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I get my "demonstration" of time dilation from the textbook thought experiment.

A laser is mounted on a cart with a reflective ceiling. At $t=0$ the cart starts moving and the laser is fired. When the laser is reflected back at the starting point the (thought) experiment stops.

Now, two different observers, one sharing the frame of the cart and another standing on the ground perpendicular to the cart will observe two different things. For the first one, the laser bounces back and then down in a straight line. For the second one, the light travels in a triangular pattern which is longer than the path observed by the first guy.

Given that the speed of light is constant, the time has to dilate/contract.

Why is the speed of light held constant here? Could we work out a physics where time is absolute but the maximum speed of light variable?

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  • $\begingroup$ it's the ceiling, not the roof. Also: what is "solidal"? $\endgroup$
    – JEB
    Commented Jan 6, 2020 at 18:42
  • $\begingroup$ It means sharing the frame of reference. $\endgroup$
    – Three Diag
    Commented Jan 6, 2020 at 18:46
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    $\begingroup$ Is there a link to a dictionary in which solidal appears? $\endgroup$
    – JEB
    Commented Jan 6, 2020 at 18:51
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    $\begingroup$ I can only find articles from italian physicists that make the same mistake as I do. Changed it. $\endgroup$
    – Three Diag
    Commented Jan 6, 2020 at 18:53
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    $\begingroup$ I put an answer down before some of the comments, but now I think it should be pointed out that the entire premise of this question seems to be wrong. We don't arbitrarily assume that the speed of light is constant in the middle of one of these examples. Relativity starts from the observation that the speed of light is constant in the Maxwell equations, as confirmed experimentally. "Why is the speed of light held constant here?" Because it was already known to be constant and these thought experiments are to tease out the consequences of that observation. $\endgroup$
    – Brick
    Commented Jan 6, 2020 at 19:32

8 Answers 8

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Keep in mind that several other Einsteinian effects are hard to explain in an absolute-time scenario and are tested. For these purposes I would concentrate on:

  • The existence of a speed limit for massive particles

    Looping accelerator systems based RF cavities only work because once the particles have enough energy their speed is effectively constant (and that speed is within a hair's breadth of $c$). But this constant speed doesn't mean constant kinetic energy or momentum: the accelerator continue to add energy and momentum with measurable consequences in the bends and the experimental halls.

  • Conversion of other energies to mass and vice versa

    We can measure the kinetic energy and mass of reaction products in particle physics experiments and when we produce heavier products than we started with the extra mass is related to lost kinetic energy in keeping with $E = mc^2$. Likewise when particles decay to lighter products the products have extra kinetic energy in keeping with the mass difference.

  • The twin paradox

    It is not just a fanciful notion you find in books, but something that we do with unstable particles in looping accelerators (example, muon-g2).

To fit all of those that into a absolute time framework will require more (and to my mind very arbitrary) assumptions. By contrast the Lorentz symmetry of special relativity explains them all in one go and is motivated by the structure of Maxwell's equations (that is has an experimental basis and is not at all arbitrary).

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    $\begingroup$ It seems, though, your solution leaves the door open for a possible (albeit somewhat arbitrarily built) physics with absolute time and compatible with experiments, in contrast with the second answer "Now if you want to find a theory that is fully Lorentz invariant such that it correctly matches the train-light-clock experiment and the other standard S.R. scenarios, then: No. Relativity is the Lorentz invariant solution." This is precisely what I would like to know. I guess it boils down to: is in any sense possible that relative space-time is really a convention ? $\endgroup$
    – Three Diag
    Commented Jan 9, 2020 at 13:51
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    $\begingroup$ Scientific investigation can never absolutely rule out "[supreme being of your choice] is messing with us" type scenarios, nor even so-called "conspiracies" (complex nature is fine-tuned to present as some simpler truth). Instead it is an engine for seeking out successful descriptions where "successful" combines getting everything right with parsimony and ellegance. The last two parts are a human convention, but they have perfromed well in the past: the more parsimonious theory is usually the one that makes the correct predictions for the next behavior you invesitate. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Jan 9, 2020 at 16:32
  • $\begingroup$ @ThreeDiag, Conventionality of distant simultaneity is well known concept: plato.stanford.edu/entries/spacetime-convensimul . In regard of empirical equivalence of absolute space – time theory (Lorentz) and Einstein relativity there was work philpapers.org/rec/JANACB It is here mpiwg-berlin.mpg.de/litserv/diss/janssen_diss/Chapter3.pdf, just change manually chapter numbers. I don't agree with conclusion; but it is valuable source of historical and scientific analysis anyway. $\endgroup$
    – user139020
    Commented Jan 9, 2020 at 16:51
  • $\begingroup$ In regard of the statement that the speed of light can be isotropic in all relatively moving reference frames it is hardly possible, rotation shows everything. Speed of light is anisotropic relatively to a rim of rotating ring, large or small: physics.stackexchange.com/questions/481231/…. Hence. (at least) speed of light relatively to the Earth surface is NOT isotropic, it is quite obvious. Of course, synchronizing clocks Einstein- way one can make it isotropic with all the ensuing consequences. $\endgroup$
    – user139020
    Commented Jan 9, 2020 at 17:06
  • $\begingroup$ @dmckee what I am interested in is the philosophical interpretation that could be supported as a consequence. If there are two distinct theory one which has dilated space-time and one in which space-time is invariant then it's a convention which you pick, and it might make sense to use the more elegant one. $\endgroup$
    – Three Diag
    Commented Jan 9, 2020 at 17:36
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There is a physics where time is constant and the speed of light is not: Newtonian with an ether.

Galilean transformations in Newtonian physics have time as a fixed parameter that ticks away uniformly for all points and states of motion.

For the speed of light to be frame dependent, one needs the ether in which it propagates at $c$. The ether then defines a preferred reference frame against which all motion is absolute.

So in the train experiment, the station (which is solidal with the ether ;-) sees light take a long path at $c$. Meanwhile, the observer on the train sees light propagating vertically more slowly:

$$ c' = \frac c {\sqrt{1+(\frac v c)^2}}$$

Now if you want to find a theory that is fully Lorentz invariant such that it correctly matches the train-light-clock experiment and the other standard S.R. scenarios, then: No. Relativity is the Lorentz invariant solution.

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    $\begingroup$ This is a little misleading in the sense that you use "a physics" to mean an alternative reality, whereas the OP seems to use it to mean an alternative theory of our reality. $\endgroup$
    – Brick
    Commented Jan 6, 2020 at 19:15
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    $\begingroup$ Of course the notion of Lorentz-Fitzgerald constraction floated about for a bit as a lash up that could save Galilean relativity in the face of Michelson-Morley at least. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Jan 6, 2020 at 19:15
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No. You're neglecting that time dilation is only one effect explained by relativity. You'd also need to take into account length contraction or, more generally, Lorentz invariance. Your "absolute time" is not going to capture the fact that there are properties of spacetime (not just time) at play here.

In light of the comments (pun intended!), a further point: The idea that the speed of light is constant is a consequence of the Maxwell equations. Relativity follows that logically and historically, it doesn't precede it. If you open the question to spacetime, then you still have the issue that the Maxwell equations are and were well-known. Special relativity is about exploring the consequences of that experimentally verified fact. It's not clear what you mean by "absolute" here, but any interpretation that comes to my mind implies a preferred frame for Maxwell, and we know that does not exist due to experiment.

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  • $\begingroup$ What about absolute space and time with variable speed of light? (Or I guess more specifically a frame dependent speed of light?) $\endgroup$
    – BioPhysicist
    Commented Jan 6, 2020 at 18:51
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    $\begingroup$ If you want to define precisely what you mean by those terms, @AaronStevens, we can answer precisely, but it's a different question. The answer is still no though. :) But maybe the question was rhetorical? $\endgroup$
    – Brick
    Commented Jan 6, 2020 at 19:03
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    $\begingroup$ Well it seems like the OP is trying to get at "Instead of the speed of light being absolute and space-time being relative, what if it is space-time that is absolute and the speed of light that is relative?" While the OP forgot to include the "space part", I think that is what they were going after $\endgroup$
    – BioPhysicist
    Commented Jan 6, 2020 at 19:05
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    $\begingroup$ Indeed, this is what I meant, I am not a physicist by any mean. $\endgroup$
    – Three Diag
    Commented Jan 6, 2020 at 19:07
  • $\begingroup$ I added some text based on the comments, although I still think that's essentially a different question. @AaronStevens $\endgroup$
    – Brick
    Commented Jan 6, 2020 at 19:13
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There are a number of alternative theories to SR that posit absolute simultaneity (and hence reject SR's relative simultaneity). There are often referred to as Lorentzian relativity or neo-lorentzian relativity, and were originally developed by Lorentz and others (such as Poincare). They preceded SR by approximately 10 years.

These theories presuppose that there is only one frame (the "preferred frame" often called the ether or ether frame) in which the speed of light is truly isotropic.

In these theories, time is absolute and does not vary with speed. Here it is theorized that there is no actual "time dilation." There is only "clock retardation." Time, as an abstract concept, does not change. However the mechanical instruments which we use to measure time (clocks) are altered by motion.

According to such theories, the speed of light is variable, and differs from frame to frame (while time does not).

However, the speed of light is always MEASURED to be C in other frames if corrections are not made for the distortion of the measuring instruments caused by increased velocity.

The idea is that all (uncorrected) frames measure C to be the same because the rods and clocks used in those frames have been distorted by velocity. So, even though the MEASURED speed of light is C, the "actual" speed is not (except in the preferred frame).

These theories are often said make the same predictions as SR (although I would dispute that). Therefore, every experiment which is said to confirm SR can also be said to confirm LR.

Sexl and Mansuri did a several part, extended analysis which compared and contrasted SR with such alternative theories. Here is an excerpt from a wiki article which summarizes their work on the topic:

"So Mansouri and Sexl spoke about the "remarkable result that a theory maintaining absolute simultaneity is equivalent to special relativity." They also noticed the similarity between this test theory and Lorentz ether theory of Hendrik Lorentz, Joseph Larmor and Henri Poincaré."

https://en.wikipedia.org/wiki/Test_theories_of_special_relativity

The essence of your question was: "Could we work out a physics were time is absolute but maximum speed of light variable?"

The answer is "yes, we can (and have)."

Edit: I see now that I am basically just re-stating, in a different form, the answer given by Albert, above.

Edit: The second part of your question was "Why is the speed of light held constant here?." Because it is a (by definition unproven) postulate of SR. Einstein himself readily acknowledged that it was a "freely chosen" premise, not one that was dictated by experimental evidence.

One the other hand, Lorenztian theories posit the (also unproven) premise that the speed of light is not "truly" constant in every inertial frame, even though we measure it to be the same.

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According to Lorentz Ether Theory simultaneity is absolute and one – way speed of light is frame dependent. One-way speed of light is isotropic only in the preferred frame, or Ether; hence in all moving in the Ether laboratories one-way speed of light is anisotropic; but introduction of length contraction and time dilation for all phenomena in a “preferred” frame of reference which plays the role of Lorentz immobile Ether leads to the complete Lorentz transformation.

Because the same mathematical formalism occurs in both, it is not possible to distinguish between Lorentz Theory and Special Relativity by experiment.

For example, this paper simulates all kinematic effects of the special theory of relativity on the simplest example of floating on water ships.

When using the term 'the speed of light’' it is sometimes necessary to make the distinction between its one-way speed and its two-way speed. The "one-way" speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector. What can however be experimentally measured is the round-trip speed (or "two-way" speed of light) from the source to the detector and back again.

A. Einstein chose a synchronization convention (Einstein synchronization) that made the one-way speed equal to the two-way speed.

As soon as observers in relatively moving frames employ the same (Einstein's) synchronization scheme of clocks they would make different conclusions whether spatially separated events occur at the same time (relativity of simultaneity).

It should be noted, that Earth rotates; hence one-way speed of light relatively to the Earth surface and any laboratory that is on the Earth surface is different in different directions (or anisotropic, see Sagnac Effect) while two-way speed of light is isotropic (see Michelson Morley experiment).

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  • $\begingroup$ It is not enough to reproduce kinematics: you must reproduce the changed dynamics as well. I list some of the necessary effects in my answer. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Jan 7, 2020 at 16:41
  • $\begingroup$ By the way, this simulation in water environment gives a hint to the reason why material bodies cannot reach the speed of light. Please note that if the carriers of interactions (as simulated in the paper) that move at the speed of light initiate events inside material bodies, this condition automatically provides for the maximum speed limit for both massless particles and particles with mass. physics.stackexchange.com/questions/496328/… $\endgroup$
    – user139020
    Commented Jan 8, 2020 at 5:41
  • $\begingroup$ As soon as we assume that the massless particles move inside the material bodies at the speed of light and the distance between the structural elements of the material body is maintained in a location-based manner, we get a special theory of relativity with all its wonders, as simulation vividly demonstrates. Again, we do not make ten different assumptions and amendments. Only that one that I have mentioned is enough. $\endgroup$
    – user139020
    Commented Jan 8, 2020 at 5:43
  • $\begingroup$ The twin paradox is the worst argument in favor of the special theory of relativity; this effect is solved in the framework of Lorentz theory by elementary algebraic methods physics.stackexchange.com/questions/483665/… $\endgroup$
    – user139020
    Commented Jan 8, 2020 at 5:44
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    $\begingroup$ If you are working in a theory with absolute time and you have reproduced the outcome of the twin paradox then you might want to look again. Seriously, there is a fundamental conflict between the two idea "absolute time" and "different amounts of time have passed when they meet again". $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Jan 8, 2020 at 17:26
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Why is the speed of light held constant here?

You are missing one important point of that thought experiment: it is meaningful after considering the Michelson-Morley experiment.

If our interpretation of the Michelson-Morley experiment is that the speed of light is constant with respect to the observer, then we can perform the thought experiment you described, using the assumption that the speed of light is constant (we justify this assumption because of the results of the Michelson-Morley experiment).

That thought experiment leads then to the formulae of time dilation and space contraction (and to the special relativity theory).

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When you consider different frames, something weird happens.

Frames result in you measuring things in weird ways that cause problems for a Newtonian explanation of the world, with a single cartesian space with galilean transformation between frames, and a single universal time.

The question is whether SR is the only way to resolve that.

Any alternative would have to give the same results as SR, so I will revise the question:

Is there any way to think about it that allows a single cartesian space with galilean transformation between frames and a single universal time, that is equivalent to SR?

To get that, we would have to somehow pile all the weirdness into the motion of electromagnetic force through space.

Here's a link to some graphics which display part of the problem, and propose a constraint that any potential solution must meet.

https://www.glowscript.org/#/user/jethomas5/folder/LW3/program/galileanrelativity

At a minimum, to save cartesian space and absolute time, then when light or EMF travels from a source charge to a target charge, the speed must vary just the right amount to get constant lightspeed $c$ relative to the target.

So two charges at the same location with different velocities would observe the same light at different times.

This is so weird. Much weirder than SR, and probably it can't be equivalent to SR. So probably there's no way to do it with cartesian space and a single time.

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  • $\begingroup$ Still, very helpful, thanks! $\endgroup$
    – Three Diag
    Commented Dec 30, 2021 at 11:37
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The speed of light is not a constant! Mathematical analysis using Maxwell’s equations of an oscillating charge shows that light is nearly instantaneous when it is created and only reduces to the speed of light at infinite distance from the source. So light is never a constant. Since Special Relativity is based on the assumption that light speed is a constant, it is wrong. Time and space are not flexible and only appear flexible. For more information google search William Walker Superluminal and Relativity.

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  • $\begingroup$ Finally, the missing piece. $\endgroup$
    – Three Diag
    Commented Jul 19, 2023 at 10:38

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