Is Space-Time Symmetrical or Asymmetrical?

[japplepie]

Is it true that the speed of light is a conversion factor between time and space?

and that D = C*T?

and if it is, how does that make any sense?

 

[CompuChip]

Yes, the speed of light is a speed - it has units of m/s. For any speed, if you multiply a time by it you get a distance and if you divide a distance by it you get a time. Of course the big deal with the speed of light is that, unlike your car on the freeway, it is constant throughout the universe.

and that D = C*T?

and if it is, how does that make any sense?

I have no idea what D, C and T mean in that equation.

 

[CompuChip]

Oh, I just realized that probably "D" stands for "Distance", "C" is the speed of light (we normally use a lower-case c for that) and "T" for "Time".

In that case: yes, this is how you would convert distance to time. For example, you will find that 1 second corresponds to 300,000 km (taking c = 300,000 km/s for convenience, it is really 299,792.458 of course).

If you have ever heard a distance expressed in light years, this is exactly what happens. People often confuse a light year for a time duration, but it is really a distance: the time that light travels in a year. If you want to convert it to kilometers, just plug in t = 1 year in d = ct.

 

[japplepie]

Does that mean that space and time are equivalent? And if they are, to what extent?

Does space exhibit all the properties of time (and vice versa)?

I've read somewhere that something that violates parity would also be time irreversible since space and time are equivalent.

 

[nikkkom]

Does that mean that space and time are equivalent? And if they are, to what extent?

Does space exhibit all the properties of time (and vice versa)?

Spatial coordinates enter metric with positive sign, temporal one has a negative sign. For a flat space-time of special relativity:

ds^2 = dx^2 + dy^2 + dz^2 - dt^2

That seems to be the only, but crucial, difference.

 

[Dale]

Spatial coordinates enter metric with positive sign, temporal one has a negative sign. For a flat space-time of special relativity:

ds^2 = dx^2 + dy^2 + dz^2 - dt^2

That seems to be the only, but crucial, difference.

Well, there is the sign of the metric and also the number of dimensions. Since there is only one time dimension you cannot have closed timelike curves in flat spacetime, while you can have closed spacelike curves since there are three dimensions of space.

 

[nikkkom]

Well, there is the sign of the metric and also the number of dimensions. Since there is only one time dimension you cannot have closed timelike curves in flat spacetime, while you can have closed spacelike curves since there are three dimensions of space.

It has nothing to do with the number of spatial dimensions. (For one, 2D space-time with just one spatial dimension works similarly to 4D case even though there is only one spatial dimension).

Moreover, there are non-flat GR space-time solutions with closed timelike curves.

In flat Minkovski space you can not go back and thus enter a closed loop not because time coordinate somehow does not allow it, but because absolute value of four-velocity of any object is 1 (i.e. the object moves into future), and *then* minus sign comes into play: the curve where |four-velocity| is 1 is not a circle (which would be the case for euclidean space), but a hyperbola because one metric component is ***-dt^2***, not dt^2!

 

[Dale]

It has nothing to do with the number of spatial dimensions. (For one, 2D space-time with just one spatial dimension works similarly to 4D case even though there is only one spatial dimension).

No, 1+1D spacetime does not work the same as 3+1D spacetime. In 1+1D flat spacetime you cannot have closed spacelike curves like you can in 3+1D spacetime. Draw any closed curve in a standard spacetime diagram and you will see timelike and spacelike portions.

In flat Minkovski space you can not go back and thus enter a closed loop not because time coordinate somehow does not allow it, but because absolute value of four-velocity of any object is 1

If you had two or more dimensions of time then you could construct a closed loop where the absolute value of the four velocity is always 1.

Again, the two things which distinguish time from space are the sign of the metric and the number of dimensions.

 

[FactChecker]

Does that mean that space and time are equivalent? And if they are, to what extent?

Does space exhibit all the properties of time (and vice versa)?

I've read somewhere that something that violates parity would also be time irreversible since space and time are equivalent.

Time is irreversible (asymmetrical) due to the second law of thermodynamics. But space is symmetrical. So they are not equivalent.