As I understand it, in special relativity, when two bodies are moving away from one another, there is no absolute sense in which one is moving away from the other (e.g. when you jump in the air it is equally true to say that the Earth is moving away from you as it is to say that you are moving away from the Earth; or when a spaceship is going deep into space it’s just as true to say that the Earth is moving away from the spaceship as it is to say the spaceship is moving away from Earth).
This has interesting implications when it comes to the more funky aspects of special relativity (i.e. time dilation, length contraction). Because this means that if Bob is moving close to light speed relative to Jane, Bob will perceive Jane as experiencing length contraction and time dilation, but Jane will not experience these things. From her point of view, it is Bob that is experiencing length contraction and time dilation. So both will always experience the other as experiencing these things, because from their point of view it is always the other person moving at near light speeds. So special relativity is symmetrical this way.
As I understand it though, this symmetry breaks when it comes to acceleration. This is how you can have a scenario where e.g. Bob ages a lot compared to Jane (because he accelerated or decelerated more).
So my question is: why does this symmetry in special relativity break when it comes to acceleration?
The tl;dr answer is that it’s axiomatic. It’s built in to the model, and if it weren’t true, the model wouldn’t work.
More broadly though, symmetry in relativity exists because there is no way of distinguishing the “truth”. No one point of reference is more correct. You can’t tell who is truly moving, because as you highlight, A is moving away from B is just as valid as B is moving away from A.
Acceleration breaks symmetry though, because you can measure it. You can tell whether it’s A or B that’s accelerating, and there is a “right” answer.
You can tell whether it’s A or B that’s accelerating, and there is a “right” answer.
This seems counterintuitive to me. Is this because of the motion itself or because of other variables (such as the fact that the acceleration can simulate gravity through the centrifugal force of whatever?)
I can’t help but feel like this post was generated from a physics discussion I had the other day here.
I can confirm that it was
Ha! Awesome. Happy to know that even though I’m not a professor anymore there are still places where I can inspire more physics questions.
I recently made a comment that “the sun and stars being holes in the fabric of the celestial sphere through which the light of heaven shines through” is a really weird way to describe gravity wells in the fabric of spacetime emotion emitting the energy of solar fusion that created the elements we’re all made of but that was mostly a joke and not directly inspired by you.
Say Jane passes Bob, travels some distance away, then turns around and comes back. For both her outward trip and return trip, her experience and Bob’s experience are symmetric—but when Jane accelerates (by turning around), she changes reference frames. In her new reference frame, the point in Bob’s history Jane sees as simultaneous with her own changes—and the farther apart they are, the greater the time shift will be. This time shift will persist for Jane’s return journey, since she’s no longer changing reference frames.
Bob, on the other hand, never perceives a comparable shift in Jane’s history, since he never changes reference frames.
To illustrate the frame shift, let’s say Jane is four light-years away and moving at a relative speed that gives a Lorentz factor of two. So just before turning around, she sees a red-shifted signal from Bob in which he’s moving at half speed. She knows the signal took four years to reach her, so she’s looking at Bob from two years in his past.
Immediately after turning around, she sees the same signal from Bob but now he’s blue-shifted, moving at double speed. Knowing the signal took four years to reach her, she now interprets the same signal from Bob as being eight years in his past—so the point in Bob’s history she considers simultaneous with her own just shifted by six years.
Or here’s a simpler way of looking at the asymmetry: Both Bob and Jane see the other’s signal go through a red-shifted phase and a blue-shifted phase. Jane experiences the two phases as being equal in duration; but because the light from Jane’s turnaround takes four years to reach him, Bob experiences the red-shifted phase being longer that the blue-shifted phase.
