I Understanding Space-Time Expansion: Debunking the Myth of Non-Physical Space

[PhanthomJay]

How can space expand when space is not a physical thing? I’ve heard some say that is not expanding but rather it is getting less dense, which to me implies the same thing.

 

[PeroK]

How can space expand when space is not a physical thing? I’ve heard some say that is not expanding but rather it is getting less dense, which to me implies the same thing.

Didn't you ask this question before?

If space is expanding, then that's your evidence that it can expand, whether it's a physical thing or not.

 

[PhanthomJay]

Didn't you ask this question before?

If space is expanding, then that's your evidence that it can expand, whether it's a physical thing or not.

I don’t remember asking it. But thanks for response

 

[Orodruin]

How can space expand when space is not a physical thing? I’ve heard some say that is not expanding but rather it is getting less dense, which to me implies the same thing.

What do you mean when you say it is not a physical thing? While it is true that what ”space” is is a rather arbitrary separation from spacetime. Cosmology generally uses a very particular coordinate system in which the universe is spatially homogeneous and isotropic. It is in those coordinates we talk about the expansion of space, which is nothing else than noting that the distance between so-called comoving objects (essentially objects at rest wrt the CMB or, equivalently, the cosmic frame) grow with time.

 

[PhanthomJay]

Thanks, but why would it not be that the galaxies, not space, are moving apart as physical objects that are "spatially extended" (I borrowed that "term" from Einstein)? I don't particularly like the balloon analogy. And is time expanding also, being part of spacetime?

 

[Drakkith]

How I usually explain it: The geometry of spacetime is such that, over time, objects not bound together through some force or through gravity will tend to get further apart. It's not that 'space itself' is expanding, it's a geometrical effect that is just like objects falling towards each other under gravity. The answer to "why do objects fall towards each other" is the same as "why do unbound objects move apart". Geometry tells them to.

 

[PeroK]

And is time expanding also, being part of spacetime?

No, it's an expansion of space over time - specifically that's how it's described in comoving coordinates.

More generally, the coordinate-free description is that spacetime is curved.

 

[Orodruin]

Thanks, but why would it not be that the galaxies, not space, are moving apart as physical objects that are "spatially extended" (I borrowed that "term" from Einstein)?

Locally (in a small enough spacetime region) it is possible to make a change of coordinates to the locally Minkowski coordinates. In those coordinates, comoving objects are indeed moving apart so it is a matter of coordinates. Hence, this is a matter of nomenclature and interpretation in a particular coordinate system.

However, it should be noted that such coordinates do not generally extend to all of spacetime. They are just going to give an approximately Minkowski picture in a small spacetime region.

Cosmological coordinates on the other hand are global. The expansion of space refers to those coordinates.

If I don’t misremember I wrote an Insight about this issue several years ago.
(Edit: Indeed, here it is https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/)

I don't particularly like the balloon analogy. And is time expanding also, being part of spacetime?

Whether you like it or not is irrelevant. The only relevant thing is how accurately it describes the theory. As far as analogies go, it is a surprisingly appropriate one for the description using cosmological coordinates.

(Cosmological) time is the parameter on which the expansion depends. It would make no sense to talk about time itself expanding. That said, there are coordinates where also the time part of the metric is multiplied by a scale factor. However, this can be removed by trivial scaling.

 

[PhanthomJay]

Once again, I want to thank you all for your time and responses. I've said it several times, but I'll say it again, you all are amazing geniuses in this field!

And I still miss Marcus.

 

[DaveC426913]

Once again, I want to thank you all for your time and responses.

OK, now answer us this: where did you disappear to for 387 days? (from Jul 8 '22 till Jul 30 '23)

 

[Jaime Rudas]

More generally, the coordinate-free description is that spacetime is curved.

I suppose this implies that an expanding flat space corresponds to a curved spacetime. That's right?

 

[PhanthomJay]

OK, now answer us this: where did you disappear to for 387 days? (from Jul 8 '22 till Jul 30 '23)

Hah, Dave , nice sense of humor! And good research! I've had some issues this past year, hope to be a regular again.

When is the next full moon over the horizon?

 

[Orodruin]

I suppose this implies that an expanding flat space corresponds to a curved spacetime. That's right?

In general, yes. There are however some pathological counter examples. The best fit Lambda-CDM model of our universe not counting among those examples.

 

[Hill]

I suppose this implies that an expanding flat space corresponds to a curved spacetime. That's right?

Here is the curvature of that spacetime, according to Wikipedia:

 

[PeterDonis]

Here is the curvature of that spacetime

One clarification is probably appropriate here: what you quoted from Wikipedia only gives the Ricci tensor, which is only a piece of the Riemann tensor. But in this particular case, the other piece of the Riemann tensor, the Weyl tensor, is zero, so the Ricci tensor does capture all of the spacetime curvature. In general that will not be the case.

 

[Hill]

One clarification is probably appropriate here: what you quoted from Wikipedia only gives the Ricci tensor, which is only a piece of the Riemann tensor. But in this particular case, the other piece of the Riemann tensor, the Weyl tensor, is zero, so the Ricci tensor does capture all of the spacetime curvature. In general that will not be the case.

Thanks a lot. I wondered about the rest of Riemann tensor. Should've asked.