# Zero-point energy density evaluation

1. Oct 20, 2014

### Helios

Dear cosmology people,
What is a theoretical value for the zero-point energy density of the vacuum? It must be hard to know or even controversial. Even though the zero point field is a QFT topic, the question seems to be cosmological, because only the cosmologist seem to be forthcoming on the matter. Furthermore, a lot of sources seem to talk up a good understanding, but then they either don't ever get around to giving up a value or they do and don't even get the dimensional units right. Pascals could be correct for energy density.

2. Oct 20, 2014

### George Jones

Staff Emeritus
Nobody knows how to calculate this. For a technical review (but interesting even when just skimmed), see

http://arxiv.org/abs/1205.3365

3. Oct 22, 2014

### Clayjay

I think the value has not been determined but but I think it has been determined the value will be negative.

4. Oct 26, 2014

### Staff: Mentor

Why do you think that? The best-fit value in our current cosmological models is positive.

5. Oct 27, 2014

### Helios

Does PeterDonis suggest that the same best-fit value applies to all our current cosmological models? That would seem incredible. Can PeterDonis cite a value he has seen?

6. Oct 27, 2014

### Staff: Mentor

First, a short note: you're allowed to address the person you're responding to directly; as in, "do you suggest..." as opposed to "does PeterDonis suggest...".

The answer to your question is yes, because the current best-fit value is based on observations with which any model must be consistent.

How so?

http://en.wikipedia.org/wiki/Cosmological_constant#Positive_value

7. Oct 27, 2014

### Helios

There is no value for the zero-point energy density of the vacuum at the link you give, ( as far as I can see ). So far, the OP question remains unanswered. I agree with Clayjay that the value is negative. That's the theory.

8. Oct 27, 2014

### Chronos

There may be some confusion here. In the article referenced by PeterDonis it is noted "A positive vacuum energy density resulting from a cosmological constant implies a negative pressure, and vice versa. If the energy density is positive, the associated negative pressure will drive an accelerated expansion of the universe, as observed." Putting a number to the vacuum energy density requires putting numbers to other values in the Einstein Field Equation, which are also unknown. Based on measurements which can be made observationally, it is easier to express the cosmological constant as a ratio of vacuum energy density to the critical energy density of the universe. Since all measurements to date suggest the universe is flat to the limit of our ability to measure, this ratio [known as omega] has been deduced to be about 0.7. So, to sum up, a positive vacuum energy density predicts an expanding universe, which is exactly what we see.

9. Oct 27, 2014

### Staff: Mentor

Did you see this?

"the cosmological constant, which is measured to be on the order of $10^{−52} m^{−2}$, in metric units."

That's a value for the vacuum energy density ("cosmological constant" is just another word for the same thing).

10. Oct 27, 2014

### Staff: Mentor

What theory? Can you give a reference?

11. Oct 27, 2014

### Helios

Chronos: I can only find the critical density of the universe value and not the critical energy density of the universe, so the calculation I can't complete.

PeterDonis: We don't agree about dimensional analysis.
energy density = pressure ( Pascals ) = Joules per cubic meter

unless metric units have some tricky meaning

12. Oct 27, 2014

### Staff: Mentor

I don't think that's the issue; the Wikipedia page was just very badly worded as regards the system of units being used. See below.

In ordinary SI units, yes. But in geometric units, which are commonly used in relativity, energy and mass have units of length, so energy density has units of length per length cubed, or inverse length squared, just like curvature. In fact, the key reason why these units are used in GR is so that the Einstein Field Equation can be written in simple form, with curvature on the left and energy density on the right and no unit conversion factors required (similar to the way time and distance are given the same units in SR to make the equations simpler).

The Wikipedia page should have said "geometric units" (or perhaps "geometric units with SI units of length"). Note, however, that it goes on to give equivalent values in other units, including $g / cm^3$, so it's clear from context that they are not using "metric units" in the ordinary sense when referring to the $10^{-52}$ value.

13. Oct 27, 2014

### Helios

OK, I see now. Energy density is positive and pressure is negative in the theoretical context. Geometric units are converted to SI ( for energy density ) by a conversion factor GC^-4.

I'm still wondering if there's a difference between the critical density of the universe and the critical energy density of the universe, that Chronos brought up.

14. Oct 27, 2014

### Staff: Mentor

For the cosmological constant/vacuum energy density, yes. (Of course this isn't true for ordinary matter or radiation.)

Exactly.

I don't think so, other than the different units that are used in different sources.

15. Oct 28, 2014

### Clayjay

The thought entered my head by way of the Richard Feynman lectures. Wheeler and Dirac made the same reference and Feynman worked with them. The thought experiment example that Feynman used was " There is enough negative energy in a teaspoon of of vacuum energy to boil away all the water on earth."

I anticipate Feynman was using a relative value context and the "positive" value is in an absolute context.

16. Oct 28, 2014

### bapowell

Negative vacuum energy densities arise in cases of nontrivial topology, for example, in spaces with boundaries as in the Casimir effect. Calculations of this nature that are relevant to cosmology were done by Ford back in the 70's: http://journals.aps.org/prd/abstract/10.1103/PhysRevD.11.3370, and I believe Birrell and Davies have more detailed accounts of similar calculations. Negative energy densities are found for certain compactified geometries like cylinders.

17. Oct 28, 2014

### Torbjorn_L

FWIW the discussion of 'what has been determined', the current best theoretical estimate for the vacuum energy given by George Jones's excellent reference is negative:

vac ≃ −2 × 108 GeV4 + [other therms]"

[p48; derived from the standard model for particles]

But that is still 50+ oom from the cosmological/astronomical values for the same.

Last edited: Oct 28, 2014
18. Oct 28, 2014

### Chronos

You have misinterpreted the paper. The '[other therms]' cannot be safely ignored and the consensus is vacuum energy density is, in fact, positive. See http://math.ucr.edu/home/baez/vacuum.html for further discussion.

19. Oct 29, 2014

### Torbjorn_L

I don't think I misunderstood the paper, it is the best current estimate. The consensus comes from the work Peter Donis and bapowell describes, how the trivial topology that is our universe in fact has positive cosmological constant. That is the 2nd part of that paper, which finishes with putting the (not complete, but "current best") estimate against what is a fact of nature.

I was inserting it in response to Clayjay up thread:

[/Sheldon]

Thanks for the reference! I remember reading it a while ago, but had no active memory of it. (Now bookmarked.)

The paper is somewhere in Baez's category 3 answer I believe (but haven't checked thoroughly). I like the moral:

"The moral is: for a question like this, you need to know not just the answer but also the assumptions and reasoning that went into the answer. Otherwise you can't make sense of why different people give different answers."

Last edited: Oct 29, 2014
20. Oct 30, 2014

### Clayjay

The "vacuum.html" for me was an excellent synthesis of perspectives that resolves the issues in this thread. Thank you for the reference. I knew the different perspectives but the synthesis of them was very helpful to me to clear up miscommunication. I mentioned "I anticipate Feynman was using a relative value context and the "positive" value is in an absolute context" and Feynman was in a GR context which leads to a negative value and the Quantum mechanics a positive value. That is a context switch and source of miscommunication.