I Vacuum energy cutoff and Lorentz invariance....

[asimov42]

Sorry, the above is not a very well posed question. If we know that in quantum gravity, one has a family of Poincare invariant Hadamard states that replace the vacuum state in flat QFT, then aren't we happy? In the sense that we have a candidate for the structure of the vacuum in QFT in curved spacetime, which doesn't violate Lorentz invariance (so has vacuum energy zero)? Why the need, then, for concerns about changes at the Planck scale? (I realize this is now, most likely, an exceedingly naive question.)

 

[A. Neumaier]

is each Hadamard state Poincare invariant?

No. And please forget vacuum energy. It is an unphysical, speculative concept only.

 

[asimov42]

Thanks Prof. Neumaier. Could you clarify what is meant by 'unphysical' in relation to vacuum energy? First we had the "vacuum catastrophe" situation, then, through renormalization, the infinite group of infinite frequency oscillators was effectively 'removed,' resulting in a vacuum energy of exactly zero. But what makes the concept unphysical?

 

[A. Neumaier]

what makes the concept unphysical?

Its unobservablilty. Something that is always zero cannot be observed.

 

[asimov42]

Has renormalization completely done away with the older idea of a Planck scale cutoff (since the oscillators are gone)? (I continue to see discussions of the vacuum catastrophe, even from Physics sources, and also claims that some type of cutoff will be needed... both of which I find a bit confusing.)

 

[asimov42]

Sorry to beat a dead horse here, and not to harp on about vacuum energy - I'd asked above about renormalization, and want to make sure I'm clear, on the process and what it actually means:

Beginning with the 'classical' (if that's the right word) vacuum in QFT (harmonic oscillators at every point, infinite energy), one applies renormalization to obtains a physical vacuum in which the oscillators are gone (in fact, as Prof. Neumaier indicated, nothing physical remains). This is much more than simply 'subtracting off the infinities,' in that, as indicated, the predicted physical structure changes. Presumably, this change in structure also fixes the problem with vacuum energy and gravity - if the vacuum energy is zero, then there is no issue with infinite curvature (in GR). Correct so far?

Now, rethinking my question above, there's no need to ask about a Planck scale cutoff, as there's nothing to 'cut off' (given the last paragraph). So, folks talking about the vacuum catastrophe (still) and cutoffs are either not familiar with, or choose not to accept, the idea of renormalization.

Final question: is it not the case that the Unruh effect requires the quantum (physical) vacuum to have a structure that includes a nonzero zero point (vacuum) energy? Without oscillators, how does one disagree on particle number in the inertial vs. the accelerate frame?

Thanks all.

 

[asimov42]

Whoops - so I'm wrong. Quoting vanhees71 is a prior post regarding zero-point energy and GR:

Even in the box-regularized case you get an infinite ground-state energy when doing the calculation in a naive way. The reason for this failure is that the field operators in quantum field theory are operator valued distributions, which you cannot multiply in a mathematically rigorous way. That's why already at this stage you have to renormalize by subtracting the infinite zero-point energy. As long as you neglect gravity, there's no way to observe the absolute value of total energy. Only energy differences between different states of the system are observable quantities, and thus there's no problem in relativistic QFT with the infinite zero-point energy arising from the sloppy calculation of the operator of the total field energy (the Hamiltonian of the free fields in this case).

In cosmology, where General Relativity becomes important, there is a really big problem with this, because even when renormalizing the zero-point energy you need to adjust the corresponding parameters of the Standard model to an extreme accuracy. The reason is that the Higgs boson is a spin-0 field and it's mass is quadratically divergent. This is known as the fine-tuning problem. The question thus is not, why there is "dark energy" but why is it 10^{120} times smaller than expected. It's one of the least understood problems in contemporary physics. A famous review on this issue is

Weinberg, Steven: The cosmological constant problem, Rev. Mod. Phys. 61, 1, 1989
http://link.aps.org/abstract/RMP/V61/P1

So renormalization does not fix the problem in GR... and it appears one does still have zero-point energy after all? Or are the Standard Model parameters adjusted in such a way that they match the physical vacuum determined by renormalization?

Apologies all - I'm just confused - if the QFT vacuum describes a state in which all (renormalized) quantum fields vanish, why do we require such fine tuning for the Standard Model? Here, I think I'm conflating different ideas - I'm unclear on how renormalization seems to solve the problem with infinities, and yet, in the case of GR, the problem seems still to exist (in the form of the need for extreme fine tuning)?

 

[PeterDonis]

So renormalization does not fix the problem in GR... and it appears one does still have zero-point energy after all?

Check out this article by John Baez:

http://math.ucr.edu/home/baez/vacuum.html

A quick summary: the cosmological constant, which our best evidence now says is not zero but small and positive, can be thought of as an energy density of the vacuum. But if we think of it that way, we have the problem that we can't understand why it is so small; our best current theories suggest it should be about 120 orders of magnitude larger.

I'm unclear on how renormalization seems to solve the problem with infinities, and yet, in the case of GR, the problem seems still to exist (in the form of the need for extreme fine tuning)?

Renormalization only solves the problem with a certain limited class of theories. QED and the Standard Model belong to this class, but quantum field theories that include gravity do not. One way of looking at the difference is that in the presence of gravity, energy density causes spacetime curvature, so it's not just differences in energy that have physical significance (as is the case in ordinary QFT in flat spacetime and which is what allows renormalization to work) but the absolute value of energy.

Note that this means the problem in the presence of gravity is not limited to the fine-tuning that vanhees71 referred to. It's more general than that; the need for fine-tuning is just one manifestation of it.

 

[vanhees71]

This old review talk of mine gives a brief intro to the problem:

http://th.physik.uni-frankfurt.de/~hees/publ/cosmo.pdf

 

[AlexCaledin]

Virtual particles do not exist, they are just a heuristic to get a feeling for some things in QFT.

But one could just as well say,

"Real" particles do not exist, they are just a heuristic to get a feeling for those tracks in a detector camera.