Thought experiment involving spacetime curvature:

[VeryConfusedP]

Peter Donis and Nugatory taught me a lot about spacetime curvature yesterday, but it has left me with so many questions.

It sounds like mass slows down time as it warps spacetime. So, I suppose this means: more mass = more spacetime curvature = less time elapsing.

Okay, in addition to that, we know that time "stands still" for the photon. I'm sure there's a more elegant way of putting this, and please let me know.

Here's my question: if--this is a big, big if--you could fill the known universe with mass, which, I suppose, would be a complete warping of spacetime, would time be nonexistent, as it is for the photon?

I know there's not enough mass and energy to do this, so you could immediately dismiss this course of thought, but I'm trying to get a better understanding of the reach of spacetime curvature.

However, if the universe (even in our ideal universe with as much mass as we need) cannot be filled completely with mass (which, again, is complete warping of spacetime), what is it about space or spacetime that prohibits this? Is there some interaction between spacetime and matter that demands that there should always be more spacetime than matter?

I think the obvious answer is: matter cannot be created or destroyed, and space is expanding. But I'm just trying to understand that a little better.

Thank you for your time.

 

[PeterDonis]

It sounds like mass slows down time as it warps spacetime.

This is not generally valid, because in the general case there is no way of defining what "slows down time" means. In the special case of a *static* mass, i.e., a mass that can be viewed as an isolated, unchanging object surrounded by empty space, then we can usefully define what "slows down time" means.

So, I suppose this means: more mass = more spacetime curvature = less time elapsing.

Again, this is not generally valid; it is only valid in the particular case of a static, isolated mass. In that case, yes, a larger mass will cause more "slowing down of time" at a given distance from the mass.

Okay, in addition to that, we know that time "stands still" for the photon.

No, we don't know that. What we know is that the concept of "elapsed time" doesn't make sense for a photon. That's not quite the same thing.

(Yes, I know a lot of popular presentations say "time stands still for a photon", or words to that effect. That's an example of why you can't use popular presentations if you actually want to learn physics.)

if--this is a big, big if--you could fill the known universe with mass

It's not a big if; it's actually the case. The universe, to a first approximation, is filled with mass--very, very low density mass, but mass nonetheless. It's hard for us to see this on ordinary distance scales because at those scales the universe is obviously lumpy, not uniformly dense; we have dense objects like the Earth or the Sun or white dwarfs or neutron stars surrounded by what seems to be empty space. (Actually it isn't quite empty; estimates of the density of interstellar space are something like one hydrogen atom per cubic meter. But that's as good as empty for ordinary purposes.) But on a distance scale of a billion light years or so, which is the distance scale of interest for cosmology, all that lumpiness averages out, and we can treat the universe, to a first approximation, as just being uniformly filled with very low density mass.

which, I suppose, would be a complete warping of spacetime

No, it wouldn't, because the mass filling the universe is not static or isolated, so it doesn't work the way a static, isolated mass works.

would time be nonexistent

No.

as it is for the photon?

As noted above, this is incorrect.

I think the obvious answer is: matter cannot be created or destroyed, and space is expanding.

Both of these are true, but I think you need to re-think how they are connected to the rest of your understanding, in the light of my comments above.

 

[VeryConfusedP]

So, Peter, are you saying that curvature of spacetime can be understood as the curvature of low-density mass?

 

[PeterDonis]

So, Peter, are you saying that curvature of spacetime can be understood as the curvature of low-density mass?

If the mass is low density, sure (except that it's not the mass that is curved, it's spacetime). Mass doesn't have to be low density--nor does it have to be high density. It can be either. It produces spacetime curvature either way.

 

[Nugatory]

So, Peter, are you saying that curvature of spacetime can be understood as the curvature of low-density mass?

You probably think of the air in a room as a substance of uniform and low density - and indeed it is, at any non-microscopic scale. But at a sufficiently small scale, the density in very non-uniform; essentially all of the mass of the air is concentrated in tiny particles (atomic nuclei) as dense as the interior of a neutron star and separated by enormous gulfs of empty space. Nonetheless, on any large scale it makes sense to treat air as a gas of uniform and low density.

Cosmologists are doing the same thing when they treat the universe as if it is filled with a uniform low-density mass; at the scale they're working with the star-sized and galaxy-sized lumps average out.