# Was Lewis Epstein right to dismiss explanations of relativity that are based on signal delay?

Ever since reading Relativity Visualized by Lewis Epstein, I believed that signal delay is not the explanation for relativistic effects. Here's a quote from the book:

"Suppose a pair of stars (or wheels) is moving side by side through space. You see the more distant star (or wheel) further in the past, and so it appears to lag behind the nearer star. Because of this effect, a box (or asteroid) moving rapidly through space appears to be turned.

If a pulsating star is moving away from you, the signal transmission delay time increases between each pulse. Each pulse is delayed more than the one before it. So the time between pulses appears to be longer than it properly is. If the star moves toward you, the effect is reversed. But don’t confuse this with Einstein’s slow time; his slow time does not depend on signal delay time or on the direction of motion.

Signal transmission delay time can even cause you to see things moving faster than the speed of light! Suppose a gun, one light year away from you, is fired directly toward you. It will take one year for the first light from the oncoming bullet or gun flash to hit you. If the bullet moves at three-quarters the speed of light, it will hit you four-thirds of a year (a year and four months) after it is fired. The last light from the bullet will hit you just before the bullet hits you. As you see it, the time between first and last light from the bullet is four months. During those four months you will see the bullet travel one light year. So the bullet appears to you to be moving three times faster than light.

Everyone knows about and allows for all these signal transmission delay time effects. There is nothing new here. There are two ways to dispose of them: (1) Subtract the delay time from the apparent time, or, easier yet, (2) get so close to the happening that you can forget about the delay. If you are close enough to the lightning, the thunder is not delayed."

This all still seems to make perfect sense to me. So I am still inclined to write off any reference to signal delays or Doppler shifts as wrongheaded.

But lately I have started to question my knowledge of relativity, and I'm wondering: could signal delay based explanations of relativity be a valid alternative to the way Epstein does it? I saw something in Wikipedia about Langevin, and maybe also Einstein, deriving relativity from signal delay and/or Doppler effects, although I'm not sure if this in now out of date thinking.

Unfortunately I can't find the Wikipedia article now. Someone had linked to the article in a Physics question or answer saying it was surprisingly "readable" for Wikipedia. And it was.

Edit: I found the article. This is it: https://en.wikipedia.org/wiki/Twin_paradox and here is a quote from it.

"In 1911, Paul Langevin gave a "striking example" by describing the story of a traveler making a trip at a Lorentz factor of γ = 100 (99.995% the speed of light). The traveler remains in a projectile for one year of his time, and then reverses direction. Upon return, the traveler will find that he has aged two years, while 200 years have passed on Earth. During the trip, both the traveler and Earth keep sending signals to each other at a constant rate, which places Langevin's story among the Doppler shift versions of the twin paradox. The relativistic effects upon the signal rates are used to account for the different aging rates. The asymmetry that occurred because only the traveler underwent acceleration is used to explain why there is any difference at all,[16][17] because "any change of velocity, or any acceleration has an absolute meaning".[A 3]".

I also recall seeing in old books such as "Relativity for the Layman" (not the one by Einstein) old versions of the Encyclopedia Britannica, the following explanation of relativity of simultaneity that never made the slightest sense to me: A spacecraft at rest receives light from two simultaneous explosions at the same time, but if it is instead moving, it receives light from one of them earlier than the other, therefore they are not simultaneous for the moving spaceship. I always thought that made no sense because the same logic would imply that if the ship was at rest, but nearer to one explosion than the other at the time of the explosions, it would likewise receive light from one them before the other, and yet no one was claiming that that indicated that the explosions were not simultaneous for that type of stationary observer. I always thought the authors just made up / fiddled the equations that accompanied these arguments. But having seen the stuff about Langevin, I figure that maybe they copied them from old textbooks.

The first video https://www.youtube.com/watch?v=894ZI68rdys I found with Google about relativity of simultaneity, and the first text https://www.fourmilab.ch/documents/RelativityOfSimultaneity/, both explain it by invoking signal delay. So it's still surprisingly widespread.

Wikipedia has three explanations in https://en.wikipedia.org/wiki/Relativity_of_simultaneity. First a shortened, low key, version of what Epstein said, then a signal delay explanation attributed to Einstein (but way back in 1917) but also with the subtle disclaimer "A popular picture for understanding this idea" at the outset. Most laymen will think "popular" means "favored" but of course, those in the know, will also think popularization of science by the mass media and oversimplification and misinformation. And then comes "It may be helpful to visualize this situation using spacetime diagrams." This is true. "May" is right. I find spacetime diagrams frustratingly incomprehensible due to math not being my strong point. End of Edit.

So my question is: was Epstein right to dismiss explanations of relativity that are based on signal delay?

• About the youtube video by Bryan W. Robers that you link to: at 4:42 into that video Bryan Roberts takes the time to warn the viewers: the case of a lightning flash and its thunder not arriving at the same time is not an instance of relativity of simultaneity: "the lightning bolt and the thunder crash really do happen at the same time [...] this is just one thing moving slower than the other but the relativity of simultaneity is deeper than that". The thing is: while relativity of simultaneity can be presented in an unambiguous way, unfortunately Bryan Roberts doesn't do that. Commented Jul 23, 2022 at 21:39
• About the fourmilab link that you give. Fourmilab is a personal website, the name of the author is John Walker. There is a wide range of subjects on the website. The author is not a professional science communicator, but on the whole the science content is good, it appears. However, the article about relativity of simultaneity that you link to is gibberish. (The abysmal quality of that article is very weird. From other material on the website it is clear that John Walker is passionate about Special Relativity.) Commented Jul 23, 2022 at 22:11
• Palash B. Pal 2003, European Journal of Physics, Volume 24, number 3 315 Nothing but Relativity Commented Jul 24, 2022 at 15:08
• As pointed out in the article itself: using Nothing But Relativity to narrow down to just Galilean and Lorentzian as viable goes back many years. The citations go back to 1965, 1966. I think it is fairly well known in the physics community. In my opinion it should be the standard way to reveal the potential of Special Relativity. Other than that: the stackexchange policy is that comments are not for extended discussion. I endorse that policy. For ongoing discussion the better option is to use a threaded forum such as physicsforums. Commented Jul 24, 2022 at 16:22
• The earliest instance of a 'Nothing But Relativity' approach is, it appears, by Ignatowski 1910. English wikisource has a translation of his article Some general remarks on the relativity principle Commented Jul 24, 2022 at 17:05

Short answer: Lewis Epstein is correct.

If you are interested in knowing what a single individual would see when looking at a relativistic phenomenon, you do have to account for signal delay effects.

However, an "observer" or "reference frame" in special relativity is actually not a single individual located at a spatial point. You can think of a reference frame as an infinitely large and dense grid of clocks connected by rulers stretching through all of space. The clocks are all synchronized and the grid as a whole is moving with a single, uniform velocity. At every node of the grid, there is a device that records events that occur at that spatial location and the time at which they occurred.

What length contraction means, is that if you use a reference frame to measure the length of a meter stick moving with respect to the reference frame, you will measure its length to be less than one meter. Here's how you measure a length with the reference frame:

• You pick a time to measure the length, $$t_{\rm obs}$$.
• At this time (in the reference frame), the node which is nearest to the left edge of the ruler says "I am the node at position $$x_1, y_1, z_1$$ and measured the left end of the ruler at time $$t_{\rm obs}$$.
• Also at this same time (in the reference frame), the node which is nearest to the right edge of the ruler says "I am the node at position $$x_2, y_2, z_2$$ and measured the right end of the ruler at time $$t_{\rm obs}$$.

Then what special relativity says is that $$$$\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2 + (z_1-z_2)^2} < {1\ {\rm m}}$$$$ It actually says more, because it tells you exactly what length will be recorded by the reference frame given the relative velocity between the meter stick and the reference frame, but we don't need to get into that level of detail for this question.

The above statement does not include any effects of propagation delays. It is a statement about the spatial distance between two events that occur at the same time, in a specific reference frame.

You can make a similar careful setup to define time dilation; there, you are comparing how much time has passed on a moving clock as it passes by two reference nodes in the reference frame grid, with how much time passed on the clocks at those two nodes attached to the reference frame.

If you want to know what an individual person would actually see if they were watching the meter stick from a fixed position, the length contraction effect would be part of the answer, but you would also need to take into account the propagation of light from the meter stick to the person. This is a subtlety that is sometimes glossed over in treatments of special relativity.

It is possible to derive special relativity from Doppler shifts. Hermann Bondi famously did it in the popular book Relativity and Common Sense. The Wikipedia article you're thinking of might be this one: Bondi k-calculus.

The idea is to take as the fundamentally non-Newtonian postulate not the constancy of the speed of light, but the reciprocity of Doppler shifts: that is, the fact that if two objects are moving symmetrically toward or away from each other, they each see the other Doppler shifted by the same factor. From that you can easily derive that the two twins in the twin-paradox setup end up as different ages (the argument is in the Wikipedia article), and with more work the rest of special relativity.

What Epstein wrote is the standard view of the nature of propagation delays in special relativity. Arguably it's correct: if special relativity were really just about signal delays then the twins wouldn't end up persistently different ages at the end of the experiment. But I think you can also make a reasonable argument that it's wrong: aging is a chemical process, whose speed is set (in a very complicated way) by various propagation delays inside your body. So it's entirely possible that you could age at a different speed (wrt some time coordinate) while moving (wrt some frame) solely because of differing propagation delays; and that is indeed what happens.

• The $k$ calculus is a neat way to present special relativity. However I think the point you make there being a reasonable argument that special relativity is about signal delays is a bit of a non-sequitur; I think the question is asking about signal delays due to the propagation of light between source and observer, and not signal delays as a synonym for a clock in a specific reference frame. Commented Jul 23, 2022 at 17:49
• In my opinion the correct end result of k-calculus approach is fortuitous. It is possible for a derivation to be on the wrong track and still arrive at the same end result as a correct derivation. For context, on the website mathpages.com Kevin Brown describes how in 1887 Woldemar Voigt explored Doppler shift, leading to expressions that have the same form as Lorentz transformation. I submit this parallel of form is the underlying explanation for how the k-calculus approach arrives at the same result as a correct approach. Commented Jul 24, 2022 at 6:27
• @Cleonis That seems unlikely, honestly; I'd bet you dollars to donuts you can derive Doppler-equivalence from special relativity and special relativity from Doppler-equivalence. If so, then saying Doppler-equivalence is "wrong" while special relativity is "right" when both make the same predictions is not even wrong. (now, both are wrong, in that general relativity makes different correct predictions that they won't). Ie, it turns out that the two are equivalent axioms; any distinction between them is a preference.
– Yakk
Commented Jul 25, 2022 at 2:09
• @Cleonis As Yakk said, you can derive Einstein's postulates from Bondi's and vice versa, so the theories are equivalent. Interpretationally they're the same too; Bondi only wanted to develop the same theory in a different way, not suggest Einstein was wrong. The problem with pre-1905 derivations of the Lorentz transformation was that it was assumed to apply to some phenomena and not to others, which leads to wrong predictions. Commented Jul 25, 2022 at 2:37
• @Andrew I'm just not sure there's any precisely articulable difference between those two cases. Atoms in your body are emitters and receivers of electromagnetic waves, and it seems somewhat arbitrary to not apply the terms "source" and "observer" to them. In QM you can limit "observation" to processes that cause decoherence/collapse, but there's nothing analogous in SR. Commented Jul 25, 2022 at 2:43

I want to make a distinction between gathering of raw data, and stages of processing the data.

In data processing we can and do take advantage of the fact that the data processing happens after the data gathering.

When there are multiple locations all the data are logged, and processed afterwards. That is, the content of the logs is communicated to some central processing facility, so that you can take your time processing the data. The natural first stage of data processing is to account for all signal delay.

Relativistic physics is:
That which is still there after signal delay has been accounted for.

There is an example that highlights that: a relativistic effect with (unfortunately) an awkward name: 'transverse Doppler effect'.

There is a historical reason for that awkward name: there is a parallel between the expression for classical Doppler effect, and the expression for the Lorentz transformation.

(It seems likely that the purported derivation of Lorentz transformation using signal delay abused this parallel.)

One way to verify transverse relativistic effect would be as follows: create a setup that will allow you to measure spectral lines of atoms moving at high transversal velocity. For instance, a cyclotron-like setup with ions maintained in circular motion. Set up spectrum measurement with the detector located at the center of the circular motion. In terms of pre-relativistic physics you do not expect shift of frequency, but in terms of relativistic physics you do expect frequency shift.

So yeah, explanation of relativity based on signal delay should be dismissed,