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I'm curious about just what is meant by time being another dimension, like the three (observable) spatial dimensions. Does this imply, according to General Relativity, that the past and the future already "exist" and that we're just moving through it, as we move through spatial dimensions? Or, is time being a dimension just a mathematical construct allowing us to calculate time dilation effects? Do we even know the answer to this question?

Intuitively, it would seem to me that the past doesn't "exist" except in our memories and that the future "hasn't happened yet" so that all that exists is the present...

Clarification

I suppose I should clarify what I mean by "exists". The three spatial dimensions definitely exist. You can travel through them and they are not just a bit of abstract mathematics.

What you can't do is travel faster than C through space. But, if you could you know when you stop, there would be something there.

Now, if you were to take the hypothetical example of time travel, there are two distinct questions here that follow this same line of reasoning. For the present, we don't have the technology to travel through time and it seems like an extremely difficult thing to do. But if you could would there be something there to travel to?

So, even if it is impossible to travel through time, our theories could still inform us whether the past and future exist in the same sense as the present does along the above lines. This was not supposed to be a time travel question... Just a question about the fundamental nature of spacetime: all "presents" existing, or only one "present", and what our current theories tell us or don't tell us about the answer to that question.

Further Clarification

So, as one of the answer's helpfully pointed out, Relativity certainly states there is no "privileged present", or a present that nature prefers and that all other points in time are measured against. I understood this before I asked the question.

But, you could still ask the question of whether in an observer's own frame of reference, does his own past and future exist?

To illustrate: Imagine instead of three spatial dimensions, we had only two. When space would stretch, it would expand or contract a grid drawn on the "paper" universe's spacetime. But, the "paper" would not move out of it's plane (NOT like a trampoline).

Time would be the third dimension, with infinitesimal space sheets stacked one after another. A stretching of time would mean pulling the sheet in or out like a trampoline.

So, in this illustrative universe, if the past and future exist, there are a nearly infinite number of sheets of present slices in array from the universe's birth till it's death. If only the present exists, there is only ever one slice and it changes over time.

Can we say which view is correct in a concrete way, not just in terms of the math? (If you haven't noticed, I'm not a math guy, but I am a picture guy)

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Good opinion how would you then explain someone near a EH owing comparatively in the future and we see them in the past "ie observationally frozen" –  Argus Jul 16 '12 at 16:36
    
In my opinion that view is actually counter intuitive. I see the present as a flow above some timelike "river" moving the particles along some dimension of causality. The information already exist and does not become the "jurisdiction" of scientific scrutiny until we can observe it. –  Argus Jul 16 '12 at 16:41
    
@Argus Good point! I didn't say that each POV wasn't relative, it is. The extreme of this is at the event horizon of a black hole. But the extreme distortion is due to the stretching spacetime. Photons still have to travel through spacetime for us to observe the person at the event horizon. So I'd say it's a matter of slowing those particles down, rather than the person at the horizon existing in a different present. –  John Jul 16 '12 at 17:35
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Another metaphysics question here. What a pity that Philosophy.SE is so pathetic. –  Anixx Jul 16 '12 at 22:42

7 Answers 7

Kurt Godel attempted to show, using his exact solution to the field equations, that time has no objective existence. See, for instance, A World Without Time. The paper can be found in Godel's Collected Works or in Living Philosophers, the Einstein edition.

http://books.google.com/books?id=tuA-cY_6HZkC&pg=PA177&lpg=PA177&dq=godel+ideality+of+time&source=bl&ots=i6PHitDb1q&sig=a1RsQD-sIWUCiNBFhFMfqWKwBPE&hl=en&sa=X&ei=hEoIUOerIMmw0QGOuPXUAw&ved=0CFUQ6AEwBQ#v=onepage&q=godel%20ideality%20of%20time&f=false

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General relativity by itself is neutral on this issue. The conventional metric of spacetime treatment seems to support eternalism aka block universe, but the equivalent ADM formalism seems to support presentism.

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Thank you for your answer, this seems promising. Can you break this down into more layman's terms and elaborate a bit? –  John Jul 19 '12 at 13:40

General relativity uses a static spacetime as a model for our universe, and it is thus natural to think that both present and future really exist. Even though topologies which allow time travel via wormholes are possible in principle, the framework does not include any sort of meta-time, ie the geometry of spacetime as a whole - and thus the energy-momentum of all matter - stays fixed, which forbids any interesting modes of time travel.

I'd also like to address some individual points of your clarification:

The three spatial dimensions definitely exist. You can travel through them and they are not just a bit of abstract mathematics.

You do not move through space alone, but through spacetime: Each second, you travel $3\cdot10^8m$ into your future.

What you can't do is travel faster than C through space. But, if you could you know when you stop, there would be something there.

Travelling faster than $c$ also means that you'd end up in someone's past. If this is your criterion, then the past does indeed exist.

For the present, we don't have the technology to travel through time and it seems like an extremely difficult thing to do.

It's not: you're already doing it right now.

It might be helpful to think about it like this: You move through spacetime with uniform velocity $c$. When accelerating, all you do is change the direction you're moving in. Because special relativity forbids accelerating from $v<c$ to $v>c$ (where $v$ would be a relative velocity in a spatial direction), you cannot move backwards in time by 'turning around'.

However, there's particle-antiparticle annihilation, which looks like Compton scattering turned right-angle in Minkowski space, ie instead of having an electron and a positron annihilate into two photons, we can interpret it as a single electron which gets bounced backwards in time.

If you take this interpretation at face value, this would mean that when you hold your hand into an antiproton beam and an interaction happens, that antiproton is a part of you moving backwards in time.

This does not mean that a human constructed from antimatter would experience time flowing backwards, as the laws of physics are (mostly) the same for matter and antimatter and the consciousness of your antimatter-self should experience time the same way you do.

The question about the subjective arrow of time can't really be answered by relativity, but the example above (holding your hand into a proton beam) actually gives a hint: In contrast to the clean electron-positron annihilation, a messy proton-antiproton annihilation creates a whole bunch of new particles, and reversing the process would mean having to recreate a multi-particle collision.

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so that all that exists is the present...

That view is called Presentism and it is clearly in conflict with both SR and GR.

In Special Relativity, the past and future "exist" simply because of the relativity of simultaneity.

Consider two relatively moving reference frames in the standard configuration and the event where both origins are co-located.

Note that all other events that are simultaneous with that event in one frame are either in the past or the future of that event in the other frame.

To put it another way, there is no privileged "present" (spacelike hyperslice)

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I'm OK with no "privileged present". I had that assumption when I asked the question, but I guess I didn't make that clear. I know that to even define a present, you must first define a frame of reference, which means every observer's present is relative. But, does the observer's own past exist? Is there a place to travel to? Do you know what I mean? –  John Jul 17 '12 at 18:38
    
I confess I don't know what you mean. You seem to be using "exist" in an odd way, as if the past is a "place" that can be visited to hang out for a while. but we can't linger at any spacetime event. Our 4-speed is invariant and equal to $c$. The events in our past exist in the sense that they are in the present of other reference frames. –  Alfred Centauri Jul 17 '12 at 18:47
    
Yeah, time is a very difficult thing to describe. I tried my best to further clarify what I mean. –  John Jul 17 '12 at 18:52
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Why can't I define the "present" of one observer as the past light-cone of this observer? It's a relativistically invariant definition. I agree that it is unnatural to make a "time pushing forward picture" of relativity, but it's not impossible, and the question is pure philosophy. –  Ron Maimon Jul 18 '12 at 2:24

General relativity, like all physical theories, is a mathematical model of the universe. By this I mean that it allows me to take some initial conditions and calculate what will happen as I move forward (or back) in time.

Speaking as a Platonist I consider that in my mathematical model the past and future exist, and the time I experience is basically just a convenient parameterisation of a trajectory through some configuration space. Actually I'd go further than this and say the configuration space exists as well.

But I'd guess you're asking about the real world, and the answer is that I don't know because I don't know whether GR and the real world are the same thing, or whether GR is just a model. You would have to go and ask a philosopher.

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You do not really need general relativity or even special relativity to get into this problem. Consider for example a generic form for Newton's second law, $$m\frac{d^2x}{dt^2}=F(x,\dot{x}),$$ where $x$ can be the one-dimensional position of a particle on a line or some kind of longer vector possibly involving multiple particles. Then you can see the differential equation as describing the dynamics of some point in $n$-dimensional space, or you can see it as describing the geometrical structure of a line in $(n+1)$-dimensional spacetime. General relativity is just an extrapolated version of this second view, where the geometrical objects in play are quite a bit more complicated, but the basic outlook is the same.

In a sense, whether time "exists" is not really a question that any theory can answer. What is a mathematical construct and what is actually there? (and what do you mean by "there"?) This isn't something you can look to the mathematics for help.

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General relativity doesn't make any assertions about existence. So the answer to your question is no.

General relativity treats time as a dimension like space (though with a different metric sign). This just means that observers with different speeds get different 3-dimensional perspective views of the same 4 dimensions, just as 2-dimensional perspective views for the same 3-dimensional object may differ.

However, general relativity is both compatible with a view that spacetime grows along a spacelike hypersurface containing all ''now''s of different observers, as with a view that space-time events are predetermined and observers just move through it. The predictions of general relativity depend on that in no way.

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...but you'd have to jump through some gnarly hoops to consistently work out the details of the "growing along a hypersurface" interpretation. Even in special relativity you can see that it (locally) picks out a special distinguished reference frame that has no operationally detectable effect on anything. So that view of GR would add a lot of extra complexity without providing any increase in predictive power. You can infer from that what you will. –  Nathaniel Jul 16 '12 at 16:57
    
@Nathaniel: But there is a consistent dynamics from moving between an arbitary spacelike hypersurface to one lying in the future of it, which is fully covariant. –  Arnold Neumaier Jul 17 '12 at 7:28
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@Nathaniel: This doesn't diminish the value of the interpretation. Whenever we interpret general relativity we have to introduce observers, ad then things become noncovariant. What an observer considers to be real is always observer dependent. (What an amoeba takes as real is very different orm what a child takes as real, and what a trained physicists takes as real. There is no objectivbe notion of reality. To use here Occam's razor woud damage all of reality - razors can be dangerous when not used appropriately.) –  Arnold Neumaier Jul 17 '12 at 14:03
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@ArnoldNeumaier: This is correct, but it should be emphasized that the intuitive "pushing forward nature of time" is nothing to do with physics, and everything to do with our perception, with the type of entities we happen to be. –  Ron Maimon Jul 18 '12 at 2:22
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@ArnoldNeumaier: I don't think it abstracts this in any way--- the perceptions of the observers regarding the flow of time are still contained in the description--- if you describe asking the observers "is time flowing forward" you have described them saying "yes" even in cases where you have the whole history pre-computed on your computer. So the fact is only superficially fundamental, the question of the pushing forward of time is positivistically ill formulated, and the positivist formulation gets rid of the mystery. –  Ron Maimon Jul 18 '12 at 16:34

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