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If I said that we are living in a Universe with 3 time dimensions and 1 spatial dimension, would I be wrong?

By that I mean if the spacetime interval was evaluated as -time1^2-time2^2-time3^2+space1^2 instead of space1^2+space2^2+space3^2-time1^2.

Is there an absolute difference between a spatial and a time dimension, or are they like the positive and negative electrical charges?

Edit: This came to me after reading a question considering more than 1 time dimensions. I think it was about a 2+2 universe, which prompted the question "Which 2 would be the time dimensions?"

So I guess the real questions is, is time's property the fact that it is a single dimension of its type/sign, instead of 3? Could we talk about spacetimes only for 1+N pseudo-euclidean spaces, but not for M+N where M>1 and N>1?

And also, if we have 3 time dimensions and 1 space dimension, and the spacetime interval was

sashoalm
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  • Related: http://physics.stackexchange.com/q/10651/2451 , http://physics.stackexchange.com/q/43322/2451 , and links therein. – Qmechanic Jan 28 '15 at 14:43
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    We actually have no idea what "time" is or how it could be defined. So time is just a word. However, there are some concepts that we relate to time, e.g. the direction of increasing entropy, that you would have to refine in your claim. – Clever Jan 28 '15 at 15:14
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    @Clever To clarify, in a 2+2 Minkowski spacetime which 2 dimensions would you call space? – sashoalm Jan 28 '15 at 15:21
  • I guess it would be difficult to read your question if he had one spatial dimension only... – Andre Holzner Jan 28 '15 at 15:26
  • @AndreHolzner But then the time dimensions would play the role of the space dimensions :) – sashoalm Jan 28 '15 at 15:34
  • possible duplicate of More than one time dimension – Brandon Enright Jan 28 '15 at 16:12
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    @sashoalm: I think that the term "time" we attribute to one dimension is exactly this: a term for one dimension. The fact that in SR time and space dimensions are mixed, states that time is no so special after all. I think a lot of terminology would be messed up in a 2+2 world (e.g. time-like and space-like and therefore light-like and probably causality ...). – Clever Jan 28 '15 at 16:21

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Time-like dimensions are those where motion is only possible in one direction (we call that forward because it's pessimistic to say you can only go backward) and observing is only possible in the reverse direction (that's a direct result of motion only being allowed in one direction). Spatial dimensions are those where motion is possible in both directions as is observation.

The spacetime interval can be written with either the mostly plus or the mostly minus signature, (+ - - -) or (- + + +), without changing the fact that there is only one time dimension and three spatial dimensions.

When you see something like "in an m+n universe", m is the number of spatial dimensions and n is the number of temporal dimensions.

Jim
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  • I think you should be very careful with that first paragraph. Human experience is that the flow of time is unidirectional, but the human view of the flow of time has no obvious significance in GR. – John Rennie Jan 28 '15 at 16:24
  • @JohnRennie I'm not talking about human view. A null path can move in either direction for spatial dimensions but a null path only moves in one direction for temporal dimensions. GR describes this well. That is why we say spatial dimensions become time-like beyond the event horizon of a black hole; null paths (and thus, any other applicable path) are only defined for one direction beyond the event horizon. – Jim Jan 28 '15 at 16:27
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    Null geodesics don't move at all. They are just curves in spacetime. – John Rennie Jan 28 '15 at 16:29
  • @JohnRennie And also a point particle is really a line in space-time, if I understand it correctly. – sashoalm Jan 28 '15 at 16:30
  • @sashoalm: the worldline of a point particle is a line – John Rennie Jan 28 '15 at 16:31
  • @JohnRennie Forgive me, I'm not the best with terminology and wording. But the point remains valid. Motion is only possible in one direction for temporal dimensions. Were motion possible in both directions, information from times ahead of an observer could travel backwards and be observed at earlier times. Since only one direction of motion is possible, information can only reach an observer by moving forward, and thus only the past is observable. Similarly, spatial dimension allow motion in both directions, so information can be observed coming from both directions – Jim Jan 28 '15 at 16:38
  • GR describes this in geodesic motion by using a path element (usually $\lambda$) to represent an increment of motion along the geodesic. We find that even null geodesics follow the path element in a direction of non-decreasing time. Any results to the contrary usually violate causality and are summarily classified as non-physical – Jim Jan 28 '15 at 16:41