Hubble Expansion

A Constant at the Speed of Light

 

All mass moving away from a center in an expanding Hubble pattern could produce observations in our Universe:

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.

 

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

·         The actual velocity of every object depends on its distance from center, increasing incrementally with distance.

·         The relative velocity between any two objects also depends on their distance apart, increasing with distance.

·         All expansion motions, actual and relative, are relatable using Hubble Law and the Hubble Constant Value associated with any moment in time.

·         Expansion motion is easier to measure (because its speed is greater) the greater the distance observed.

·         Expansion motion is difficult to measure in “local” objects, and the scope of “local” expands with expansion age.

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

·         If expansion was homogeneous when all was at cente, it will remain homogeneous throughout the history of it.

·         Gravity can clump mass together, but the center of momentum will remain consistent with this expansion pattern and preserve the illusions, including that of center.

·         The Hubble Value reduces with each tick of the clock, as objects spread apart and as the density of the universe drops.

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

·         Light delayed viewing of distant objects will offer a Hubble Constant value (velocity and distance relationship) 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 will present any observer with the same value of the Hubble Constant value, no matter how much time is between their observations, or the path 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 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.

 

A Simple Plan for a Spherical Expansion Simulator:

I started out studying a stretching elastic strip.  I could see an illusion of center for every observer placed at any point along its length as it is stretched.  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 disk cut from it, then it would be true for the whole sphere.  The sliver would have to include the center of the sphere, extracting a thin round disk.

I placed objects within my extracted disk and drew an axis through each from center. To simulate expansion, I imagined thousands of elastic strips attached at its center (each axis), with objects attached anywhere on them.  I then stretched (expanded) the disk by pulling each strip simultaneously away from center, all at the same steady rate. --  I found that I could also stretch my disk at an accelerated rate and still yield observations. Some of those simulations are included below, but over time I became convinced of steady rate. --  Strange observations emerged from my simulations, but I researched each and learned they are actually being observed. Running both accelerated and steady rate simulations.  I concluded over time, based on actual observations I was learning about, that if our Universe is expanding in this pattern it is more likely a steady rate, all objects moving away from a center under inertia, gravity, and speed of light parallax.  

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”:

 

R= Radius of circle around Observer

y=distance from center of disk to object being observed

θ = angle from Observer’s axis to the Object being observed

x = opposite side of Observer’s view of object

d=distance from center of disk to Observer

α = Angle at center of disk between object and Observer

a= adjacent side of Observer’s view of object

z = distance from center of disk to x

O = radius of disk

 

 

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 = vy / (new y) = vR / (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:

I as ran more simulations, I could see that local relative motion was slowing with time.  Below are two simulations with objects at the same initial distances from Observer Y but this time starting at 5,000 seconds into expansion.  The second simulation is a new observer also watching “local” objects and Observer Y and his objects.

The first two charts below are Observer Y still watching Objects A and E, plus 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.  In my original charts, his R=50cm circle of objects began at H=0.0667/s. His new circle at R=50 will begin at H=0.0002/s (H =1/t=1/5000s). 

For my second simulation of local relative motion in more advanced aged expansion, 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 new Circle of Observation for him to watch, and at the same perspective that Y had for his A and B (same R and θ).  

At this older point in expansion, Observer Y will have moved further away from center, on their mutual axis, to 25,000cm. Object A will now be at 36,323cm from center, and its Circle of Observation radius around Y will have increased to 16,664cm.  E will have moved to 39,413cm, and its radius around Y expanded to 18,577.  I let Observer Z watch the motion of Observer Y’s A and E objects.

 

 

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 at 50cm apart now had virtually the same speed as the observer (α is very small).  At 10 seconds into expansion he was moving at the same 5cm/sec but objects at 50cm were moving at significantly higher speeds relative to him.

 

 

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

 

Aging the expansion expanded the scope of objects “local” for each observer.  Local is the range where relative expansion motion is difficult to discern. At 10 seconds of expansion, an observer looking at objects 50cm away in any direction will measure their velocity at 3.33cm/sec. At 10 seconds, object H would be moving at relative velocity, v=.01cm/sec, R= v / h = .01 / .067 = .15cm (away from Observer Y).  At 5,000 seconds, Object H will move to R=50cm from center, and still receding from the observer at the same near undiscernible (local) expansion motion, 0.01cm/sec .  Yet, at 5,000 seconds, Observer Y’s original objects, 50cm at 10 seconds into expansion, had moved to a new radius of R=16,664cm, still moving directly away from him at the original observed velocity of 3.33cm/sec, and still at the same angle in his sky.  No object changed velocity, only the faster moving objects moved further away from him.  The Hubble Motion itself was expanding, that is, the space between all objects moving at set velocities was expanding evenly with time, the Hubble Constant value for each moment decreasing as a result.

 

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

 

 

This simulation suggests that in order for two observers to see the same expansion motion for a given configuration they would have to be peering out into space at the same moment. Observer Z was placed at the exact perspective where Y started, 75cm from center, with objects on a circle of observation of 50cm (F and G).  Their data charts changed for distances of 50cm just because the expansion had aged. These measurements show a slowing down of local expansion motion due to the aging of expansion. Objects A and E are moving along at the same “actual” velocity when Observer Y observed them.  Observer Y measures no change in their velocities, only they are much further away.  The relative velocities (“Observed Charts”) for Y and Z at 50cm are identical, yet the “actual local” motions around each are quite different. Both might declare that local expansion motion has virtually stopped.

The Hubble value is constantly changing in this model (H = velocity/distance). That change suggests that actual expansion motion in this pattern makes the “observed” rates of expansion decrease with time at set distances, but the velocities of the individual objects do not.  The charts suggest that the reason observation in our Universe of local expansion is so difficult is because as time passes objects moving at different velocities from us have moved out of our local space.  Faster moving objects have moved away from the observer, and he has moved away from slower moving objects. As time passes, more and more of the objects closest to him are the objects that have always been moving closest to him, at near the same expansion velocity away from center and at the lowest α’s. Therefore, discernable “local” relative motion is falling toward insignificant differences as expansion grows old. The data suggests that as expansion ages the objects that will present measurable relative (observable) expansion motion will be those furthest away.  It also shows that the larger the disk grows the greater distances from an observer that would be considered “local” in scope.

This pattern of motion maintains an illusion of center, everything receding away from everything else at increasing speeds proportional to distance, for every observer, and from every perspective. 

 

 

The Pattern as an Accelerating Expansion

If the expansion motion is a steady rate, then the Hubble value at each pause is H =1/Age of expansion.  If it is an acceleration, the value at each pause becomes H = 2/Age of expansion. Instead of objects moving away from center at constant velocities, the values of which increase with distance from center, now objects are moving with constant accelerations, the values of which increase with distance from center.  At each pause in the simulation you cannot tell whether the motion is steady rate or accelerating, except the H value.  With the altered H, the related motions of all objects can be discerned using the Hubble Law, v = H * d.  All observer’s still record all objects receding directly away, but with an acceleration.  

 

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

 

 

There are other differences between steady rate and accelerated expansion under this divergent angle motion, which show up when observational delays from the speed of light are added to the simulation.  With steady rate expansion, the objects stay in the same position in the observer’s sky as they recede from him in all directions, even when observational delay by the speed of light is considered (shown later).  Accelerating Expansion with instantaneous viewing (no delays from the speed of light) likewise holds each object in their original position in the observer’s sky (as seen above).   Unlike steady rate, this turns out not to be the case when speed of light delays are added. I will show later that the speed of light under acceleration causes objects to drift across the observer’s sky and the H calculated from observational data to be skewed.  I will also show that distance, and therefore greater relative velocities, diminish these skewing affects down to almost undiscernible. If the expansion is an acceleration, the actual motion of all objects will exhibit Hubble motion.  The the observed light will for objects at relatively close objects will not.  But, as distance increases, and therefore velocities, the disruptive affects of light delay diminish, and the observations move back toward Hubble motion, roughly.  With very great distances, it is restored, but it looks like steady rate.

 

 

The Source of the Illusions of Center

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

 

Object’s expansion velocity vectors as viewed by observer:

 

 

= θα    

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

Vp = Va cos(Ω)

Vt = Va sin(Ω)

 

 

 

 

 

Using data from the chart above, Object A was observed at 50cm, 60 degrees, moving at 3.33cm/sec. 

The Actual velocity of Object A along its path was 7.27cm/sec

The viewing vectors for the actual speed of the object at that moment:

     Ω = 60- 23.41 = 36.59

     Va = 7.27 cm/sec   (from data chart)

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

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

 

 

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

 

θ = observer’s angle to object

Vp = - Va cos(θ)

Vt = - Va sin(θ)

                               

 

 

 

 

The Observer measures the relative motion, the combined vectors of his motion and the object’s. The observer was moving along his path at 5.00cm/sec.

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

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

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

Observer Y’s measured perpendicular motion for object A is the sum of their two “actual motion” vectors;  5.84 – 2.50 = 3.34 cm/sec.  This difference agrees with the “observed” rate of expansion from our data table of 3.33cm/sec, which was calculated just by moving all objects along their own axes. If expansion motion is moving away from a center in this pattern, an observer (us) cannot separate his own relative motion from the observed objects because he cannot discern his own expansion motion. Everything around him is caught up in it. This pattern skews the motion of the observed object, modifying it by the value of the observer’s perpendicular vector projected onto the object. This pattern accomplishes this masking of this vector proportionally in every position around each circle of viewing.

The observed tangential expansion motion is also the sum of the two:  4.33 – 4.33 = 0. This relationship is likewise true all the way around each circle.  In this pattern of motion, our observer cannot see this vector of the object’s expansion motion because his own is exactly masking it to nil. If this so as the radius of the circle grows, then it is true that the ratio of the velocity of the object over the velocity of the observer = sin(Ω) / sin(θ).  Since the data shows that Ω  and θ are not changing, the radio of the object’s speed divided by the observer’s is constant as the circle grows with time. This hidden vector is the reason objects on his viewing circles appear to remain in the same positions in his sky, in all directions, as they move away from, not him, but center of the disk.

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.  

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

 

 

 

 

 

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.

 

 

Observationsdelayed by the Speed of Light: Hubble Motion, and illusions, 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.  :

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

VE 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

Emitter

time span viewed

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

Emitter

time span viewed

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

Emitter

time span viewed

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 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 (VRm – velocity at the bottom of the Rm column) and the speed of light, C (or VL as denoted in my original equations.) 

 

L can also be determined using:

 

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

Using the Hubble formula,

VRm = Rm * Hm, since Rm is the observed distance traveled by the emitted light, then Rm = C * tr ,

therefore VRm =   (C * tr) Hm

If L= 1 – VRm / C , then

L = 1 – Hm  * tr

 

Since the age of expansion when the light was emitted is tm = ta – tr, then tr = ta - tm, then;  

L = 1 – Hm (ta – tm)

 

From my formulas for L,  tm = L * ta

L = 1 – Hm (ta – L * ta)

L – 1 = Hm * ta  (L - 1)

Hm = 1 / ta

 

Since 1/ta = Ha ,

     Hm = Ha

 

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. Also, the light emitted by the object in the past, and therefore under an older H, will be converted to the observer’s H at the time of observation.

 

 

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 the Gravitational Lensing simulation, I programmed it to move all three objects back to that moment in time (Fig 1).  I then let the system expand until the light reached the Lensing Object (Fig 2).  I then let the light continue from that point toward 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

 

 

 

 

    

 

 

Data (all simulations below start out at 9,800 seconds in to expansion):

 

Initial Observation Chart:  Observation of Light Traveling directly from Emitting Object to Observer (Observer starts out at 6,000cm from center, Emitting object at α=70, 6,000cm from center)

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

Observer

Calculated

100,000

0.0000100000000

6,122.45

6,122.45

0.02341128

7,023.38

6,122.45

0.070233841

0.0000100000000

100,100

0.0000099900100

6,128.57

6,128.57

0.02343469

7,030.41

6,128.57

0.070233841

0.0000099900100

100,200

0.0000099800399

6,134.69

6,134.69

0.0234581

7,037.43

6,134.69

0.070233841

0.0000099800399

100,300

0.0000099700897

6,140.82

6,140.82

0.02348151

7,044.45

6,140.81

0.070233841

0.0000099700897

100,400

0.0000099601594

6,146.94

6,146.94

0.02350493

7,051.48

6,146.94

0.070233841

0.0000099601594

2.100000E+17

4.761905E-18

1.2857142857E+16

1.2857142857E+16

49,163,688,789

1.47491066E+16

1.285713985E+16

0.070233841

4.76190500E-18

2.200000E+17

4.545455E-18

1.3469387755E+16

1.3469387755E+16

51,504,816,827

1.54514450E+16

1.346938460E+16

0.070233841

4.54545500E-18

2.300000E+17

4.347826E-18

1.4081632653E+16

1.4081632653E+16

53,845,944,864

1.61537835E+16

1.408162936E+16

0.070233841

4.34782600E-18

2.400000E+17

4.166667E-18

1.4693877551E+16

1.4693877551E+16

56,187,072,902

1.68561219E+16

1.469387411E+16

0.070233841

4.16666700E-18

2.500000E+17

4.000000E-18

1.5306122449E+16

1.5306122449E+16

58,528,200,939

1.75584603E+16

1.530611887E+16

0.070233841

4.00000000E-18

 

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

(Lensing Object starts out at α=35, 6,000cm from center)

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

0.0000099999975

0.024547

7,364.22

0.073642

0.0000100000000

0.0000100000000

100,100

0.0000099900100

100,100.02

0.0000099900075

0.024572

7,371.59

0.073642

0.0000099900100

0.0000099900100

100,200

0.0000099800399

100,200.02

0.0000099800375

0.024597

7,378.95

0.073642

0.0000099800399

0.0000099800399

100,300

0.0000099700897

100,300.02

0.0000099700873

0.024621

7,386.32

0.073642

0.0000099700897

0.0000099700897

100,400

0.0000099601594

100,400.02

0.0000099601569

0.024646

7,393.68

0.073642

0.0000099601594

0.0000099601594

2.100000E+17

4.761905E-18

2.10000051550E+17

4.761904E-18

5.154956E+10

1.546487E+16

0.073642

4.761905E-18

4.761905E-18

2.200000E+17

4.545455E-18

2.20000054004E+17

4.545453E-18

5.400430E+10

1.620129E+16

0.073642

4.545455E-18

4.545455E-18

2.300000E+17

4.347826E-18

2.30000056459E+17

4.347825E-18

5.645904E+10

1.693771E+16

0.073642

4.347826E-18

4.347826E-18

2.400000E+17

4.166667E-18

2.40000058914E+17

4.166666E-18

5.891378E+10

1.767413E+16

0.073642

4.166667E-18

4.166667E-18

2.500000E+17

4.000000E-18

2.50000061369E+17

3.999999E-18

6.136852E+10

1.841056E+16

0.073642

4.000000E-18

4.000000E-18

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

 

Analysis:

The observe will see two images from the Emitter, each originating from the emitted at the same moment in time. The first will travel directly to the observer and the second will arrive later.  What my simulator offers is that the H value calculated by both images will be the same.  To my surprise, the H value at the moment of the second viewing was not the value of the expansion at the moment of viewing, but whether the value of the first viewing.  The values offered to the observer were the same.  The velocity and the distance at the second viewing had changed but the Hubble formula produced the H value to the time of first viewing. Also, I found that 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 initial viewing.

 

 

This means you could use Gravitational Lensing to calculate the distance traveled by any two images having only the velocity (from red shift) of each and the synchronized time interval between the receipt of each.

     or    

     where C is the speed of light

 

At expansion time,2.1 E17 seconds,

 

(matches the observed distance in the Initial Observation Chart).

 

I placed a second lensing object in the path of the emitter.  This one was much closer to the emitting object and offset closer toward center.  I can then set up a scenario of two independent objects deflecting light from the emitter and then observed from three very different paths.

 

Tertiary Observation Chart:    Observation of Light Emitted at the same moment traveling from Emitting Object, around Lensing Object, to Observer

  (Lensing Object starts out at α=55, 5,900cm from center)

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

0.02398621

7,195.86

0.071958634

0.0000100000000

0.0000100000000

100,100

0.0000099900100

100,100.02

0.0000099900076

0.0240102

7,203.06

0.071958634

0.0000099900100

0.0000099900100

100,200

0.0000099800399

100,200.02

0.0000099800375

0.02403418

7,210.26

0.071958634

0.0000099800399

0.0000099800399

100,300

0.0000099700897

100,300.02

0.0000099700873

0.02405817

7,217.45

0.071958634

0.0000099700897

0.0000099700897

100,400

0.0000099601594

100,400.02

0.0000099601570

0.02408216

7,224.65

0.071958634

0.0000099601594

0.0000099601594

2.100000E+17

4.761905E-18

2.10000050371E+17

4.76190400E-18

5.037104E+10

1.511131E+16

0.071958634

4.761905E-18

4.761905E-18

2.200000E+17

4.545455E-18

2.20000052770E+17

4.54545300E-18

5.276967E+10

1.583090E+16

0.071958634

4.545455E-18

4.545455E-18

2.300000E+17

4.347826E-18

2.30000055168E+17

4.34782500E-18

5.516829E+10

1.655049E+16

0.071958634

4.347826E-18

4.347826E-18

2.400000E+17

4.166667E-18

2.40000057567E+17

4.16666600E-18

5.756691E+10

1.727007E+16

0.071958634

4.166667E-18

4.166667E-18

2.500000E+17

4.000000E-18

2.50000059966E+17

3.99999900E-18

5.996553E+10

1.798966E+16

0.071958634

4.000000E-18

4.000000E-18

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

Using the data from the Secondary Object and the Tertiary:

 

At expansion time,2.1 E17 seconds using chart “f” to determine light travel distance for “t”,

 

 

 

At expansion time,2.1 E17 seconds using chart “t” to determine light travel distance for “f”,

 

 

It appears that if you can observer light from a specific emitter, emitted at the same moment, no matter the path, you can determine the distance the light traveled to the observer for both using only the red shift of each and the time interval between the observations.

 

The Calculated Hubble Value Gets Locked in:

 

I ran many more simulations, letting light from this “backed up” emitter position reach the same observer from different paths.  The light emitted from that backed up position, and moment in time, will offer the observer the Hubble Value at his time of observation as if there were no observational delays (the distance to the emitters actual position at time of observation).  This is true no matter the path it takes to reach the observer, who is moving along as the light propagates. In other words, no matter the path, no matter how long the light emitted at that moment is bouncing or bending around in space, when it reaches the observer it will offer him altered values for relative velocity measurements and distances that the light traveled, but he will always calculate the same Hubble Value.  The value is locked in between that light burst and that observer.  If the observer every sees it, it is going to present the the observer’s Hubble Value when the light would have first reach him via an unaltered path.

I ran additional simulations of the two different emitters emitting light at the same moment in expansion and arriving at the observer at different times, but these simulations did not produce the same Hubble Constant value (unless expansion age was advanced and I didn’t look at significant enough digits).  That only happened when the light was emitted at the same moment from the same source and arrived at the observer at different times.  Gravitational Lensing is the only scenario that produced that criteria.

 

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:  Steady Rate Expansion offers Relative Acceleration

I started by calculating the Center of Momentum (CoM) of objects placed at different distances from center on a common axis within this pattern.  I used varying masses, but always velocities dictated by this pattern, proportional to their distances from center.  What I found was that the CoM of any two pairs was always moving at the correct velocity for its location within the pattern.  Since gravity conserves momentum then two objects merging due to gravity should not alter the pattern, and therefore preserve all relationships of motion and the illusions.

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 motion in this tiny universe moving in, or at least some semblance of, the 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 in this pattern, it is certain that an observer, caught in a large orbit around a center of mass, will individually be out of sync to some degree.

With gravity in mind, I wanted to see what happens to observations if objects are 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.  I decided to include this scenario in my simulations of “Out of Sync” motion.

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 am going to 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, and failed to reflect the clear relationships of Hubble Motion.

3.       Objects appeared to the observer to be accelerating. This acceleration is only present in the relative motion between observer and Emitter. There was no acceleration in the actual expansion motion of either.

All three effects diminish with distance between the observer and the Emitter, and even go away completely at extreme distances.  In the many simulations I ran, this was consistent. The change in the angle  was greatest when objects are closer, but with distance it becomes increasingly difficult to see. The H approaches the correct value, and the drifting across the sky slows.  At greater and greater distances the presence of “relative acceleration” becomes increasingly hard to discern, and for all practical purposes, goes away. 

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:  deceleration and 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

 

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