Hubble Constant

An Expansion Simulator

(built from a prayer and a vision)

 

Expansion motion away from a center, under inertia, could produce observations in our Universe, including relative acceleration:

To whom it may concern:  This is not a scientific paper.  I was reading an article about science building an underground laboratory to search for Dark Energy and I stopped to pray.  I am a Christian and I prayed saying, “Lord, what is this Dark Energy they’re looking for?”  Instantly, I had a vision.  Just as instantly I felt I had seen that space itself was expanding.  I searched the internet for “space itself expanding”, and learned this is exactly what science believes.  With that, I realized that the vision had shown me what they were looking for. That was enough for me, but that weekend I ran into a friend who was taking an astronomy class at a local university. I told him my vision and he said, “The Universe doesn’t have a center.”  Because of the vision, I objected.

Two years later, I heard someone talking about Dark Energy again on the radio.  That brought the vision back into my mind and I designed a simulator based on the motion I had seen.  That motion was all mass expanding away from a center in the pattern of stretching elastic attached at center.  I still knew little to nothing about observations made in our Universe, only what I read about the day I googled “space itself expanding, which is what Dr. Hubble saw. 

Below is a list of strange observations coming out of my simulations. When I googled them, I found they are not so strange. I learned that modern theory insists space has no center, because it was not possible that we are at center.  My expansion motion had all mass moving away from a clear center, and was offering another explanation of how it is that every observer perceives himself at the center of it.  I tried to get comments about my results, but because my expansion pattern offered a clear center, I could not get anyone to hear me, much less help me.  I had to do it myself.  Since I have no math skills, I built a simulator.

Observations offered by this Simulator:

·        An illusion of center, no matter where the observer is, or when.

·        The actual velocity of every object is away from center. Its value depends on its distance from center.  In fact, it’s simply (velocity directly away from center) = (Distance from center) / (Age of Expansion).

·        The relative velocity, with which every object is moving away from every other, also depends on their distance apart, Relative Velocity = (distance separated)/(Age of Expansion).

·        All expansion motions, actual and relative, are related.  There is a relationship factor unique to the moment in time of Expansion by which any motion can be determined by knowing this factor and how far the object is from center or its velocity: H = 1/t = v/d.

·        H is easier to calculate by measuring distant objects, the further the better, because the “noise” in distance measurements is smoothed out.

·        H is difficult to measure in “local” objects, because they are just not diverging away from the observer significantly, the closer the more difficult, and the scope of “local” expands with expansion age.

·        The Hubble Value reduces with each tick of the clock (H = 1/t).

·        With extreme age of Expansion, the Hubble Value will appear to become a solid constant, good for longer and longer periods of time, depending on the sensitivity of measurements.

·        If everything is moving away from everything else under this relationship, and if at the beginning the Universe is homogeneous, then gravity is naturalized and it will remain homogeneous throughout the history of it, except, maybe, the outer reaches.

·        If an observer, and his Center of Momentum, gets out of sync in this expansion pattern, acceleration shows up in his observed (relative) expansion motions, when there is none in the actual expansion motion.

·        As gravity clumps mass together, it will pull objects out of sync in the pattern, but the center of momentum will remain in sync, preserving the illusions, including that of center for all observers.

·        Light delayed viewing will present to the observer a Hubble Constant Value consistent with the time it is observed, rather than the time the light was emitted.

·        Gravitational Lensing, producing multiple images of the same light emission source, will present any observer with the same value of the Hubble Constant value, no matter how much time is between receipt of the images, or the path of each to the observer.  (This simulator also suggests that lensing could be used to determine the distance traveled by the light of every path without knowing the distance of either path of light, if the images are synced.

·        Dark Flow is an observation reported by NASA of the appearance of strange local motion, or a local expansion within the broader expansion.  This model predicts such a motion and it is an illusion.

·        This simulator might offer a reason CMB and observations offer two different Hubble Constant values. In fact, it suggests the two would only be the same if Expansion and the “flash” happened at the same time. It also offers a relationship between the two values.

 

The Vision:

In the vision, I saw a giant hand come in from the right. In it was a strip of elastic. It attached one end to a surface and then pulled the other.  As it stretched, I perceived, “This is what they are looking for.”   It is the motion I saw in that stretching band that I used to build my simulator.  At first, I felt He had shown me that space itself was expanding, but my simulator showed me, maybe, but not necessarily. In my simulator, space itself did not have to be physically expanding to yield the observations listed above.  It could be just mass moving away from a center under inertia, but in this pattern.  I am not a scientist, I knew virtually nothing about Cosmology, and I was not looking for any specific characteristics in my simulation other than an illusion of center, which I quickly found.  The features listed above just came out of it.  Therefore, I offer my journey through my simulations below, to whomever is interested.  I just want to know, in the end, if the vision was so.  One thing I already know about it, I now understand what they are looking for.

 

An Expansion Simulator:

I started out studying what I had seen by placing multiple dots evenly spaced on an elastic strip and stretching it from one end.  I could see an illusion of center for every observer placed at any point along its length as it is stretched.  I could also see that the density of the objects dropped evenly as the strip was stretched.  I could also see that each object’s velocity depended on its distance from the attached end, and that, even though any observer would see all objects moving away from him, all objects were always moving directly away from the attached end.  

I then wanted to know if the same would be true within a stretching sphere.  I imagined a sphere and determined that if I could show this is true with a thin disk cut from it, then it would be true for the whole sphere.  The sliver would have to include the center of the sphere, the observer and an object being observed.

To simulate expansion of my thin disk, I imagined thousands of elastic strips attached at its center, with objects and observers attached anywhere on them.  I then stretched (expanded) the disk by pulling each strip simultaneously away from center, all at the same steady rate.   When I stretched the disk, strange observations emerged from my simulations, but when I googled them, I learned they are actually being observed.

Each object moved with the stretching band it was attached to (its axis is its path away from center).  In the charts below, I stretched each axis for a set time before pausing to evaluate how each object was moving.   At each pause (steady rate or accelerating), the new position of each object could be determined in various ways. (On the day I read about the Hubble Motion formula, I applied it to my charts and saw how it worked and added it, but by then, I had already seen in a disk what Dr. Hubble had seen in space.) 

If the stretching was a steady rate, all objects had a steady velocity, moving away from center, and each object’s speed depended on its distance from center, the value increasing with distance.  Each pause had its own Hubble Value that could be used to show a relationship of all actual motion away from center.  The same Hubble Value showed the same relationship between all relative motion between any two objects. It was Hubble Motion within Hubble Motion, just like with the stretching band.  This is what Dr. Hubble might have witnessed.    

I determined the change of position of each object at each pause (steady rate or accelerating) by multiplying the new length of the axis (new radius of the disk at each pause) by the ratio of the object’s starting distance from center divided by the starting length of the band (original radius of disk). 

            New position of object = (initial distance of object from center / initial length of axis) * (rate of expansion * age of expansion)

If this expansion is an acceleration;

            New position of object = (initial distance of object from center / initial length of axis) * (.5 * acceleration rate * age of expansion^2)

It turned out that the position of each object could have been determined through time once the velocity of each object is known, using d = v * Age of Expansion.  This model assumes everything started out at center, which meant that for my model, H = v/d = 1/Age of Expansion.

 

The Simulations:

I randomly placed an observer within my disk and drew an axis that passed through him and the center of the disk (see image below). I started out assuming no gravity and no delays of observation due to light propagation. I drew a “circle of observation” of a random radius around my observer. I placed objects on this circle for him to watch and to collect data as the disk expanded (data charts below). As I placed each object on his circle, I calculated the angle at disk center between the observer and his objects and the distance of the object from center.  Just like with my observer, I drew an axis from center through each object that I could “stretch” and give it motion due only to expansion.

I expanded my tiny sphere by “pulling” each axis at the same rate simultaneously, pulling each outward from center. The resulting motion of each object was solely due to expansion determined by its position on each stretching axis.  Each axis represented the actual path of each object’s motion.  For my first simulation, I pulled each axis at a steady rate, all expansion motion was therefore away from center at steady velocities. I later ran simulations pulling at accelerated rates.  In both forms of expansion, the Hubble Law remained valid throughout, and all observations present within this pattern of motion were preserved. All actual motion was away from center, and the illusions of center were present in all relative motions.

My initial goal was to examine how this movement affects my observer’s perspective of each object on his observation circle(s). Later, I added the delays of observation due to the speed of light and the effects of gravity.

My analysis suggests that this pattern of motion could explain what Dr. Hubble observed.  He was looking into an illusion of center.  He was indeed seeing from the perspective of center, as if at center, yet not.

 

Expansion motion, and a “Circle of Observation”:

 

 

 

Steady Rate Expansion:

The idea here is that all mass began compacted at center, but my first pause to examine the expansion began at 15 seconds into the expansion process.  I stretched the disk at a steady 10cm/sec (disk radius change rate).  I randomly placed my Observer (“Y”) at 75cm from disk center and created three “Circles of Observation” around him. One of radius 50cm, one at 60, and another at 55.73.  I placed objects on each circle by randomly selecting angles in his sky where he can see them. (The angle is between his axis and the objects.)  As the “stretching” progressed, I could track where those objects are in his sky, how that angle changes.

 

Locate the position of y (distance from center) for all objects placed on the Observer’s “Circles of Observation” based on Observer Y’s distance from center (75cm).  Radius R of each circle is selected at random, as well as positions in degrees (θ) in the observer’s sky for each object.

 

  

 

Distance of objects from center of disk

Time into expansion	Hubble Value	Radius of Disk after each expansion (Initial O)	Observer Y (Initial d)	Object A R = 50 θ=60 deg (Initial y)	Object B R = 50 θ=200 deg (Initial y)	Object C R = 60 θ=60 deg (Initial y)	Object D R = 60 θ=200 deg (Initial y)	Object E R = 55.73 θ=51.1 deg (Initial y)
15 sec	0.066667	150cm	75cm	108.97	32.82	117.15	27.71	118.24

 

 

What is the angle at center of the disk between the observer and the object being observed?

 

 

Angle from center between observer and each object

Time into expansion	Radius of Disk after each expansion (Initial O)	Observer Y	Object A R = 50 θ=60 deg   α	Object B R = 50 θ=200 deg   α	Object C R = 60 θ=60 deg   α	Object D R = 60 θ=200 deg   α	Object E R = 55.73 θ=51.1 deg   α
15 sec	150cm	---	23.41	-31.40	26.33	-47.78	21.52

 

Then stretch the disk by “pulling” each axis at a set rate for a set amount of time. I paused the stretch to calculate how each object moved along its own axis.  This will be the motion of objects along their axis due only to this expansion pattern.

 

                       

 

Actual Motion away from center of each object along its own axis as expansion progresses

Time into expansion	Hubble Value 1/Time	Radius of Disk after each expansion (new O)	Observer Y   (new d)	Object A R = 50 θ=60 deg   (new y)	Object B R = 50 θ=200 deg   (new y)	Object C R = 60 θ=60 deg   (new y)	Object D R = 60 θ=200 deg   (new y)	Object E R = 55.73 θ=51.1 deg   (new y)
16 sec	0.062500	160 cm	80.00	116.24	35.01	124.96	29.56	126.12
50 sec	0.020000	500cm	250.00	363.23	109.40	390.50	92.37	394.13
51 sec	0.019608	510cm	255.00	370.50	111.59	398.31	94.21	402.02
5000 sec	0.000200	50,000cm	25,000.00	36,323.33	10,940.00	39,050.00	9,237.50	39,413.33
5001 sec	0.000200	50,010cm	25,005.00	36,330.60	10,942.19	39,057.81	9,239.35	39,421.22
Actual velocity due to expansion motion		---	5cm/sec	7.27cm/sec	2.18cm/sec	7.81cm/sec	1.85cm/sec	7.89cm/sec

Calculations of position came from the motion generated as each axis is being stretched like elastic pinned at center, but the resulting motions are a steady velocity. 

Therefore, this motion could be a simple drifting away from a center under inertia.

 

For each movement, strictly by the expansion process, re-calculate the new angle θ of each object with respect to the observer, where will he now have to look to find that object in his sky?

 

 

 

Observed Position: Effect of expansion motion on the position of each object in our observer’s sky

Time	Object A R = 50, θ=60 deg   new θ	Object B R = 50, θ=200 deg   new θ	Object C R = 60, θ=60 deg   new θ	Object D R = 60, θ=200 deg   new θ	Object E R = 60, θ=60 deg   new θ
15 sec	60	200	60	200	51.1
16 sec	60	200	60	200	51.1
50 sec	60	200	60	200	51.1
51 sec	60	200	60	200	51.1
5000 sec	60	200	60	200	51.1
5001 sec	60	200	60	200	51.1
Change of position in observer’s sky	unchanged	unchanged	unchanged	unchanged	Unchanged

 

At each pause, how has the radius of each “circle of observation” been affected?  This is measured by the relative motion of each object to the observer, the actual distance between them.

 

 

Relative (Observed) Motion: Distance measured by observer to each object

Time	Hubble Value	Object A R = 50, θ=60 deg   new R	Object B R = 50, θ=200 deg   new R	Object C R = 60, θ=60 deg   new R	Object D R = 60, θ=200 deg   new R	Object E R = 55.73, θ=51.1 deg   new R
15 sec	0.066667	50.00	50.00	60.00	60.00	55.73
16 sec	0.062500	53.33	53.33	64.00	64.01	59.45
50 sec	0.020000	166.67	166.67	200.00	200.00	185.77
51 sec	0.019608	170.00	170.00	204.00	204.00	189.48
5000 sec	0.000200	16,664.78	16,667.07	19,999.15	19,999.04	18,577.41
5001 sec	0.000200	16,668.12	16,670.40	20,003.14	20,003.03	18,581.13
Relative velocity due to expansion		3.33 cm/sec	3.33 cm/sec	4.00 cm/sec	4.00 cm/sec	3.72 cm/sec

 

 

Analysis:

All motion was due to pulling every axis at a steady rate. Each object’s motion was directly away from center.  The resulting calculations show that this motion kept each object on the observer’s original circle of observation in the exact position where he first saw it. This expansion motion accomplished this while simultaneously increasing the radius of each circle, moving every object on the circle away from the observer. Each pause could be evaluated using the Hubble formula. This motion created an illusion that the observer was standing at the center of an expansion process, every object receding from him in all directions.  Each object was moving away from center at a constant velocity, proportional to distance from center.  Each object was moving away from every observer at a constant relative velocity, also proportional to distance.  Every object was moving away from center at a divergent angle (α) to every other.  Every observer would record a redshift when viewing every other object.

 

The “Observed Motion” chart turns out to be identical if I place my observer at different locations with the same configuration for the same time span of expansion, but his “Actual Motion” chart will change with position. He cannot tell from his observations that he is in a different place. Since this includes him standing on true center this pattern of motion presents every observer with a view of expansion as if he were standing at true center.  He is seeing center, yet not, it is an illusion of center for every observer.

If we place another observer at dead center with the same configuration of objects his “Observed Motion” chart would be identical to his “Actual Motion” chart.  His “Observed” chart would be identical to Observer Y’s “Observed” Chart, if data is collected at the same moment of expansion.  When an observer is standing on true center, his “observed” motion is the “actual” motion. Every other observer is observing relative motions and cannot discern the actual, either his own or the objects he is observing.  He thinks he is at the center of an expansion.

At each pause, the Hubble value calculated is the same by all observers. An observer standing at true center watching Observer Y at 50 seconds into expansion would calculate a Hubble value of v/d = 5cm/sec / 250cm = .02/sec.  Observer Y, at the same moment, watching Object A (“Observed Motion”) would calculate his H as 3.33/166.67 = .02/sec.  

Each observer is caught up in their own relationship of relative motions. Each observer’s relative motions mimic what is observed at center.  This tiny model could therefore be another explanation of why Dr. Hubble saw an appearance of center.

 

When I started my simulations all I knew about Cosmology was Dr. Hubble seeing everything receding.  I was unaware of the Hubble formula. When my data charts resembled what Dr Hubble saw I began to read more about him.  That is when I learned about the Hubble formula. I began to divide separations between objects in my chart and saw that it nicely describes the relationships between the observer and all his objects at each pause (row).  For each pause, it could be used to calculate any position from a known velocity or a velocity from a known position.  In time, I saw that in my charts H = 1/t, where t is the age of the expansion at the time of the pause.  I just needed to know the time of the pause to know H, or I could calculate it from H = v_y / (new y) = v_R / (new R).  I could see that the Hubble formula was really just d = vt and this formula could be used to replace my elastic stretching formula, but I didn’t do that. For example, in my “Actual Motion” chart, once I knew Observer Y was moving along at 5cm/s, I could have determined his distance from center by (new O) = 5cm/51sec = 255cm.  The Hubble formula is better for expansion, because it expresses d=vt as a relationship between all the objects caught up in the expansion process.

 

 

 

 

“Locally” Observed Expansion Motion slowing with time:

As I ran more simulations, I could see that close-range relative motion was slowing with Expansion age. I setup two new simulations to examine “local” vs “distant” observations of Expansion Motion.

In my first simulation of local Expansion Motion, Observer Y is still watching Objects A and E, but now the expansion has aged to 5,000 seconds. At 5,000 seconds, Observer Y will have moved to 25,000cm away from center. I added two new objects in his sky, H and J.  These two new objects are starting out on his original “Circle of Observation” of R=50cm, to represent “local” observation of Expansion.  Objects A and E will represent “distant” observation of Expansion Motion.  They will have move away from Observer Y to 16,664cm and 18,577cm, respectively,  and away from center of disk to 36,323cm and 39,413cm, respectively.

For my second simulation of local relative motion, I placed a new observer Z at the same 5,000 seconds mark.  He is on Observer Y’s axis, and at Y’s original vantage point of 75cm from center. I added Objects F and G on a Circle of Observation for him to watch at the same perspective that Y had for his A and B (starting at the same R and θ).  

I let Observer Z see the motion of objects A and E.

 

Actual Motion: Observer Y and his objects starting at 5,000 seconds into expansion

				New Local Objects		Original Non-Local Objects
Time into expansion	Hubble Value	Radius of Disk after each expansion	Observer Y   new d	Object H R = 50 θ=60 deg   new y	Object J R = 50 θ=200 deg   new y	Object A R = 16,664 θ=60 deg   new y	Object E R = 18,577 θ=51.1 deg   new y
α				0.10	-0.04	23.41	21.52
5000 sec	0.000200	50,000cm	25,000.00	25,025.04	24,953.02	36,323.33	39,413.33
5001 sec	0.000200	50,010cm	25,005.00	25,030.04	24,958.01	36,330.59	39,421.21
5002 sec	0.000200	50,020 cm	25,010.00	25,035.05	24,963.00	36,337.86	39,429.09
5100 sec	0.000196	51,000 cm	25,500.00	25,525.54	25,452.08	37,049.80	40,201.60
5200 sec	0.000192	52,000 cm	26,000.00	26,026.04	25,951.14	37,776.26	40,989.86
Actual velocity due to expansion			5.00 cm/sec	5.01 cm/sec	4.99 cm/sec	7.26 cm/sec	7.88 cm/sec

 

At 5,000 seconds into expansion objects 50cm away from the observer now had virtually the same speed as the observer (divergent angle α is very small between them).  This contrasts with objects at the same distance from him when expansion was just 10 seconds old.

 

 

Observed Motion: Distance measured by Observer Y to each object

		Local Objects		Non-Local Objects
Time	Hubble Value	Object H R = 50 θ=60 deg   new R	Object J R = 50 θ=200 deg   new R	Object A R = 16,664 θ=60 deg   new R	Object E R = 18,577 θ=51.1 deg   new R
5000 sec	0.000200	50.00	49.94	16,664.12	18,577.52
5001 sec	0.000200	50.01	49.95	16,667.45	18,581.24
5002 sec	0.000200	50.02	49.96	16,670.79	18,584.96
5100 sec	0.000196	51.00	50.93	16,997.40	18,949.08
5200 sec	0.000192	52.00	51.93	17,330.68	19,320.63
Relative velocity due to expansion		0.01 cm/sec	0.01 cm/sec	3.33 cm/sec	3.72 cm/sec

 

 

“Local” (grey box) verses Distant Actual Expansion Motion

 

 

“Local” (grey box) verses Distant Observed (Relative) Expansion Motion

 

At 15 seconds into Expansion, Observer Y was 50cm from Object A and moving away at an expansion motion of 3.33cm/s.  Observer Y could easily measure their relative velocity.  When the Expansion aged to 5,000 seconds, A had moved to 36,363cm away, but still moving directly away at an expansion motion of 3.33cm/s. Observer Y could still easily measure the relative velocity.  However, 5,000 seconds I added the new object H at 50cm away from Y.  Y then measured an expansion motion for H of 0.01cm/s.  At 15 seconds into Expansion, object H would have been 75.01cm from center and just 0.15cm away from the Observer.  At 15 seconds into expansion, this example of "local" Expansion Motion was about 0.2cm, but expanded to 50cm at 4,985 seconds later.

For my simulation of Observer Z, I calculated his perspective of A and E (distance and θ); where are they in his sky?

Actual Motion: Observer Z and his objects starting at 5,000 seconds into expansion

				Local Objects		Non-Local Objects
Time into expansion	Hubble Value	Radius of Disk after each expansion	Observer Z   new d	Object F R = 50 θ=60 deg   new y	Object G R = 50 θ=200 deg   new y	Object A R = 36,254 θ=23.46 deg   new y	Object E R = 39,344 θ= 21.56 deg   new y
α		---	---	23.41	-31.40	23.41	21.52
5,000 sec	0.000200	50,000cm	75.00	108.97	32.82	36,323.33	39,413.33
5,001 sec	0.000200	50,010cm	75.02	109.00	32.83	36,330.59	39,421.21
5,002sec	0.000200	50,020cm	75.03	109.02	32.83	36,337.86	39,429.09
5,100 sec	0.000196	51,000cm	76.50	111.15	33.48	37,049.80	40,201.60
5,200 sec	0.000192	52,000cm	78.00	113.33	34.13	37,776.26	40,989.86
Actual velocity due to expansion		---	.02 cm/sec	.02 cm/sec	.01 cm/sec	7.26 cm/sec	7.88 cm/sec

 

 

Observed Motion: Distance measured by Observer Z to each object

		Local Objects		Non-Local Objects
Time	Hubble Value	Object F R = 50 θ=60 deg   new R	Object G R = 50 θ=200 deg   new R	Object A R = 36,254.52 θ=23.46 deg   new R	Object E R = 39,343.68 Θ=21.56 deg   new R
5000 sec	0.000200	50.00	50.00	36,254.52	39,343.68
5001 sec	0.000200	50.01	50.01	36,257.53	39,351.55
5002 sec	0.000200	50.01	50.01	36,264.78	39,359.42
5100 sec	0.000196	50.99	51.00	36,975.28	40,130.68
5200 sec	0.000192	51.99	51.99	37,700.28	40,918.68
Relative velocity due to expansion		.01 cm/sec	.01 cm/sec	7.25 cm/sec	7.87cm/sec

 

The charts suggest that the reason observation of local expansion in our Universe is so difficult is because as time passes objects moving with significant relative Expansion Motion have moved out of our local space. As Expansion progresses, more and more of the objects close to us are barely showing any relative Expansion Motion, although it is there.  Those objects have always been moving with very slow relative Expansion Motion.  From the beginning, these are objects that are moving at virtually the same speed away from center and at very small angles of divergence (α).

Therefore, relative (observed) Expansion Motion of close objects will fall toward insignificance as expansion grows old. The data charts suggest that distances from an observer considered “local” in scope (Expansion Motion difficult to observe) grows larger and larger as expansion ages.

 

The Pattern as an Accelerating Expansion – pulling each axis at an accelerated rate

If Expansion Motion is an acceleration can simulate it by pulling each axis at an accelerated rate, but unlike steady rate expansion this could not be inertia.

Instead of objects moving away from center at constant velocities at values that increase with distance from center, now objects are moving with constant accelerations at values that increase with distance from center.  At each pause, there is still a Hubble Formula relationship between all objects caught up in the expansion, H = v/d, but now H = 2/(Age of Expansion).

If looking at a single pause in the simulation you cannot tell whether the motion is steady rate or accelerating, except the H value.  All observer’s still record all objects receding directly away, but now relative motion is an acceleration.  

If Expansion Motion slows and speeds up this simulation can do either and still present observations of center, homogeneous expansion, and insignificant local relative motion.

 

Object A: Actual Motion with a forced acceleration of each object along its own axis away from center (without viewing delays of light propagation)

Time into expansion	Hubble Value 2/Time	Observer Y   new d	Observer Y Velocity (d)	Object A R = 50 θ=60 deg (y)	Object A Velocity	Object A Observed Distance	Object A Observed Velocity	Object A θ
15 sec	0.13333	75.00	10.00	108.97	14.53	49.99	6.67	60
16 sec	0.125	85.33	10.67	123.98	15.50	56.88	7.11	60
50 sec	0.04	833.33	33.33	1,210.78	48.43	555.49	22.22	60
51 sec	0.03922	867.00	34.00	1,259.69	49.40	577.93	22.66	60
5000 sec	0.0004	8,333,333.33	3,333.33	12,107,777.78	4,843.11	5,554,928.73	2,221.97	60
5001 sec	0.0004	8,336,667.00	3,334.00	12,112,621.37	4,844.08	5,557,150.92	2,222.42	60
Acceleration due to expansion			0.67cm/s/s		0.97cm/s/s		0.44cm/s/s

                      

Object B: Actual Motion with a forced acceleration of each object along its own axis away from center (without viewing delays of light propagation)

Time into expansion	Hubble Value 2/Time	Observer Y (d)	Observer Y Velocity	Object B R = 50 θ=200 deg (y)	Object B Velocity	Object B Observed Distance	Object B Observed Velocity	Object B θ
15 sec	0.13333	75.00	10.00	32.82	4.38	50.00	6.67	200
16 sec	0.125	85.33	10.67	37.34	4.67	56.89	7.11	200
50 sec	0.04	833.33	33.33	364.67	14.59	555.57	22.22	200
51 sec	0.03922	867.00	34.00	379.4	14.88	578.01	22.67	200
5000 sec	0.0004	8,333,333.33	3,333.33	3,646,666.67	1,458.67	5,555,690.92	2,222.28	200
5001 sec	0.0004	8,336,667.00	3,334.00	3,648,125.48	1,458.96	5,557,913.41	2,222.72	200
Acceleration due to expansion			0.67cm/s/s		0.29cm/s/s		0.44cm/s/s

 

 

 

The Source of the Illusion of Center

The source of the illusion of center, all objects receding directly away at the same rate per distance in all directions of the observer’s sky, is in the observer’s inability to perceive his own motion due to expansion.  The illusion is in the interaction of vector motions within this pattern.

 

Object’s Expansion velocity vectors as viewed by observer:

 

Ω = θ – α    

 (θ = angle of the object on the viewing circle)

V_p = V_a cos(Ω)

V_t = V_a sin(Ω)

 

 

 

 

 

Observer’s Expansion Velocity vectors as projected onto the observed object:

 

 

θ = observer’s angle to object

V_p = - V_a cos(θ)

V_t = - V_a sin(θ)

                              

 

 

 

 

Using data from the original chart above, Observer Y was watching Object A when it was 50cm away and 60 degrees from his expansion motion. He determined that it was moving directly away from him at 3.33cm/sec. He found that every object 50cm away was moving directly away from him at the same speed. 

The actual Expansion velocity of Object A was 7.27cm/sec directly away from disk center, and the divergent angle between the observer and Y at true center was 23.41 degrees.

 

Vectors of Observer Y’s Expansion motion projected onto Object A:

     Ω = 60 - 23.41 = 36.59 degrees

V_a = 7.27 cm/sec 

V_p = 7.27cm/sec * cos(36.59) = 5.84 cm/sec

V_t = 7.27 cm/sec * sin(36.59) = 4.33 cm/sec

Object A’s Expansion motion as viewed by Observer Y:

                              V_a = - 5.00 cm/sec   (from data chart)

                               V_p = - 5.00 cm/sec * cos(60) = - 2.50 cm/sec

V_t = - 5.00 cm/sec * sin(60) = - 4.33 cm/sec

 

For this expansion pattern all movement is part of the Hubble relationships (v=Hd):

 

 

 

Observer Y’s relative Expansion velocity (measured perpendicular motion) for object A is the sum of their two “actual motion” perpendicular vectors; 

 

Observed Velocity = 5.84 – 2.50 = 3.34 cm/sec.

 

Observer Y’s tangential Expansion velocity is the sum of their two tangential vectors:

 

Tangential Motion in the observer’s sky = 4.33 – 4.33 = 0.

 

This relationship is true between all objects moving away from center in this Expansion pattern.  In this pattern of motion, our observer cannot see the tangential vector of Expansion Motion, because his own is exactly masking the object’s to nil.

The result is that each object on each circle is viewed as moving the same speed directly away from him, when in fact they are neither moving directly away, nor the same speeds, unless the observer happens to be special, standing on dead-center of the disk.  Center is an illusion.

 

 

The Hubble Constant

The Hubble Constant is defined as H = v / d.  In this model, v is the observed or actual velocity, and d is the distance from observer or from center, respectively.  Here, H is not a constant but a value good for “moments” in time. As the expansion ages, H does become more of a constant. At any moment in time an H can be measured anywhere in the disk, and then be used for the whole within that moment, but its value changes as expansion advances. Dr. Hubble would have been measuring “observed” motion within the illusion, a product of relative motion, and his measurement of H would be accurate for the “actual”, which he could not discern.

Using “Actual” motion of Object A, at the 15 second mark, yields H = 7.27/108.97 = .067. Using the “Observed” motion at the same moment, Observer Y would calculate H = 3.33/50 = .067.  If Dr. Hubble was looking out into this universe, he was not able to see the actual motion, yet his data gave him the actual H of expansion for that moment.

I designed my data such that Object A and Object E start out at 10cm apart at the 15 second moment in expansion. If H at 15 seconds is .067, then the two objects should be expanding away from each other at v = H * d = .67cm/sec. To check that, I calculated the actual distance between the two objects due to expansion motion at the 16 second mark. The separation grew to 10.67cm, which is a velocity of .67 cm/sec.  The two results agree.

As expansion gets older, the H value becomes increasingly stable. At the 5,000 seconds mark the H value dropped to .002. It stayed that value for a long period of time (at 3 significant digits). In the second data chart when the expansion age was even more advanced, H dropped to 0.00026.  At this more advanced stage, even using 5 significant digits, the H value did not register change over 200 seconds.  Calculated values for H would be more and more of an estimate as the universe ages.

Hubble Value of this expansion model:

H = Actual velocity of any object away from center / distance from center

OR

H= Observed velocity/observer’s distance to object

OR

H = Observed net velocity between two objects / separation between them

OR

If H = v / d,    (for pure expansion motion that is not an acceleration)

v = (distance between any two objects) / (Age of the Universe)

(Any position can count as an object, even if there is nothing there)

d = (distance between same two objects)

then,

H = 1 / (Age of the Universe). 

 

If expansion is an acceleration:

 

 

For steady rate expansion, the Hubble value for an expanding disk is the reciprocal of the age of the expansion process. H is therefore independent of the rate of expansion. If I stretch my disk at 10cm/sec it will have the same Hubble value at any given time as a disk being stretched at 500cm/sec. An object that is at 75cm from center 15 seconds into the expansion of a disk being stretched at 10cm/sec will be at 3,750cm if the same disk is being stretch for 15 seconds at 500cm/sec.

The current Hubble Value reported for our Universe, derived from observations:

 

H (derived from observation) =  =  = 2.33 E ^-18 /s

 

If this is so, and H is changing with time, then at the current age of our Universe it would take 58.6M years to observe H changing.

  -  = 1 / (2.32E-18/sec)  –  1 /(2.33E-18/sec) = 1,849,933,402,397,513sec = 58.6M years

At 4 significant digits, 1 / (2.332E-18/sec)  –  1 /(2.333E-18/sec) = 183,804,743,485,776sec = 5.8M years

At 5 significant digits, 1 / (2.3332E-18/sec)  –  1 /(2.3333E-18/sec) = 18,368,658,970,850sec = 582K years

At 6 significant digits, 1 / (2.33332E-18/sec)  –  1 /(2.33333E-18/sec) = 1,836,747,813,490sec= 58K years

At advanced age of the expansion, to the observer H will appear to be a constant.

 

 

The Speed of Light: Hubble Motion and illusions of center preserved

 

The calculated data in my original charts assumed no gravity and no speed of light parallax. The illusions of this pattern are true instantaneously, but astronomers view objects from great distances, seeing light emitted from their past. I felt surely that this delay of our Universe would reap havoc on the illusions seen in this model. Instead, not only does it maintain Hubble motion and the illusions of center, but it adds a new illusion. In steady rate expansion the delay somehow converts the Hubble value at the time the light was emitted, in the past, to the value at the moment of observation.  For steady rate, the speed of light parallax makes the Hubble value at the time of observation appear to be valid throughout history, when it’s not.

 

To add this to my simulation of steady rate expansion, I had to know where the emitter was when the observed light was emitted. I developed equations (below) to yield the time required for emitted light from an object to intercept any desired observer, who would be moving along his axis during the time the light was in transit.  Knowing this time, I could back the emitting object down its axis from its “actual” location (according to expansion in this pattern) at the moment of observation, to the position where the light was emitted.  The distance to the object that the observer would measure would be this location to the point where the light intercepted him.

 

Determining the delay time (t) from emission to observation of the beams of light.0

α is the angle from center between the observer and the emitter.  :

V_L is the velocity of light (for my model I made it 4,300cm/sec)

V_E is the velocity of the emitter

O is the distance from center of the Observer at the time of observation

E is the distance from center of the Emitter at the time of observation

         (determined by this expansion motion)

t = the time required for emitted light to intercept the observer,

          and the amount of time that the emitter moved after emission

 

Solving for t, both equations reduce to the same solution. This will give me the amount of time the light takes to travel from the point of emission from its axis to the point it intercepts the observer on his axis.  Solving for t doesn’t matter rather the emitter is further from center, or closer:

 

 

Using my solution for “time for light to travel”, I populated a new data chart (below). When the chart was complete I saw that the delay somehow converts the information in the light received to the Hubble value of the observer, the H at the time of observation (H = 1/observation time). Every object he observed was emitted at different times in the expansion history, yet it all presents him with the current value of H for the expansion process.  The observer does not have to determine the H value at the time of emission to analyze his data but can use the current value of H at the moment the light is received.  This was consistent in every scenario I tried. This new illusion will make the current H value of expansion appear to be “the” value of H throughout the history of expansion, but it’s not so.

 

One thing that became clear is that the delay of observation changes the mechanics of presenting the illusion of center to the observer.  I could no longer draw a “Circle of Observation” around my observer and then let him watch that circle expand evenly.  The observer could still have such a circle and watch it expand evenly, but the selected objects that make up that circle would look like a circle only to him. Looking at the disk from overhead, it would be warped.

 

This time, I started my disk at 5 seconds into expansion, and stretched my disk at a rate of 500cm/sec. I placed my observer at 10,000cm from true center with three objects in a Circle of Observation around him of radius 866cm.  The objects (light emitters) will be in his sky at 60, 90, and 200 degrees from his axis.  That means two will be further away from center than my observer and one closer.  I will set the speed of light in my model to 4,300cm/sec.

 

 

Emitter 1:  (α =  27.626 degrees    Viewer’s angle of 60 degrees is altered by the delay to 62.3 degrees and it is maintained)

Pattern without Observational Delay					Speed of Light Observational Delay
Time of Observation ta	Ha at Time of Observation	Observer distance from center	Emitter distance from center at time of Observation Ea	Unmodified Observed Distance Ra	tr Time for emitted light  to reach Observer	Time Of Emission tm	HEm at time of emission	Emitter distance from center at time of emission Em	Modified observed distance Rm	Observer calculated Hm
5sec	0.2000000	1,000	1,617.4	866.00	0.189	4.81	0.2078786	1,556.10	814.90	0.2000010
10sec	0.0100000	2,000	3,234.8	17,320.41	0.379	9.62	0.1039397	3,112.19	1,629.79	0.0100005
5,100sec	0.0002000	1,020,000	1,649,762	883,340.73	193.303	4,906.70	0.0002038	1,587,231.789	831,204.17	0.0001961
15,100sec	0.0000662	2,020,000	4,884,588	2,615,381.37	572.329	14,527.67	0.0000688	4,699,450.956	2,461,016.26	0.0000662
15,095sec		200cm/sec	323.48cm/sec	173cm/sec	0.03790/sec	14,522.86sec		311.22cm/sec	162.98cm/sec

Observer sees 0.962 seconds of the emitter motion for every second of his own time.  L = 0.962

 

Emitter 2:  (α =  40.893 degrees    Viewer’s angle of 90 degrees is altered by the delay to 93.4 degrees and it is maintained)

Pattern without Observational Delay					Speed of Light Observational Delay
Time of Observation ta	Ha at Time of Observation	Observer distance from center	Emitter distance from center at time of Observation Ea	Unmodified Observed Distance Ra	tr Time for emitted light  to reach Observer	Time Of Emission tm	HEm at time of emission	Emitter distance from center at time of emission Em	Modified observed distance Rm	Observer calculated Hm
5sec	0.2000000	1,000	1,322.85	866.00	0.197	4.80	0.2082000	1270.74	846.85	0.1968117
100sec	0.0100000	20,000	26,457.5	17,320.37	3.87	96.13	0.0104030	25,432.02	1,6667.07cm	0.0100000
5,100sec	0.0002000	1,020,000	1,349,333	883,338.93	197.68	4,902.32	0.0002040	1,297,033.25	850,020.45cm	0.0001961
15,100sec	0.0000662	3,020,000	3,995,085	2,615,376.04	585.28	14,514.72	0.0000689	3,840,235.71	2,516,727.22cm	0.0000662
15,095sec		200cm/sec	264.57cm/sec	173.2cm/sec	0.03876/sec	14,509.92sec		254.33cm/sec	166.67cm/sec

Observer sees 0.961 seconds of the emitter motion for every second of his own time. L = 0.961

 

Emitter 3:  (α =  57.845 degrees    Viewer’s angle of 200 degrees is altered by the delay to 199 degrees and it is maintained)

Pattern without Observational Delay					Speed of Light Observational Delay
Time of Observation ta	Ha at Time of Observation	Observer distance from center	Emitter distance from center at time of Observation Ea	Unmodified Observed Distance Ra	tr Time for emitted light  to reach Observer	Time Of Emission tm	HEm at time of emission	Emitter distance from center at time of emission Em	Modified observed distance Rm	Observer calculated Hm
5sec	0.2000000	1,000	349.85	866.00	0.202	4.80	0.2084254	335.71	869.12	0.1926278
100sec	0.0100000	20,000	6,997.27	17,320.53	4.035	95.97	0.0104204	6,714.95	17,350.19	0.0100000
5,100sec	0.0002000	1,020,000	356,861	883,346.87	205.781	4,894.22	0.0002043	342,462.48	884,859.49	0.0001961
15,100sec	0.0000662	3,020,000	1,056,588	2,615,399.55	609.274	14,490.73	0.0000690	1,013,957.54	2,619,878.11	0.0000662
15,095sec		200cm/sec	69.97cm/sec	173.2cm/sec	0.0403/sec	14,485.93sec		67.15cm/sec	173.50cm/sec

Observer sees 0.960 seconds of the emitter motion for every second of his own time.   L = 0.96

 

 

 

 

 

 

 

The light observed was emitted by the object in the past, and therefore under an older H. Yet, it will present the Hubble Constant Value at the time of observation.  This is true, because the motion of the “image” presented to the observer is moving in sync for an object that would be actually at that distance from center at the time of observation and being observed with no delay.  This is always true, so this “phantom” position and “phantom” motion of the object created by the speed of light is always in sync with the pattern and will always present the observer with the current H at time of observation.  The delayed observations caused by the speed of light will not disrupt any of the illusions of this pattern, including the illusion of center.

The observations delayed by the speed of light alters the ratio of the distance from center of the observer and the object being observed. Without the delay of viewing this ratio remained a constant within this pattern.  With the delay it continues to be a constant, but of a different value.

 

 

At the moment the light is emitted, is the correct ratio for the actual motion of the pair.  During the time the emitted light is traveling toward the observer the observer’s distance from center (new d) is changing but the Emitter’s (new y) is frozen. Under observational delay this ratio for actual motion is different than observed motion. This is why θ is altered by the delay of the speed of light, but since the altered ratio is likewise constant, the observed θ is constant.  If the delay alters θ then it alters R.

 

 

I could see that there is a conversion factor (L) for each observed object. I found that L can be determined by the observer from his observed velocity (V_Rm – velocity at the bottom of the R_m column) and the speed of light, C (or V_L as denoted in my original equations.) 

 

L can also be determined using:

 

My data charts suggested that the Hubble Constant calculated by the observer (H_m determined from the delayed observed light), is the current H (H_a), even though his data is altered by the delayed observations:

Using the Hubble formula,

V_Rm = R_m * H_m, since R_m is the observed distance traveled by the emitted light, then R_m = C * t_r ,

therefore V_Rm =   (C * t_r) H_m

If L= 1 – V_Rm / C , then

L = 1 – H_m  * t_r

 

Since the age of expansion when the light was emitted is t_m = t_a – t_r, then t_r = t_a - t_m, then;  

L = 1 – H_m (t_a – t_m)

 

From my formulas for L,  t_m = L * t_a

L = 1 – H_m (t_a – L * t_a)

L – 1 = H_m * t_a  (L - 1)

H_m = 1 / t_a

 

Since 1/t_a = H_a ,

     H_m = H_a

 

Also, since the ratio of the distance from center before the delay and after are both constant, then

      where P is a conversion factor that relates them

Therefore: 

 

 

The vector analysis of how light delayed observations continue to maintain the illusions of center and recession:

Emitter’s perpendicular observed velocity:  Vp = 311.22 * cos(62.3 – 27.626) = 255.95cm/sec

Observer’s projected perpendicular observed velocity: Vp= - 200 * cos(62.3) =  - 92.97cm/sec

Emitter’s tangential observed velocity: Vt = 311.22 * sin(62.3 – 27.626) = 177.05cm/sec

Observer’s projected tangential observed velocity: Vt=  - 200 * sin(62.3) = - 177.08cm/sec

Just like in the “ideal” pattern (no gravity and no delay), the observer’s tangential velocities cancel out, even with the altered angle.  The observer still sees the objects moving only directly away from him at the sum of the perpendiculars…

                                        Vp = 255.95 – 92.97 = 162.98cm/sec

 

This shows that within this pattern, the illusion of center, everything receding, is preserved by the speed of light for every observer, and by the same mechanism of vector interaction. Every observed object will be red shifted, still.

 

 

An illusion of Slow Motion, of time slowed down:

This chart reveals yet another illusion from light delay.  Each successive emission of light takes a little longer than the one before it to reach the observer. As a result, the passage of time of the emitted object appears to the observer to move slower.  This is true within this pattern whether he is moving toward the emitted light (closer to center), or away from it (further out). The result is that the observed emitters in all directions continue to appear to be receding directly away from the observer with velocities proportional to distance, but now they are moving in an observed slow motion.

At each data point, the equations for travel time were used to move the emitter back down its axis to the point where the light was emitted. If the observer is looking back toward center, the observed distance is increased, if toward outer edge, decreased, but regardless of which way he looks, there is a slowing of motion. For Emitter 1, the delay decreased the apparent distance traveled by the emitting object on its own axis during the 15,095seconds of observation from the true 4,882,970.60cm to 4,697,894.86cm.  This altered data presents the object as moving only 311.22cm/sec along its path of motion when it was actually moving 323.48cm/sec.

I wondered how delayed observation would affect measurements between distant pairs of objects, and would the expansion going on between them also present the current value of H?  Both are viewed from the past, and both presenting independent delay affects to the observer. The observer’s evaluation of the relationship between them would be a culmination of these two independent delays. My first two charts below evaluate the independent observations of each object, which are then the source of my combined evaluation of the two together (third chart).  I could not perceive how the observation of the expansion going on between them, measured under all this noise, might offer the current H to the observer. Turns out, they did, every time, and it is accomplished by this slowed down observation of distant motion.

I set two new objects in my expanding disk at the 100 second mark and with expansion of the whole disk still at 500cm/sec.  I set the two objects at the same distance from disk center and at angles of 27.626 degrees and 32.626 degrees from my observer.  This means each will have identical actual motion away from center, yet each will be viewed differently by my observer because each will have a different angle α from him. I wanted the two objects to be moving away from center at a decent velocity, and diverging away from each other at a moderate expansion velocity.  I then let the observer watch them for four seconds, as he moved along his own axis with expansion motion.  What I found is that the delay still presents the incoming motion as the current H, and it does so by slowing down the passage of time within the observation, but not in reality.

 

Observation of Emitter 1

Without Delay					With Light Delay
Time	Expansion H	Observer Distance from center	Emitter 1 Distance from center	Viewing Angle (Degrees)	Delay	Emitter time span viewed	H At moment of emission	Emitter 1 Distance from center at emission	Observed Distance	Altered Viewing Angle	H Calculated by observer
100 sec	0.01000	20,000	32,348.3	60.0	3.79 sec	96.21	0.01039	31,122.22	16,298.15	62.31	0.01000
101 sec	0.00990	20,200	32,671.8	60.0	3.83 sec	97.17	0.01029	31,433.45	16,461.13	62.31	0.00990
102 sec	0.00980	20,400	32,995.3	60.0	3.87 sec	98.13	0.01019	31,744.67	16,624.11	62.31	0.00980
103 sec	0.00970	20,600	33,318.7	60.0	3.90 sec	99.10	0.01009	32,055.89	16,787.09	62.31	0.00971
104 sec	0.00960	20,800	33,642.2	60.0	3.94 sec	100.06	0.01009	32,367.11	16,950.07	62.31	0.00961
4 sec		200 cm/sec	323.48 cm/sec			3.85		311.22 cm/sec	162.98 cm/sec

The observer viewed 4 seconds, but the light viewed during that time was emitted over 3.83 seconds. The emitter was viewed in slow motion.  Emitter 1 moved 1,294cm on its own axis during the 4 seconds, but the distance observed was offset down the emitter’s axis and covered only 1,245 cm.  The observed velocity without the delay is 173.2 cm/sec. With the delay, it was recorded moving at 162.98 cm/sec.

 

 

Observation of Emitter 2

Without Delay						With Light Delay
Time	Expansion H	Observer Distance from center	Emitter 2 Distance from center	Viewing Angle (Degrees)	Delay		Emitter time span viewed	H At moment of emission	Emitter 2 Distance from center at emission	Observed Distance	Altered Viewing Angle	H Calculated by observer
100 sec	0.01000	20,000	32,348.3	67.4	4.14 sec		95.86	0.01043	31,009.08	17,802.23	69.91	0.01000
101 sec	0.00990	20,200	32,671.8	67.4	4.18 sec		96.82	0.01033	31,319.17	17,980.25	69.91	0.00990
102 sec	0.00980	20,400	32,995.3	67.4	4.22 sec		97.78	0.01023	31,629.26	18,158.27	69.91	0.00980
103 sec	0.00970	20,600	33,318.7	67.4	4.26 sec		98.74	0.01013	31,939.35	18,336.30	69.91	0.00971
104 sec	0.00960	20,800	33,642.2	67.4	4.31 sec		99.69	0.01003	32,249.44	18,514.32	69.91	0.00961
4 sec		200 cm/sec	323.48 cm/sec				3.83		310.09 cm/sec	178.02 cm/sec

The observer viewed 4 seconds, but the light viewed during that time was emitted over 3.85 seconds. The emitter was viewed in slow motion.  Emitter 2 moved 1,294cm on its own axis during the 4 seconds, but the distance observed was offset down the emitter’s axis and covered only 1,240 cm.  The observed velocity without the delay is 188.8 cm/sec. With the delay, it was recorded moving at 178.02 cm/sec.

 

 

The slowing down of time within the observed light seems to translate the Hubble values, presented to the observer, to the current expansion value.  At the 100 second mark (H = 1/100 = 0.0100), Emitter 1 was moving along its axis at 323.48 cm/sec at 32,348 cm from center; H = 323.48 / 32348.3 = 0.0100.  The delay of observation showed that the light was actually emitted at the 96.21 second mark. At that moment, H for Emitter 1 was 323.48 / 31122.22 = 1 / 96.21 = 0.0104.  But the light received by the observer present itself as just emitted, H = 311.22 / 31122.22 = 0.0100.  The age of the emission was therefore offered as t = 1 / H = 1/0.0100 = 100 seconds.  The same is true for Emitter 2, actual emission time was 95.86 seconds, but presented to the observer as H = 162.98 / 16298.15 = 0.0100, t = 1 / H = 100 seconds.

These two objects were moving at the same distance from center and at the same velocities but on different axes. The altered time ratios observed for each was different. That combined with different observed distances and velocities would make it seem unlikely that the illusions offered to every observer embedded within this pattern would be preserved, but they were. It would seem even more unlikely that observing the expansion happening between these two distance objects would preserve anything, but it did.  The delay likewise converted the information within the light to the current expansion value and preserved all the illusions.  I’m not sure how.

 

Actual motion of expansion between E1 and E2 (no delays)

Time	Actual H	α	Emitter 1 Actual Distance from Center	Emitter 2 Actual Distance from Center	Actual Distance between E1 and E2	H between 1 & 2
100 sec	0.01000	1.8	32,348.30	32,348.30	2,822.03	0.01000
101 sec	0.00990	1.8	32,671.78	32,671.78	2,850.25	0.00990
102 sec	0.00980	1.8	32,995.27	32,995.27	2,878.49	0.00980
103 sec	0.00971	1.8	33,318.75	33,318.75	2,906.69	0.00971
104 sec	0.00961	1.8	33,642.23	33,642.23	2,934.91	0.00961
4 sec			323.48cm/sec	323.48cm/sec	28.22 cm/sec

Total distance of actual motion between E1 and E2 during the 4 seconds of observation was

112.88cm at 28.22 cm/sec.

 

Observed motion of expansion between E1 and E2 with light delays

Time	Actual H	Observer’s Angle of viewing	Observed Emitter 1 Offset position	Observed Emitter 2 Offset position	Observed Distance between them	H btw 1 & 2 Calculated by observer
100 sec	0.01000	7.6	31,122.22	31,009.08	2,712.89	0.01000
101 sec	0.00990	7.6	31,433.45	31,319.17	2,740.02	0.00990
102 sec	0.00980	7.6	31,744.67	31,629.26	2,767.15	0.00980
103 sec	0.00971	7.6	32,055.89	31,939.35	2,794.27	0.00971
104 sec	0.00961	7.6	32,367.11	32,249.44	2,821.40	0.00961
4 sec			311.22 cm/sec	310.09 cm/sec	27.13 cm/sec

Total distance of observed motion between E1 and E2 during the 4 seconds of observation was

108.50cm at 27.12 cm/sec.

 

 

The delay of receiving the emitted light makes A and E appear to move in slow motion, but within this the proportional alterations of velocity and distance corrected the H to the current value at time of observation.  If speed of light delay with the observation of the motion of two objects moving apart are made to appear to move slower than they really are, then other actions at a distance would likewise appear so since together they are likewise diverging.  If Emitter 1 were a binary star system rotating around each other at 3 times per second, my observer should have viewed 12 full rotations, but instead would have recorded 11.55.  If he did not discern this pattern of motion, he would incorrectly report a rate of 2.89 rotations per second.  Every observation would have a different ratio of time slowdown. If the same binary pair were at the position of Emitter 2, the observer would report 11.49 rotations at 2.87 rotations per second.

 

Gravitational Lensing

 

I read that scientist were using Gravitational Lensing to study the expansion rate of the Universe, and that it had confirmed the value of H offered by recession observations.  I looked for raw data to understand how they were using these observations, but could find only the declaration that it confirmed current values of H.  I decided to build Gravitational Lensing into my simulator.

To do that, I let the simulator place a “Lensing Object” between any observer and the object being observed. It halves the angle of divergence between them (α) and places the Lensing Object at a distance from center that is the average distance from center of the observer and his object.  The Lensing Object will then be slightly offset from unbent light that will travel directly to the observer (Fig 1).

 

 

 

 

I let my simulator generate a standard data chart with no lensing.  At each pause in my chart, the simulator had moved the Emitter back toward center to find the point of emission for observed light.  For the Gravitational Lensing simulation, I programmed it to then move all three objects back to that moment in time (Fig 1).  I then built in a sub-simulator to let the system expand from that moment in the past until the light reached the Lensing Object (Fig 2).  It would then continue until the light reached the observer (Fig 3).

To accomplish this, I had to rework the equations that I had used to move the Emitter back in time. I needed one that moves the target object forward in time to the point of interception, (Figs 2 and 3).

 

 

 

      

 

                where C is the speed of light

 

 

 

 

    

 

 

Evaluation of Light Observed from an Emitting Object at 160,075 Seconds into Expansion History

I started the simulation at 1,000 seconds into Expansion (beginning point not shown in charts):

Observer: 6,000cm from center

Emitting Object:  6,000cm from center, α=90 degrees

Lensing Object 1:  6,366cm from center, α=40 degrees

Lensing Object 2:  5,376cm from center, α=40 degrees

Seed of Light (C): 200 cm/s

 

Emitting Object  (Undeflected viewing of emitted light -- shortest possible path to the observer)

Expansion Time at First Observation	H at First Observation	Observer Distance from Center	Emitter Distance from Center at time of Observation α = 90	Actual Distance between  Emitter and  Observer	Time for Emitted Light To Reach Observer	Expansion Time when Observed light was Emitted	H At time Observed Light was Emitted	Emitter Distance From Center at time of Emission	Distance Between Observer and Emission Point at Observation	Observer Calculated
100,000	1.0000E-05	600,000.00	600,000.00	848,528.14	4,155.43	95,844.57	1.0434E-05	575,067.44	831,085.17	1.0000E-05
150,000	6.6667E-06	900,000.00	900,000.00	1,272,792.21	6,233.14	143,766.86	6.9557E-06	862,601.17	1,246,627.76	6.6667E-06
200,000	5.0000E-06	1,200,000.00	1,200,000.00	1,697,056.27	8,310.85	191,689.15	5.2168E-06	1,150,134.89	1,662,170.35	5.0000E-06
1s/s		6.00cm/s	6.00cm/s	8.48cm/s	0.0416s/s	95,844.58s 0.958s/s		5.75cm/s	vO=8.31cm/s

   L=0.958

 

Deflecting Object 1 Data (Deflection and observation of second beam of light, emitted at the same moment):

Expansion Time when Observed light was Emitted	Expansion Time at Deflection	Deflector Distance from Center at Deflection	Time for Deflected Light To reach Observer	Expansion Time at Second (Deflected) Observation	Actual H at time of Second Observation	Observer Distance from Center at Second Observation	Distance Deflected Light Traveled (Perceived Relative Distance)	Observer Calculated HL	Observer Calculated HL
95,844.57	98,206.41	540,135.25	4,322.04	100,166.61	9.9834E-06	600,999.66	864,407.10	1.0000E-05	1.0000E-05
143,766.86	147,309.61	810,202.88	6,483.05	150,249.91	6.6556E-06	901,499.49	1,296,610.64	6.6667E-06	6.6667E-06
191,689.15	196,412.82	1,080,270.51	8,644.07	200,333.22	4.9917E-06	1,201,999.32	1,728,814.19	5.0000E-06	5.0000E-06
		5.50cm/s				6.00cm/s	Vf = 8.64cm/s

 

 

Object 1 Perceived (Projected) Location and Motion (Phantom Object 1)

Expansion Time at Second (Deflected) Observation	Actual H at time of Second Observation	Projected Location of Phantom Emission Point (Distance from Center) dP	Phantom Divergent Angle From Observer	Observer Distance From Phantom Emission Point	Expected Expansion Velocity for an Object at Projected Distance from Center   ()
100,166.61	9.9834E-06	785,097.58	76.13	866,825.49	7.84cm/s
150,249.91	6.6556E-06	1,177,646.37	76.13	1,300,238.23	7.84cm/s
200,333.22	4.9917E-06	1,570,195.16	76.13	1,733,650.97	7.84cm/s
		7.85cm/s		8.65cm/s

 

 

 

 

 

 

 

 

Deflecting Object 2 Data (Deflection and observation of second beam of light, emitted at the same moment):

Expansion Time when Observed light was Emitted	Expansion Time at Deflection	Deflector Distance from Center at Deflection	Time for Deflected Light To reach Observer	Expansion Time at Second (Deflected) Observation	Actual H at time of Second Observation	Observer Distance from Center at Second Observation	Distance Deflected Light Traveled (Perceived Relative Distance)	Observer Calculated HL	Observer Calculated HL
95,844.57	98,428.36	639,784.37	4,682.70	100,527.28	9.9475E-06	603,163.67	936,540.80	1.0000E-05	1.0000E-05
143,766.86	147,642.55	959,676.55	7,024.06	150,790.92	6.6317E-06	904,745.50	1,404,811.20	6.6667E-06	6.6667E-06
191,689.15	196,856.73	1,279,568.73	9,365.41	201,054.56	4.9738E-06	1,206,327.34	1,873,081.60	5.0000E-06	5.0000E-06
		8.50/cm/s				6.00cm/s	Vf = 9.36cm/s

 

 

Object 1 Perceived (Projected) Location and Motion (Phantom Object 1)

Expansion Time at Second (Deflected) Observation	Actual H at time of Second Observation	Projected Location of Phantom Emission Point (Distance from Center) dP	Phantom Divergent Angle From Observer	Observer Distance From Phantom Emission Point	Expected Expansion Velocity for an Object at Projected Distance from Center   ()
100,527.28	9.9475E-06	974,331.46	68.88	943,259.65	9.69
150,790.92	6.6317E-06	1,461,497.18	68.88	1,414,889.47	9.69
201,054.56	4.9738E-06	1,948,662.91	68.88	1,886,519.29	9.69
		9.69cm/s		9.38cm/s

 

 

 

 

 

 

 

 

Plot of Data Charts for Deflecting Object 1:

 

 

Analysis:

If an emission source were to “flash” on and back off, the observer could see two (or more) blips of light due to Gravitational Lensing. There will be an “undeflected” path to every observer, but a few observers will see the same flash again via deflected light. It appears that using data collected from those deflected flashes will present the same Hubble Constant Value as the undeflected observation.  This seems true no matter the path and no matter how many times a flash is deflected.  This pattern of Expansion will adjust the observed (relative) velocity according to the added distance traveled by the light.  This suggests that there are likely stars viewed that are not where they appear to be, deflections placing them in our sky far from their true location and motion.  From this simulator, it could be that Expansion data collected from these location illusions will present a calculation of H that is too high, depending on how long after the first observation is the flash is seen.

This simulation also suggests that a flash, once synchronized with the original observation, can be used to calculate the distance that the light traveled to reach the observer using only the red shift and the interval between sightings.  If so, this would be a way to measure distances with greater precision, and therefore the Hubble Constant Value.

The difference in speed between the two viewings divided by the difference in time between the two values times the speed of light, also provides the H value at the time of unobstructed viewing.

   

I wondered if this could be used to evaluate the Hubble Constant Value in terms of directly measured values, Δv and Δt.

         

 

Since

 

 

This means you could use Gravitational Lensing to calculate the distance traveled by the light having any two observations of simultaneously emitted light that travels different paths to the observer. 

     or    

     where C is the speed of light

 

Using observations at 160,075 seconds into expansion to determine the distance traveled by emitted light around Deflecting Object 1:

If observed light is seen and sync’ed for unaltered light and Deflecting Object 1

 

 

If observed light is seen and sync’ed for Deflecting Object 2 and Deflecting Object 1

 

 

From the Data Chart, the distance traveled by deflected light around:

Object 1 observed at 100,167 seconds into expansion was 864,407.0965 cm.  

Object 2 observed at 201,054 seconds into Expansion was 1,873,081.5986cm.

 

It appears that if you can observer two beams of light from a specific emitter, with each beam being emitted at the same moment (sync’ed), no matter the path, you can determine the distance the light traveled to get to the observer for both paths using only the red shift of each and the time interval between the two observations.  This could be done with greater precision than H = v/d, where d is an attempt to measure distance directy.

 

 

Speed of light delay in an accelerating expansion – the H for acceleration is reduced to the H of steady rate.

(I had to use a computer algorithm to determine “Time for light to reach Observer”, and I bumped up the speed of light in this simulation to 300,000cm/s).

.

Example 1: Observer will start at 500cm from center watching an object located at 1,000cm from center, α = 30 degrees

Pattern without Observational Delay								Speed of Light Observational Delay
Time of Observation	H at Time of Observation 2/t	Observer distance from center	Observer Velocity	Emitter distance from center at time of Observation	Emitter Actual Velocity	Distance between Observer and Object	Relative Velocity	Time for emitted light to reach observer	Emitter distance from center at time of emission	Actual Delayed Velocity	Observed distance	Observed Velocity	H Calculated from observation v/d	H For a steady rate expansion 1/t
10	0.200000	500	100	1,000.00	200.00	619.66	123.93	0.01	999.59	149.93	619.28	92.88	0.1499806	0.100000
50	0.040000	12,500.00	500	25,000.00	1000.00	15,491.42	619.66	0.05	24,948.55	598.72	15,444.35	370.63	0.0239976	0.020000
100	0.020000	50,000.00	1,000.00	100,000.00	2,000.00	61,965.68	1,239.31	0.21	99,589.82	1,194.91	61,590.59	738.94	0.0119976	0.010000
150	0.013333	112,500.00	1,500.00	225,000.00	3,000.00	139,422.79	1,858.97	0.46	223,620.50	2,480.61	138,161.67	1,531.42	0.0110843	0.006667
1000	0.002000	5.000E+06	1.000E+04	1.000E+07	2.000E+04	6.197E+06	12393.14	19.49	9.614E+06	1.105E+04	5.846E+06	6.715E+03	0.0011487	0.001000
1500	0.001333	1.125E+07	1.500E+04	2.250E+07	3.000E+04	1.394E+07	18589.71	42.66	2.124E+07	2.325E+04	1.280E+07	1.390E+04	0.0010865	0.000667
5000	0.000400	1.250E+08	5.000E+04	2.500E+08	1.000E+05	1.549E+08	6.197E+04	402.050	2.114E+08	5.434E+04	1.206E+08	3.080E+04	0.0002554	0.000200
50000	0.000040	1.250E+10	5.000E+05	2.500E+10	1.000E+06	1.549E+10	6.197E+05	36621.630	1.790E+09	3.508E+04	1.099E+10	2.415E+05	0.0000220	0.000020
			10.00cm/s/s		20.00cm/s/s		12.39cm/s/s			Decreasing acceleration		Decreasing acceleration

 

Example 2: Observer will start at 4,000cm from center watching an object located at 175,500cm from center, α = 30 degrees

Pattern without Observational Delay								Speed of Light Observational Delay
Time of Observation	H For an accelerating expansion	Observer distance from center	Observer Velocity	Emitter distance from center at time of Observation	Emitter Actual Velocity	Observed Distance	Relative Velocity	tr Time for emitted light  to reach Observer	Observed distance	Observed Velocity	Observer calculated H	H For a steady rate expansion 1/t
10	0.200000	4,000.00	800	175,500.00	35,100.00	172,047.52	34,409.50	0.51	154,444.03	21,355.69	0.1382746	0.100000
50	0.040000	100,000.00	4,000.00	4,387,500.00	175,500.00	4,301,188.09	172,047.52	9.37	2.811E+06	66,413.74	0.0236264	0.020000
100	0.020000	400,000.00	8,000.00	17,550,000.00	351,000.00	17,204,752.35	344,095.05	28.64	8.592E+06	115,629.02	0.0134571	0.010000
500	0.004000	1.000E+07	4.000E+04	4.388E+08	1.755E+06	4.301E+08	1.720E+06	273.02	8.191E+07	183,286.60	0.0022377	0.002000
1000	0.002000	4.000E+07	8.000E+04	1.755E+09	3.510E+06	1.720E+09	3.441E+06	641.18	1.924E+08	220,896.51	0.0011484	0.001000
			80.00cm/s/s		3,510.00cm/s/s		3,440.95cm/s/s			Decreasing acceleration

 

As with steady rate expansion, Observers see a slow motion, but in an accelerating expansion this slowing down of viewed motion grows slower with time.  The conversion constant L is no longer a constant but changes with time.  The speed of light in an accelerating expansion is disruptive to the perception of Hubble Motion, whereas in steady rate, it was not.

As with steady rate acceleration, the motion radio (new d/ new y) is a constant between two objects.  Unlike steady rate, accelerating expansion does not present this ratio as a constant to the observer who is having to deal with the effects of the speed of light.  If the motion ratio is changing for the observer, θ will be changing for the observer. The observer will see the object drifting across his sky. (To save space, I did not include the Emitter distance from Center at time of observation [new y] after delay or the changing θ.)  

These effects on observation caused by the speed of light diminish with distance. With great distance the rate of change of the motion ratio as the two diverge away from slows down, becoming close to a constant again and the drifting across the sky will slow to unobservable.

Unlike steady rate expansion, at closer range the H calculated after observational delays is altered to a value that does not reflect Hubble Motion, a relationship of motions. The observations made at the same moments (time) in the above charts should offer the same H values under Hubble Motion, but they don’t.   In Example 1 at 10 seconds, H = 0.14998/s. At the same 10 second moment of expansion Example 2 is H = 0.13827/s.  This is not Hubble motion but just d = v * t. (To me, Hubble motion is simply d = v * t, but it is more than this and should be expressed differently.  Hubble Motion, v = H * d, expresses a relationship of motions, which is compromised in an accelerating expansion by the speed of light. Just like with the motion ratio, this problem diminishes at great distances.

Observed motion begins to return to a meaningful Hubble relationships at great distances, but with a twist, the motion begins to look like steady rate expansion.  The greater the distance between objects (therefore the greater the relative velocity), the more speed of light delays helps accelerating expansion presents itself as steady rate.  At great distances, using actual distances, accelerations, and velocities, H = 2/t, but with observations under the influence of light propagation, H ≃ 1/t, steady rate.  

A problem with accelerating expansion is that actual velocities and relative velocities soon exceed light speed, and I had to end the simulations not knowing how to proceed. (I never had to struggle with this under steady rate, except with relative velocities, which likewise ended my simulations but just meant the objects no longer saw each other’s light.)  But up until those points, as my acceleration simulations approached these greater distances, the H calculated from observation looked more and more like the H of steady rate, but were always high.  I ran my simulations out to 20,000 years + and the H calculated seemed to be moving closer and closer to steady rate values, always high, but never quite got there. I felt this disproved this pattern as a model, if the expansion in our Universe is indeed an acceleration, but then I remembered something I had read.

 

 

Gravity:  Introducing Relative Acceleration

I knew that so far my simulator was clean motion, that is, nothing disturbs it.  I knew in the real Universe gravity alters motion so I felt I needed to see how gravity would affect these observations. I knew gravity causes objects to come together or move together around a Center of Momentum (CoM).  To start incorporating gravity into my simulator I wanted to know how it would affect two objects moving in this pattern as it pulled them together. Using the law of Conservation of Momentum, I discovered that as two objects are being pulled together each object is out-of-sync with the pattern, but their CoM is always in-sync.

I found that I could place two objects of any mass at different distances from center, and on the same axis of Expansion Motion, and their merged positions or orbits would remain in-sync in the pattern.  I determined their velocities based on this pattern, d=vH, and let gravity pull them towards each other.

Using data from my chart at 100 seconds into expansion (H=.01), I made the mass of the observer (20,000cm from center, 200cm/sec) to be 100kg.  The emitter (32,348cm from center, 323.48cm/sec) to be 200kg.

CoM = (20,000 * 100 + 32,348 * 200) / (100 + 200) = 28,232cm from center              

Velocity of CoM:  (200 * 100 + 323.48 * 200) / (100 + 200) = 282.32cm/sec

 

If the CoM is located at 28,232cm, the pattern velocity of my expanding disk would be

Pattern velocity = H * CoM = .01 * 28,232 = 282.32cm/sec

All objects pulled together by gravity eventually merge at CoM, or circle it. By the Law of Conservation of Momentum, it appears that gravity will leave common motion in this tiny universe moving in-sync with this expansion pattern. In other words, the relationships and illusions will be preserved in some form.

Even if merged masses and masses bound by gravity manage to stay in-sync, it is certain that an observer would be entangled in an orbit around a CoM of his own.  He is going to be out-of-sync.

I read that earth is part of a super group of galaxies moving against the CMB at about 600km/sec.  Earth is roughly moving 300km/sec.  That could mean that we are being currently slung by our network of orbits in the opposite direction of the motion of our group (but I could not find any published data comparing the vector directions).  If our super cluster is moving away from center, then we could be getting slung by our orbit back toward center at half the speed. 

To let my simulator help me examine the possible affects of the observer and his objects moving out-of-sync, I coded a parameter put the observer or one of his objects moving too slow or too fast directly away from center.

I set my observer at 6,000cm from center and the object being observed at 50,000cm.  If in-sync with the pattern, the Emitter will be moving at 5,000cm/sec away from center and the Observer at 600cm/sec.  For the simulation I set the observer out of sync too high and too low by 300cm/sec.   

 

Scenario 1:  α = 45 degrees, all motion in sync

Observations without Light Delay						Observations with Light Delay
Age of Expansion	H	Observer distance from center	Emitter Distance from center	Observed distance	Observed Velocity	Time for light to travel	Emitter Distance from center at time of emission	Observed Distance	Observed Velocity	Calculated H	θ
10	0.1000000	6,000.00	50,000.00	45,953.63	4,595.36	0.15	49,246.61	45,203.51	4,520.35	0.1000000	50.39
100	0.0100000	60,000.00	500,000.00	459,536.28	4,595.36	1.51	492,466.08	452,035.08	4,520.35	0.0100000	50.39
50000	0.0000200	3.00E+07	2.50E+08	2.30E+08	4,595.36	7.53E+02	2.46E+08	2.26E+08	4,520.35	0.0000200	50.39
10000000	0.0000001	6.00E+09	5.00E+10	4.60E+10	4,595.36	1.51E+05	4.92E+10	4.52E+10	4,520.35	0.0000001	50.39
		600.00cm/sec	5,000cm/sec		4,595.36	0.15s/s	49,246.61	45,203.51	4,520.35

 

Scenario 2:  α = 45 degrees, Observer is moving 300cm/sec out of sync too fast

Observations without Light Delay						Observations with Light Delay
Age of Expansion	H	Observer distance from center	Emitter Distance from center	Observed distance	Observed Velocity	Time for light to travel	Emitter Distance from center at time of emission	Observed Distance	Observed Velocity	Calculated H	θ
10	0.1000000000000	6,000.00	50,000.00	45,953.63	4,403.78	0.1507	49,246.61	45,203.51	4,332.24	0.0958385753672	50.39
100	0.0100000000000	87,000.00	500,000.00	442,776.14	4,409.14	1.452	492,740.20	435,587.92	4,337.60	0.0099580460911	53.12
1000	0.0010000000000	897,000.00	5,000,000.00	4,411,559.95	4,409.76	14.4666	4,927,666.82	4,339,990.75	4,338.23	0.0009995932285	53.40
10000	0.0001000000000	8.997000E+06	5.000000E+07	4.409946E+07	4,409.77	144.6136	4.927693E+07	4.338408E+07	4,338.23	0.0000999959457	53.43
50000	0.0000200000000	4.499700E+07	2.500000E+08	2.204901E+08	4,409.77	723.0445	2.463848E+08	2.169134E+08	4,338.23	0.0000199998379	53.44
10000000	0.0000001000000	8.999997E+09	5.000000E+10	4.409766E+10	4,409.77	144,607.74	4.927696E+10	4.338232E+10	4,338.23	0.0000001000000	53.44
		900.00cm/sec	5,000cm/sec		0.060cm/s/s	0.0151s/s			Decreasing acceleration

Scenario 3:  α = 45 degrees, Observer is moving 300cm/sec out of sync too slow

Observations without Light Delay						Observations with Light Delay
Age of Expansion	H	Observer distance from center	Emitter Distance from center	Observed distance	Observed Velocity	Time for light to travel	Emitter Distance from center at time of emission	Observed Distance	Observed Velocity	Calculated H	θ
10	0.1000000000000	6,000.00	50,000.00	45,953.63	4,403.78	0.1507	49,246.61	45,203.51	4,332.24	0.1030903753679	50.39
100	0.0100000000000	33,000.00	500,000.00	477,236.29	4,792.03	1.5647	492,176.30	469,422.10	4,713.54	0.0100411546840	47.85
1000	0.0010000000000	3.030000E+05	5.000000E+06	4,790,540.20	4,792.56	15.707	4.921465E+06	4.712085E+06	4,714.07	0.0010004212413	47.61
10000	0.0001000000000	3.003000E+06	5.000000E+07	4.79236E+07	4,792.57	157.1292	4.921435E+07	4.713876E+07	4,714.08	0.0001000042216	47.58
50000	0.0000200000000	1.500300E+07	2.500000E+08	2.39626E+08	4,792.57	785.6726	2.460716E+08	2.357018E+08	4,714.08	0.0000200001689	47.58
10000000	0.0000001000000	3.000003E+09	5.000000E+10	4.79256E+10	4,792.57	157,135.84	4.921432E+10	4.714075E+10	4,714.08	0.0000001000000	47.58
		300.00cm/sec	5,000cm/sec		0.060cm/s/s	0.015sec/sec			Decreasing acceleration

 

 

 There were 3 firsts for these simulations:

1.      The angle of observation (θ) changed with time. From my analysis of the vector motions to understand how this pattern made every object appear to be receding from every observer, I could see that for θ to remain constant the Motion Ratios (new d/ new y) must remain constant. If this pattern is undisturbed that remains true, but an out of sync situation causes that ratio to change with time even in the “actual” motion.  As a result, θ is changing, which means objects can now be seen to move across the observer’s sky within expansion motion.  If the altered relative motion is increased by the out of sync motion, the movement across the sky was clockwise, θ is decreasing.  If it is decreased, it was counterclockwise, θ is increasing.

2.      The H calculated by the observer was too high or too low, at close range and failed to reflect the clear relationships of Hubble Motion. This affected faded with distance.

3.      Objects appeared to the observer to be accelerating. Objects closest to the observer exhibit the appearance of accelerating.  The rate of acceleration decreases with the distance from observer, in directions, whether the observer is moving too slow or too fast. This “Relative Acceleration” faded away with distance away from observer, and is only present in the relative motion between observer and Emitter. There was no “actual” acceleration in the Expansion Motion of either. Expansion Acceleration is an illusion.

All three affects diminish with distance away from the observer, and even go away completely after a certain range.  In the many simulations I ran, this was consistent. The change in the angle  was greatest when objects are closer, but with distance it also becomes increasingly difficult to see. With distance the Hubble Constant Value calculated by the observer approaches the correct value, and the drifting across the sky slows and becomes undetectable. 

The reason the observed object appears to the observer to be accelerating and moving across the sky, is a disruption in the interaction between the merged vectors of motion from the two objects, the backbone of the illusions of all objects receding.  Out of sync motion causes the Motion Ratio (new d/ new y) to change with time.

If altered the velocity of any single object being observed, that object had its own profile of out of sync motion, but likewise maintained the appearance of recession and Hubble Motion unless I made the out of syn extreme.

 

The observer’s perspective:  a viewed acceleration in steady rate expansion.

I decided to examine a single point in time in the expansion process using a steady rate expansion, multiple objects at different distances, and with the observer out of sync. 

In the simulations below, I set up an observer and several objects all at the same distance from center (6000cm) and therefore all moving the same speed away from center, if all in sync.  The first chart represents all moving in sync with the pattern.  I choose 100,000 seconds into expansion as my observation time; H = .00001/s.  Each row of each chart represents a different object being observed at a different angle α from observer.  The charts that follow it represent out of sync expansions under the same starting scenario.

 

  Chart 1: Observer and Emitters at 6,000cm from center, no out of sync motion.

H=.0000100000000/s

Α	Time for Emitted Light to Reach Observer	Observed Distance	Observed Velocity	Observed Acceleration	Calculated H
10	0.0036	1,067.21	0.0107	0	0.0000100000000	1.0000000000000
45	0.0155	4,662.49	0.0469	0	0.0000100000000	1.0000000000000
70	0.0234	7,023.38	0.0702	0	0.0000100000000	1.0000000000000
90	0.0289	8,658.45	0.0866	0	0.0000100000000	1.0000000000000
130	0.0370	11,097.64	0.1110	0	0.0000100000000	1.0000000000000
160	0.0402	12,058.87	0.1206	0	0.0000100000000	1.0000000000000
180	0.0408	12,244.90	0.1224	0	0.0000100000000	1.0000000000000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chart 2:  Observer and Emitters at 6,000cm from center, Observer out of sync too slow.

H=.0000100000000/s

Α	Time for Emitted Light to Reach Observer	Observed Distance	Observed Velocity	Observed Acceleration	Calculated H
10	0.0035	1,064.47	0.0096	7.3632E-07	0.0000089980515	0.8998051542760
45	0.0156	4,670.76	0.0393	1.4435E-07	0.0000084210633	0.8421063252110
70	0.0233	7,000.52	0.0588	7.5711E-08	0.0000084035275	0.8403527545570
90	0.0288	8,630.21	0.0725	4.5763E-08	0.0000083987158	0.8398715792460
130	0.0369	11,061.40	0.0929	1.2754E-08	0.0000083950938	0.8395093766560
160	0.0401	12,019.48	0.1009	1.9816E-09	0.0000083942313	0.8394231254310
180	0.0407	12,204.90	0.1024	0.0000E+00	0.0000083940874	0.8394087352020

 

 

Chart 3: observer and emitters at 6,000cm, observer moving out of sync too fast.

H=.0000100000000/s

α	Time for Emitted Light to Reach Observer	Observed Distance	Observed Velocity	Observed Acceleration	Calculated H
10	0.0036	1,071.44	0.0131	7.2794E-07	0.0000121881228	1.2188122784470
45	0.0157	4,701.37	0.0546	1.4270E-07	0.0000116219269	1.1621926923980
70	0.0235	7,046.40	0.0818	7.4849E-08	0.0000116047190	1.1604718976200
90	0.0290	8,686.78	0.1008	4.5241E-08 0	0.0000115999971	1.1599997050810
130	0.0371	11,133.91	0.1291	1.2609E-08	0.0000115964425	1.1596442538460
160	0.0403	12,098.26	0.1403	1.9590E-09	0.0000115955961	1.1595596074170
180	0.0409	12,284.90	0.1424	7.2720E-18	0.0000115954548	1.1595454847500

 

 

 

Plot of Near Objects with Observer Moving Out-of-Sync (Different data from charts)

 

                                                                                         

Same Data Points as Objects Move Further Away from Observer

 

 

 

Chart 4:  Chart 2 at 6.6 million years into expansion.

H = 4.76E-18/s

α	Time for Emitted Light to Reach Observer	Observed Distance	Observed Velocity	Observed Acceleration	Calculated H
10	1.64329E+10	4.92986E+15	0.0235	0	4.76191E-18	1.0000000000000
45	4.02915E+10	1.20875E+16	0.0576	0	4.76191E-18	1.0000000000000
70	5.83322E+10	1.74997E+16	0.0833	0	4.76191E-18	1.0000000000000
90	7.12002E+10	2.13601E+16	0.1017	0	4.76191E-18	1.0000000000000
130	9.05653E+10	2.71696E+16	0.1294	0	4.76191E-18	1.0000000000000
160	9.82295E+10	2.94688E+16	0.1403	0	4.76191E-18	1.0000000000000
180	9.97143E+10	2.99143E+16	0.1424	0	4.76191E-18	1.0000000000000

 

 

My simulator could not reduce α significantly to examine much closer observed distances.  In order to see what closer distances look like I placed my observer at center, set him drifting slightly out of sync (his velocity within the pattern at center should be zero), and I let him watch 11 objects on the same axis at different distances.

 

Chart 5:  6.6 million years into expansion at closer/further observed distances, observer out of sync too slow.

H = 4.76E-18/s

Time for Emitted Light to Reach Observer	Observed Distance	Observed Velocity	Observed Acceleration	Calculated H
0.0633	18,992.58	9.9965E-14	0	5.26335E-18	1.1053041412590
0.3085	92,545.36	4.3447E-13	0	4.69472E-18	0.9858912703770
3,499.96	1.049987E+09	5.0073E-09	0	4.76190E-18	0.9999986531220
34,999,999.95	1.050000E+13	5.0000E-05	0	4.76191E-18	0.9999999998650
3.499994E+11	1.049998E+17	0.50000	0	4.76191E-18	1.0000000000000
3.442623E+15	1.032787E+21	4,918.03279	0	4.76191E-18	1.0000000000000
3.000000E+16	9.000000E+21	42,857.14286	0	4.76191E-18	1.0000000000000
1.981132E+17	5.943396E+22	283,018.86792	1.20000E-20	4.76191E-18	1.0000000000000
2.087475E+17	6.262425E+22	298,210.73559	2.14500E-18	4.76191E-18	1.0000000000000
2.098741E+17	6.296222E+22	299,820.10791	2.04405E-16	4.76191E-18	0.9999999999990
2.099874E+17	6.299622E+22	299,981.99588	2.01038E-14	4.76191E-18	0.9999999981090

 

At this extreme age of expansion, great distances appear to wash out the out of sync affects, restoring the appearance of clean Hubble Motion relationships, but closer distances show some distortion. At very close distances, there is no detectable relative motion.  At these closer distances, with the observer out of sync, the Hubble Values are off, even offering an appearance within the relative motion of acceleration that increases with distance.  Objects far off wash out the effects from out of sync motion.

I read that the value of H as calculated from observation is higher than the value derived from the CMB.  Since scenario 3 is based motion from actual calculated motion of earth (and our super cluster) relative to the CMB, this could suggest that current observations from our expanding Universe are offering a H that might be high.  This model could offer a way to bring them closer together, suggesting that the value calculated from observations might be high.

 

H (derived from observation) =  =  = 2.33 E ^-18 /s

H (derived from CMB) =  = = 2.07 E ^-18 /s

 

“Dark Flow”

NASA reports an observation that suggest a local expansion within the greater expansion of the cosmos. They named it “dark flow” and have no explanation for it. Out of sync observation motion within this suggested pattern produces an observation that sounds much like that.  θ changes in the observer’s sky because his out of sync motion allows him to see the perpendicular motion vectors.  This motion makes his objects move in his sky (see image below).  If he is watching two objects out in front of him, one on each side of his expansion axis, he will perceive them to be moving away from each other. He will perceive no cause for this associated with gravity or expansion motion.  It will appear to him to be an expansion within the expansion.  Since distance reduces his observation of θ changing, this extra motion will appear to be very local and fading away altogether with distance.

 

Observer out of sync too fast with light speed delays   ·        Looking in the direction of expansion motion the observer will see all objects expanding away from him but they will also appear to be moving away from his expansion axis, away from each other. ·        In the opposite direction, he will see objects moving towards his axis, towards each other.	Observer out of sync too slow with light speed delays   ·        Looking in the direction of expansion motion the observer will see all objects expanding away from him but they will also appear to be moving towards his expansion axis, towards each other. ·        In the opposite direction, he will see objects moving away his axis, away from each other.
·        This rate of change of the additional expansion motion will increase with parpendicular position to his expansion axis, being most noticible around 60 degrees (with observer moving too fast, around 120 if moving too slow). ·        With increasing distance from observer, this affect deminishes and goes away. ·        This expansion within expansion will appear to be “local” in scope and non-existant at greater distances.

 

I coded my simulator to place objects at near and far distances from the observer at the same angle in the observer’s sky, and I set my observer moving out of sync too fast.  In other words, I let the observer stare off into space at a set angle and see objects at different distances (see data charts below).  I wanted to more quantify the shape of the expansion-within-expansion (“dark flow”) when the observer is moving out of sync.  What I could clearly see is that if the observer is looking in the direction of his motion, the rate of expansion within expansion will increase with distance away from his axis. In addition, the closer the object is to him the greater the observed rate of this expansion away from his axis, with distance this expansion away from his axis goes away completely, just like relative acceleration.  If he looks in the opposite direction, he will see a contraction toward his axis. However, that contraction will be much slower, even for objects that are a comparable distance out in front of him, and therefore the contraction will be more difficult to see.  The rates of expansion and contraction will depend on how much he is out of sync.

If he is moving too slow, at the same rate he was moving too fast, the affect is exactly opposite, the data charts are exactly reversed. The expansion away from his axis will now be happening behind him and at exactly the rate he would see in front of him if he is moving too fast.  The contraction will now be in front of him and happening at the same much more subtle rate.  His out of sync motion (if along his axis of expansion motion) will help him locate his axis of motion away form center, but not his direction along it.  He will not be able to tell if he is moving too fast or too slow, looking toward center or away from it.

 

15 degrees	30 degrees	60 degrees
Obj starting at 1,000cm from observer t Observed Distance Observed θ Δθ 100 999.77 15.003   200 1,065.75 29.058 0.14055 300 1,186.75 40.864 0.11806 400 1,348.04 50.173 0.09309 500 1,536.99 57.347 0.07175	Obj starting at 1,000cm from observer t Observed Distance Observed θ Δθ 100 999.79 30.006   200 1,239.13 53.804 0.23798 300 1,614.67 68.274 0.1447 400 2,053.00 76.948 0.08674 500 2,521.59 82.49 0.05542	Obj starting at 1,000cm from observer t Observed Distance Observed θ Δθ 100 999.87 60   200 1,732.00 90 0.30002 300 2,645.78 101 0.10893 400 3,605.67 106 0.05209 500 4,582.78 109 0.03004
Obj starting at 4,000cm from observer t Observed Distance Observed θ Δθ 100 3,998.69 15.003   200 7,036.55 17.111 0.02108 300 10,078.19 17.947 0.00836 400 13,120.97 18.396 0.00448 500 16,164.26 18.675 0.00280	Obj starting at 4,000cm from observer t Observed Distance Observed θ Δθ 100 3,998.77 30.006   200 7,149.34 34.016 0.04010 300 10,313.48 35.57 0.01554 400 13,481.65 36.394 0.00824 500 16,651.54 36.904 0.00510	Obj starting at 4,000cm from observer t Observed Distance Observed θ Δθ 100 3,999.07 60   200 7,548.23 66.6 0.06588 300 11,133.26 69 0.02362 400 14,727.99 70.2 0.01210 500 18,326.70 70.9 0.00735
Obj starting at 6,000cm from observer t Observed Distance Observed θ Delta θ 100 5,997.64 15.003   200 11,032.79 16.347 0.01344 300 16,070.20 16.849 0.00502 400 21,108.25 17.111 0.00262 500 26,146.57 17.272 0.00161	Obj starting at 6,000cm from observer t Observed Distance Observed θ Δθ 100 5,997.76 30.006   200 11,141.09 32.578 0.02572 300 16,292.69 33.525 0.00947 400 21,446.59 34.016 0.00492 500 26,601.46 34.318 0.00301	Obj starting at 6,000cm from observer t Observed Distance Observed θ Δθ 100 5,998.20 60   200 11,529.26 64.3 0.04308 300 17,083.21 65.8 0.01511 400 22,643.21 66.6 0.00769 500 28,205.67 67.1 0.00466
Obj starting at 10,000cm from observer t Observed Distance Observed θ Δθ 100 9,994.74 15.003   200 19,025.83 15.782 0.00779 300 28,058.18 16.060 0.00278 400 37,090.86 16.202 0.00142 500 46,123.69 16.289 0.00087	Obj starting at 10,000cm from observer t Observed Distance Observed θ Δ 100 9,994.94 30.006 0 200 19,130.87 31.503 0.01498 300 28,271.42 32.033 0.00529 400 37,413.20 32.303 0.00271 500 46,555.50 32.468 0.00164	Obj starting at 10,000cm from observer t Observed Distance Observed θ Δθ 100 9,995.67 60.00   200 19,510.93 62.60 0.02544 300 29,039.42 63.40 0.00875 400 38,571.34 63.90 0.00443 500 48,104.65 64.10 0.00267
Obj starting at 40,000cm from observer t Observed Distance Observed θ Δθ 100 39,939.03 15.00   200 78,914.05 15.19 0.0019 300 117,889.35 15.26 0.0006 400 156,864.73 15.29 0.0003 500 195,840.13 15.31 0.0002	Obj starting at 40,000cm from observer t Observed Distance Observed θ Δθ 100 39,939.83 30.01   200 79,016.57 30.37 0.0036 300 118,094.37 30.49 0.0012 400 157,172.45 30.55 0.0006 500 196,250.63 30.59 0.0004	Obj starting at 40,000cm from observer t Observed Distance Observed θ Δθ 100 39,942.75 60.00   200 79,391.08 60.60 0.00625 300 118,842.58 60.80 0.00210 400 158,294.89 61.00 0.00105 500 197,747.51 61.00 0.00063
Obj starting at 80,000cm from observer t Observed Distance Observed θ Δθ 100 79,771.86 15.00   200 158,580.78 15.10 0.0009 300 237,389.84 15.13 0.0003 400 316,198.93 15.14 0.0002 500 395,008.04 15.15 9E-05	Obj starting at 80,000cm from observer t Observed Distance Observed θ Δθ 100 79,773.45 30.01   200 158,684.17 30.19 0.0018 300 237,595.41 30.25 0.0006 400 316,506.79 30.28 0.0003 500 395,418.22 30.30 0.0002	Obj starting at 80,000cm from observer t Observed Distance Observed θ Δθ 100 79,779.28 60.00   200 159,062.44 60.30 0.00312 300 238,347.17 60.40 0.00104 400 317,632.30 60.50 0.00052 500 396,917.58 60.50 0.00031
Obj starting at 10,000,000cm from observer t Observed Distance Observed θ Δθ 100 967,561.05 15.00   200 1,934,187.53 15.00 0 300 2,900,814.03 15.00 0 400 3,867,440.53 15.00 0 500 4,834,067.03 15.00 0	Obj starting at 10,000,000cm from observer t Observed Distance Observed θ Δθ 100 967,579.76 30.006   200 1,934,321.68 30.021 0.00015 300 2,901,063.64 30.025 0.00005 400 3,867,805.61 30.028 0.00002 500 4,834,547.58 30.029 0.00001	Obj starting at 10,000,000cm from observer t Observed Distance Observed θ Δθ 100 967,648.31 60.010   200 1,934,813.12 60.036 0.00026 300 2,901,978.06 60.044 0.00009 400 3,869,143.03 60.048 0.00004 500 4,836,308.02 60.051 0.00003

 

120 degrees	150 degrees	165 degrees
Obj starting at 1,000cm from observer t Observed Distance Observed θ Δθ 100 1,000.07 120.010   200 2,646.07 139.115 0.19105 300 4,359.47 143.421 0.04306 400 6,083.58 145.292 0.01872 500 7,811.32 146.337 0.01044	Obj starting at 1,000cm from observer t Observed Distance Observed θ Δθ 100 1,000.14 150.006   200 2,909.76 159.900 0.09895 300 4,837.32 161.936 0.02036 400 6,767.51 162.812 0.00875 500 8,698.57 163.298 0.00487	Obj starting at 1,000cm from observer t Observed Distance Observed θ Δθ 100 1,000.16 165.003   200 2,977.68 169.989 0.04986 300 4,959.76 170.994 0.01004 400 6,942.48 171.424 0.00431 500 8,925.43 171.664 0.00239
Obj starting at 4,000cm from observer t Observed Distance Observed θ Δθ 100 3,999.87 120.01   200 8,543.87 125.828 0.05818 300 13,114.74 127.599 0.01772 400 17,691.67 128.455 0.00855 500 22,270.92 128.958 0.00504	Obj starting at 4,000cm from observer t Observed Distance Observed θ Δθ 100 4,000.16 150.006   200 8,880.52 153.233 0.03228 300 13,769.06 154.171 0.00937 400 18,659.36 154.617 0.00446 500 23,550.32 154.877 0.00261	Obj starting at 4,000cm from observer t Observed Distance Observed θ Δθ 100 4,000.24 165.003   200 8,970.21 166.656 0.01653 300 13,942.33 167.131 0.00474 400 18,914.89 167.356 0.00225 500 23,887.63 167.487 0.00131
Obj starting at 4,000cm from observer t Observed Distance Observed θ Δθ 100 99,677.71 120.01   200 199,855.83 120.258 0.00248 300 300,035.19 120.341 0.00082 400 400,214.86 120.382 0.00041 500 500,394.66 120.407 0.00025	Obj starting at 1,000,000cm from observer t Observed Distance Observed θ Δθ 100 967,904.18 150.006   200 1,936,646.70 150.021 0.00015 300 2,905,389.26 150.025 0.00005 400 3,874,131.83 150.028 0.00002 500 4,842,874.40 150.029 0.00001	Obj starting at 1,000,000cm from observer t Observed Distance Observed θ Δθ 100 967,922.89 165.003   200 1,936,780.76 165.011 0.00008 300 2,905,638.63 165.013 0.00003 400 3,874,496.51 165.014 0.00001 500 4,843,354.39 165.015 0.00001

 

 

 

Out of Sync Gravitational Lensing

When everything was in sync, Gravitational Lensing generated the same H for all lensed light as if it were not lensed.  The raw data, speed and distance reflected the alteration, but the H they produced was the same.  This is not so if the observer is out of sync.  But, as separation grows, the effect of the out of sync goes away, Gravitational Lensing returns to offering the same H for all light emitted by the observed object, lensed or not. 

The results remain consistent with past simulations; if the observer is out of sync too slow, the H value calculated by the observer is low compared to the actual expansion value at the time of observation but becomes accurate at greater distances.  If too high, the H calculated is high, but becomes accurate with greater distances.

 

Initial Observation Chart:  Observation of Light Traveling directly from Emitting Object to Observer with Observer out of sync too slow

Expansion Time at First Observation	H at First Observation	Observer Distance from Center	Emitter Distance from Center α = 70	Time for Light to Reach Observer	Observed Distance	Emitter Distance at time of Emission	Observed Velocity	Observed Acceleration	Observer Calculated
100,000	0.0000100000000	6,062.45	6,122.45	0.02329714	6,989.14	6,122.45	0.05320224	2.521688E-07	0.0000076085184
100,100	0.0000099900100	6,065.57	6,128.57	0.02331488	6,994.46	6,128.57	0.05321060	8.360912E-08	0.0000076063364
100,200	0.0000099800399	6,068.69	6,134.69	0.02333261	6,999.78	6,134.69	0.05321894	8.341860E-08	0.0000076017487
100,300	0.0000099700897	6,071.82	6,140.82	0.02335035	7,005.11	6,140.81	0.05322726	8.322862E-08	0.0000075971643
100,400	0.0000099601594	6,074.94	6,146.94	0.02336809	7,010.43	6,146.94	0.05844419	2.500000E-20	0.0000075925833
2.100000E+17	4.761905E-18	6.557143E+15	1.2857142857E+16	40,910,934,093	1.2273280228E+16	1.2857140352E+16	0.05844419	0	4.76190500E-18
2.200000E+17	4.545455E-18	6.869388E+15	1.3469387755E+16	42,859,073,812	1.2857722144E+16	1.3469385131E+16	0.05844419	0	4.54545500E-18
2.300000E+17	4.347826E-18	7.181633E+15	1.4081632653E+16	44,807,213,531	1.3442164059E+16	1.4081629910E+16	0.05844419	0	4.34782600E-18
2.400000E+17	4.166667E-18	7.493878E+15	1.4693877551E+16	46,755,353,250	1.4026605975E+16	1.4693874688E+16	0.05844419	0	4.16666700E-18
2.500000E+17	4.000000E-18	7.806122E+15	1.5306122449E+16	48,703,492,968	1.4611047891E+16	1.5306119467E+16	0.05844419	0	4.00000000E-18

 

Secondary Observation Chart:  Observation of Light Emitted at the same moment traveling from Emitting Object, around Lensing Object, to Observer who is out of sync to slow

Expansion Time at First Observation	H at First Observation	Expansion Time at Second Observation	H at Second Observation	Time for Light to Reach Observer	Distance Light Traveled	Observed Velocity	Observer Calculated H	Observer Calculated H
100,000	0.0000100000000	100,000.02	0.0000099999976	0.02448876	7,346.63	0.06507526	0.0000088489689	0.0000331008736
100,100	0.0000099900100	100,100.02	0.0000099900075	0.02451045	7,353.13	0.06509687	0.0000088500024	0.0000331027310
100,200	0.0000099800399	100,200.02	0.0000099800375	0.02453215	7,359.64	0.06511843	0.0000088451108	0.0000330302118
100,300	0.0000099700897	100,300.02	0.0000099700873	0.02455385	7,366.16	0.06513994	0.0000088402186	0.0000329579641
100,400	0.0000099601594	100,400.02	0.0000099601569	0.02457557	7,372.67	0.07671415	0.0000088353257	0.0000328859862
2.100000E+17	4.761905E-18	2.10000054E+17	4.76190400E-18	5.369991E+10	1.610997E+16	0.07671415	4.761905E-18	4.761905E-18
2.200000E+17	4.545455E-18	2.20000056E+17	4.54545300E-18	5.625704E+10	1.687711E+16	0.07671415	4.545455E-18	4.545455E-18
2.300000E+17	4.347826E-18	2.30000059E+17	4.34782500E-18	5.881418E+10	1.764425E+16	0.07671415	4.347826E-18	4.347826E-18
2.400000E+17	4.166667E-18	2.40000061E+17	4.16666600E-18	6.137132E+10	1.841140E+16	0.07671415	4.166667E-18	4.166667E-18
2.500000E+17	4.000000E-18	2.50000064E+17	3.99999900E-18	6.392846E+10	1.917854E+16	0.07671415	4.000000E-18	4.000000E-18

Where subscript “f” is values from the second observation, and “o” is from the first

 

Orbital Out of Sync Motion

Above, I explored “out of sync motion” by setting the observer out of sync with the overall expansion motion with the observer moving directly away from center.  I had explored the idea that Conservation of Momentum (COM), mass clumps moving together, might be what is moving in sync with the pattern, not the observer.  The observer would be in orbit around his COM.  Likewise, the objects he is observer would be in orbit around their COM.  The observer and the objects being observed would not be in sync but held close to in-sync by their COM’s.   I decided to write another simulator to move COM points away from center in this Expansion pattern, instead of objects, and added code to a single object in orbit around each (the observer included). 

To do that, I added parameters to each point (COM)  moving away from center to describe an object moving in a circle around it.  For each object, these parameters could alter the radius of orbit, the time it takes to complete a single orbit, and a starting angle of orbit measured from the COM’s axis of motion.  For my first simulation, I created 13 COM points with orbital parameters manually chosen at random.   When I plotted the results, it looked familiar, like charts I see every time I google “Hubble Value”.

 

A Sample Chart from the Webb:

 

 

Configuration of My Manually Selected Random Objects

In these charts, the COM’s are moving away from center in-sync with this Expansion Motion pattern.  Each has an object orbiting (one is the observer). But, the out of sync motion is held in check within the pattern by its COM.

 

 

My Initial Charts: 

 

Data Chart 1 – Several objects are observed Blue Shifted

 

 

 

Data Chart 2  – All objects observed Red Shifted

 

 

Data Chart 3 – All objects observed Red Shifted

 

 

When I averaged the Hubble Constant Values calculated from each object being observed, the value was consistently high.  When I thought about it, I could see how the orbits could create this problem, especially seeing how lopsided I had created the distribution of COM’s around the observer’s COM. 

I ran another simulation with just two objects for the observer.  Each object’s COM was the same distance from the observer’s COM, 180 degrees apart, and with all orbits the same radius and in sync.  When the Expanison was young, this configuration gave the observer an accurate Hubble Constant Value with a percent error of 0.00% and in all positions of the observer’s orbit around his COM.  The error increased to 2.70% as the Expansion age reached 1 billion years.  The2 .7% was consistent consistent all the way around the observer’s orbit.   It was clear to me that two objects 180 degrees apart, with their distances from their respective COMs to the observer’s COM being equal, and orbits in sync, offered an offset of the errors introduced by the observer’s orbit.

I let my simulator generate evenly distributed COM/object pairs in circles around my observer and his COM.  I left all orbits in sync and the same radius. I then ran multiple simulations with the observer’s starting orbital angles off his COM’s axis away from center to 0, 90, 180, and 270 degrees.

 

Evenly Spaced COMs around the Observer and His COM

 

In the early stages of Expansion for this configuration, the average H was accurate to within 0.0%    As the Expansion aged the accuracy dropped, but after 1 million years it only dropped to about 3%, comparable to watching just two objects of perfect placement.  What was most different was that the observer calculated a large range of individual H values that averaged out the errors caused by the observer’s orbit.  The result was an accurate Hubble Constant Value, no matter what quadrant the observer was in around his COM.  I let the age of Expansion go out to 1 billion years. 

 

Lopsided Configuration of Many Objects

I set up the simulator to again generate many COM/object pairs around my observer’s COM.  This time, I let it place the pairs unevenly in different quadrants.

 

Observer Moving in First Quadrant of His Orbit Around His Center of Momentum

 

 

Observer Moving in Second Quadrant of His Orbit Around His Center of Momentum

 

 

Observer Moving in Third Quadrant of His Orbit Around His Center of Momentum

 

 

 

Observer Moving in Third Quadrant of His Orbit Around His Center of Momentum

 

 

In this configuration of objects, uneven density around the observer and his COM, none of the pauses to make observations yielded an accurate Hubble Constant Value. The more lopsided the distribution around him the more off the results and the direction of the errors for a given configuration were influenced by what quadrant the observer was in.

 

Randomly Generated “Homogeneuos” COM/Object Configuration, with Randomly Generated Orbital Parameters

Adding orbits to COM’s in sync proved problematic to get an accurate Hubble Constant Value, even from averages.  The difficulty depended a complicated mix of the configuration of the observer and the observation points presenting him with data. I found that lopsided data (objects mostly in one direction in his sky) presented the most difficulty for an observer to calculate an accurate Hubble Constant Value. Not only is it difficult to cancel out the skewing of results caused by the orbits by just adding many objects, but the much easier task of canceling out skewing caused by the observer’s orbit was not happening.

When the observer had an even distribution of objects around him (for every object in one direction and distance there was an equal object 180 degrees) and all the orbits were in sync, then the percent error went down to within a few percentage points.  If I let the simulator randomly build the orbits around the objects, it became problematic to get a reasonable estimate of the Hubble Constant Value.  Even with the skewing caused by the observer’s orbits being averaged out, the orbits were causing chaos.  Quantity of objects helped, but strangely, as I let the simulator expand the disk, the accuracy went up and down.  It could range from 3% percent error to 25%.  Distance helped also, but when I let this simulator get very old it became flakey, it seemed like the percent error was stabilizing into a range from 5 to 25%.

Even when the percent error was high, I could search through the data to find two COM points that were 180 degrees apart around the observer’s COM and the same distance away from the observer’s COM.  If the orbits where at least somewhat in-sync,  I could then calculate a Hubble Constant Value from the two objects and get an accurate estimate from their average.  This did not work if the objects selected were too much out of phase in their orbits.  If I instead found several object pairs in this configuration the average was much more accurate, but the observer had no way to check the results. From the observer’s perspective, it was always impossible to know if current observations from even a carefully selected homogeneous configuration was going to offer a good result. Sometimes it did, sometimes it didn’t.  The problem was not in the accuracy of the individual measurements but the complexity of the interactions of orbits within the given configuration of observation points.

 

Relative and Observed Acceleration

I have not yet coded this new simulator to allow me to set the COM’s out of sync.  I suspect that if I do it will add the Relative Acceleration or Deceleration in the closest objects.  When the observer’s orbit is throwing the observer away from center, he will observer a slight Relative Acceleration in objects closest to him and that acceleration will decrease with objects that are increasingly far away.  If his orbit is throwing him back toward center, he will see slight Relative Deceleration for objects closest to him, likewise decreasing with distance away.  All of my individual observation points showed orbital acceleration and deceleration caused by the swinging of the observer toward or away from his center by his orbit and the same for each object.  Relative Acceleration/Deceleration would be seen only in “local” or close objects and it would fade away as distance increases.  If I add COM out of sync motion to this simulation, I suspect Relative Acceleration/Deceleration will be a composite and more confusing.

Neither have I coded light delays into this new simulator, which will be interesting because it will slow or increase the observed rates of orbit for each object.

 

CMB verses Observation: Observation questionable

If this Expansion Motion is current, it could suggest that an observer will be unlikely to yield an accurate value of the Hubble Constant Value from observations, especially if he thinks all the data points should yield the same values.  However, I could be that with extreme Expansion Age a given configuration of distant objects would settle into a given range.  If a second configuration of objects is viewed at the same time that are within a different range, say much closer, then the results could give a much lower or higher value, depending on the lopsidedness and the observer’s orbit around his COM.  Closer objects would also be more susceptible to change by adding or remove observation points.

 

More Possible Real Observations Extracted from this Simulator

As I plotted these data charts, I recognized them.  I posted a chart,  at the beginning of these simulations of orbital motions, made by Dr. Hubble that looks like the plots that emerge from these new simulations. 

The struggle to reconcile the Hubble Values from CMB verses Observation be a struggle predicted by these simulations.    I also just read that a new value has come out of a study based on Red Giants.  That value landed in between the two old opposing values.  This simulation would suggest that this different set of data points, if grouped from a closer range or heavily clumped arose a specific arc of the sky, could, and likely would, yield a significantly different value.

 

The Age of Expansion:

Without the disruptions in the pattern due to gravity and light propagation (or even in those cases, at extreme distances), an observer is able to use any expansion rate measured between two objects to determine how long the disk has been expanding.  Assuming that all points were once together in one location at the beginning of the expansion, this would be the age of the universe. The velocity observed between two objects divided by its velocity will produce how long they have been diverging. The result should be the same for every rate of expansion between two objects everywhere in the disk, so long as the pattern is intact.  Even if the

The speeds, or relative speeds, between the objects will bring them back together in the same amount of time as all other objects. All will come together back at center. In reality, during the time the two objects are moving back together (he could be one of the two objects), he will not realize that he will be returning to center himself. He would see the objects moving directly toward him when they are actually both (or all) moving back down their own axis toward center. His perceived reunion will be a mutual return to center. In the time it takes them to unite, everything everywhere in the disk will return to center with them.  Objects badly skewed be gravity will affect the accuracy.

An example from our data: Observer Y measured Object A at 166.67cm moving directly away from him at 3.33 cm/sec.  That means it would take that object 50.0 seconds to return to him at that speed. If motion were reversed, he would see it coming directly toward him, but it is an illusion.  From the “actual” motion chart, at that same moment, Object A was moving directly away from true center at 7.27cm/sec and was 360cm from center.  Observer Y was moving directly away from center at 5cm/sec and was 250cm from center. It would take both of them 50 seconds to return to center, and this would be their “actual” return motion.

 

 

Accelerating Expansion verses Set Velocities

The motion in this model can be either an actual expansion of the fabric of space or just mass drifting away from center under inertia. If an actual expansion of space itself, then this simulation could also be done by “pulling” each axis at an accelerated rate.  If so, the data charts will show each object accelerating away from center at a rate proportional to its distance from center (see charts below – each axis is pulled at a rate of 5cm/s/s).  At each pause, the velocities of each object will still conform to the Hubble formula, v = H * d, and all observations, illusions, and machanics will work the same way. Therefore, in this model steady expansion or accelerated expansion will both yield Hubble motion.

A difference will be in calculations of H.  H = 1/t when expansion was steady will no longer be valid:

 

The H in an accelerating expansion will be double the value in a steady rate expansion.  Likewise, the age of the universe can no longer be determined from dividing the distance observed by the corresponding velocity observed. If the expansion is accelerating, you will have to determine the observed acceleration and then decelerate the object toward closing the observed gaps.  This could help determine whether the expansion of the universe is an acceleration or steady speed. If the age of the universe is known, either the formula derived from steady rate expansion motion or the accelerated rate motion should yield a reasonable estimate, but not both. If the universe started out accelerating and then stopped, or started out steady and acceleration started later, then neither formula would yield a reasonable approximation.

If this model is a steady speed expansion:

Convert current measurement of H units/sec:

AgeOfUniverse = 1/H = 1/2.333 X E-18/sec =4.28569XE17sec = 13,589,847,934 years

 

If this model is an accelerated expansion:

AgeOfUniverse = 2/H = 27,179,695,868 years

 

 

Actual and Observed motion for Observer Y and Object A, if the expansion is an acceleration of 5cm/s/s

Time into expansion	Hubble Value	Radius of Disk after each expansion	Velocity of expansion (outer most object)	Observer Y   new d	Velocity of Y	Object A R = 50 θ=60 deg   new y	Velocity of A	Observed Distance	Observed Velocity	Observed θ
α						23.41
15 sec	0.133333	562.50	75	75.00	10	108.97	14.529	50.00	6.67	60
16 sec	0.125000	640.00	80	85.33	10.66	123.98	15.50	56.88	7.11	60
50 sec	0.040000	6250.00	250	833.33	33.33	1,210.78	31.96	555.49	22.22	60
51 sec	0.039216	6,502.50	255	867.00	34.00	1,259.69	48.91	577.93	22.67	60
5000 sec	0.000400	62,500,000.00	25,000.00	8,333,333.33	3,333.33	12,107,777.78	2,446.25	5,554,928.73	2,222.22	60
5001 sec	0.000400	62,525,002.50	25,005.00	8,336,667.00	3,334.00	12,112,621.37	4,843.59	5,557,150.92	2,222.67	60
Acceleration of each object due to expansion			5.00cm/s/s		0.667cm/s/s		0.9686cm/s/s		0.4444cm/s/s

 

 

Actual and Observed motion for Observer Y and Object B, if the expansion is an acceleration of 5cm/s/s

Time into expansion	Hubble Value	Radius of Disk after each expansion	Velocity of expansion (outer most object)	Observer Y   new d	Velocity of Y	Object B R = 50 θ=200 deg   new y	Velocity of B	Observed Distance	Observed Velocity	Observed θ
α						-31.40
15 sec	0.133333	562.50	75	75.00	10.00	32.82	4.38	50.00	6.67	200
16 sec	0.125000	640.00	80	85.33	10.67	37.34	4.67	56.88	7.11	200
50 sec	0.040000	6250.00	250	833.33	33.33	364.67	14.59	555.61	22.22	200
51 sec	0.039216	6,502.50	255	867.00	34.00	379.40	14.88	578.06	22.67	200
5000 sec	0.000400	62,500,000.00	25,000	8,333,333.33	3,333.33	3,646,666.67	1,458.67	5,555,690.91	2,222.22	200
5001 sec	0.000400	62,525,002.50	25,005	8,336,667.00	3,334.00	3,648,125.48	1,458.96	5,558,823.70	2,222.67	200
Acceleration of each object due to expansion			5.00cm/s/s		0.667cm/s/s	0.2917cm/s/s	0.2917cm/s/s/		0.4444cm/s/s

 

 

Universal Flash:  CMB verses Observation

 

I read about a disparity between observation verses CMB in the search for the current Hubble Constant value.  It seemed to me that if the light waves that make up the CMB are directionless, and all emitted at a common moment (relatively speaking) in expansion, a “flash” in the Universe’s past, then maybe I could use my simulator to play with something like that.

I wanted to use my simulator to create a universal flash with a stationary observer to see through time.  My observer would need to receive an unlimited supply of light from increasingly far away distances in all directions.  Every second would bring new photons from objects that were just a little further away than the object that emitted the light he just measured.

I came up with a way to view this in my expansion simulator. I could set my observer at center (which would render him expansion motionless) and then every direction he looked would be α=0.  Instead of placing billions of objects spaced evenly apart along his line of sight, I could just use several objects and treat them as samplings.  I could then let the simulator expand the universe as it was designed to do.  I could then simulate a flash by extracting the data from each object’s chart for a randomly selected moment for the flash.  I could place the extracted data (one row per object) in a new data chart as if was data from one source, a composite object. The new chart would record the emission position of each object at the time of the flash.

It occurred to me that the many flashes from many sources coming from one direction would look to him like one continuous beam of light, as if emitted from a single source.  A continuous stream of photons from lined-up sources could create the appearance of a single star in the sky receding from him.  It would be a “Phantom” object.

The composite chart would show how much time it takes for each object’s light to reach the observer, how far away the emission point was, and a offer a trace of the emission points observed and its virtual velocity.  I felt that information could be used to calculate a “Flash Hubble Value” using the Hubble formula. 

I had to alter the code that determines the length of time that light travels between emitter and observer. Instead of knowing the observing position and pushing the emitter back down its axis to know when the light he is seeing was emitted (in the past), now the light emission point is frozen in place and I had to know when its light will intercept the observer (in the future).  Since the observer is sitting still and the emission points frozen, the light bursts will be the only movement.

In the sample data below, I selected 1000 seconds (H_E=0.001) into the expansion as the flash point. 

 

 

In the first composite chart below the observer is set at center, so not moving.  I placed 5 objects on his axis of motion, α = 0 and θ = 0, so all the objects are lined up.  Each row below is an extract from the individual object’s data charts at 1000 seconds, the flash point for each of them.  Since the location of the flash points is frozen in time (all light observed in the future will point back to them), the only thing moving is the emitted light,   In the two charts that follow it I set the observe moving slightly (using the out of sync motion settings).

 

 

Data in chart below extracted from regular expansion data charts.  For each object data was selected from the 1,000 second point, H_E=0.001:

Composite Chart 1 - Phantom Object: Observer at center, not moving.  Flash points are frozen in time: (no expansion motion, the only motion is light), C=200cm/sec

	Emitter Distance from center at time of flash	Observer distance from center at time of observation	Light Travel Time (since flash) tf	Expansion Time at Observation	Hubble Value at Observation	Hubble Value of travel Time (Hf = 1/tf)	Phantom Object Observed Distance Dr	Observed Hubble Constant vr/Dr	Observed θ
Obj 1	60,000.00	0	300	1,300.00	0.000769	0.003333	60,000.00		0
Obj 2	100,000.00	0	500	1,500.00	0.000667	0.002000	100,000.00	0.002000	0
Obj 3	200,000.00	0	1,000.00	2,000.00	0.000500	0.001000	200,000.00	0.001000	0
Obj 4	400,000.00	0	2,000.00	3,000.00	0.000333	0.000500	400,000.00	0.000500	0
Obj 5	1,000,000.00	0	5,000.00	6,000.00	0.000167	0.000200	1,000,000.00	0.000200	0
	940,000cm vP=200cm/s	0 vO=0cm/s	4,700 sec	4,700 sec			940,000cm vr=200cm/s

V_r =  = C

 

Composite Chart 2 - Phantom Object: Observer at center, moving at 10cm/sec.  Flash points are frozen in time, C=200cm/sec

	Emitter Distance from center at time of flash	Observer distance from center at time of observation	Light Travel Time (since flash) tf	Expansion Time at Observation	Hubble Value at Observation	Hubble Value of travel Time (Hf = 1/tf)	Phantom Object Observed Distance Dr	Observed Hubble Constant vr/Dr	Observed θ
Obj 1	60,000.00	11,428.57	242.8571	1,242.86	0.000805	0.004118	48,571.43		0
Obj 2	100,000.00	13,333.33	433.3333	1,433.33	0.000698	0.002308	86,666.67	0.002308	0
Obj 3	200,000.00	18,095.24	909.5238	1,909.52	0.000524	0.001099	181,904.76	0.001099	0
Obj 4	400,000.00	27,619.05	1,861.90	2,861.90	0.000350	0.000537	372,380.95	0.000537	0
Obj 5	1,000,000.00	56,190.48	4,719.05	5,719.05	0.000175	0.000212	943,809.52	0.000212	0
	940,000cm vP=210cm/s	44,761.9 vO=10cm/s 1	4,476 sec	4,476.19 sec			895,238cm vr=200cm/s

 

 

 

Composite Chart 3 - Phantom Object: Observer at center, moving at -10cm/sec.  Flash points are frozen in time, C=200cm/sec

	Emitter Distance from center at time of flash	Observer distance from center at time of observation	Light Travel Time (since flash) tf	Expansion Time at Observation	Hubble Value at Observation	Hubble Value of travel Time (Hf = 1/tf)	Phantom Object Observed Distance Dr	Observed Hubble Constant vr/Dr	Observed θ
Obj 1	60,000.00	-12,631.58	363.1579	1,363.16	0.000734	0.002756	72,631.58		0
Obj 2	100,000.00	-14,736.84	573.6842	1,573.68	0.000635	0.001743	114,736.84	0.001743	0
Obj 3	200,000.00	-20,000.00	1,100.00	2,100.00	0.000476	0.000909	220,000.00	0.000909	0
Obj 4	400,000.00	-30,526.32	2,152.63	3,152.63	0.000317	0.000465	430,526.32	0.000465	0
Obj 5	1,000,000.00	-62,105.26	5,310.53	6,310.53	0.000158	0.000188	1,062,105.26	0.000188	0
	940,000cm vP=190cm/s	-49,473.68 vO= -10cm/s	4,947.37 sec	4,947.37 sec			989,473cm vr=200cm/s

 

·        The observer sees every Phantom Object moving directly away from him at the speed of light, whether he is sitting still or moving.

·        There is a Flash Hubble Constant Value H_f = 1/t_f , where t_f = Age of flash. 

·        Every “flash” has an independent Hubble Expansion, its own Hubble Constant Values.

·        Since the relationship of the Phantom Object and the observer is Hubble Motion, H_f is reducing with time.

·        With age, H_f becomes more and more of a constant, depending on sensitivity of data.

·        If the observer is set in motion, looking in the direction of motion, the perceived density of the emission points will increase and the time to view them will decrease.

·        If the observer is set in motion, looking in the opposite direction of motion, the perceived density of the emission points will decrease and the time to view them will increase.

 

 

The observation of receding objects and the observation of the remnants of a flash both present Hubble Motion relationships that are independent of each other:

 

 

Chart 1 is an observer siting still and observing the light from the flash as it reaches him.  In Charts 2 & 3, the observer is in motion.  I used my formula for a conversion constant that I derived from light propagation delays to try to express the compression rates in the bottom rows of the charts.  The distances are not to real objects but to light burst points.  It is more like a frequency of light bursts being viewed:

 

where v_O=velocity of observer, and C is the speed of light (v_r=C).

 

It seemed to almost work.  This formula was off by a consistent factor unique to each chart for all my simulations of phantom objects with my observer in motion.  By trial and error (so not sure why this works) I found a formula that expresses the factor I needed for each chart to make my old formula work.  I used it to come up with a conversion formula for phantom objects in motion, as viewed by an observer not in motion, to motion observed for the same phantom object while he is in motion.  I called the conversion factor L_P:

 

The correction factor is the reciprocal of

 

From this conversion factor I could translate observations of compression of time and distance (totals in the bottom rows) from my observer not in motion to my observer in motion:

 

 

            

 

 

From Chart 2 (Observations of the flash in the direction the observer is moving; C = 200, v_O = 10)

 

 

 

From Chart 3 (Observations of the flash in the opposite direction the observer is moving; C = 200, v_O = -10)

 

 

 

For every scenario, observed light bursts present the observer with a Phantom object moving away from him at the speed of light (v_r).  When the observer is in motion the flux of emission points changes, observed frequencies increase or decrease (v_P).

 

 

New Simulator: Flash motion

 

My Expansion simulator couldn’t examine a flash at various angles, so I coded a new simulator to focus on flash events.  To do that, I worked backwards from the observation to the virtual motion of the Phantom object (which again is not a physical object but a trace of the emission points that provide the light of observation, as if it was a single object doing the emitting.  The trace would provide the rate, or frequency, that emission points are viewed.)  I built into this new simulator the ability of the observer to watch at various angles.

I built the new simulator to conform the observer to the expansion pattern of the previous simulator, (v=distance from center/age of expansion, moving directly away from expansion center). As I ran more and more simulations, I began to see that this was not necessary because the observation of a flash turned out to be completely dependent on the motion of the observer, in sync or not, and  independent of the ongoing expansion round him.

Step one of my new simulator was to determine the distance from the observer’s current position to the emission point of the current pulse of light being viewed;

               Observed distance = (Age of Flash) * C

From that physical distance, I calculated the physical location based on the angle he is looking.  From that, the distance to the center of expansion and the divergent angle α.

This was how my simulator worked. I began running simulations and plotted the results. On my first plot I could see that the emission points were forming a straight line. I could see immediately that α was changing with time.  Yet, when I drew a line through them the trace it created was a straight line.  The line did not pass through expansion center.  It traced a virtual path that intersected the real path of the observer at his position, where he was, when the flash happened.

The data and plots resembled the suggestions from my expansion simulator, that the Flash has its own expansion motion relationships, its own Hubble Motion Values, and now I could clearly see them starting at the moment of the flash.  I then added a calculation of α at the “Flash Point” along the observer’s path and reran the simulations.  This new α did not change with time.  There was Hubble Motion between the observer and the Phantom Object, both would have left a common point at a set velocity.

The virtual velocities of some of the phantom objects exceeded the speed of light and some didn’t. Since these are not real objects, but frequencies of emission points, this was not a violation. The paths aren’t a velocity but represent the distribution of emission points observed at the angle of observation. The virtual path was providing the rate, or flux, at which the observer was seeing light pulses go past him.  The relative velocity of the “observed” phantom objects, no matter how many pulses per second were representing them, is always the speed of light, but the trace of the emission points creating it might be above or below it.  When I plotted full simulations I saw how important this was, a boundary appeared between red and blue shift observations.

 

Plot of a simulation with observer at center, not moving. 

The speed of light in this simulation is 200cm/s.  Therefore, this plot represents the base (at rest) frequency of observed pulses, which turns out to always be C * density of emitters at the time of the flash.

 

Observer velocity: 0cm/s

Θ = varying degrees (all look the same to the observer when he is not moving)

Flash point:  1000 seconds into expansion

 

Data Chart of Observer not Moving

 

Observer velocity: 0cm/s

Θ = 0 degrees

Flash point:  1000 seconds into expansion

C=200cm/s

Age of Expansion	α at center of expansion	Observer Distance From Expansion Center	Emission Point Distance from Center	α at flash point (Position of Observer at time of flash)	Emission Point Distance from Flash Point df	Time For Light to reach Observer tf	Observed Distance Dr	Calculated Hp (vr /Dr) (1/ tf)
2000	0	0.00	200,000.00	0	200,000.00	1,000.00	200,000.00	0.0010000
2100	0	0.00	220,000.00	0	220,000.00	1,100.00	220,000.00	0.0009090
2200	0	0.00	240,000.00	0	240,000.00	1,200.00	240,000.00	0.0008333
2300	0	0.00	260,000.00	0	260,000.00	1,300.00	260,000.00	0.0007692
		DO=0cm vO=0cm/s			Df=60,000cm vP=200.00cm/s		Dr=60,000cm vr =200cm/s

If there were 3 per cm emitters at the moment of the flash then the observer is seeing: v_p  * 3 = 600.00 pulses per second (at rest frequency)

 

 

 

Data Chart of Observer Moving at 10cm/s and looking 30 degrees from his forward motion axis:

 

Observer velocity: 10cm/s

Θ = 30 degrees

Flash point:  1000 seconds into expansion

C=200cm/s

Age of Expansion	α at center of expansion	Observer Distance From Expansion Center	Emission Point Distance from Center	α at flash point (Position of Observer at time of flash)	Emission Point Distance from Flash Point	Time For Light to reach Observer tf	Observed Distance Dr	Calculated Hp (vr /Dr) (1/ tf)
2000	27.37	20,000.00	217,550.46	28.62	208,720.15	1,000.00	200,000.00	0.0010000
2100	27.48	21,000.00	238,417.86	28.62	229,592.17	1,100.00	220,000.00	0.0009090
2200	27.57	22,000.00	259,286.00	28.62	250,464.18	1,200.00	240,000.00	0.0008333
2300	27.65	23,000.00	280,154.71	28.62	271,336.20	1,300.00	260,000.00	0.0007692
		DO=3,000cm vO=10cm/s			Df= 62,616.05cm vP=208.72cm/s		Dr=60,000cm vr =200cm/s

If there were 3 per cm emitters at the moment of the flash then the observer is seeing: v_p  * 3 = 626.16 pulses per second

 

 

Plot of the above chart

 

Plot of the same data but from the observer’s perspective (observed or relative motion)

 

 

Data Chart of Observer looking 170 degrees from forward motion axis:

Observer velocity: 10cm/s

Θ = 170 degrees

Flash point:  1000 seconds into expansion

C=200cm/s

Age of Expansion	α at center of expansion	Observer Distance From Expansion Center	Emission Point Distance from Center	α at flash point (Position of Observer at time of flash)	Emission Point Distance from Flash Point	Time For Light to reach Observer tf	Observed Distance Dr	Calculated Hp (vr /Dr) (1/ tf)
2000	168.90	20,000.00	180,337.29	169.48	190,159.85	1,000.00	200,000.00	0.0010000
2100	168.95	21,000.00	199,352.39	169.48	209,175.84	1,100.00	220,000.00	0.0009090
2200	169.00	22,000.00	218,367.65	169.48	228,191.82	1,200.00	240,000.00	0.0008333
2300	169.04	23,000.00	237,383.02	169.48	247,207.81	1,300.00	260,000.00	0.0007692
		DO=3,000cm vO=10cm/s	s		Df= 57,047.96cm vp=190.16cm/s		Dr=60,000cm vr =200cm/s

If there were 3 emitters per cm at the moment of the flash then the observer is seeing: v_p * 3 = 570.48 pulses per second

 

 

Plot of Relative Motion from above chart

 

 

Observer looking directly behind him.

 

Observer velocity: 10cm/s

Θ = 180 degrees

Flash point:  1000 seconds into expansion

C=200cm/s

Age of Expansion	α at center of expansion	Observer Distance From Expansion Center	Emission Point Distance from Center	α at flash point (Position of Observer at time of flash)	Emission Point Distance from Flash Point df	Time For Light to reach Observer tf	Observed Distance Dr	Calculated Hp (vr /Dr) (1/ tf)
2000	0	20,000.00	180,000.00	0	190,000.00	1,000.00	200,000.00	0.0010000
2100	0	21,000.00	199,000.00	0	209,000.00	1,100.00	220,000.00	0.0009090
2200	0	22,000.00	218,000.00	0	228,000.00	1,200.00	240,000.00	0.0008333
2300	0	23,000.00	237,000.00	0	247,000.00	1,300.00	260,000.00	0.0007692
		vO=10cm/s			Df=57,000.00cm vp=190.00cm/s		Dr=60,000cm vr =200cm/s

If there were 3 emitters per cm emitters at the moment of the flash then the observer is seeing: v_p * 3 = 570.00 pulses per second

 

(It turns out that the observer’s position at flash is also virtual, not necessarily on his axis away from expansion center.  With this Flash analysis, his current axis of motion points back to a projected position where he would have been at time of flash based on his current velocity.  He may never have actually been in that position.  In this analysis, if he changes direction his “projected location at the moment of the flash” instantly moves with him.)

 

The data from my first simulator used to evaluate observation of a past universal flash was from the perspective of watching a common set of flash points with my observer at different speeds.  To compare this Flash Simulator’s data to that data the same span of emission points needs to be watched. Since that was not the way this simulator works, I had to calculate it:

 

 

 

Using the data chart for the observer moving at 10cm/s and watching at 30 degrees:

 

 

I had to reevaluate the conversion factor formula derived from the Flash analysis in the Expansion simulator to take into account different angles of observation:

 

 

From the equations derived using the first simulator:

 

            

 

           

 

The two simulators are producing the same relationship of motions.  The Expansion Simulator could only watch a set of emission points from different observational perspectives.  The Flash Simulator gives a perspective of observations from light emitted at set moments in time for the observer.  It also allows for evaluations of movement relationships at any direction desired.

 

Determining the speed of the trace (v_pt)

 (the virtual velocity of the Phantom object)

 

 

v_p = speed of Phantom object (or trace of emission objects through space)

v_o = speed of observer

θ = angle observer is watching against his forward motion

t = time since flash

 

 

 

 

Vector Analysis:

Since the motion of the observer and the relationships with the Phantom object create Hubble Motion, I can explore a flash using relationships from “Source of the Illusions”.

Since in “prefect” Hubble Motion the horizontal vectors cancel out only the observed (relative) perpendicular velocity vectors are needed to evaluate Phantom object motion:

 

 

Since the observed (relative) velocity (v_r ) for a phantom object is always C:

 

The velocity of the Phantom object (v_p) is going to be greater than light speed and can be calculated:

 

 

Therefore, I should be able to determine α (the angle between the observer and his emission points path at the projected position where the observer was be at the point of flash):

 

Phantom objects are not real objects, but represent flash points observed since the flash, a frequency of light bursts in objects/cm.

If ρ_f is the density of emitting objects at the time of the flesh (emission points/cm) then the frequency of observed emission points is,

 

 

 

The frequency observed of the flash when the observer is at rest (v_O=0) is measured when the observer is not moving, that is when he is located at the center of expansion.  When the observer is at rest the velocity of the phantom objects in every direction will be C (that is, the trace will be moving across the sky at C).

 

 

 

 

Therefore:

 

 

Using the vector relationships this can also be expressed as

 

 

Plot of full simulation: Observer’s Perspective at rest (located at true expansion center)

 

Plot of full simulation: Observer in motion (velocity = 75% of light speed):

 

 

Plot of full simulation: Observer in motion (velocity = 5% of light speed):

 

 

 

Reducing the speed of the observer alters the frequencies shift of observed emission points, and the angles of the Red/Blue shift transition boundaries.  Only the speed of light alters the base frequency rate at which that boundary is defined.

 

I ran many simulations using various speeds for light.  The plots above are samples using 200cm/sec.  I used values as high as 300,000cm/s.  The higher the speed of light the higher the frequency values observed for emission points at any angle.  No matter what value I used there was a boundary (an angle) between Red and Blue Shift observations that was defined by the speed of light.  That was true because the Red/Blue Shift Boundary was demarcated by the frequency of observed mission points with observer at rest, which is C *density of the universe at the time of the flash.  The upper boundary, when my observer’s speed was approaching the speed of light was 120 degrees, regardless of the speed light I used. The lower boundary was when he was approaching 0 speed. Each speed of light has its own unique at rest frequency that defines this boundary.

 

The angle of the Blue/Red Boundary depends on the observer’s motion and appears to be a factor of his speed as a percentage of the speed of light.

 

 

 

 

 

This Red/Blue Shift Doppler boundary for any flash is demarcated by the angle at which the virtual velocity of the trace path (v_p) is equal to the observed (relative) velocity of the Phantom object which is always C,( v_P = v_r = C).  v_P and v_r are equal when the observer is at rest.  Therefore, at this angle, the observed frequency of pulses equals the frequency observed when the observer is at rest.

 

 

 

Therefore,

 

 

 

 

There are two points around a circle that will yield this value of cos. The other is,

 

 

 

 

 

This could be the first hope of the observer determining his velocity in the universe.  If he can get a frequency reading of the flash all the way around him and find the Angle of Red/Blue Shift, he can determine his velocity, but still no way to orient himself toward center. (Not knowing the nature of his out-of-sync situation.)

 

In the “Plot of Full Simulation” the simulation discovered the boundary to be at 112.03 degrees.  From this observation, the observer can calculate his speed in the universe, but it tells him nothing about his direction:

 

 

v_o =  - 2C cos(“Angle of Red/Blue Shift Boundary”) = - 2C  cos(112.03) = 150.04cm/s

 

 

The actual velocity I set for the observer was 150cm/s (75% the speed of light). 

 

 

Both simulators suggest that the Hubble Constant value for a flash, H_f, is not the same as that of the observational expansion, H_E.  In this simulator, H_E – H_f, will give the observer the time in history of the flash.  That implies that if H_E < H_f,  , the flash happened before physical expansion began.  That doesn’t play well with current theories.

 

Even so, I am including this idea -- for one, because I have been including whatever comes out of my simulator even when it seemed that actual observations would invalidate it (only to then learn that it doesn’t). I decided to include it also because I wonder now if light propagation from a flash event, with emission points frozen in place, just might not ever offer the same Hubble Constant Value as an ongoing expansion motion of light emitting objects. Unless the flash and the expansion are simultaneous, they do not make the same presentation.   Observation of a flash is always a straight line between the point of emission and the point of observation.  Moving emitting objects dictate location of the emission points that make up the continuous beam of light.  A flash can substitute emission points to maintain motion of a phantom object, keeping it always directly away from the observer, wherever he looks.  A flash presentation doesn’t care what generated the light.

Current theory about space itself expanding might demand that the red shift of received light comes from the expansion of the space it is traveling through. If that theory requires the two offer the same value, but they don’t, it might mean that stretching space is not what is stretching wavelengths.

 

When the flash happened:  Density of the Universe

There may be a way the observer can determine the time, within the expansion, that the flash occurred (that is, if the flash is a part of the expansion).  In the expansion pattern of the first simulator, if the density of all mass starts out homogeneous then it will remain so throughout expansion, from the center of the expansion to the outer reaches, density will decrease evenly with time. If the light was emitted from mass caught up in the expansion, then it contains information about the physical density of the Universe at the time of the flash (emission points per cm). If that is discernable, and if he can determine the current physical density, then an observer can use that link between the two determine when the flash happened.

In this simulation, to determine the density of his universe in the present, the observer can measure the distance (d_R) to a far-off object (where measurable Hubble motion is linear -- out beyond relative acceleration and dark flow) and count the number of objects between him and it.

 

=

where v_R is relative velocity of the observed object

 

Since this is Hubble relationships, the object count between the observer and his distant object is constant so he can use his count and Hubble Motion parameters of the outer object to determine the density of the universe at any time in history,

 

where t is the historical time desired and H_E is the current Hubble Constant Value from observation.

 

The flash point positions are frozen in time and each flash point represents the position of the emitter (object) at the time of flash. The emission points he is observing contain a record of the density of the Universe at the time of the flash.

 

where v_P is the speed of the trace of observed emission points.

      Δt is the timespan that emission points are counted.

 

 If he measures his emission points while looking at the angle of red/blue boundary, then v_P=C,

 

 

This simulator offers a way to determine the density of universe at the time of the flash (ρ_f) from observable parameters:

 

The observer can measure the emission point frequency of the flash at 0 and 180 degrees.

 

 

Also, at θ = 90 degrees,

 

 

Solve both for v_o and setting them equal, he can solve for the density at the time of the flash in terms of strictly observable data:

 

 

He can also determine his own velocity in the universe from strictly observable data

 

 

 

If he knows his velocity…

he can determination the density of the universe at the time of the Flash using a single reading taken at the Red/Blue shift Boundary:

 

 

 

Or from a reading made at ANY angle

 

 

 

Knowing the density of the universe at the time of the flash, he can determine when the flash happened.  The flash would have happened when the density of the universe was the same as the density recorded within the flash,

 

    where t is the time of the flash

 

 

 

Therefore, the density of the Universe can be used to determine the expansion Hubble Constant Value at the time of the flash:

 

H_{E(at flash)} = 1/t_{E(at flash)}

 

In the simulation that generated Chart 3 I set the density at the time of flash at 3 objects per cm.  I set the time of the flash to be 1,000 seconds into expansion.  So, if my observer watches at his red/blue shift angle for 5 seconds he will count 3,000 emission points (objects).  He would then calculate the density of the Universe at the time of the flash:

 

  

 

He can confirm this using direct observation data (the values below extracted from data used to create Chart 3):

f_0degrees = 630.0000 e/s (observed emission points/s at time of observation which represent objects/s viewed at time of flash)

f_90degrees = 600.7495 e /s

f_180degrees = 570.0000 e /s

 

 

 

Knowing the density observed in the flash, the time of the flash can be calculated. Chart 3 started at 2,000 seconds into expansion.  If my observer spots an object 10,000cm away (and it is in sync) he will measure its relative velocity to be 5cm/second (v_E =Hd_E, where H=0.0005).  He would count 15,000 objects between it and him.

 

 

This calculation is not the time since the flash, from which the Hubble Constant for the flash could be determined. This is the expansion time at the time of the flash.  I want to know the H of the flash verses the H of expansion.

The “Flash Hubble Constant Value” at time of observation can be directly measured from current observations of the flash combined with current observations of the universe.  If the observer selects a distant object moving away from him in clean Hubble motion:

 

 

ð 

 

where

H_E = Current Expansion Hubble Constant Value

H_f = Current Flash Hubble Constant Value

v_R  =  the relative velocity of the observed object

d = distance to observed object

#objs = number of objects between the observer and the observed object

ρ_E = Current density of the universe (#objs/d)

ρ_f = Density of the universe at the time of the flash

 

 

The Flash Hubble Value can be calculated from current measurable flash and expansion parameters:

 

where

f is the emission points counted in the observed light from the flash

 

What’s true in this disk is true in a sphere:

Since our disk was sliced from a sphere such that the center, the observer, and the observed object define the slice, and since you could therefore rotate this disk within the sphere in any direction or orientation, all observations remain true anywhere within the sphere.

 

Homogeneous Expansion:

If you place evenly distributed dots on a rubber band and stretch it, the space between each dot increase at the same rate, proportional to the length of the band. The density drops with time, inversely proportional to the length of the band. Current observations offer that space is homogeneous, if that were not so this model would be ruled out.

 

Example:

If we look at two circles of observation around the observer and make the distribution of objects around each to start out with the same density, how will the densities compare as Expansion Motion progresses?

At 10,000 seconds into Expansion Motion

First Circle:  R = 1,000cm from center (or the Observer). 

Therefore, rate of expansion away from center (or observer):  .1cm/s.

Circumference of circle: 6,283cm

Number of objects on circle: 628

Arch distance between objects: 10cm (approx.)

Density:  0.1 objects/cm

 

Second Circle:  R = 5,000cm from center (Observer)

Rate of expansion away from center (or observer):  .5cm/s.

Circumference of circle: 31,416cm

Number of objects on circle: 3,142

Arch distance between objects: 10cm (approx.)

Density:  0.1 objects/cm

 

 

At 50,000 seconds into Expansion Motion

First Circle:  R = 5,000cm from center (or Observer). 

Rate of expansion away from center (or observer):  .1cm/s.

Circumference of circle: 31,416cm

Number of objects on circle: 628

Arch distance between objects: 50cm (approx.)

Density:  0.02 objects/cm

 

Second Circle:  R = 25,000cm from center (or Observer)

Rate of expansion away from center (or observer):  .5cm/s.

Circumference of circle: 157,080cm

Number of objects on circle: 3,142

Arch distance between objects: 50cm (approx.)

Density:  0.02 objects/cm

 

 

If the event that gave mass this motion also distributed mass evenly (homogeneously), then every unit of mass would experience every other moving away at the same rates.  If truly homogeneous, the net force of gravity on each unit of mass would be net zero (perhaps even at the atomic force level).  From the center of the sphere, where everything is moving the slowest, until you approach the outer edges, density would drop with time, but remain the same everywhere.  (It would seem reasonable that as you approach the outer most fringes mass would feel a pull back toward center.) 

Even once disrupted, the merged masses and Centers of Momentum will reflect the original distribution at the start of Expansion Motion, and this pattern of motion.

 

 

Luminosity and Acceleration

Just a thought:  When reading about “Dark Flow” in one article a scientist wrote that under Hubble Motion theory holds that there should never be lateral motion caused by Expansion.  I also read that the reason Dr. Adam Weiss declared the Expansion of our Universe to be accelerating is because very distant galaxies appear dimmer than they should be at their calculated distance due to Hubble Motion.  I assume that under current Expansion Theory the angle of Expansion motion between two objects will always be zero.  I found a basic General Relativity equation for luminosity (I think).

Using this equation, relativistic beta’s influence on the apparent brightness of a star would be minimum for Expansion motions under current Expansion Theory (since cos θ = 1).  Therefore, under current Expansion Motion theory General Relativity would dim luminosity at a minimum.

 

 

However, in the pattern of my simulator θ would rarely be zero (see image below).  In my simulations, θ spans the range of 0 to 90 degrees. Every observed object is much more likely to have a value > 0 and less than 90.  Therefore, if General Relativity were applied to the pattern of Expansion in my simulator, virtually every far distant object (with relative velocities approaching large values) would be expected to exhibit a lowered luminosity, which Dr. Weiss reports is observed and under current Expansion Theory, would require our Universe to be under an accelerating Expansion.  Or, combined with not being able to detect Dark Energy, it could be a clue that the current theory is not right. 

 

 

 

This model would not have to be an ongoing expansion force:

If objects are moving away from each other due to the fabric of space expanding, that suggests an interface, or friction, between space and mass. If so, how is it that we observe mass traveling frictionless through space? If there is friction when space moves past mass, then there is friction when mass moves through space.

This pattern suggests a way that the universe would not have to be an ongoing expansion of space itself for every observer to perceive himself located at center. Some event would only have to set mass in this pattern of motion and then let inertia take over. Perhaps space was an initial expansion of 100% energy, or a field, and at some state there was a conversion to mass, which inherited the motion and drifted away in this expanding Hubble motion pattern.  On the other hand, this could be an expanding fabric of space.

Either way, whether this expansion pattern is driven or maintained by inertia, this pattern presents everything observer everywhere with an illusion of center.