Cosmic expansion in quantum gravity

[palmer eldtrich]

Ive often heard that in quantum gravity space time is discrete. One analogy I've heard is to think of spacetime as being made up on space time atoms. In these models when the universe expands, is the number of space time atoms thought to increase?

 

[wabbit]

Hmm... Interesting questions, will see what the experts have to say about this.

My take on this would be to say "yes" because what we call spacetime atoms are more or less Planck-size chuncks so they have a fixed volume, and the larger the total volume, the more "atoms" there should be.

One qualification though : as you said, we are talking about spacetime atoms, and spacetime doesn't expand or change in any way, it is just "there".
But my understanding is that since patial volume is quantized in QG as well, it may be meaningful to talk of "an increasing number(*) of space atoms", or of spacetime atoms intersecting a given (expanding) spatial volume.

And lastly, I think the talk of atoms here, while suggestive, does not refer to something as concrete as ordinary atoms, rather as you say it is a way to talk about the "discreteness" of spacetime.

(*) provided we can meaningfully talk of "number" here: what does it mean to count atoms of space, other than measuring a volume?

Edit: this piece by Smolin, published in Scientific American, may be of interest to you here : Atoms of Space and Time

 

[Quds Akbar]

Maybe yes, because the particles themselves do not expand, but isn't space time has no boundary, we also do not have a complete quantum theory of gravity. But I would say yes, though I am not sure.

 

[mfb]

If you talk about spacetime, then you cannot consider an additional time direction (or you get very exotic models). Spacetime exists, it does not change over time in the same way a ruler does not "change over its length" - it just exists everywhere.

 

[Chalnoth]

I don't think we can be sure without a full quantum theory of gravity, but I strongly suspect the answer is yes: graviton number is not a conserved quantity.

That said, there's a reasonable argument to be had that the total number of degrees of freedom in the universe is an invariant which does not change through time at all. This is a necessary consequence of unitary laws of physics, which are often thought to be a requirement to have a sensible notion of causality.

 

[palmer eldtrich]

Thanks, yes the piece by Smolin, got me thinking about this.
In LQC there is a maximum density to the universe, would that imply there is a minimum number of spacetime atoms?

 

[wabbit]

I was starting to answer your question, by I ended up putting so many qualifications and question marks that it was useless.

In short and handwavingly I would say : if the universe is finite it should reach a minimum volume at the bounce, and inasmuch as counting atoms is the same as measuring volume, then this means a minimum number of atoms.

But I think there are many subtelties here which I do not master, so at best I expect this to be a somewhat true statement in a broad sense.

 

[wabbit]

I don't think we can be sure without a full quantum theory of gravity, but I strongly suspect the answer is yes: graviton number is not a conserved quantity.

Could you please clarify this for me : I am a bit confused by the identification you appear to make of space or spacetime atoms with gravitons, because graviton do not play as far as I know a fundamental role in LQG (and might not be defined in general, especially around high energy configurations such as the bounce), while something like space/spacetime atoms is in a handwaving way present in the spin network/spinfoam description which is I believe general. I must admit it is not clear to me what the graviton looks like in a spinfoam description so I'm probably missing something.

Thanks

Edit : the question was about QG in general, not LQG, so at least that is something I had missed. Still, the sense in which gravitons are spacetime atoms eludes me, beyond something like "they are fundamental excitation of the field so they should be whatever we call atoms", but this still leaves me confused.

 

[Chalnoth]

Could you please clarify this for me : I am a bit confused by the identification you appear to make of space or spacetime atoms with gravitons, because graviton do not play as far as I know a fundamental role in LQG (and might not be defined in general, especially around high energy configurations such as the bounce), while something like space/spacetime atoms is in a way present in the spin network/spinfoam description which is I believe general. I must admit it is not clear to me what the graviton looks like in a spinfoam description so I'm probably missing something.

Thanks

A "spacetime atom" is a fictitious concept that has no bearing in physics. A graviton is a quantized component of the gravitational field, and if anything acts as a "spacetime atom", it's a graviton. And yes, the graviton is a feature of LQG.

 

[wabbit]

A "spacetime atom" is a fictitious concept that has no bearing in physics.

Right, thanks. I was trying to get too much out of a loose analogy here based on the spinfoam picture.
Perhaps not a good analogy either, beyond saying something vague about the discreteness of spacetime.

 

[wabbit]

yes, the graviton is a feature of LQG.

I wasn't doubting that, rather its fundamental status and its applicability around the bounce.

 

[wabbit]

provided we can meaningfully talk of "number" here: what does it mean to count atoms of space, other than measuring a volume?

I'm afraid this statement is misleading : the volume operator of LQG doesn't count anything, because its spectrum while discrete, does not consist of multiples of its smallest eigenvalue.

See http://arxiv.org/abs/gr-qc/0405060 for some horrendously complicated calculations about this spectrum and page 37 therein for a sample table of eigenvalues.

Sorry about that.

 

[CaptDude]

I posted this same question awhile back in a different context. In thay post, Peter Donis gave a good answer to your question you may want to look at. In addition TEFLing also posted a link that fits into your question that I found facinating. That post was titled
Is all the space there is here now, or is space being created?
Here is a link to take you there.

https://www.physicsforums.com/threa...is-here-now-or-is-space-being-created.795973/