# The Nature of Time?

1. Apr 2, 2007

Because i received an infraction for posting my explanation for why time shouldn't be considered a 4th dimension, instead, i would like to address the issue as a question instead of an assertion.
Why should time be considered as a 4th dimension?

cheers,

2. Apr 2, 2007

### mathman

The simple explanation is that relativity theory has the concept built into it. For example when changing inertial frames in special relativity, time and space change together.

3. Apr 2, 2007

### rbj

i would add that time is still the "funky" 4th dimension. it has a different sign attached to it in that $\eta$ metric. there is also no "arrow of space" that i am aware of (except i guess in black hole). t is not qualitatively identical to x, y, or z, the latter 3 which are qualitatively identical.

4. Apr 2, 2007

### MeJennifer

In Galilean space-time you could consider time the fourth dimension, but in relativity time is not the fourth dimension!

In relativity, the relative measure of time between any two observers is related to their relative orientations in space-time.

The only difference between an Euclidean 4-dimensional Galilean space-time and a Minkowski space-time is that the rotations work differently.

Both the Galilean E4 and the Lorentz O(1,3) make a 10-dimensional symmetry group.

So actually there is not that much of a difference!

Last edited: Apr 2, 2007
5. Apr 2, 2007

### robphy

The Lorentz metric is invertible, whereas the Galilean metric is not invertible.
The Lorentz metric yields three classes of vectors [spacelike, timelike, and null], whereas the Galilean metric yields only two classes...with spacelike and null coinciding.
The Lorentz group and the Galilean group have different sets of eigenvectors.

6. Apr 3, 2007

### yogi

Time has the property that when scaled by c, (i.e., multiplied by the velocity of light) there results the dimension of distance. The other three dimensions (X, Y and Z) are also distances. When Minkowski unified time and space he scaled the temporal distance as "ct" This isn't something arbitrary - If you can think of it metaphorically as all objects always moving at a constant rate equal to c - then you traveled 3 x 10^8 meters in one second w/o even moving from your chair. This becomes a useful tool that leads to the invariance of the interval - all objects move at c, therefore while you are sitting at rest, you are traveling in time a distance ct whereas an object in motion (with uniform relative velocity v) would travel a distance
[(ct')^2 + (vt)^2]^1/2 where vt is the spatial component and ct' is the temporal component, both of which have units of distance. Rather than thinking of c as local light speed, think of it as the rate of expansion of the Hubble sphere - you like everything else are being effortlessly carried along a distance ct each second

7. Apr 3, 2007

### robphy

The above (e.g. a statement like "all objects move at c") would only apply to objects with nonzero rest-mass. That is, the above does not apply to light.

8. Apr 3, 2007

### Garth

Because the position of an event cannot be described except at a specific time and the time of an event cannot be described except at a specific position. (Albert Einstein)

Furthermore, using a space-time continuum also resolves certain problems in 19th Century physics, such as the invariance of the speed of light in the Michelson-Morley experiment and it makes Maxwell's equations invariant between different inertial frames of reference.

Garth

Last edited: Apr 3, 2007
9. Apr 3, 2007

### masudr

It must be stressed here that time being the 4th dimension is coordinate time. This is very different from the time that clocks will measure (the so-called proper time): that is proportional to lengths of paths in spacetime and can involve as much space as they do time.

10. Apr 3, 2007

### robphy

Given a 3D-Euclidean space, it does make sense to define a new, fourth dimension that can be defined as perpendicular to that space. That new dimension is associated with the "time" associated with that given 3D space. Mystical as this may sound at first, this construction is used in describing the evolution of 3D systems in Galilean physics.... however, its interpretation as a spacetime geometry is not as familiar as Minkowski spacetime.

11. Apr 3, 2007

thanks all, thats quite a complicated variety of answers to chew on...
so far none of these answers tackles the fundamental nature of time as compared to that of space. Thats understandable, since time is something we thing with and only perilously about...

12. Apr 3, 2007

Perhaps i'm misinterpreting this explanation, but it seems to me you are saying: "Time should be treated as a 4th dimension because we treat it as a 4th dimension." That seems a bit circular to my question. I don't see your example as an explanation either, since it leaves room to assume the reason time and space change together in inertial frames could be due to the way they are arranged in an equation, not whats indicated by nature.
thanks,

13. Apr 3, 2007

what does the sign indicate? You have pointed out how different time is to a spacial dimension, why then should it be treated as a dimension? Perhaps this is a question of semantics, but if it is called a "4th dimension", that implies it is built upon the former 3 dimensions, just as the Y-dimension is only thus in reference to the X- dimension, etc.
I am interested in hearing more about the arrow of time in a black hole.
thanks,

14. Apr 3, 2007

### HallsofIvy

I would be interested in hearing what you think the word "dimension" means.

15. Apr 3, 2007

### Garth

The question is: "How are events connected up in space and time?"

Take an infinitesimal interval ds separating two events:

Now the separation in 2 dimensions is given by Pythagoras' theorem:

dx2 + dy2 = ds2

now expand it to 3 dimensions:

dx2 + dy2 + dz2 = ds2

now expand it to 4 dimensions where the fourth dimension is time; do we get

dx2 + dy2 + dz2 + dt2= ds2???

Unfortunately this isn't correct, there are two things wrong with it.

First there is a question of units, we have added the squares of 'apples' and oranges'! We need a conversion factor to convert time into distance, such a factor has the dimension of velocity, so call it c, we have to multiply dt2 by c2.

Secondly in SR we do not add the time2 but subtract it. This changes the 4D space we are constructing from Euclidean space to Minkowski space. You may ask why do we do this, the first answer is because that is the way the world works, and this approach has been verified in all the experiments that verify SR.

In Minkowski space the maximum velocity is c, massive objects can only approach c asymptotically and massless objects such as photons can only travel in vacuo at c, so c is the speed of light in vacuo.

We now have:

dx2 + dy2 + dz2 - c2 dt2= ds2.

This is called the Minkowskian metric and accurately describes the behaviour of objects with clocks and rulers moving relatively to each other at high speed.

The result of this construction of a 'space-time' continuum out of space and time is that time is seen to be a dimension like the other three but with a difference. It bears the same mathematical relationship to them that the Imaginary numbers do the the Real. The fact that if time is a dimension then it is not exactly the same as the others is intuitively self-evident.

I hope this helps.

Garth

Last edited: Apr 3, 2007
16. Apr 3, 2007

### rewebster

It's too bad that there are so many 'definitions' of what 'time' 'means' to fit each theory---and how it is incorporated at 'what' level of those theories.

maybe time will tell which times are tales

17. Apr 3, 2007

### Staff: Mentor

That really isn't true, rewebster. To scientists and engineers, this issue is unambiguous.

18. Apr 3, 2007

### MeJennifer

Out of curiosity Garth. why do you call this fourth dimension time?

To me time is measured by the metric, not by the t coordinate.

Last edited: Apr 3, 2007
19. Apr 3, 2007

### Garth

If there is no motion when moving between the two events then dx, dy and dz are all zero. Then
ds2 = -c2dt2 and the space-like interval is i x time. One could write everything in terms of the time-like interval d$\tau$:

dt2 - c-2dx2 - c-2dy2 - c-2 dz2 = d$\tau$ 2

in which case if dx, dy and dz are all zero then d$\tau$ is dt, the interval is time in the rest frame.

Using this form of the metric $\tau$ is the proper time or time-like space-time interval between the two events.

Garth

20. Apr 3, 2007

### MeJennifer

I fully understand what you are saying but I don't look at it that way at all.
To me space-time is a frame independent representation of reality.

In the case you mention, the proper time vector happens to be pointing in the same direction as the t axis. This is the trivial case.

But clearly, in a more general case, where we have several objects that are in relative motion with each other, we immediate see that not all the directions of the proper time vectors point towards the t axis.

Then if we analyze this situation a bit further we can see that the t axis does not measure time but instead is a means to describe relative angles between the individual proper time vectors.

Last edited: Apr 3, 2007