Is there any difference left between time and space left?

[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?

 

[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 .

 

[Meir Achuz]

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.

 

[A.T.]

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

Which can be regarded as a dimension as well, instead of coordinate time:
https://www.physicsforums.com/showthread.php?p=2328057
In that Euclidean space-time the 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.

between space and time dimensions vanish.

 

[Bob_for_short]

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?

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.

 

[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!

 

[I_am_learning]

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

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

 

[atyy]

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

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.

 

[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.

 

[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).

 

[Dale]

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.

I would also add:

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.

 

[Naty1]

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

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??

 

[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.

 

[A.T.]

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

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

 

[Dale]

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

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.

 

[Cleonis]

Is it that only due to our institution we think time and space as different entities?

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

 

[matheinste]

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.

Cleonis

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.

 

[I_am_learning]

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).
Cleonis

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' ?

 

[matheinste]

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' ?

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

 

[Cleonis]

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.

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 traveled 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

 

[matheinste]

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 traveled 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.
Cleonis

Proper time is a measure of distance traveled 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.