What is presented below is not a typical thought experiment. It predicts an outcome that can be empirically tested – with more moderate lengths and speeds than used here. The experiment contains an asymmetry that is used to demonstrate the fallacy of the Lorentz Transformation and the second principle of SRT.

Imagine a large planet on which there is a straight railroad track, several million miles long, and a train that is about 300,000 km long, that can reach a speed of 1/2 the speed of light, or 150,000 km/sec. A man stands on the embankment, and when the rear of the train reaches him he triggers two short light pulses, blue ones, one from a source at the rear of the train and one from a source on the embankment where he stands. Both pulses will be reflected back from a mirror located at the front of the train and will reach a detector at the rear of the train. According to the second principle of SRT another man can stand at a spot along the embankment where he will see the rear of the train pass and simultaneously see both light pulses return to the detector at the rear of the train. In addition, according to the second principle of SRT, both pulses should reach the mirror at the front of the train at the same time.

It is best to think of this as two separate experiments – one with a source on the embankment, another with a source on the train. Let us call A the pulse originating on the train and B the pulse originating on the embankment. It is easy to calculate just where the second man must be stationed to observe the return of pulse A. For pulse A, originating on, and at the rear of the train, the location of the observer, in the frame of the embankment, is 300,000 km beyond the point of initiation, sinced by the first principle of SRT the speed of light is the same on the train for the source on the train, and along the embankment for the source on the embankment. We can also grant Einstein’s assumption that the speed is the same in both directions. Without appeal to SRT, the A pulse requires two seconds for the round trip on the train and at that time the rear of the train has advanced 300,000km.

For pulse B, originating on the embankment at the same time and place as pulse A, the answer is either 450,000 km, or 1.5 light-seconds, or possibly 400,000 km. This pulse is chasing the train and after one second it has reached the point where the front of the train was at the time the pulse was initiated. By that time the front has advanced 0.5 light-seconds, and by the time the pulse reaches that point the front has advanced another 0.25 light-seconds, etc. Pulse B reaches the front of the train after 2 seconds and at that point the rear has traveled 300,000 km. Because the front of the train is moving away from the source there will be a Doppler effect, so the pulse reaching the mirror will be red, instead of blue. On the return trip pulse B requires only one second to travel the 300,000 km distance to the rear of the train (if we assume it now travels on the train), and at that point in time, 3 seconds from the time of initiation the rear of the train is at the 450,000 km mark. Furthermore, using this scenario, the color of the light pulse B, remains unchanged, during the reverse journey. It is red.

The mirror adds an interesting facet to this experiment – whether or not we use the LT. Its function is to produce a similar pulse, for each pulse received at the front of the train, that travels in the reverse direction of the train. For pulse A, the pulse on the train, the mirror is stationary, but for pulse B, the pulse from the embankment, the mirror moves away from this pulse. It is therefore arguable whether the mirror merely reverses the sign of pulse B, and allows the reverse pulse to move with velocity c in the frame of the embankment; or if it generates, or regenerates a light pulse, and that pulse has speed c in the system in which the mirror is stationary, i.e. the train. Since both scenarios are conceivable, both solutions are offered.

If the returning pulse remains in the embankment frame, we should take into consideration that the rear of the train moves towards the point, in the embankment frame, from which pulse B is reflected back. Then it takes only 2/3 seconds for the second leg, and the rear of the train has then reached the 400,000 km mark. In this case the returning pulse experiences a blue shift as a result of the approaching rear of the train, so that the color shift is reversed, and the arriving pulse is blue.

An observer stationed at the front of the train would note that pulse A gets there first, and would deduce that it is speedier – not realizing that pulse B travels a longer distance. The pulses do not reach the front at the same time and the color of A is blue while that of pulse B is red. Since the source for pulse B is in relative motion to the source of pulse A, considered in the frame of the train, the second principle assertion, that they should reach the front of the train at the same time, is false.

The energy of a blow, for example from a boxer, is dependent on whether the destination (the opponent) is moving towards or away from the source of the blow. The kinetic energy is not just in the blow; it is in the relation, the relative movement of source and destination. That is why the color of the light, which reflects its energy, (remembering Planck’s law) depends on the relative motion of two systems – that is the message of the Doppler effect.

AN ALTERNATIVE VIEW

As a result of an e-mail exchange with a physicist who has taught and written about Special Relativity for many years and who wishes to remain anonymous, I now have an alternative solution which uses SRT to come to the conclusion that one observer will see both pulses return to the rear of the train at the same time. Here is a sketch of that approach:

For pulse A we need to calculate by means of the Lorentz Transformation the apparent contraction of the embankment in the frame of the train. According to this physicist, this would put the rear of the train at the 346,410 km mark at the time pulse A returns to the rear. This result is obtained by using time dilation. Note that it now takes more than two seconds, in the frame of the embankment. Since the time of travel is the same in both directions the rear of the train is at the 346,410/2 = 173,205 mark when the pulse reaches the front..

The length of the train is only 259,808 km as it appears in the frame of the embankment, and as a result pulse B, moving at the speed c in that frame, takes only 1.73205 seconds to reach the front of the train, at which time the rear has traveled 259,808 km. Also, in the frame of the embankment, the rear of the train is moving towards the point at which the front is located when pulse B is reflected, so that the pulse requires only 2/3 the length of the train to reach the rear or (2/3)x259,808/300,000 = .57735 seconds. During this time the train has traveled an additional 86,602 km. When we note that 259,808 + 86,602 = 346,410 km, we see that, according to the LT, both pulses return to the same spot along the track, but it is at the 346,410 km mark – not 300,000, and not 450,000, nor 400,000.

This calculation says nothing about the Doppler effect, which would be evident to an observer located at the front of the train, in the case of pulse B, but not in the case of pulse A. It would also be evident at the rear of the train if the returning pulse B traveled the return path in the frame of the train. (in a normal two-way Doppler process the one way Doppler factors multiply since source and receiver continue to separate – that is not the case in this experiment.)

Note that pule A reaches the front of the train when the rear has advanced 346,410/2 = 173,205 km and not 259,808 km as is the case for pulse B. So the two pulses do not arrive at the front at the same time. The one-way LT contradicts the claim of the second principle that the speed of light is independent of the movement of the source. Since with, or without the LT the second principle is violated for a single direct path, we can conclude that the second principle, and hence SRT, is false. SRT can force the two pulses to return to the same spot on the embankment, at the same time, by invoking the LT for a two way path – it is however most likely the wrong spot. The LT is derived using a two way trip, and, additionally, using the second principle, so it is not surprising to get a solution bringing both pulses back to the same spot. The mathematics is consistent, but if the second principle is wrong this consistency is useless.

Lorentz derived his transform beginning with the hypothesis of the aether theory of light. Einstein, along with most physicists, rejected this theory. It is inconsistent with the M&M experiment. Einstein substituted his second principle, from which he derived the two way LT, and then went on (erroneously) to derive the one way LT using the square root. As we see from the above this does not work. Nor can we infer the truth of the second principle from the two way LT – that is a circular argument. The second principle, like the aether theory, is inconsistent with empirical observations, like the M&M experiment, and thought experiments, like the one above.

Some form of empirical experiment would help to resolve the question as to where on the embankment the two pulses return to the rear of the train. If SRT is invalid, as can be inferred from the forward direction, we would expect the answer to be 300,000 km for pulse A and either 400,000 or 450,000 for pulse B.

Table of Contents

PUBLISHED BOOK 2005

HOME PAGE
INTRODUCTION
THE PRINCIPLE OF RELATIVITY
SPECIAL RELATIVITY - 1905
SPECIAL RELATIVITY - 1917

THE MICHELSON-MORLEY EXPERIMENT
THE LORENTZ TRANSFORMATION
MICHELSON-MORLEY PLUS LORENTZ, CONDENSED

THE DOPPLER EFFECT
A COUNTER EXAMPLE TO SRT
A COUNTER EXAMPLE TO GRT
THE AGE OF THE UNIVERSE

CONCLUSIONS
APPENDIX I: TYPE 1A SUPERNOVAE
APPENDIX II: A EUCLIDEAN MODEL OF THE UNIVERSE
APPENDIX III: MASS AND ENERGY
All contents copyright 1997, 2005
Revised 6/30/2005