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maybe also Einstein, deriving relativity from signal delay and/or Doppler effects, although I'm not sure if this in now out of date thinking.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?
Best Answer
Short answer: Lewis Epstein is correct.
Longer answer:
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:
Then what special relativity says is that \begin{equation} \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2 + (z_1-z_2)^2} < {1\ {\rm m}} \end{equation} 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.