Does time ever go backwards in Special Relativity

Question

If I move away from an obsverer at high speed, does that obsverer go backwards in time relative to me? Due to things like surfaces of simultaneity?

Or is this overinterpreting of coordinates and things just flow forward.

Answer 1

I'm going to guess this will get migrated to physics SE. But I'm brave.

What you will see is not "go backwards in time." You will see that different observers disagree about which points in space-time have the same time coordinate value. And they will disagree about their clocks, this one insisting the other guy's clock is slower, for example.

No observer will see another observer going backward in time. That is, they will never see the other observer getting younger. They may see the other observer aging more slowly. (Or quicker, depending on the situation.)

Answer 2

Time doesn't go forwards or backwards. Rather, time is a direction you can move in, and mass is always moving in the forward direction, towards the future.

So if the question is, does special relativity allow you to move backwards in time? In theory, yes, but only if you travel faster than c, so no.

If you'd like to know why you can't, it's an interesting answer to a different question.

Answer 3

No. In GR, time is defined around light moving from place to place, so the propagation of signals. For time to go backwards the information flow would have to be reversed - which, we would experience in a given restframe observing, as time going forwards..!

Einstein said on Thermodynamics:

“It is the only physical theory of universal content, which I am convinced, that within the framework of applicability of its basic concepts will never be overthrown.”

His estimate from Brownian Motion of the size of atoms, was crucial experimental evidence of atoms and so of Boltzmann's ideas; with Ernst Mach insisting as late as 1903 that matter is a continuum. We find in thermodynamics, that time is also about information, or correlations, spreading out. Only here there are also consequences that affect all systems: entropy increases, as it does so (from the work of Shannon).

If you have an isolated quantum system (and this can be macroscopic if isolated enough) then it's information is not spreading out. It is still governed by Conservation Laws, but within those all it's configurations become possible, according to the rules we call it's wavefunction. Many things indicate this is fundamentally time-independent, like the time-independence of the Wheeler-DeWitt equation which is arguably the furthest step in fully accepted physics to unite Relativity and Quantum behaviour.

Feynman found that in terms of Conservation Laws, we find antiparticles behave like particles, going 'backwards' in time. He rejected that having physical reality, but his mentor Wheeler didn't, whose more radical idea of the One Electron Universe had provoked Feynman's insight.

I imagine it like this, a sea of ripples, on the surface of which are hairs or iron filings all facing the same way. Our experience of events is like when the tips of the hairs bend over and hit other hairs, or sometimes multiple hairs at once (quantum interference). The nap of the hairs forces things placed on the surface to move one way. But the sea can have waves going in any direction, colliding with hard edges say and bouncing into antiparticles.

Or you can think of it like an isolated quantum system has full dimensionality, like a hypercube say, and we can only experience one face of the object (existing simultaneously in Many Worlds), which subdivision we call 'the world', and we only get reminded we are attached the higher dimensional part by observing isolated systems. I would relate this higher dimensionality to the Conservation of Information, also called the 'No Hiding Theorem' (see Noether's Theorem on how Conservation Laws & continuous symmetries relate). This fits perfectly, because information can increase, but not decrease, that is there is an asymmetric symmetry in the direction of time, that in the context of the mechanics of solid inelastic bodies can be treated as though it were symmetric in time (reversible).

TL;DR: It looks like in very specific ways we can think of objects going backwards in time, but signals cannot, which we can understand as resulting from the fact truly going back in time would involve concentrating information instead of it spreading out, and so leave no trace.

Answer 4

No, time never goes backwards. You might have heard of the Andromeda 'paradox', for example, in which a person on Earth and a person very far distant are stationary relative to each other, so that 'now' is the same time for each of them. If the person far away now begins to move, then their plane of simultaneity tilts, so that what might be 'now' for them in Andromeda, say, might be yesterday here on Earth. However, the present on Earth is still today, so really it is just a case of the person on Andromeda assigning a different time coordinate to it. The distant person never sees anything go backwards in time.