Vacuum energy spectrum, density and constant term....

[asimov42]

Hi all,

A question about the vacuum energy density and spectrum. The only spectrum that is frame invariant involves the cube of the frequency. Is it also possible to have a constant offset term (which would also be frame invariant), to 'adjust' the energy density so it doesn't turn out to be huge? The constant offset would correspond to a harmonic oscillator with frequency zero, which wouldn't make sense. I'm wondering a) if such a term (a constant) has been considered, and b) if there are any hypotheses as to the 'meaning' of the term? (i.e., what would the constant negative offset correspond to physically?)

Thanks!

 

[bhobba]

Vacuum energy was actually one of the first indications of sickness in QFT because its infinite. There is a technique called normal ordering that makes it zero:
https://www.physicsforums.com/threads/zero-point-energy-and-qed-vacuum-state.820670/

Really though its one of the infinities that plague QFT that renormalisation is needed to fix up. Renormalisation is, like most things in QFT, complex. I however did write an insights paper to at least try and give an idea what its on about:
https://www.physicsforums.com/insights/renormalisation-made-easy/

So the answer to your question is most QFT's need a cut-off to make sense - this is the modern Wilsonian view he got a Nobel Prize for. We may not know what that cut-off is, but you need it. With such a cut-off you simply redefine the zero energy to be the cut-off and you don't have a problem.

As I explained in other threads you started vacuum energy doesn't have any observable consequences so its rather moot if its any concern at all. Certainly nobody has figured out how to extract its energy..

Thanks
Bill

 

[asimov42]

Hi Bill,

Ah, great thanks - the other threads were very helpful as well. Re: the vacuum energy not having any observable consequences - shouldn't this affect spacetime curvature in some way?

Thanks again.
J.

 

[bhobba]

Ah, great thanks - the other threads were very helpful as well. Re: the vacuum energy not having any observable consequences - shouldn't this affect spacetime curvature in some way?

Yes it should - but like all things in QFT the situation is complex:
http://math.ucr.edu/home/baez/vacuum.html

As John Baez points out, and I mentioned, in QFT only energy differences matter so it has no observable consequences. But gravity is the issue - that gives an unambiguous indication. This is a BIG problem that to the best of my knowledge has no current solution.

But of course solutions have been proposed.
http://www.calphysics.org/zpe.html

But right now we simply do not know.

Thanks
Bill