# Why is the time dimension different from the 3 space dimensions

1. Jul 27, 2011

### scottbekerham

General relativity states that our universe is four dimensional curved space so time dimension is not separated from space dimensions .Why then is the time dimension different from the 3 space dimensions ? and why there must be 3 space dimensions and not 4 for example ?

2. Jul 27, 2011

### nitsuj

I'm having a simular issue understanding the time "dimension".

In 3D you need 3 coordinates for a location, what is the fourth coordinate for? Is it equivelant to "meet me at xyz @ 10:30am"? Is that 4D coordinates?

3. Jul 27, 2011

### TrickyDicky

Exactly.

4. Jul 27, 2011

### Passionflower

It is in a Galilean spacetime but not in a Minskowski or Lorentzian spacetime.

5. Jul 27, 2011

### nitsuj

What is the time coordinate a reference to?

6. Jul 27, 2011

### Passionflower

Time between two events is the length of the path in spacetime not a dimension of spacetime.

In simple spacetimes we can chose a map or chart where one dimension uniquely represents time, however in more complex spacetimes that is not possible.

7. Jul 27, 2011

### bcrowell

Staff Emeritus
There is no known reason why spacetime has to be be 3+1 (3 spatial dimensions plus one time dimension) and not 4+1, 2+1, etc. Various speculative theories such a string theory or loop quantum gravity may be able to explain this, but those theories are actually not really full-fledged theories yet, and they have never been tested against experiment, so there's currently no way to know if they're right.

8. Jul 27, 2011

### nitsuj

Yea, back to my trouble with understanding why time is referred to as a dimension.

In at least some remote sense, is the time dimension similar to an index for the other 3Ds when measuring a distance?

Last edited: Jul 27, 2011
9. Jul 27, 2011

### Passionflower

Many seem to do so, something I do not understand.

Clearly time is a dimension in Galilean spacetime and I do not believe anyone would disagree with that. In a Galilean spacetime time is the same for all observers, and "10:30" is "10:30" for everybody however that is not the case in a Minkowski or Lorentzian spacetime.

Why some people persists in calling time a separate dimension in Minkowski or Lorentzian spacetime is beyond my comprehension, because I consider it inaccurate. Because they just do so as a matter of speaking.

10. Jul 27, 2011

### nitsuj

Oh

I actually thought about it, trying to understand in what sense it was a dimension.

Why not 3D + a constant [STRIKE]for forces[/STRIKE]

Last edited: Jul 27, 2011
11. Jul 27, 2011

### WannabeNewton

In the case of a 4 -manifold, if you decided to keep any one $x^{\alpha }$ = const. then you're just defining a hyper-surface of that $x^{\alpha }$, kind of like keeping t = const., thereby defining a 3 - surface at some instant of time. If you want a 4 - manifold though (as is needed with space - time) you need four functions $x^{\alpha }$ as ,roughly speaking, keeping one or some constant defines a sub manifold of that 4 - manifold.

Last edited: Jul 27, 2011
12. Jul 27, 2011

### nitsuj

My cats breath smells like cat food...

I have no idea what your saying. What you are calling manifolds, were called dimensions in the previous post.

13. Jul 27, 2011

### WannabeNewton

What I'm trying to say is that if you keep one of the coordinates constant then you can't have a 4 - dimensional space - time. If, say, you kept time constant then you're looking at a 3 - dimensional surface at that instant of time. Now you have me wondering what cat food smells like though.

14. Jul 27, 2011

### atyy

Yes, that's right. When people talk about time as a dimension, they are referring to coordinate time of a Lorentz inertial frame. It is a dimension in the sense that switching to another Lorentz inertial frame, what was previously coordinate time is now mixed up as coordinate space and coordinate time. In a sense, you can rotate the axes in spacetime, just as you can rotate them in space.

15. Jul 27, 2011

### atyy

It is better to say that time directions are different from space directions. A time direction is a direction in spacetime in which a stationary observer moves. Let's say some guy A is stationary, moving only in time. Another guy B moving at speed v relative to A will have a different time. But we can make B stationary too, by considering A to be moving at speed -v relative to B. Since B can be considered stationary, he too defines a time direction. Since we can have people moving at all sorts of velocities relative to A, and we can similarly define many other time directions. However, there are no observers moving faster than the speed of light relative to A. All the faster than light directions are therefore considered space directions.

16. Jul 28, 2011

### TrickyDicky

No wonder nitsuj (or any relativity newbie) are confused about this if they keep getting this kind of apparently contradictory answersassionflower: no, time is not a dimension -atty: yes, it is.
At least atty clarifies that he is talking about coordinate time (dt^2 in a Lorentzian manifold line element, with positive or negative sign depending on the signature convention used:(3,1) or (1,3)), which is clearly a dimension in Lorentzian spacetimes, if it wasn't we wouldn't talk about 4-spacetimes instead of 3-spaces.
I guess Passionflower must be referring to proper time (d$\tau^2$ or ds^2 in Minkoski line element) when he says that in Minkowski spacetime time is not a dimension, if so he should have made that clear IMO considering not everyone will know the difference.

17. Jul 28, 2011

### ZealScience

I think there is no necessity that time and space are the same. Because time is closely related to space measurement, change in space components affects time component. I think this is the only reason that time is another dimension. Also, looking at the tensors, sometimes just those special properties of time lead to the special features of geometry of space-time.

18. Jul 28, 2011

### nitsuj

c is constant

19. Jul 28, 2011

### WannabeNewton

C isn't a coordinate though.

20. Jul 28, 2011

### nitsuj

Oh good point! c is not a coordinate.

3D + a constant for forces

is hardly me suggesting time is a coordinate.