Two ships pass one another at 0.5c. Do they both see their own clock as the fast clock and their own meter stick as the long meter stick? Or is there a fast clock and a slow clock; a long meter stick and a short meter stick with both ships agreeing which is which?
Imagine two ships with atomic clocks, a large display on their surface display the timing of the clock and the ability to accelerate very fast to 0.5c. The two ships separate by one AU with a signal directly between them.
When the flash of the signal reaches the ships both zero their clocks and one of the ship accelerates instantly to 0.5c. When the two ships pass one another (akin to jousting) they can both see each others clock output.
Is this situation symmetric? Do they both think their clock is fast and the other ship is slow? Or instead do they see a fast clock and a slow clock and they agree which is which?
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@Irigi Sure. Just post the link to the experimental confirmation and I’ll resolve it right now.
@JoeCharlier Would you resolve based on experiment with atoms / elementary particles? Or you really want relativistic ships?
How does this resolve? If it's based on scientific consensus at closing time, then this is pretty much certain to resolve YES.
Also, the title of this market doesn't match the description. I was going to ask which is correct, but it looks like you already confirmed that the description is correct and not the title. Even if Lorentz symmetry is violated (which is what the title asks), there is absolutely no way in hell that two ships passing each other at 0.5c would see each other's clocks ticking at the same rate. For that to be true, all of special relativity would have to be false, even though effects like time dilation have been experimentally observed for a long time. It's about as likely as finding out that the Earth is flat.
@PlasmaBallin To clarify, this isn’t asking if the ships clocks match one another. It’s asking if both ships will see their own as the faster.
And yes this isn’t ask for scientific consensus it is asking about an experimental (past or future) result generally believe to be valid. If no such experiment is performed I’ll N/A this or extend the time (if possible)
@JoeCharlier That doesn't really affect what I said about there being absolutely no chance. For either of the ships to not see their own clock as ticking faster, it would require relativity to be completely wrong (and by "completely wrong", I don't mean "wrong" in the sense that Newtonian mechanics is wrong because it's only an approximation to relativity - I mean it wouldn't even have a domain of validity beyond that of Newtonian mechanics or be a useful approximation to anything).
I'm still not clear about what kind of experiment you're asking about. Does it have to involve two space ships traveling past each other at exactly 0.5c, or would a slower speed do? And how would each ship measure the relative ticking speed of the two clocks?
@PlasmaBallin Certainly the experiment as described won’t be possible for centuries (or more). Any experiment fast enough to detect the signal would suffice.
It is actually fairly straightforward to construct a system that recreates all of special relativity except for this symmetry; a result of which being a trivial resolution of the twin paradox.
I have created an iOS/macOS app that does just that including simulations of dilation and contraction: https://apps.apple.com/us/app/aexels/id935727868
@JoeCharlier I don't have iOS, so I don't know what the simulations in the app do, but I don't see how a simulation could recreate all of special relativity except those specific observations. If you've already gotten rid of time dilation and length contraction by having neither observer consider their own clocks/rulers to be the fastest/longest, then there's not much left of special relativity to recreate.
Dilation:
https://youtu.be/6EuBceZx3pw?si=kaYVqvLAo3AgnRfY
Contraction:
https://youtu.be/Fc6_McWXFuQ?si=eFB07VDVNTcarkCI
PDF of app text:
https://github.com/aepryus/Aexels/releases/download/v3.0.3/Aexels30.pdf
GitHub of app:
@JoeCharlier Maybe I am misunderstanding what you are asking about in the description, but these don't look like the scenario you described of two ships passing each other at 0.5c and both being able to agree which clock/stick is faster/longer. In the simulations, you act as an external observer watching ships pass you at 0.5c, and it demonstrates that time is slowed down for them in your reference frame. But that's just the standard SR picture. We observe that the light pulse takes longer to travel between the two dots when they're moving, but from the perspective of an observer on one of those dots, it would take the same amount of time.
@PlasmaBallin Yes, each spaceship when performing the experiment will see the exact same results. But, if they watch the experiment on the other spaceship how will it compare to their own?
In the case that SR is always symmetrical, both observers will see the other ship’s experiment taking longer to complete than their own.
But this question asks if it’s possible Ship A will see Ship B’s experiment taking longer; but ship B sees Ship A’s experiment completing quicker than their own?
How literally do you mean "see" (i.e., are you talking about transformations between coordinate frames, or about the Doppler effect and Terrell rotation)?
Would Lorentz invariance violations much milder than in the description (e.g. A "seeing" their own clock as 1.15 times as fast as B's and B "seeing" their own clock as 1.16 times as fast as A's) also count?
@ArmandodiMatteo No, that wouldn’t count. This is looking for anti-symmetrical observations not slightly away from symmetrical. So the scenario you suggested would still resolve this to YES.
@JoeCharlier well, Lorentz invariance has been tested to waaaaaaaay better precision than we need to know the sign of effects at 0.5c
https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation
@ArmandodiMatteo Lorentz invariance does not require symmetrical frames only that all the physics is the same for all frames. This question is definitely not arguing against Lorentz invariance.
@ArmandodiMatteo Both see the other clocks as moving slower; both see the other (correctly aligned) meters sticks as being shorter. Neither sees the other clock as faster or the other meter stick as longer than their own.
@JoeCharlier that's a weaker condition than Lorentz invariance, not a stronger one (e.g. my example above would be "symmetrical" by your definition but not invariant)
@ArmandodiMatteo Lorentz covariance says the speed of light is the same in all directions for all inertial frames of reference. This doesn’t require that all frames see their clocks moving the fastest. This question is asking if all frames always see their clock as fastest? If it was ever shown that a frame saw some other frame’s clock as faster than their own this question would resolve as NO.
@JoeCharlier "Lorentz covariance says the speed of light is the same in all directions for all inertial frames of reference."
All laws of physics, not just the speed of light.
"This doesn’t require that all frames see their clocks moving the fastest."
Yes it does.
@JoeCharlier I dunno whether there are clocks precise enough to tell on the ISS but the ones in GPS satellites we see pretty much the way general relativity predicts (if we didn't the system wouldn't even work)
@JoeCharlier the example in the question description would even require violation of invariance for rotations by 180°
(Assume both ships agree Alice's clock is faster. Consider an observer halfway between the two ships, with Alice's to their right. They'd describe the physics as "if two ships pass one another at 0.5c, both agree that the clock on the ship to my right is faster than that on the ship to my left". Make them turn around and now they'd describe it the other way around.)
@JoeCharlier Are observations based on doppler shift acceptable or do we need material rods and clocks?
@mariopasquato The symmetry stipulated here is unrelated to the doppler shift. One should be able to back out the shift and still see the symmetry (if they are in fact symmetrical).