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The Use of Moved Clocks: How this challenges Special Relativity:

D.M. Marett (2010)

Einstein's special relativity has as one of it's primary tenants that the speed of light is exactly C for all inertial observers. Herein I explore a thought experiment which demonstrates that if one uses synchronized clocks and meter sticks to measure the speed of light in one direction, and then back, that the speed of light has to be different in the two directions for at least one  inertial observer.  This requires making some assumptions that are not much of a stretch - you need to be able to synchronize clocks (already done in GPS), and you need to be able to define which observer is moving faster. We also need to ignore the Einstein clock synchronization method usually used in special relativity (SR). One of the big problems with the theory of relativity has to do with how it synchronizes clocks. According to Einstein’s method, the speed of light is defined by measuring the time for a two way propagation of light to proceed from one clock to a distance mirror and back.  But what if C is not the same in both directions? Relativity assumes it to be so a priori. Our thought experiment is designed to settle the issue by looking at the predictions made by any medium of space theory where there is a preferred frame for light, and comparing this to predictions made by SR where the speed of light is supposed to be constant for all inertial observers.

To perform such a test, first we establish how we will synchronize our clocks. We take two clocks, synchronized immediately next to one another by some electromagnetic means. We then move one at a velocity v = 10m/s to 1000m away ( takes 100 seconds). This clock has then slowed by:

100 s x (1-v^2/c^2)^1/2 – 100 = 1/2t*v^2/c^2 = 5.55555555555555709876543209 E -14 seconds  [4]

If this amount is then added to the moved clock, then the two clocks can be considered synchronized, as long as the two clocks remain in a fixed position relative to one another in the same moving frame. Following this procedure the one way speed of light can be measured. When light leaves the first clock, the time is marked. When light reaches the second clock, the time is marked. The difference in the two readings is the elapsed time. Similarly, if the same procedure is performed in the opposite direction, then the time of flight back can also be independently calculated. According to the theory of relativity, Cf = Cr = C. We begin by asking what would be the predicted result if there is a preferred frame for light in space vs. no preferred frame (SR) if these two clocks are on the translating Earth in its orbit around the Sun at 30 Km/s:

From the Preferred Frame Perspective:

For the Forward Path:

C = 3 E 8 m/s  V = - 3 E 4 m/s   C + V = 2.9997 E 8 t m = 1000 m     t =3.3336666 E -6 s

(velocity is negative, since C is being slowed by media)

For the Reverse Path:

C = 3 E 8 m/s  V = 3 E 4 m/s   C + V = 3.0003 E 8 t m = 1000 m      t =  3.3330000 E -6 s

(velocity is positive, since C is travelling with media)

The total time difference is: 3.3330000E -6 s + 3.3336666E -6 s = 6.6666667 E-6 s

From the Relativity Perspective:

For the Forward Path:

C = 3 E 8 m/s  V = 0   C + V = 3 E 8 t m = 1000 m     t =3.3333333 E -6 s

For the Reverse Path:

C = 3 E 8 m/s  V = 0   C + V = 3 E 8 t m = 1000 m      t =  3.3333333 E -6 s

The total time difference is: 3.3333333E -6 s + 3.3333333E -6 s = 6.6666667 E-6 s

The two perspectives agree on the arrival time of the light back at the first clock, but they disagree on the one-way travel times, since if space is a preferred frame, one would need to add and subtract the velocity of the Earth from that of the light, whereas if relativity is correct, then the speed of light does not change. If we look at the preferred frame scenario, the synchronized clocks on Earth show two different one-way propagation speeds, but if the clocks were in space at rest in the preferred frame instead, then we would see the speed of light as constant (c) in both directions, and we would expect the paths to be measured as different lengths. Lets now perform a second thought experiment, this time using clocks that are all synchronized, both in space and also on the Earth as shown in Figure 1:

Fig. 1:

Referring to Fig. 1A, for clocks in space, these are synchronized to each other by the method described above, and adjusted to Earth time (Earth time will be our standard) by slowing them down by (1-v2/c2)1/2 to account for the velocity of Earth. The Earth

clocks are also synchronized and counting in Earth time.

The space clock S1 is positioned to be directly beside the Earth clock E1 when Earth passes by S1 in its orbit, and starts at the same time as when the beam of light leaves E1. Synchronization is not a problem because they are side by side at that moment (verified by contact). The space clock S2 is at the exact position where the mirror will be on the Earth (at clock E2) when the light beam on Earth reaches it and is triggered at the same time because at that moment they are also side by side. Finally, clock S3, synchronized with the first two, is at the exact position where clock E1 on Earth will be when the return light beam arrives.

It might be considered a problem coordinating the positions of the space clocks to match those of the Earth clocks - to remidy this, we could think of space as having a line of consecutive synchronized clocks, and the clocks that are triggered are the ones that are in the correct position when the light reaches each Earth clock.

A common standard of length is used - a meter stick on Earth. If two clocks on Earth are 1000 Earth meters apart, then the two corresponding clocks in space will be 1000 Earth meters apart, since they trigger only when they are in the same space at the same time. Therefore there is simultaneity of both length and time. We are not concerned that the length of the Earth meter may appear to be longer (relativity) or may actually be longer (Lorentz theory) in the space frame, - if we want to switch reference lengths we can easily do this by adjusting the meter length by the factor 1/(1-v2/c2)1/2 when it is moved from the Earth to space.

The important point is that the spaces clocks are in exactly the same place at the same time as the Earth clocks when they meet the beam, so that we can be sure that the lengths between them are perfectly correlated, regardless of which meter stick we use to measure with.

We then measure the forward and return speed of light on a two way path (1000m each way)  on Earth, from the perspective of clocks synchronized to a common time (Earth time) both on Earth and in space. The predicted results of the two scenarios (preferred frame, SR) are shown below:

Table 1: On Earth Prediction: Space is preferred frame, Earth is moving at V with respect to it.

 Beam Direction: Speed of light (C) Velocity of Earth Frame (V) C+V Distance (D) total Earth time (t) on Earth Clocks Earth Forward 3 E 8 m/s - 3 E 4 m/s 2.9997 E 8 m/s 1000 m 3.3336666 E-6 s Earth Reverse 3 E 8 m/s + 3 E 4 m/s 3.0003 E 8 m/s 1000 m 3.3330000 E-6 s

The total Earth time difference forward and reverse is : 3.3330000E -6 s + 3.3336666E -6 s = 6.6666667 E-6 s

Table 2: In Space Prediction: Space is preferred frame, Earth is moving at V with respect to it.

 Beam Direction: Speed of light (C) Velocity of Space Frame (V) C+V Distance (D) total Earth time (t) on Space Clocks Earth Forward 3 E 8 m/s 0 3.0000 E 8 m/s 1000.1 m 3.3336666 E-6 s Earth Reverse 3 E 8 m/s 0 3.0000 E 8 m/s 999.9 m 3.3330000 E-6 s

The total Space time difference forward and reverse is: 3.3330000E -6 s + 3.3336666E -6 s = 6.6666667 E-6 s

Table 3: Earth or Space Prediction of Special Relativity: Earth V has no effect on C.

 Beam Direction: Speed of light (C) Velocity of Earth Frame (V) C+V Distance (D) total Earth time (t) on Earth/Space Clocks Earth Forward 3 E 8 m/s no effect on C 3.0000 E 8 m/s 1000 m 3.3333333 E-6 s Earth Reverse 3 E 8 m/s no effect on C 3.0000 E 8 m/s 1000 m 3.3333333 E-6 s

The total Earth / space time difference forward and reverse is : 3.3333333E -6 s + 3.3333333E -6 s = 6.6666667 E-6 s

What is happening with the space clocks:

Space Clocks: Earth Forward Path:

C = 3 E 8 m/s    V = 0  C+ V =  1000.1 meters   t = 3.3336666 E-6 s   (Earth clock)

t = 3.3340000 E-6 s   (uncorrected space clock)

t = 3.3336666 E-6 s   (corrected space clock)

Since the Earth frame is moving - clock E2 has moved 0.1 meters with respect to space when it is triggered, which is added to the space length measured.

Space Clocks: Earth Reverse Path:

C = 3 E 8 m/s    V = 0  C+ V =  999.9 meters     t = 3.3330000E-6 s     (Earth clock)

t = 3.3333333E-6 s     (uncorrected space clock)

t = 3.3330000E-6 s     (corrected space clock)

Since the Earth frame is moving - clock E3 has now moved 0.2 meters with respect to space when it is triggered. This is subtracted from the first 1000.1 meters to get 999.9 meters as the length measured in space.

Space clocks display absolute Earth time, slowed down from uncorrected space time by the factor:  (1-v2/c2)1/2.

Earth clocks display Earth time, and can display uncorrected space time if they are sped up by 1/(1-v2/c2)1/2.

Uncorrected space time round trip:                  t = 3.334000 E-6 s +  3.33333333E-6 s = 6.667333 E -6 s

Corrected space time/Earth time round trip:      t = 3.33366 E-6 s  +  3.3330000 E–6 s = 6.66666667 E -6 s

We find that mathematically, if the clocks are all reading at an identical rate, and they trigger at an identical time, then the one way speed of light must be C-V in the forward direction, and C+V in the return direction. If this were not true, then the Earth could not be moving relative to space clocks. The only situation that would agree with SR under these conditions is if there was no relative movement. We then take as our correct result below:

Table 1: Speed of Light (Earth Observer): = C+V, C-V, distance is 1000 meters both ways

Table 2: Speed of Light (Space Observer): = C both ways, distance is 1000.1 m and 999.9 meters.

In considering Fig. 1A, the Earth time and space time that has elapsed (corrected to Earth time) agree on the one-way elapsed time for the preferred frame model, but not the Relativity model. We find that they agree because the speed of light is different in the two directions for an Earth observer but the distance is the same, but for a space observer it is the reverse, the speed of light is the same in the different directions but the distance is different. When one then uncorrects the space clock to count in the actual time that it would display on its face, one gets a longer elapsed time. According to this time, the speed of light is no longer C in space, but 2.9997E8 m/s on average. We arrive at a situation similar to that of the Sagnac interferometer - one observer (on the axis) sees the speed of light as constant  and the distance different in each direction, the other observer (on the rim) sees the distance as the same, but the speed of light different in each direction. Correcting the clocks to one another does not change this relationship, nor does correcting for the length viewed in Earth meters vs. space meters. The ultimate result of using a synchronized time and a synchronized length is that the speed of light must by definition be C+V and C-V in at least one of the frames, contradicting the postulate of relativity that the speed of light is constant for all inertial observers. This is why relativity must use the Einstein time synchronization method and suggests that clocks in different inertial frames can't be synchronized, since otherwise we lead to this (real) contradiction (1). The only requirement to get to this result is that we need to know to begin with which way to calibrate the moving clocks, i.e. is space moving slower that the Earth, or is it moving faster. In most situations this is definable - the Earth's orbital frame is moving faster than the Sun (heliocentric) frame, the Earths diurnal rotation frame (ECEF) is moving faster than the frame of the Earth's pole (ECI frame), etc. And ultimately, the relative velocity of objects can be referenced to the Cosmic Microwave Background, which appears to be a true rest frame for the universe.

Is this just an artifact of picking the Earth as the moving frame? If we look at the next simulation in Fig. 1B, where we reverse things and have space moving hypothetically and the Earth is at rest, we arrive at a similar result. On Earth the speed of light is measured as 3 E 8 m/s in both directions, and the distance is measured to be 1000 meters using the Earth meter. In space, the distances measured and the speeds of light in either direction now become C-V and C+V:

Table 4: On Earth Prediction: Earth is a preferred frame, Space is moving at V with respect to it.

 Beam Direction: Speed of light (C) Velocity of Earth Frame (V) C+V Distance (D) total Earth time (t) on Earth Clocks Earth Forward 3 E 8 m/s 0 m/s 3 E 8 m/s 1000 m 3.3333333 E-6 s Earth Reverse 3 E 8 m/s 0 m/s 3 E 8 m/s 1000 m 3.3333333 E-6 s

The total Earth time difference forward and reverse is : 3.3333333E -6 s + 3.3333333E -6 s = 6.6666667 E-6 s

Table 5: In Space Prediction: Earth is preferred frame, space is moving at V with respect to it.

 Beam Direction: Speed of light (C) Velocity of Space Frame (V) C+V Distance (D) total Earth time (t) on Space Clocks Earth Forward 3 E 8 m/s -3 E 4 m/s 2.9997 E 8 m/s 999.9 m 3.3333333 E-6 s Earth Reverse 3 E 8 m/s + 3 e 4 m/s 3.0003 E 8 m/s 1000.1 m 3.3333333 E-6 s

The total Earth time difference forward and reverse is : 3.3333333E -6 s + 3.3333333E -6 s = 6.6666667 E-6 s

The frame that is moving faster is consistently the one where the speed of light doesn't equal C in either direction once all clocks and lengths are synchronized.

GPS is the first practical system which uses synchronized clocks in daily practice. Do GPS one-way propagation range times provide any clarification on this? Yes, it does. The satellite is in a frame moving with the Earth in its orbit, and the receiver is in a frame also moving with the Earth in its orbit as well as rotating diurnally. GPS range times suggest that the one-way speed of light is constant in the frame of the orbiting Earth (ECI frame), but the velocity is C+V and C-V in the frame of the rotating Earth (ECEF frame), where V is the Earth's rotational velocity. Again, two frames, and in one the speed of light is not C. This contradiction was pointed out by Herbert Ives in “Genesis of a Query “Is there an Ether?” (3) where Ives says:

“From the contractions of length and clock rate with motion contained in these transformations it is possible to determine the Epoch of the moved clock. When this is done, and time is measured by the moved clock, the velocity of a one way signal turns out to be a function involving the moved clock velocity, that is, it is not “c”, contradicting the initial postulate.”

Conclusion:

This exercise shows that it is possible to synchronize clocks in two velocity frames, by moving them in accordance with the corrections due for velocity and distance, and correcting them for their relative velocity. When this is performed, the clocks agree that the one way speed of light adds and subtracts with the velocity of relative movement between the frames, and uncorrected clocks reading in one frame or the other will give erroneous and contradictory readings. This is a consequence of our fore-knowledge of which frame is faster, information which is usually available to us, as well as our objective acceptance that relative motion is tangible and measurable. After synchronization, if we go backward and re-apply all relativistic corrections to that of a local observer, the difference in the one way speeds of light do not go away, since the corrections affect the one way speeds of light in an equal manner. If a result of synchronizing clocks and lengths in two frames is that the speed of light can be shown to no longer be constant, then the premise of real time dilation collapses - this suggests that it is the clocks, and not actual time, that are affected by velocity.

References:

1) Tyapkin, A.A., (1973) "On the Impossibility of the First-Order Relativity Test." Lettere Al Nuovo Cimento Vo. 7, No. 15, 760-764.

2) Su, C. C.,(2001)  "A local-ether model of propagation of electromagnetic wave."

3) Ives, Herbert, (1953) "Is there an Ether?"

4) Einstein, Albert, (1905) "On the Electrodynamics of Moving Bodies." P.10