Entropy and Expansion in a Simple Universe

[PeterDonis]

Isn't that just because the curvature has not been detected yet

You say "yet". How do you know spatial curvature will ever be detected?

Our best current model is spatially flat because that's the model that best fits the data we have.

it's still an open question if the universe is spatially finite or infinite

Only in the sense that the error bars in our measurements cannot conclusively rule out the possibility that the universe is spatially closed. But we have no positive evidence of spatial curvature. And at some point, as the error bars continue to narrow, we might be able to rule out spatial closure as a possibility, if future measurements continue in the pattern of the data we have now.

Whatever the flat-lambda model says should be compatible even if the universe was a finite, closed system.

No, it won't; if we ever get positive evidence that the universe is not spatially flat (which we do not currently have--see above), we will have to change our best fit model; it will no longer be the flat lambda CDM model. It might be a spatially closed lambda CDM model, but that's still a different model.

 

[PeterDonis]

the system you are describing is an ideal gas

No, it isn't. A single particle is not a continuous fluid. Also, there is no piston in the "single particle in an otherwise empty universe" model. As has already been pointed out, such a model is either flat Minkowski spacetime (if the single particle has negligible mass) or Schwarzschild spacetime (if the single particle has non-negligible mass). If you want to reason about entropy, you need to do it using one of those two models; the model you used is neither.

 

[Mark Harder]

No, it isn't. A single particle is not a continuous fluid.

That's not the ideal gas model with which I'm familiar. The statistical mechanics of an ideal gas assumes that it consists of particles in thermal, i.e. ramdom, motion. That can't be a continuous fluid. The particles must occupy zero volume and do not participate in any energetic interaction with other particles. A very unreal situation, but one that can be approximated experimentally by helium and some other gases, especially at low concentrations that minimize inter-particle collisions.

 

[durant35]

You say "yet". How do you know spatial curvature will ever be detected?

Well, I don't but the same can be said about you and the claim that it won't. At this point it is pointless to claim anything about it.

Only in the sense that the error bars in our measurements cannot conclusively rule out the possibility that the universe is spatially closed. But we have no positive evidence of spatial curvature. And at some point, as the error bars continue to narrow, we might be able to rule out spatial closure as a possibility, if future measurements continue in the pattern of the data we have now.

What if only our region is flat and the rest is not?

You seem to be pretty optimistic about the potential extrapolations of a measurement that is local and inconclusive about the greater scale. Sure, it can be said that there's no evidence in my claim but your claims are incredibly strong wrt to available measurements.

No, it won't; if we ever get positive evidence that the universe is not spatially flat (which we do not currently have--see above), we will have to change our best fit model; it will no longer be the flat lambda CDM model. It might be a spatially closed lambda CDM model, but that's still a different model.

What would be different?

 

[PeterDonis]

At this point it is pointless to claim anything about it.

I wasn't. You were the one making an implicit claim when you used the word "yet". If you had left out that word your statement would just have been a description of our current evidence, which is fine.

What if only our region is flat and the rest is not?

Then we will have to change models--assuming we could observe the non-flatness outside "our region" at some point.

your claims are incredibly strong wrt to available measurements

My "claims" are just a description of our current best fit model. It is our current best fit model because it best fits all of our available evidence--more precisely, it is the simplest model which fits all of our available evidence. It is the simplest because it assumes that the rest of the universe that we can't see looks similar to the part of it that we can see. Your questions (such as "what if only our region is flat and the rest is not?") assume a more complex universe in which the region we can see is somehow special, different from the rest. If we ever get positive evidence that that's the case, then yes, we'll need to revise our model, but in the meantime Occam's Razor tells us to use the simplest model that fits the data. So that's what we do. If that's "incredibly strong wrt to available measurements", then so are practically all of our current scientific theories.

What would be different?

Um, the universe would be spatially closed and have positive spatial curvature, instead of being spatially flat and having zero curvature? Is it not obvious that those are different models?

 

[PeterDonis]

The statistical mechanics of an ideal gas assumes that it consists of particles in thermal, i.e. ramdom, motion.

No, the statistical mechanics justification for using the ideal gas model assumes that the gas consists of particles in random thermal motion, and then shows how, given that assumption (plus a few others, such as zero interaction between the particles except elastic collisions on contact), you can ignore the motions of the individual particles and just model the gas as a continuous fluid with a few simple thermodynamic properties. And for that justification to work, you need a very large number of particles; just one won't do.