Superluminal Speeds and All That Jazz

[oldman]

More Jazz

When trying in a dim sort of way to comprehend the consensus model of the universe --- the one Marcus is trying to build a 'same page to get on' about --- I've found it useful to imagine toy models in which extreme circumstances prevail. Sometimes this leads on to questions that I don't have answers for. Hence this further Jazz.

I find the vastness of the model observed universe quite unimaginable, with its remote boundary now at a proper distance of about 46 million light years. This distance is imposed by the tiny Hubble constant, presently about 2.4 x 10 ^ -19 per second.

Since I have no idea at all what determines the numerical value of the Hubble constant, I feel free to imagine a toy model that expands as absurdly fast as I like. Why not? --- Alan Guth did just this!

Sometimes I find it more comfortable to imagine a table-top model of the observed universe, choosing a Hubble constant of the order of 10 ^ +7 per second. The observed-universe boundary is then only a few tens of meters away. I also like to imagine the Hubble constant to be eternally constant, so that there are absolutely no gravitational tidal forces that can distort the shapes of everyday objects like myself, my steel ruler and mechanical tick-tock clock with which I set up coordinates and explore simple physics, as ruled by SR with the ordinary value for c.

Just as I begin to think that in this tabletop universe I could ignore such an absurd rate of expansion of the universe around me, and expect ordinary physics to prevail, I remember that in this toy universe extreme redshifts would occur for light signals transmitted between points of spacetime. I imagine that large redshifts would in this case affect the workings of atomic and particle physics, e.g. interparticle interactions.

Which brings me to the general question: GR assumes that local physics obeys the same covariant laws with the same c throughout spacetime. Should one imagine an upper limit for the Hubble constant in an expanding universe, to ensure that the expansion leaves enough local 'room' in spacetime for the workings of say, QED or QCD as we understand these theories, to remain perceptibly unaffected? Or is local physics likely to be somehow changed by very rapid expansion, as occurs in, say, the inflationary scenario?

 

[marcus]

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...I find the vastness of the model observed universe quite unimaginable, with its remote boundary now at a proper distance of about 46 million light years.

three orders of magnitude

This distance is imposed by the tiny Hubble constant, presently about 2.4 x 10 ^ -19 per second.

one order of magnitude

... no idea at all what determines the numerical value of the Hubble constant,

General Relativity. It's determined dynamically by GR. The Friedmann eqns derive from GR, and the first Friedmann eqn (which dates from around 1922) specifies the changing numerical value of the Hubble parameter. Indeed, the square of that parameter constitutes the righthand side of that equation. Calling it a constant was an unfortunate misnomer. You can see from the equation that the square is proportional to density, so it has to decline as the universe thins out. It has always been known not to be constant.

... I also like to imagine the Hubble constant to be eternally constant, ...

Then you are choosing to take leave of General Relativity. You'll be needing a new theory of gravity. Hope you find one and it goes all right.

 

[oldman]

General Relativity. It's determined dynamically by GR. The Friedmann eqns derive from GR, and the first Friedmann eqn (which dates from around 1922) specifies the changing numerical value of the Hubble parameter. Indeed, the square of that parameter constitutes the righthand side of that equation. Calling it a constant was an unfortunate misnomer. You can see from the equation that the square is proportional to density, so it has to decline as the universe thins out. It has always been known not to be constant...

I'm not clear what your comments about orders of magnitude mean. Have I got numbers wrong, perhaps? Probably.

But let me clarify why I said that I have no idea what determines the numerical value of H.

H is, via Friedmann I, and for a spatially flat geometry, expressed in terms of two variables: namely mean density and Lambda. We have some idea of what the density of our universe is, but no idea at all of what determines Lambda. To match the presently observed H and flat geometry we accept an appropriate value for Lambda, perhaps calling it dark energy. We have no idea why Lambda, and hence our H, have the values they now do. So I still do have no idea why H is what it is!

If I choose to imagine an absurdly large value for H in my toy model, I am in effect choosing a Lambda to suit my fancy. Since there is a 10 ^ 120 discrepancy between the postulated value of Lambda and its rationale as vacuum energy, what's wrong with this liberty?

I take your point about H varying. I was trying to exclude from consideration the tidal forces that are caused by the rate of expansion varying. These might be confused with non-existent forces that are often erroneously attributed to expansion itself.

Thanks muchly for your good wishes about my getting hold a new theory of gravity. I'll remember them kindly. But for the moment I'll stick with GR!