B Is Time Expanding Along with Space in the Expanding Universe?

[lomidrevo]

Hello all,
at the beginning, let me say that I haven't studied General relativity yet, I might have some knowledge at popsci level only... So I apologize if the question looks stupid...

At cosmological scale we observe that universe is expanding. If I understood well, this includes only the spatial coordinates of the spacetime.
How do we know that time is not expanding together with space?

 

[PeroK]

Hello all,
at the beginning, let me say that I haven't studied General relativity yet, I might have some knowledge at popsci level only... So I apologize if the question looks stupid...

At cosmological scale we observe that universe is expanding. If I understood well, this includes only the spatial coordinates of the spacetime.
How do we know that time is not expanding together with space?

How would you define the expansion of time?

 

[Orodruin]

When we say that the Universe is expanding, this is the translation of a very precise mathematical statement to English for a particular way of describing it. The corresponding statement for time would be meaningless.

 

[lomidrevo]

thanks guys, I needed to think about it twice to understand that such question doesn't make sense indeed

initially, my thinking was as following:
we have 4 coordinates of spacetime: x,y,z,t. During expansion x,y,z coordinates are "stretched". I imagined that time coordinate can defined as ct, in order to be measured in the same units as x,y,z. So if the x,y,z are scaled by the expansion, why couldn't be ct?

Now I realized, that whatever I understand by expansion, it must be evolving with time. So expanding time as the time evolves, makes no sense indeed.

 

[Orodruin]

So if the x,y,z are scaled by the expansion, why couldn't be ct?

Time is different. Expansion means that the distances defined by the spatial coordinates change with time. You can try to do the same with time, but differences in time changing with time can be removed by a simple change of coordinates.

 

[Orodruin]

To take a similar example in a more familiar geometry:

Consider a set of circles in the plane. As you go to larger and larger radius, the circles become larger and larger. In the same language, we would say that the circumference of the circle expands with radius. However, it would be unclear (and not well defined what you meant) if you stated that the radius expanded with the radius (yes, you go to larger values of r, but the distance between r and r+dr is dr by definition).

In the expanding universe, time plays the role of r in this example.

 

[lomidrevo]

To take a similar example in a more familiar geometry:

Consider a set of circles in the plane. As you go to larger and larger radius, the circles become larger and larger. In the same language, we would say that the circumference of the circle expands with radius. However, it would be unclear (and not well defined what you meant) if you stated that the radius expanded with the radius (yes, you go to larger values of r, but the distance between r and r+dr is dr by definition).

In the expanding universe, time plays the role of r in this example.

Thank you for this example, it is clear now :)