Evidence that space and time has equal footing?

[Gerenuk]

Space-time is supposed to be one unity making time in a way equivalent to spatial dimensions. Of course in the metric for time has a different sign though.

But what if it's just a mathematical accident that space and time take very similar positions in physical equations?

What is the best evidence that time and space are somehow the same?

The point is, if they weren't, then time-travel and all similar ideas with past/future would be a senseless idea.

 

[HallsofIvy]

Space-time is supposed to be one unity making time in a way equivalent to spatial dimensions. Of course in the metric for time has a different sign though.

But what if it's just a mathematical accident that space and time take very similar positions in physical equations?

What is the best evidence that time and space are somehow the same?

The point is, if they weren't, then time-travel and all similar ideas with past/future would be a senseless idea.

What do you mean by "equal footing". If "space and time take very similar positions in physical equations" isn't that itself "equal footing"?

But then you ask for evidence that time and space are "somehow the same". They aren't. For one thing, space and time coordinates have different "signatures" in the metric tensor.

 

[yuiop]

What is the best evidence that time and space are somehow the same?

I guess the best evidence that time and space are somehow the same is the conventional interpretation of the inside of a black hole where time becomes space and space becomes time. That is worth exploring in this context ;)

The point is, if they weren't, then time-travel and all similar ideas with past/future would be a senseless idea.

Well time-travel probably IS a senseless idea. There is absolutely no evidence for it outside of holywood movies. If time travel is ever destined to be invented millions of years in the future, why is there no evidence of time tourists now? There is also Steven Hawking's "grandfather paradox" which basically implies that time travel would make a mess of causality.

 

[JesseM]

I guess the best evidence that time and space are somehow the same is the conventional interpretation of the inside of a black hole where time becomes space and space becomes time. That is worth exploring in this context ;)

Only in certain coordinate systems which are badly-behaved at the horizon like Schwarzschild coordinates, there is nothing physically significant about this. You could design badly-behaved coordinate systems around the Earth where one coordinate switched from being spacelike to timelike when you crossed the boundary of the upper atmosphere, and another coordinate switched from being timelike to spacelike. In GR you are basically free to pick any crazy coordinate system you can think of, thanks to the principle of "diffeomorphism invariance".

Well time-travel probably IS a senseless idea. There is absolutely no evidence for it outside of holywood movies. If time travel is ever destined to be invented millions of years in the future, why is there no evidence of time tourists now? There is also Steven Hawking's "grandfather paradox" which basically implies that time travel would make a mess of causality.

The grandfather paradox predates Hawking by quite a lot, and even if time travel were possible, the paradox could be avoided using something like the Novikov self-consistency principle. Certain spacetime solutions in GR do allow time travel in the form of closed timelike curves, although many physicists have put forward arguments suggesting that in a theory of quantum gravity which integrates general relativity with quantum mechanics, these loopholes would likely be cut off (as suggested by Hawking's chronology protection conjecture, which may have been what you were thinking of)

 

[twofish-quant]

But what if it's just a mathematical accident that space and time take very similar positions in physical equations?

It's not so much of an accident but rather a consequence of the fact that two observers flying past each other will measure the same velocities. If the velocities are the same, and they have different measurements of space, then measurements of time will have to change to get them the same velocity.

Once you start with the premise that the speed of light is constant in all reference frames, then a *lot* of stuff follows.