## A fresh look at a famous thought-experiment

In 1920, Albert Einstein published the now well-known book titled, “Relativity: The Special and the General Theory”. In Section IX of that document, The Relativity of Simultaneity, he relates the famous thought experiment that compares observations from two differing inertial frames. The first frame is a stationary one , on the embankment alongside a railroad line. In this instance, an observer, designated M, is located at a point on the embankment equidistant between the locations of two simultaneous lightning strikes alongside the embankment. By means of two mirrors, arranged at 90 to each other, the observer, M, is able to determine that the two strikes appear to be simultaneous, based on their equidistance and on the finite constancy of the velocity of light. Because of the distances involved of course, his observation of the lightning strikes occurs at a measurable interval of time after the actual occurrence of the events themselves, but since that we know that his observations were also simultaneous, that is of no importance to the outcome of the observation.

At the same time another observer, M1, was travelling past M’s point of observation on a speeding train, at a velocity that was a significant increment of the velocity of light, (let us say at about 1,000 kilometers/second, one three-hundredth of the velocity of light). Observer M1 is also equipped with an observing device similar to that of M. M1’s observation of the two lightning flashes is not the same as that of M. In the case of M1, the flashes do not appear to have occurred simultaneously, but the one from the direction of the train’s motion arrives earlier and that from the opposite direction arrives later, by a measurable interval. Hence , his observations would seem to indicate that the two events were not simultaneous.

Now, Professor Einstein’s conclusion from this set of circumstances is as follows, and I quote.

“Now, in reality (considered with reference to the railway embankment) he is hastening toward the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time: unless we are told the reference-body to which the time refers, there is no meaning to a statement of the time of an event.” (italics mine)

It is important to note that Einstein opens this statement with the words, “Now, in reality—”, because he then immediately reverts to a discussion of, not the reality of the simultaneous events, but to the observations of them by two observers in different reference-bodies.

There is a logical disconnect here. Bertrand Russell in the Principia and elsewhere points out the importance of understanding that an event is one logical type and observations of it are another. The observation of the event from the moving train did not change the event itself. It had its own independent reality. This can be illustrated by the following transcript of an exchange between the two observers, M and M1, at breakfast the following morning:

Observer M: It seems that you, too saw the remarkable lightning strikes last evening!

Observer M1: Yes, it was amazing. I had always heard that lightning never strikes twice in the same place, but I never thought that two bolts might strike at the same time. They were amazingly close.

Observer M: Actually they did occur simultaneously. They appeared to be so on my detector, but to be sure, I measured their distance from my observation point and found the distances exactly equal. Since we know that light travels at a constant velocity regardless of its direction, I was instantly convinced.

Observer M1: That is very interesting. Since, as you know, I was on the train passing by your post at that same instant, the flash from ahead of the train appeared to arrive earlier than that from behind the train. We were travelling at a high rate of speed but I was able to measure the interval between the two flashes with some precision.

Observer M: I have heard that, according to some theories, that clocks travelling at high speeds actually run slower than those at rest. Could that have been what you observed?

Observer M1: Oh, no. The clocks are set precisely the same. We arrived precisely on time at our destination. It is just that the train had moved closer to the one point and further from the other in the interval that it took the light to arrive at my detector.

Observer M: That is good to know. The clock speed question has bothered me.

Observer M1: Yes, this way, knowing the length of the interval between the flashes was important in helping me to calculate the exact velocity of the train as we passed you. Those who think that clock speed changes with physical velocity must not understand that an event and its observation are two distinct and different logical types, two different levels of abstraction.

xxxxxx

What does this leave us with? Well, one thing is that there are now two apparent explanations for the difference between the two sets of observations. Einstein’s assertion that “Every reference-body (co-ordinate system) has its own particular time: unless we are told the reference-body to which the time refers, there is no meaning to a statement of the time of an event.” and, on the other hand the one described in the hypothetical breakfast-table conversation, which uses Newtonian logic and Newtonian mathematics to explain the discrepancy. Examining the details of Einstein’s description of his thought-experiment reveals a gap in his reasoning that is not explained anywhere in his overall account. The concept of “different time measurements or rates of occurrence” does not appear elsewhere in the narrative. The assertion about each different reference frame having its own particular time appears full-blown without precedent. Is this just an inadvertent jump in the experimenter’s narrative?

What may have happened here is a situation where the so-called thought experiment may have been intended only as an explanation of a result previously arrived at mathematically, in a narrative otherwise intentionally free of mathematics, or, it may be only a slightly incomplete narrative. At any rate this has been the accepted explanation for whatever reason, with almost  a hundred years of consequences in critical thought about relativity.

So, which explanation is correct? The common-sense Newtonian one, or the relativistic uncommon-sense one. We should perhaps look at the question of whether thought experiments are repeatable to confirm their initial results, as we would require with real-world experiments, or if they were and are actually just-so stories to explain a pre-conceived outcome. I leave it to the reader to decide.