Special Relativity and Hypersurface of Simultaneity?

Question

In Special Relativity when I move backwards and forwards my hypersurface of simultaneity moves too.

Does time really oscillate backwards and forwards as I move around? Or is it just the application of coordinates? Is it just a matter of perspective. No physical change?

Some pop books I've seen say time does actually move around crazily. But I didn't think time could move backwards, but this seems to say if I walk around with you, you move back in time...

But surely physical processes don't reverse when I move.

Answer 1

Nothing happens. The hyperplane perpendicular to your worldline does not figure into the laws of nature in any way. It's an invention of human beings who have trouble thinking fourth-dimensionally. It's not even a "plane of simultaneity" in anything but name.

It has no bearing on presentism vs eternalism in philosophy. The belief that it does is just another facet of the same cognitive error. The meaning of coordinate independence is that you can use any coordinate system, not that you must use every coordinate system. If you want to simulate a universe, you can pick the coordinates you want to do it in. If you want to save RAM by throwing away earlier time steps after computing the next one (which makes your simulated universe "presentist"), you can do that. If a simulated person in that universe is moving relative to the coordinates you chose, you will still correctly simulate all of their experiences. It doesn't matter that their "plane of simultaneity" is partly in the future of your simulation and partly in the past, because their "plane of simultaneity" has no relevance to any physical law. You can just ignore it. It's meaningless.

Answer 2

No combination of Lorentz boosts exists which reverses any part of the order of any process. Only unrelated events (for which distance $s \gt c\Delta t$ as measured in any frame) may have their apparent order reversed.

Answer 3

It depends on your stance on the philosophical question of Presentism versus Eternalism.

'Presentism' is the philosophical position that only the present exists, and the past and future don't. The past existed but no longer exists. The future does not yet exist, but will.

'Eternalism' is the philosophical position that all times, past, present, and future, are real and continually exist. The future is 'already there', laid out ahead of us. The past still exists. All time is laid out in an unchanging, 4-dimensional 'block universe'.

Special relativity poses serious problems for Presentism. If the existing 'now' is the plane of simultaneity of a given observer, then yes, existence does appear to 'wiggle' and oscillate backwards and forwards as the observer moves around. (There are alternatives to the observer's plane of simultaneity we could pick, but they all have similar problems.)

If you take the position of Eternalism, this isn't so much of a problem. Your 'now' moves around back and forth in time, but it entails no physical changes. Past and future are always there, and 'now' is just a choice of coordinate system - an entirely imaginary construct slicing through a 4-dimensional block.

Eternalism means the future is fixed and free will is an illusion (arguably), so lots of people want to dispute it for other reasons. And a lot of people have Presentist intuitions about time, so it provides that 'mindblowing' impact in pop science presentations to get the public interested. But if you find the Eternalist perspective natural (as most physicists do after working with relativity for a while), then it seems almost trivial and obvious.

The question gets interesting again when we think about issues of wavefunction collapse in quantum physics, which takes a somewhat Presentist stance. The future is undecided and undetermined until the moment of observation, the branching future is open while the past is not, and the influence of a collapse supposedly propagates 'instantaneously', faster than light. It's not actually entirely straightforward, even from the perspective of modern physics. But that's a separate question well-covered elsewhere.

Answer 4

If you consider the Universe to be everywhere, now, then yes: your definition of now changes. Details are known as the Rietdijk-Putnam Argument (aka: The Andromeda Paradox), of which David Mermin concludes:

"That no inherent meaning can be assigned to the simultaneity of distant events is the single most important lesson to be learned from relativity."

-David Mermin, It's About Time

If you draw a Minkowski diagram and move the origin around and select the various $x'$ coordinates, you'll see that every point in the light-cone defines a different "now" for every boost...which is philosophically challenging.

Meanwhile, any frames that share the same now are space-like separated.

In the Twin Paradox, both twins see the other's clock running slower, at all times, by $\gamma$. Thus Earth twin experiences $T$, and sees $T/\gamma$ pass for the space twin. Thus, space twin sees $T/\gamma^2$ pass on Earth.

Where does the missing $(T-T/\gamma^2) = \beta^2T$ go?

Well "now on Earth" jumps forward by $\beta^2 T$ for the space-twin when he switches direction. It doesn't pass or get dilated, rather, the clock bias changes.

You are correct that it is a coordinate thing, nothing physical happens, but when space-twin returns: $T$ has passed for the Earth twin.

See David Mermin's quote for explanation.

Answer 5

Benrg's 'Nothing happens' is exactly right. One bit of advice I would like to share is that whenever you are contemplating the meaning of SR, bear in mind that effects such as time dilation, length contraction and so on are all reciprocated, so if I am time dilated in your frame, you are time dilated in mine, and so on.

Now let's return to your specific question. Suppose it were true that when you walk down the street, time on Andromeda shifts forward a week. Then consider the reverse. Suppose there is a person on Andromeda who starts walking down the street- does time on Earth shift forward a week? More importantly, suppose there are n people on Andromeda who each start walking down streets at different speeds and directions- how can the time on Earth shift by n different amounts at once?

And as for 'what if eternalism is true?', by asking that question you are effectively ignoring what you have been told. It is like asking whether gold or hydrogen is more dense, and then asking 'but what if hydrogen is more dense' having been told that gold is. In any case, suppose eternalism were true (whatever that means), I still do not move backwards and forwards in time by n different amounts when n people walk at different speeds on Andromeda.