That problem is solved using the Sagnac effect, not relativity.
Assuming that acceleration was not needed for a clock to move around, we could pretend that it is the blue one that moves away and that comes back later, and we would simply get reversed results. We can only make predictions when we know for sure which clock has accelerated.
Do you have a reference for this claim?
The reason I ask is that I was under the impression that the light clock is a pedagogical tool, used to explain relativity. And by the way, it is not the only way to explain it. Look, for example, at Bondi's k-calculus approach. No light clocks there!
Have you considered the possibility that the muon example and the twin trip example are fundamentally different? Analysis of the former involves only one measurement of proper time whereas the latter requires two.
In other words, when the twins reunite what they're comparing is the amount of proper time that has elapsed for each twin. But in the muon example there is only one amount of elapsed proper time involved, and that is the amount of proper time elapsed for the muon.
Proper time is the time that elapses between two events that occur at the same place. It's a relativistic invariant, meaning all observers will agree on its value regardless of their motion relative to it.
Again, "not accelerated" is not the same as "motionless".
Motion is relative, so we cannot tell for sure if a body is in motion or not because we don't have an absolute reference frame in hand, but acceleration is absolute, so if we know a clock has accelerated, why not use that information to eliminate all the other possibilities?
Because it is unnecessary. While you keep claiming that it is necessary.
Einstein didn't say it this way, but he used the light clock mind experiment to explain SR, and all his space-time concept is based on the way light moves between moving bodies.
No light clock traveling sideways to their motion in my simulation either, just light exchanged between inline moving mirrors. No need to calculate the time it takes, just to reverse its direction when it hits the mirrors and stop the watch each time it makes a roundtrip. There are often many ways to do things, but in principle, the simpler way is often the better.
It actually takes the proper time of our clocks to know that the lab Muon decays faster than the atmospheric one, but we also have to know the distance the Muon had to travel before hitting the earth's surface, thus we have to know where it started accelerating towards us.
It is necessary if we want to make constant predictions, not to understand how light moves between moving bodies. I could have chosen not to consider acceleration in my simulation, and it would have given the same simulation, but it is the blue clock that would have suffered time dilation. From a relative viewpoint, the only thing that differentiates the clocks is acceleration.
But the muon isn't accelerating at any point, as has been pointed out before.
Time dilation is not the same as differential aging. No clock "suffers" time dilation ever.
A Muon is a massive particle that has to get its speed from acceleration, so it has to accelerate from the point where it is created. It may get that speed quite fast, but it cannot get it instantly because, being massive, it has to resist being accelerated.
You are here assuming an absolute rest frame, in contradiction to relativity.
The thread has gone off topic and the original qustion has been answered. Thread closed.
To clear up a couple of misstatements:
The "Sagnac effect" is not something separate from "relativity". It's a prediction of relativity.
Not if it's produced from something that already has that speed (relative to Earth, which is the "speed" you are implicitly assuming, though you have persistently refused to say so). Muons in the Earth's upper atmosphere are produced from the interaction of cosmic ray particles with air molecules. The speed the muons have relative to the Earth is the same as the center of mass speed of the system consisting of the incoming cosmic ray particles + the air molecules before the interaction. So the muons don't have to accelerate at all.
@Raymond Potvin feel free to PM me if you have questions about these responses; this thread will remain closed.
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