How to apply Einstein's STOR to expansion

[thetexan]

Einstein's STOR states that if I was in an upward accelerating elevator I would not be able to tell if the weight I would be experiencing was due to acceleration or gravity from my frame of reference. This identical appearance idea work for expansion also?

It has been stated many times that the expansion of the universe is not as a result of an 'explosion' at the big bang but rather an expansion of space/time.

My question is how could you tell? Expansion and an explosive event are both theories, the former more accepted than the latter. How would the two look different? How can you prove JUST by observation that what you are looking at is one or the other since the results would look the same (I'm assuming)? Wouldn't the continuously increasing distance between objects occur in either case? Wouldn't the impression that every object is moving away from our vantage point be the same. Wouldn't the dots on the balloon analogy work in either case?

tex

 

[Chalnoth]

Einstein's STOR states that if I was in an upward accelerating elevator I would not be able to tell if the weight I would be experiencing was due to acceleration or gravity from my frame of reference.

Almost. Gravity gets weaker as you move away from the source, so that, for example, in an elevator sitting on the Earth's surface, the measured acceleration will be ever so slightly less at the top of the elevator than the bottom.

Other than that, though, they are equivalent.

This identical appearance idea work for expansion also?

I don't think that the analogy extends that far. Galaxies in an expanding universe are all in free-fall.

It has been stated many times that the expansion of the universe is not as a result of an 'explosion' at the big bang but rather an expansion of space/time.

My question is how could you tell?

Explosions are extremely disordered events. The early expanding universe was extremely ordered.

 

[PeterDonis]

Gravity gets weaker as you move away from the source, so that, for example, in an elevator sitting on the Earth's surface, the measured acceleration will be ever so slightly less at the top of the elevator than the bottom.

This is also true in an "elevator" that is accelerating in flat spacetime. The only difference is the rate of variation with height. But the assumption of the equivalence principle is that we are considering a small enough range of height that these differences are not measurable.

 

[timmdeeg]

Explosions are extremely disordered events. The early expanding universe was extremely ordered.

In the case of the empty universe an observer can't distinguish expansion from explosion. Could you explain which observation would allow us to distinguish both models in case the initial state of the matter containing universe was highly ordered. Can this perhaps be excluded by certain reasons regarding the Milne like explosion scenario?

 

[Chalnoth]

In the case of the empty universe an observer can't distinguish expansion from explosion. Could you explain which observation would allow us to distinguish both models in case the initial state of the matter containing universe was highly ordered. Can this perhaps be excluded by certain reasons regarding the Milne like explosion scenario?

Well, first of all, the Milne universe isn't really expanding. With no matter or energy around, there's nothing to expand, so expansion is meaningless.

With that out of the way, an explosion is disordered. Expansion is not.

An explosion occurs when there is a large increase in temperature in a localized area. That increase in temperature rapidly pushes the material outward into the surrounding space.

In an expanding universe, there is no surrounding space. The entire manifold is expanding, and there is no "outside" at all. The expanding universe is described by objects within the universe getting further apart, so it's only meaningful if there is some form of matter or energy around to change with the expansion.

 

[timmdeeg]

Well, first of all, the Milne universe isn't really expanding. With no matter or energy around, there's nothing to expand, so expansion is meaningless.

But isn't the FRW-universe expanding, even in the absence of any energy density? So it seems that it is merely the choice of coordinates whether or not the empty universe is expanding. One could think of test particles in the Milne universe which then are drifting apart from each other.

I don't think that it really makes sense. Just theoretically, according to the standard model we assume a very homogenous initial state. Why shouldn't we assume the same for a hypothetical explosion scenario?

 

[haushofer]

The expansion of FRW is due to the cosmological constant.

 

[PeterDonis]

The expansion of FRW is due to the cosmological constant.

The accelerating expansion is due to the cosmological constant--at least, that's the simplest hypothesis (others are a scalar field or some other kind of dark energy). But there are certainly FRW models with zero cosmological constant (and scalar field, etc.) that show expansion.

 

[PeterDonis]

it seems that it is merely the choice of coordinates whether or not the empty universe is expanding.

It is for a purely empty universe, i.e., zero stress-energy tensor everywhere and zero cosmological constant. But it isn't for a universe that has nonzero stress-energy or a nonzero cosmological constant. Our actual universe has both.

theoretically, according to the standard model we assume a very homogenous initial state. Why shouldn't we assume the same for a hypothetical explosion scenario?

Because in an ordinary explosion, the asymmetry in the initial state is what causes the explosion. A perfectly homogeneous initial state cannot cause an ordinary explosion.

 

[timmdeeg]

Because in an ordinary explosion, the asymmetry in the initial state is what causes the explosion. A perfectly homogeneous initial state cannot cause an ordinary explosion.

Thanks for your answer. My point is a bit different though. We don't know how the initial state comes into existence, physics doesn't describe that. May due to a quantum fluctuation, may be due to something else. In the FLRW case the universe starts to expand according to postulated initial parameters. Why can't we think of certain initial parameters being the cause of an isotropic explosion in space? In that case the homogeneity exists, but isn't the cause.

Surely explosion can be ruled out by observational data, I'm just interested if the assumption is unphysical if one is free to postulate said initial parameters.

 

[Vanadium 50]

Our universe is, as far as we can tell, homogeneous and isotropic. An explosion into pre-existing space does not produce a universe that is homogeneous and isotropic.

 

[Haelfix]

To be fair, you could write down a Newtonian cosmology, that for all intents and purposes mimics the dynamics given by the Friedman equation. There one consider a spherically symmetric ball of expanding matter that is homogeneous and isotropic.

The only difference is that in the Newtonian version the constant k appearing in the Friedman equations is left unspecified, whereas GR limits it to -1,0,1. The cosmological constant would have to be a sort of repulsive force term in this scenario.

It is interesting that GR really only shows a difference precisely when things are NOT homogeneous and isotropic.