# Is there any difference left between time and space left?

1. Aug 30, 2009

### I_am_learning

In special relativity we often use co-ordinate x,y,z,t in similar way. They undergo transformation in similar way.
Is it that they are all the same, just a method to signify an event?
Is it that only due to our institution we think time and space as different entities?
Is there as much difference between x & z co-ordinate as x & t co-ordinate?

2. Aug 30, 2009

### atyy

Time is just a bit more private, not a universal coordinate. Each person still has his own time - proper time.

Mathematically, the signature of metric is 2, so in that sense time is not emergent, although many are looking for such a theory. See David Gross's remarks around 1:31:00 - 1:33:35 .

Last edited by a moderator: Sep 25, 2014
3. Aug 31, 2009

### clem

There are two significant differences:
1. In the metric length ds^2=dt^2-dx^2, so time has the opposite sign from space.
2. Time moves only forward.

4. Aug 31, 2009

### A.T.

Which can be regarded as a dimension as well, instead of coordinate time:
In that Euclidean space-time the differences:
between space and time dimensions vanish.

5. Aug 31, 2009

### Bob_for_short

The very first time the "geometrical" symmetry was discovered by H. Poincaré but he did not think it was worth to follow this symmetry too literally, for the obvious reason: the time is different from the length. See Principle of relativity and Lorentz transformations at http://en.wikipedia.org/wiki/Henri_poincaré.

6. Aug 31, 2009

### Naty1

Is there anything less undertood than time?? except maybe space?

We know space and time have some relationship via Lorentz transformations. But are there others as yet undiscovered....I'd guess yes.

As a personal observation: I keep wondering if time and space are different manifestations of a fundamental entity analogous to all the forces appearing to be different in our low energy environment but likely having a common high energy origin....or maybe they ALL emerge from a common source!!!

Last edited: Aug 31, 2009
7. Aug 31, 2009

### I_am_learning

Equivalently each person also has proper length and co-ordinates.I don't think Thats really is a ditinguishing factor .

8. Aug 31, 2009

### atyy

It is in this sense - special relativity asserts the existence of objects called "ideal clocks". If an arbitrarily moving person carries an ideal clock with him, he will read the proper time elapsed on his clock.

Furthermore, the signature of the metric means that there is a light cone at every point in spacetime which divdes spacetime into timelike, lightlike and spacelike directions.

Unlike coordinate space and coordinate time which can be rotated into each other - proper time, and timelike, lightlike and spacelike directions are frame independent quantities, and in that sense, are objective.

9. Aug 31, 2009

### LAncienne

For a fairly far-out take on this, take a look at Wolfram's book "A New Kind of Science", both the chapter on Physics and the accompanying notes. Can all be had on-line, but I don't have the website immediately at hand, Google Wolfram.

10. Aug 31, 2009

### LAncienne

Minor point, probably already mentioned. Minkowski and GR spaces are semi-Riemannian manifolds, R4, S4 etc are Riemannian. Speaking of directions, I think you can have transformations that invert the time axis and you can always look at what happened in the past, it is just that changing it is not a physically possible operation (causality, etc).

11. Aug 31, 2009

### Staff: Mentor

3. There are three dimensions of space and only one dimension of time.

That is related to 2., but I would make it a separate point anyway.

12. Aug 31, 2009

### Naty1

That's conventional relativity, of course, but how do we know that considering there may be more dimensions of space. I just never thought about it: do we have any experimental or theoretical basis for that??

13. Aug 31, 2009

### matheinste

Hello all.

Perhaps another distinction between a space, of more than one dimension, and time, is that points in such a dimensional space cannot be totally ordered while points in time, like those in a one dimensional space or line, can be ordered.

Matheinste.

14. Aug 31, 2009

### A.T.

And the difference between summer and the other seasons is, that there are three other seasons but only one summer.

15. Aug 31, 2009

### Staff: Mentor

In this case it is more significant than that, there are specific geometric consequences of this. For example, if there were two dimensions of time then you could have a closed timelike curve in flat spacetime.

16. Aug 31, 2009

### Cleonis

It seems to me that the twin scenario lends itself to focusing on the difference between time and space.

When the twins rejoin they find that as they anticipated on the basis of relativistic physics a different amount of proper time has elapsed for each of them (if they have traveled different spatial distances).

Does relativistic physics exclude the counterpart? That is: is it impossible that on rejoining the twins find that they have ended up being different in length? In fact, WE exclude that possibility: it is regarded as unphysical.

Notably, in the 1920's Herman Weyl found himself up against that. He was exploring avenues to unify electromagnetism and gravitation. At some point it was discovered that the new theory implied the existence of wordlines where two objects part ways and upon rejoining are found to have become different in length. Weyl then abandoned that theory. (I don't know the content of Weyl's theory, but I assume it was consistent with the [+,-,-,-] metric signature)

Wrapping it up:
Only the interpretation in which the twins find that a different amount of proper time has elapsed for each of them is regarded as physical.
That interpretation is consistent with the known experimental results, and no known experimental result compels/suggests another interpretation.

In formal mathematical operations on spacetime coordinates time and space seem to be on equal footing. Other than that we find that time and space are treated as entirely different entities.

Cleonis

17. Aug 31, 2009

### matheinste

When the twins reunite their clock rates are the same as are their meter rules. The counterpart of different elapsed times or proper times, is not a difference in meter rules but a difference in spatial distances travelled.

Matheinste.

18. Aug 31, 2009

### I_am_learning

May be I am thinking too crazily but can't we view this in this way. The two twins changed their x,y,z co-ordinate with respect to t in different way and when they meet i.e. x=x', y=y' and z=z' then t <>(desn't equal) t'.

Equivalently aren't there scenarios in special relativity where when y=y', z=z', t=t' then x<>x' ?

19. Aug 31, 2009

### matheinste

When the twins meet again they are colocated and so all their x,y,z and t coordinates are the same no matter what their relative motions have been. What is different is that the values of x,y,z they have traversed is different and their clocks will show different elapsed times.

Matheinste

20. Sep 1, 2009

### Cleonis

Ah, yes, I erred.
I wrongfooted myself by thinking that the questions "how old am I" and "How tall am I" are similar.

Not all is lost, it seems; there is another way in which the twin scenario illustrates difference between time and space:
The difference in elapsed proper time is to an extent a record of the past worldlines of the twins. The twin who has aged the least has travelled a longer pathlength in space. I take the exact shape of a worldline to correspond to a particular amount of information. Since there are three spatial dimensions and one time dimension many distinct worldlines will end up with the same difference in elapsed proper time. In other words, some of the worldline information finds its way to the difference in elapsed proper time, but not all; some information is lost in the process.

It's interesting to see how in Minkowski spacetime such a thing as irreversibility comes into play. Any such irreversibiltity is absent in Euclidean space and time; Euclidean space and time is memoryless.

Cleonis

Last edited: Sep 1, 2009
21. Sep 1, 2009

### matheinste

Proper time is a measure of distance travelled through spacetime. In the case of an inertial observer, such as the stay at home, proper time and coordinate time are the same, as the spatial component is zero, because the inertial observer can consider himself at rest throughout. In the case of a non inertal observer, such as the traveler, who cannot regard himself as at rest throughout, proper time is made up of spatial and time coponents. Although information can be said to have ben lost, it is only in the sense that the exact path taken may not be known, but the spatial distance is incorporated in the value of proper time.

Matheinste.