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Light Drag Effect of Vacuum Tube Versus Light Propagation in Stationary Vacuum Tube with Moving Source and Receiver

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Light Drag Effect of Vacuum Tube Versus Light Propagation in Stationary Vacuum Tube with Moving Source and Receiver
Ruyong Wanga,*, Li Zhanb, Le Heb, Wenyan Zhangb, Liang Zhangb a St. Cloud State University, St. Cloud, MN 56301, USA b State Key Laboratory of Advanced Optical Communication Systems and Networks, Key Laboratory for Laser
Plasmas (Ministry of Education), Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
Abstract We presented a new way to examine the principle of relativity of Special Relativity. According to the principle of
relativity, the light dragging by moving media and the light propagation in stationary media with moving source and receiver should be two totally equivalent phenomena. We select a vacuum tube with two glass rods at two ends as the optical media. The length of the middle vacuum cell is L and the thicknesses of the glass rods with refractive index n are D1 and D2 . The light drag effect of the moving vacuum tube with speed v is a first-order effect, t  2(n 1)(D1  D2 )v / c2 , which is independent of L because vacuum does not perform a drag effect. Predicted by the principle of relativity, the change of the light propagation time interval with stationary vacuum tube and moving source and receiver must be the same, i.e.,   t  2(n 1)(D1  D2 )v / c2 . However all analyses have shown that the change of the propagation time interval  is caused by the motion of the receiver during the light propagation in the vacuum tube. Thus, the contribution of the glass rods in  is 2n(D1  D2 )v / c2 , not 2(n 1)(D1  D2 )v / c2 in t . Importantly, the contribution of the vacuum cell in  is 2Lv / c2 , not zero in t .
Our analyses are solid in optics. The genuine tests of the prediction of the principle of relativity can be conducted by the experiments with two atomic clocks, or the experiments with fiber Sagnac interferometers. Keywords: Light drag effect; Light propagation; Special Relativity; Principle of relativity
*Corresponding author: ruwang@stcloudstate.edu 1

1. Introduction
In 1980, it was indicated that the principle of relativity of Special Relativity had not been verified by experiments in a system moving relative to the Earth and a new Michelson-Morley experiment in Space Lab was proposed [1]. Popper thought conducting such an experiment to examine the principle of relativity was a good idea [2]. Unfortunately, nothing ever came of it and no experiment has been carried out in a system moving relative to the Earth to date.
The principle of relativity states that in any system of coordinates in uniform translatory motion, the speed of light is a constant c . The generalized Sagnac experiments [3,4], also called linear Sagnac experiments, have shown that in an air-core fiber segment of length l and in uniform translatory motion with speed v , the travel time difference between two counter-propagating light beams is a first-order effect, t  2vl / c2 .
In this paper, we presented a new way to examine the principle of relativity. The principle of relativity of Special Relativity states that the physical laws are the same for all the observers in uniform translatory motion regardless of their different motion statuses. Therefore all the phenomena must be the same in these two cases: a moving vacuum tube with stationary source and receiver and a stationary vacuum tube with moving source and receiver. We conducted the analyses based on optics, and therefore, this way is solid in the analyses. We also indicated the possible experiments. Importantly, the experiments are based on the first-order effect. As comparisons, Lorentz contraction and relativistic time dilation are the second-order effect. Obviously these two cases represent two different moving statuses relative to the Earth. The proposed experiments are the first-order experiments examining the principle of relativity in two systems.

Relativity, all the physical phenomena, including the light propagation time interval, are the same in these two cases. In fact, if we have Observers 1 on the group of optical media and Observer 2 on the receiver, for these two observers in uniform translatory motion, they won't be able to identify the difference between these two cases.

Stationary Source

l Moving Group of Media

Stationary Receiver

v
Moving Source
v

Observer 1 (a)
l
Stationary Group of Media
Observer 1 (b)

Observer 2
Moving Receiver
v
Observer 2

Source

Vacuum Tube

Receiver

Glass

Vacuum

Glass

(c)

Fig. 1. Moving group of optical media versus moving source and co-moving receiver. The group of optical media - a vacuum tube with two glass rods.

The light drag effect of moving media has been an important topic in optics for many years. However, according to the principle of relativity, this effect can be treated as a different problem: light propagation in stationary media with moving source and receiver. Is it really true?
Apparently the previous statements should be true for any optical media. Here we select a vacuum tube, a tube having two glass rods with very low dispersion as two ends and the air is extracted as shown in Fig. 1c.
3. Primary analysis

2. New way of examining the principle of relativity

The sizes of the vacuum tube are shown in Fig. 2a. The

We present a new way of examining the principle of relativity: moving source and receiver versus moving group of optical media where the source and receiver always move together with the same speed as shown in Fig. 1. Therefore from the viewpoint of relative motion, there are only two entities: a source and a receiver versus a group of optical media, and we investigate two cases: moving group of media with stationary source and receiver (Fig. 1a); stationary group of media with moving source and co-moving receiver (Fig. 1b). It is well known that the former is the light drag effect. The latter is the light propagation in stationary media with moving source and receiver. According to the principle of relativity of Special

lengths of the two glass rods are D1 and D2 and the length of the vacuum cell is L . The whole tube is called a vacuum tube and the part without two glass rods is the vacuum cell.
The propagation time interval for a light beam which starts from a stationary source, passes the stationary vacuum tube, then arrives the stationary receiver is denoted as t0 (Fig. 2a). Accordingly, the time interval in Fig. 2b
is t and the time interval in Fig. 2c is  .
In all these cases, the time interval of a light beam propagating from the source to the receiver always consists of three periods: before entering the vacuum tube, inside the vacuum tube, and after leaving the vacuum tube.

2

For the case in Fig. 2a, we have

t0  t01  t02  t03

(1)

 lL / c  (nD1 / c  L / c  nD2 / c)  lR / c

where n is the refractive index of the glass.

lL D1

Stationary Source A

BC Glass Rod

L Stationary Vacuum Cell
(a)

D2 lR

DE Glass Rod

Stationary F Receiver

1  1  t01  0

(4)

For the second period  2 inside the stationary
vacuum tube, although the motion of the source causes a Doppler effect, the change of the frequency of incoming light beam in the vacuum tube, the dispersion of the glass rods is very low, so the change of the frequency does not cause any noticeable change of the propagation time interval in the vacuum tube. Hence we have

2  2  t02  0

(5)

Stationary
Source A v B C

Moving (b)

DE

Stationary F Receiver

Moving
Source A v B C

Stationary (c)

Moving
Receiver
v
D E FF

Fig. 2. Moving vacuum tube vs stationary vacuum tube.

Let us examine two cases in Fig. 2b and in Fig. 2c. First the case in Fig. 2b. It is the case of light dragging by optical media and it has been fully investigated. Compared with the stationary vacuum tube, the drag effect in this case [5] is

t  t  t0  (n 1)(D1  D2 )v / c2

(2)

Obviously only the glass rods contribute to the drag effect while the vacuum cell does not contribute anything to the drag effects. Here we neglect the dispersion term. Actually if including the dispersion term, we have t  (n 1 dn / d)(D1  D2 )v / c2 [6-9], and the amount contributed by the dispersion term is small even for dispersive glasses.
Then the case in Fig. 2c. Based on the principle of relativity of Special Relativity, this case is totally equivalent to the case in Fig. 2b because as we mentioned above, for each observer of the two observers 1 and 2, these two cases are the same. Therefore, we must have

    t0  t  (n 1)(D1  D2 )v / c2

(3)

Therefore the travel time difference  predicted by
the principle of relativity should exist only in the third
period  3 , that is 3  3  t03  
 (n 1)(D1  D2 )v / c2 . As shown in Fig. 2c, when the light beam exits from
the right end of the vacuum tube E, the receiver has moved
from F to F' and FF  v(1 2 )  lLv / c
n(D1  D2 )v / c  Lv / c . Clearly the light beam has to spend more time to catch the moving receiver, and the time increase is FF / c  lLv / c2  n(D1  D2 )v / c2  Lv / c2 . If we list the predicted 3  (n 1)(D1  D2 )v / c2 here, we can find two differences between these two results. Firstly,
the existence of the two glass rods causes a time increase of n(D1  D2 )v / c2 , how does this match with 3  (n 1)(D1  D2 )v / c2 ? Where does the factor (n 1) come from in this case? (We will further discuss this
problem in Appendix.) Secondly and more seriously, the
existence of the vacuum cell causes a time increase of Lv / c2 . However, required by the principle of relativity, this time increase does not contribute any time difference
for 3 . Actually if the principle of relativity of Special
Relativity is true in this scenario, the light beam in the
vacuum tube must have a very strange and selective
behavior: when light beam passes the glass rods, no matter
how short the rods are, 1 m, 1 dm, or even 1 cm, 1 mm, they will contribute a finite g . However when the light beam passes the vacuum cell, no matter how long the
vacuum cell is, 1 m, 10 m, or even 100 m, 1000 m, the vacuum cell will not contribute any finite  . That is,
VC  0 is required.
In summary, the prediction of the principle of relativity   t  (n 1)(D1  D2 )v / c2 is unlikely true.

Now let us examine whether this prediction of the
principle of relativity is true. The whole travel time difference  must exist in three time periods, i.e.,
  1  2  3 . For the first period 1 before entering the stationary
vacuum tube, because the speed of light is independent of
the motion of the source, we have

4. Analysis for specific cases
It would be very interesting to analyze the prediction of the principle of relativity with two vacuum tubes as shown in Fig. 3. Tube A has glass rods with length DA and a vacuum cell with length LA . Tube B has glass rods with length DB and a vacuum cell with length LB . And

3

we choose DA =100DB (e.g., DA =10 cm and DB =1 mm ) and LA =0.01LB (e.g., LA =10 cm and LB =10 m ).
Let us first conduct the light drag experiments (Fig.
3a). Clearly we will have the following results.

Stationary

lL DA LA DA lR

Stationary

Source SA v

Vacuum

Glass Glass

RA Receiver

RARA  RBRB contradicts with A3 =100B3 and the
latter is an extremely odd prediction of the principle of relativity.
5. Theoretical analysis of the light propagation in the vacuum tube
Now let us analyze the light propagation in the vacuum tube theoretically and we consider the light propagation in two opposite directions (Fig. 4).

lL DB Stationary

Source SB

v
Glass

LB Vacuum

DB lR Stationary
Glass RB Receiver

(a)

Moving

lL

Source SA v

DA LA DA Vacuum
Glass Glass

Moving lR Receiver
RA R'A v

Moving

lL DB

Source SB v Glass

LB Vacuum

Moving DB lR Receiver
Glass RB v R'B

(b)

Fig. 3. Two vacuum tubes with different lengths of the glass rods and vacuum cells, DA 100DB and LA  0.01LB .

lL D1

Stationary
Source or Receiver A

BC Glass Rod

L Stationary
Vacuum Cell (a)

D2 lR

DE Glass Rod

Stationary
Receiver F or Source

Stationary Source or
Receiver A v B C
Moving Source or
Receiver A v B C

Moving (b)
Stationary (c)

DE

Stationary Receiver F or Source

Moving Receiver or Source
Fv
DE

Comparing with the case where all parts are stationary, we have drag effects

Fig. 4. Light propagation in two opposite directions - in moving vacuum tube vs in stationary vacuum tube.

tA  2(n 1)DAv / c2 tB  2(n 1)DBv / c2

(6)

a) First, all the source and receiver and vacuum

tube are stationary (Fig. 4a).

and tA =100tB , because DA =100DB . Now let us conduct the experiment with stationary
vacuum tubes and moving sources and receivers (Fig. 3b). According to the principle of relativity, the experimental results should be

 A  tA  2(n 1)DAv / c2

(7)

 B  tB  2(n 1)DBv / c2

For a light beam propagating from A to F, we have

t0  t01  t02  t03

(9)

 lL / c  (nD1 / c  L / c  nD2 / c)  lR / c

For a light beam from F to A, we have

t0  t03  t02  t01

(10)

 lR / c  (nD1 / c  L / c  nD2 / c)  lL / c  t0

b) A and F are stationary and the vacuum tube is

moving left with a speed v (Fig. 4b). For the light

and A =100B . As indicated above,  is entirely contributed by

propagation time from A to F, it is a problem of light dragging by moving vacuum tube. It has been investigated

3 , then we have
 A3 = A  2(n 1)DAv / c2  B3 = B  2(n 1)DBv / c2

theoretically and experimentally and we should have the
drag effect of the glass rods and the vacuum cell does not
(8) have a drag effect [5]. The difference between the propagation time intervals of two beams in opposite

directions is

and A3 =100B3 .

As shown in Fig. 3b, the time period that a light beam

t  t  t  2(n 1)(D1  D2 )v / c2

(11)

propagates inside Tube A is much shorter than that inside Tube B. Hence, the moving distance of receiver RA during this period is much shorter than the moving distance of receiver R B , i.e., RARA  RBRB . Obviously

c) When A and F are co-moving right with a speed v and the vacuum tube is stationary (Fig. 4c), for the light propagation time interval from A to F, we have

4

 1 2 3

(12)

1  lL / c

(13)

because the speed of light is independent of the motion of the source.

2  nD1 / c  L / c  nD2 / c

(14)

As mentioned before, the vacuum tube is stationary

and the frequency change caused by the Doppler effect of

the moving source does not yield a noticeable change to the

time interval inside the vacuum tube.

When the light beam leaves the right end of the

vacuum tube E, time (1 2 ) has passed, so F has moved a distance of v(1 2 ) farther.
Therefore we have

3  [lR  v(1  2 )] / c

(15)

 lR / c  [lL  n(D1  D2 )  L]v / c2

and

  [lL  n(D1  D2 )  L  lR ] / c

(16)

[lL  n(D1  D2 )  L]v / c2

For the light propagation time from F to A, we have

6. The genuine tests of the principle of relativity

For the cases we mentioned above, the principle of

relativity of Special Relativity gives an odd and, to put it in

Popper's words, a risky prediction [10],   t  2(n 1)(D1  D2 )v / c2 . That is to say, the travel time difference  can neither be zero, nor be related to the length of the vacuum cell, L .  can only be related to the lengths of the glass rods, D1 and D2 , and the factor has to be (n 1) . Therefore the experiments examining

whether the prediction is true or not will be the genuine

tests of the principle of relativity.

Moving Source or Receiver

Glass
v
D1

Stationary Vacuum
L (a)

Glass D2

Moving Receiver or Source
v

Moving Source A & Detector A

Stationary

Moving Reflector B &
Detector B

v

v

D1

L

D2

Transmission Line

Transmission Line

    3 2 1

(17)

 3  lR / c

(18)

 2  nD2 / c  L / c  nD1 / c

(19)

When the light beam leaves the left end of the vacuum

tube B, time ( 3  2 ) has passed, so A has moved a distance of v( 3  2 ) closer.
Therefore we have

 1  [lL  v( 3  2 )] / c

(20)

 lR / c  [lR  n(D1  D2 )  L]v / c2

and

   [lR  n(D1  D2 )  L  lL ] / c

(21)

[lR  n(D1  D2 )  L]v / c2

Hence, the travel time difference between two

counter-propagating light beams is

      [lL  2n(D1  D2 )  2L  lR ]v / c2

(22)

Apparently the analysis shows that   t and their difference is   t  [lL  2(D1  D2 )  2L  lR ]v / c2 . Besides, each part's contribution to the total time difference
is also different. The contribution of the glass rods is 2n(D1  D2 )v / c2 in  , not 2(n 1)(D1  D2 )v / c2 in t . The contribution of the vacuum cell is 2Lv / c2 in  ,
not zero in t .

Atomic

Atomic

Clock A

Clock B

(b)

Moving Source A & Detector A
v
D1
Transmission Line
v
Atomic Clock A

Stationary L
(c)

Moving Reflector B &
Detector B
v
D2
Transmission Line
v
Atomic Clock B

Fig. 5. Clock version of the genuine tests.

There are two ways of conducting the genuine tests. First the clock version of the experiments is shown as Fig. 5b and the light path mentioned above is also placed there as Fig. 5a. Clearly the light path in Fig. 5b matches with the light path needed for the experiment.
When v  0 , for a light beam, we record the time leaving A with Clock A as t0 (A) and the time arriving B with Clock B as t0 (B) ; when it reflects back from B, record the time arriving A with Clock A as t0 (A) and we have

[t0 (A)  t0 (B)] [t0 (B)  t0 (A)]  T

(23)

T can be positive or negative or zero because two clocks

5

are not synchronized. Now we set T  0 to synchronize two clocks. That is, the two clocks are synchronized if the recordings of clock B are added by T / 2 .
When the speed is v , do these again: record the time leaving A with Clock A as  (A) and the time arriving B with Clock B as  (B) when it reflects back, record the time arriving A with Clock A as  (A) and we have

  [(A)  (B)] [ (B)  (A)]

(24)

Predicted by the principle of the relativity, the result must be   2(n 1)(D1  D2 )v / c2 .
In Fig. 5b, two atomic clocks are stationary, so they are always synchronized. The two transmission lines are deforming. However their deformation does not cause a net effect because they are relatively short and they have the same deformation, A better, but more difficult configuration is shown in Fig. 5c where two atomic clocks are co-moving with speed v . In this case, the two clocks are still synchronized because their speeds are the same. Therefore it is expected two configurations in Fig. 5b and Fig. 5c yield the same results.

Moving Source or Receiver

D1
v
Glass

Moving Source A & Detector A D1

L
Air Stationary
(a)
L

D2 Glass

Moving Receiver or Source
v

Moving Reflector B & D2 Detector B

-v

+v Stationary

Air

Stationary -v

+v

Glass Fiber

Glass Fiber

Moving Source or Receiver

D1
v
Glass

Collimator D1
v
Glass

L
Vacuum Stationary
(a)
L
Vacuum Stationary

D2 Glass

Moving Receiver or Source
v

D2 Collimator
v
Glass

Laser

Coupler

Cancel each other Stationary, Δt=0

Detector (b)

D1

L

D2

v

Air

v

Glass

Stationary

Glass

Laser

Coupler

Detector

Cancel each other Stationary, Δt=0
(c)

D1

L

D2

v
Stationary

Air

Stationary

v

Glass Rod

Glass Rod

Laser

Cancel each other

Coupler

Stationary, Δt=0

Detector (d)

L

v

Air–Core Fiber

v

Atomic

Atomic

Clock A

Clock B

(b)

Fig. 6. Clock version of the genuine tests with two spaced

Laser

Coupler

Detector

Cancel each other Stationary, Δt=0
(e)

stationary fibers.

Fig. 7. Experiments of stationary media with moving source and

Because the refractive index of the air is very close to

receiver using a fiber Sagnac interferometer.

1, we can use a glass tube without extracting the air as

For the interferometric experiment, we place the light

shown in Fig. 6a. Its clock version is shown as Fig. 6b path of the genuine test of the principle of relativity again

there two stationary glass fibers are used to replace the in Fig. 7a. When we conduct an interferometric experiment,

glass rods, so their lengths can be very long and the the light paths of an interferometer constitute a loop so its

distance between the two spaced fibers can be very large as light paths must be more than the light path needed.

well. The experiment can be conducted with two cases of Therefore, similarly to the linear Sagnac experiments [4]

speeds v and -v , and the final result  will be where a fiber parallelogram is used, we can build a fiber

doubled if we compare those two cases.

parallelogram with two collimators as shown in Fig. 7b for

the genuine test. In the fiber parallelogram, the top arm

moves with a constant speed v and the bottom arm is

stationary. While moving, the two relatively short

6

side-arms are kept the same shape so that the travel time

differences in these two side-arms cancel each other and

there is no travel time difference in the bottom stationary

arm. Therefore, the detected travel time difference of the

interferometer is contributed solely by the motion of the top

arm, and light path of the top arm in Fig. 7b matches with

the light path needed for the experiment.

Because the refractive index of the air is very close to

unity, we can use a glass tube without extracting the air as

shown in Fig. 7c and therefore, the configuration in Fig. 7d

is also the same.

It is not difficult to check whether the experimental result is   2(n 1)(D1  D2 )v / c2 exactly as predicted by the principle of relativity. As comparisons, the analysis

above

gives

the

result

  [lL  2n(D1  D2 )  2L  lR ]v / c2 and the parallelogram

experiment of the linear Sagnac effect with an air-core fiber

segment [4] is shown in Fig. 7c and the experimental result

is t  2Lv / c2 .

Based on these, it is expected that the prediction of the principle of relativity,   2(n 1)(D1  D2 )v / c2 , most likely cannot pass the genuine tests.

l1

l2=l

l3

Stationary Source

Stationary Non-Dispersive Medium (a)

Stationary Receiver

Stationary Source

v Moving Non-Dispersive Medium

A A

B B (b)

Stationary Receiver

Moving Source

Stationary Non-Dispersive Medium Moving Receiver

vA

B RvR

(c) Fig. 8. Moving non-dispersive medium versus moving source and receiver.

When all the medium, source and receiver are stationary (Fig. 8a), we have

t0  t01  t02  t03  l1 / c  nl / c  l3 / c

(A.1)

For the drag effect of the moving medium as shown in Fig. 8b, we have

7. Conclusions

t  t1  t2  t3

(A.2)

To summarize, we have presented a new way of examining the principle of relativity of Special Relativity. We select a vacuum tube with two glass rods at two ends as the optical media. The drag effect of the moving vacuum tube is t  2(n 1)(D1  D2 )v / c2 , which is independent of the length of the vacuum cell. Predicted by the principle of relativity, the change of the light propagation time interval with stationary vacuum tube and moving source and receiver should be the same. Our analyses show that the change of the propagation time interval  is caused by the motion of the receiver during the propagation of the light beam in the vacuum tube. The contribution of the glass rods in  is 2n(D1  D2 )v / c2 , not 2(n 1)(D1  D2 )v / c2 . More importantly, the contribution of the vacuum cell in  is 2Lv / c2 , not zero. The genuine tests of the prediction can be conducted with the experiments with two atomic clocks, or the experiments with fiber Sagnac interferometers.
Appendix

The drag effect of a non-dispersive medium is t  t  t0  (n 1)vl / c2 . That is, there is a factor (n 1) in vl / c2 . Obviously it is correct because the drag effect of vacuum (n  1) is zero. Let us find where t  (n 1)vl / c2 comes from.
Firstly, because the medium is moving left, the
propagation time interval inside the medium becomes
shorter [4, 5] and the difference is

t2  t2  t02  vl / c2

(A.3)

Secondly when the light beam left the right end of the medium, B has moved to B’ and the moving distance is vt2  v(nl / c  vl / c2 ) . Therefore the light beam will spend more time to arrive the stationary receiver and the difference is

t3  vt2 / c  v(nl / c  vl / c2 ) / c  nvl / c2

(A.4)

Hence we have the total difference of the propagation time interval

For a non-dispersive medium, we investigate its drag effect and the light propagation in stationary medium with moving source and co-moving receiver.
In Fig. 8, the time interval of a light beam propagating from S to R always consists of three periods: before

t  t2  t3  (n 1)vl / c2

(A.5)

For the light propagation in stationary non-dispersive medium with moving source and receiver (Fig. 8c), we have

entering the medium, inside the medium, and after leaving the medium.

 1 2 3

(A.6)

7

Because the speed of light is independent of the motion

l

of the source and the non-dispersive medium is stationary, we have

v

v

Stationary Non-Dispersive Medium

1  0, 1  t01  l1 / c  2  0,  2  t02  nl / c

Moving

Source A &

Detector A

l

(A.7)
Moving Reflector B &
Detector B

Laser

Coupler

Detector

Cancel each other Stationary, Δt=0
(a)

v Stationary Non-Dispersive Medium

v

l

v Stationary Non-Dispersive Fiber

v

Atomic Clock A
Moving Source A & Detector A

Atomic

Clock B

(a)

Moving

Reflector B &

l

Detector B

v Stationary Non-Dispersive Fiber

v

Atomic

Atomic

Clock A

Clock B

(b)

Moving Source A & Detector A
v

L
Stationary NonDispersive Fiber Coil

Moving Reflector B &
Detector B
v

Atomic Clock A
(c)

Atomic Clock B

Fig. 9. Clock version of the experiment.

The principle of relativity of Special Relativity in this case requires 3    t  (n 1)vl / c2 . Could this possibly be true?
Actually when the light beam leaves the right end of medium B, the receiver has moved to R’ and the moving
distance is v(1 2 )  v(l1 / c  nl / c) .
Therefore the light beam will spend more time to catch the moving receiver and the difference is

3  v(1  2 ) / c  vl1 / c2  nvl / c2

(A.8)

Generally, l1 is much shorter than l , and we have

  3  nvl / c2

(A.9)

Laser

Coupler

Detector

Cancel each other Stationary, Δt=0
(b)

L

v

Stationary Non-

v

Laser

Dispersive Fiber Coil

Coupler

Cancel each other Stationary, Δt=0

Detector (c)

Fig. 10. Experiments of stationary non-dispersive medium with moving source and receiver using a fiber Sagnac interferometer.

In conclusion, we find not only 2  t2 , but also   t . Contrary to what the principle of relativity

predicts, we have

t  (n 1)vl / c2   nvl / c2

(A.10)

It is clear that the difference between them is that one

has a factor (n 1) , and the other has a factor n .

To examine whether the factor is n or (n 1) for

 , we can conduct the experiments as shown in Fig. 9.

Fig. 9a is the clock version of the experiment. In Fig. 9 b, a

non-dispersive fiber is used so the length l can be much

longer. Because in these configurations the non-dispersive

medium is stationary and the total propagation time interval

inside the medium is proportional to the length of the

medium, we can greatly increase the total time interval by

using a non-dispersive fiber coil with total length L as

shown in Fig. 9c. Apparently in this case   nvL / c2

and it is not difficult to examine whether it is really the

case.

Experiments in Fig. 10 are the interferometric

counterparts of the experiments in Fig. 9.

8

References
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[2] K. Popper, private communication, Karl Popper Archive, 1981.
[3] R. Wang, Y. Zheng, A. Yao, D. Langley, ”ModifiedSagnac Experiment for Measuring Travel-Time Difference between Counter-Propagating Light Beams in a Uniformly Moving Fiber”, Physics Letters A, 312 (2003) 7.
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[5] Yuan Zhong Zhang, Special Relativity and Its Experimental Foundations, World Scientific Publishing, 1997, Singapore.
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Observation of the Fizeau-Effect in Solid Substances”, Proc. Royal Acad. Amsterdam, 22 (1920) 462. [7] P. Zeeman, A. Snethlage, “The Propagation of Light in Moving Transparent Solid Substances. II. Measurements on the Fizeau-Effect in Quartz”, Proc. Royal Acad. Amsterdam, 22 (1920) 512. [8] P. Zeeman, W. de Groot, A. Snethlage, and G. C. Diebetz, “The Propagation of Light in Moving Transparent Solid Substances. III. Measurements on the Fizeau-Effect in Flint Glass”, Proc. Royal Acad. Amsterdam, 23 (1922) 1402. [9] A. Safari, I. De Leon, M. Mirhosseini, O. S. Maganã-Loaiza, R. W. Boyd, “Light-Drag Enhancement by a Highly Dispersive Rubidium Vapor”, Phys. Rev. Lett. 116 (2016) 013601. [10] K. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, Routledge, 1963.

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