# Is time a vector? if it is, what is its direction?

1. Jul 6, 2015

### Superleopard21

Hi,everyone,I just got a deep-thinking question about time.

I s time a vector?IF it is,what is the direction of it?My personal view is the direction of time is every direction
or no direction(there is no direction in mutil-dimesion of the universe?) or no inclonclusion?

2. Jul 6, 2015

### Mr-R

Well , when I do Differential Geometry, I think of it as a vector moving on the time axis (dimension). And it can only flow towards the positive direction.
But a vector on the x axis (imagine a line), can move towards +x or -x and you generalize this to whatever dimension. Time is another type of dimension. Restricted to flow to the positive direction.

Note that my answer is not rigorous and someone will probably correct me.

3. Jul 6, 2015

### Ibix

Time is a dimension in relativity. There are three spatial dimensions, which are (loosely) up/down, left/right and forwards/backwards. The time dimension would be past/future.

It does in some sense have a direction, but it doesn't point in any spatial direction. Just as you can't move to the left by any combination of up/down and forward/backward movements, because those movements don't point left/right.

Different people can have different definitions of future and past, just as people approaching a crossroads have different definitions of "forwards". This is basically where time dilation comes from.

Time is similar to the other dimensions, but it is not the same - which should be obvious. The differences explain why time travel isn't as easy as turning round, and may well be impossible.

4. Jul 6, 2015

### Finny

Not really the best way to think of time. Depends which formulation of physics, that is, which mathematical models, you are considering.

In everyday math, say, d = v x t, or d = 1/2 at2one usually thinks of distance as increasing in the same direction as v, and time as a scalar...as an independent parameter.

Locally, in GR, my time ticks along at the same old fixed pace we usually attribute to, say, wrist watch ticks. So does yours. No big mystery.

But Einstein taught us that distant observers in relative motion see other's space and time as mixed up...your space and my time appear differently than I view your space and your time; and that 'craziness' has been experimentally verified many times in many ways. [This is special relativity] Then Einstein figures out not only does relative velocity [a vector] change distant observers relative passage of time, so does gravity....that is, gravitational potential. So time is more complex than a simple vector. [This is general relativity.]

Carlo Rovelli, a well respected theoretician, makes these interesting observations:

" In GR there is no external time parameter… a notion of proper time is associated ….[with] each timelike worldline; yet in quantum theory there are no physical individual trajectories… only transition probabilities between observables….
Conventional QFT relies ….on the existence of a non–dynamical background spacetime metric..[but]…with GR we have understood that there is no such non–dynamical background spacetime metric in nature…. " "

[And here are some comments of his regarding time in relativity....not how we usually think of 'simple old time'.]

"...In special relativity, this notion of time is weakened. Clocks do not measure a universal time variable, but only the proper time elapsed along inertial trajectories. .....In general relativity, when we describe the dynamics of the gravitational field ...., there is no external time variable that can play the role of observable independent evolution variable. The field equations are written in terms of an evolution parameter, which is the time coordinate x0, but this coordinate, does not correspond to anything directly observable. ..... properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable.....

http://arxiv.org/abs/gr-qc/0604045
Unfinished revolution
[This paper is about relativity and quantum theory. 'Spacetime' [space and time] plays a major role in trying to reconcile these rather different theories.

5. Jul 6, 2015

### Finny

Also, Check out
https://en.wikipedia.org/wiki/Problem_of_time

While I don't like some of the phrasing there, try reading the first two paragraphs and you'll likely come away with a different perspective of time.

6. Jul 6, 2015

### Mentz114

In GR one can construct a set of four basis vectors to define the local space of an observer on a time-like curve. ( See tetrad fields ). The time basis vector will take the form $T\partial_t \pm Y$ where $Y$ is a combination of spatial directions and T is a positive function of the coordinates. It must be positive if the local clocks are to move forward, that is, in the same direction as coordinate time $t$.

7. Jul 7, 2015

8. Jul 7, 2015

### pervect

Staff Emeritus
There are occasions when we talk about something equivalent to he direction of time. But all of the answers I can think of that go into any detail strike me as a bit technical for what I'm guessing the level of the original poster's question.

In General Relativity, he least technical thing I can think of to say is that space-time is a manifold, but that locally each point on the manifold has a tangent space. It's the tangent space that has the structure of a vector space.

Which is pretty technical.

An analogy is a bit simpler, but perhaps off-topic. It's probably simpler to talk about the special relativity case first, which you'd need to understand the GR case anyway.. In special relativity, space-time is flat, and it does have a vector structure, you don't need to worry about manifolds. Time is just another one of the vectors that describe the unified concept of space--time.

This treatment is different from the usual one in which we treat time separately from space. But it's needed in special relativity, because observers moving at different velocities have a different idea of how to split up space-time (the unified entity) into the parts we call "space" and the parts we call "time". The Lorentz transformation, in particular, involves elements of both time and space that "mix together".

9. Jul 7, 2015

### Staff: Mentor

More precisely, any given vector will be of one of three types, "timelike", "null", or "spacelike". There isn't a single vector that can be labeled "time", because, as you note later in your post, Lorentz transformations mix "space" and "time" together. The best we can do is to classify a vector into one of the three types.

10. Jul 7, 2015

### Maxila

That's because physically they are coincident and experienced as the result of a single phenomenon, the change in position of energy or matter. While being represented mathematically and in thought as being separate; space cannot be experienced without a change of position represented by time, and time cannot be experienced without a change of position in space. It makes spacetime the simplest of axioms and it would help if more people understood the physical bond that cannot exist separately. Time in that respect, is by far the harder one for most people to comprehend due to deeply ingrained intuitions.

11. Jul 7, 2015

### Staff: Mentor

This looks like a personal theory to me. Please bear in mind the PF rules about personal theories.

12. Jul 8, 2015

### Superleopard21

thanks very much,all your awesome science !

13. Jul 8, 2015

### Superleopard21

mAYbe time is not a vector,it may just be a mattter g3enerated by the universe.

14. Jul 8, 2015

### Staff: Mentor

Time is not the same thing as matter.

15. Jul 8, 2015

### Superleopard21

thanks for leading me out of craziness.!yeah,time is not a matter,that is true

16. Jul 9, 2015

### Staff: Mentor

This seems like a good place to close the thread to avoid personal speculation.