Does Time Expand? Universe Expansion Explained

[moving finger]

I'm not sure of the exact meaning of expansion of space... I had always assumed it had to do with the way the distance between test particles following geodesics would increase over time.

ok... and maybe the expansion of time has to do with the way the time between test particles following geodesics would increase over space...
MF

 

[JesseM]

ok... and maybe the expansion of time has to do with the way the time between test particles following geodesics would increase over space...

But that doesn't make any sense, unless the test particles are tachyons (and I don't think you can define the notion of a geodesic for tachyons)--if you slice spacetime into a series of non-spacelike-sections, you won't have the same collection of test particles in each slice, you'll just get particles randomly appearing and disappearing from one slice to the next. Try to visualize a spacetime filled with worldines, and what happens if you take a series of slices along the time axis vs. what happens if you take a series of slices along a spatial axis, hopefully you can see what I mean.

 

[moving finger]

But that doesn't make any sense, unless the test particles are tachyons (and I don't think you can define the notion of a geodesic for tachyons)--if you slice spacetime into a series of non-spacelike-sections, you won't have the same collection of test particles in each slice, you'll just get particles randomly appearing and disappearing from one slice to the next. Try to visualize a spacetime filled with worldines, and what happens if you take a series of slices along the time axis vs. what happens if you take a series of slices along a spatial axis, hopefully you can see what I mean.

It makes sense. I think the reason you cannot make sense of it is because you are stuck in thinking of test particles which have worldlines with a unique separation in their "space values" for each "time value".
Try to think of it instead as two spacetime events rather than as test particles or worldlines.
Let us define "time-simultaneous" as meaning the two events take place at the same time but at different points in space (I know, I know, simultaneity is relative! but let's assume a non-relativistic scenario), and let us define "space-simultaneous" as meaning the two events take place at the same location in space but at different points in time.

Now, what is being said is the following :
In the "space" case the "space interval" between two time-simultaneous events depends on their location in time - for expanding space the events are further apart in space if the events take place at later times - for contracting space the events are closer together in space if the events take place at later times.

In the "time" case the "time interval" between two space-simultaneous events depends on their location in space - the two events are either further apart or closer together in time depending on their location in space.

Now one might ask - how can the time-interval between two space-simultaneous events be different, depending upon their location in space?

Think of gravitational time-dilation. Near a massive body, this is exactly what happens - the time-interval between two space-simultaneous events near the massive body IS different (it is greater) compared to the time-interval between two space-simultaneous events in empty space.

MF

 

[JesseM]

It makes sense. I think the reason you cannot make sense of it is because you are stuck in thinking of test particles which have worldlines with a unique separation in their "space values" for each "time value".
Try to think of it instead as two spacetime events rather than as test particles or worldlines.
Let us define "time-simultaneous" as meaning the two events take place at the same time but at different points in space (I know, I know, simultaneity is relative! but let's assume a non-relativistic scenario), and let us define "space-simultaneous" as meaning the two events take place at the same location in space but at different points in time.

OK, but the point is that when you take spacelike slices along the time axis, you can say the two events are just the positions of the particles at that moment in time, so you can compare the distance of the two events in one spacelike slice to with the distance of the "corresponding" two events in a later slice (ie the position of the same two particles at the later time). But what correspondence is there between events in one slice taken along a space axis with events in another slice taken along the same space axis?

In the "space" case the "space interval" between two time-simultaneous events depends on their location in time - for expanding space the events are further apart in space if the events take place at later times

What events are further apart? Any two pairs of random events in different slices will be further apart, regardless of how you choose them? If in the first slice I choose the events "clock on Earth reads 2005" and "clock on Earth reads 3005", and in another slice I choose the events "clock on Alpha Centauri reads 2005" and "clock on Alpha Centauri reads 2008", does that mean time has shrunk? What if I had instead chosen the events "clock on Alpha Centauri reads 2005" and "clock on Alpha Centauri reads 4005"? Without some correspondence between the events on one slice and another, without some kind of rule saying "if you pick events A and B in your first slice, you must always pick events A' and B' in the second one", then your choice of which two events in each slice to pick will be totally arbitrary, so there will be no well-defined procedure to decide whether "time is expanding" or not. So, your argument still makes no sense to me.

 

[Chronos]

I haven't followed this whole thing in detail, but time and space are interchangeable. A lazy way to visualize an event is by imagining a four dimensional hypersphere whose virtual surface is:

X^3 + Y^3 + Z^3 + T^3 = 1 [or other arbitrary constant].

Note: cubing the factors is a lazy way of preserving CPT symmetry.