Tuesday, December 04, 2007

Lawrence Krauss and the Casimir effect

The December issue of Physics World contains a number of features on dark energy, including this ludicrous piece by Lawrence Krauss. Consider the following statements made by Krauss:

Quantum mechanics, combined with relativity, implies that empty space is full of a wild brew of virtual particles that pop in and out of existence so quickly that we cannot directly detect them. Nevertheless, these particles leave a measurable imprint on everything from the spacing between atomic energy levels to the Casimir force that pushes apart metal plates brought very close together.

One might expect these virtual particles to contribute an energy to empty space, which would result in an identical term to Einstein's original cosmological constant that would lead to universal repulsion and hence an accelerating universe. This form of 'vacuum energy' is gravitationally repulsive because it possesses a negative pressure that is equal and opposite in magnitude to its energy density. In other words, the ratio of the pressure to the energy density — called the 'equation of state' parameter, w — has a value of –1.

This is factually incorrect in a very straightforward fashion: whilst there will be a repulsive force between a concentric pair of spheres, those effects which have typically been considered to be Casimir effects, are examples of an attractive force between a pair of parallel metal plates! The editor of Physics World might have wished to check previous articles on the Casimir effect within his own journal to verify this type of thing, but I guess he must have been otherwise engaged on this occasion.

Theory predicts that the vacuum expectation value for the energy density of the electromagnetic field, will not only be non-zero between the plates, but will be negative. Thus, it is believed by some that the Casimir effect demonstrates the physical existence of negative energy, at least on small scales. This is exactly why the Casimir effect was invoked as a mechanism for holding open wormholes in space, given that the latter require negative energy densities. The vacuum fluctuations between a pair of metal plates do indeed suggest an equation of state with a parameter of w =-1, but in the case of plates which are attracted together, this implies a positive pressure and a negative energy. This is the exact opposite of the conclusion which Krauss attempts to establish, that vacuum energy repels things due to the presence of negative pressure.

Krauss then proceeds to express some doubt that we can ever establish that dark energy is a cosmological constant. His argument is, once again, quite bizarre:

The only way we can determine from observations that dark energy is not a cosmological constant is to somehow measure its equation of state parameter, w, and find that it is not, or was not, equal to –1. If the measured value is indistinguishable from –1 within experimental uncertainties, then we have not learned anything at all because dark energy could either be a cosmological constant or something else less (or more) exotic that behaved very much like it.

If one applied this criterion generally in science, then one would have to conclude that the predicted value of a quantity could never be verified because, well, there are always some error bars associated with the measurement. On the contrary, if a theoretical hypothesis predicts a certain value for some quantity, and the value of that quantity is subsequently measured to agree with the predicted value to within, say, two multiples of the standard deviation due to measurement uncertainties, then one can say that: (i) the prediction has been verified, and (ii) the probability that the hypothesis is true has been considerably increased, in accordance with Bayes' theorem. Of course, if there is an alternative theory, which predicts a similar value for the quantity, then the measured value doesn't enable one to discriminate between the two theories. But, in the case of dark energy, there is, as yet, no theory of any 'exotic' something that behaves like the cosmological constant.

It was Krauss, of course, who suggested a couple of weeks ago that mankind may have reduced the life-expectancy of the universe...


Susan's Husband said...

I don't think you're doing a good job of critiquing Krauss. My two key issues:

1) Negative pressure would mean an attractive force, as normal pressure is a repulsive one. Things move from high pressure to low pressure, the opposite of gravity where things move from low gravity to high gravity. So I completely fail to understand what Kraus means by "gravitationally repulsive because it possesses a negative pressure", as "gravitationally repulsive" is positive pressure. Or is pressure in this field defined oppositely to how it is in statistical mechanics?

2) In the Casimir effect, it's not clear what's being treated as the region of interest. Is it the normal vacuum outside the plates repulsing the plates, i.e. having positive pressure? Or the internal vacuum having negative pressure and attracting the plates? It seems that Kraus is taking the first view, but neither you nor he seems to be explicit about this.

Gordon McCabe said...

1) In general relativity, if a matter field with negative pressure is inserted into the Einstein field equations, it corresponds to a repulsive gravitational force. It is indeed different from statistical mechanics.

2) In the Casimir effect, it is the vacuum fluctuations, and the consequent equation of state, between the metal plates which are under consideration.

Susan's Husband said...

Does "negative pressure" have any meaning other than "a repulsive gravitational force in the Einstein field equations"? I have to say, it seems an extremely poor choice of terminology, even for physicists.

With regard to the Casimir effect, don't you need the external vacuum as well to "push" on the plates? I.e., the net force is a result of differential in the amount of virtual vacuum fluctuations, rather than something intrinsic purely to the internal vacuum? If so, that would be in line with Kraus' claim of "native" vacuum being repulsive, so you get a net attraction since there's less vacuum energy (i.e., negative energy) between the plates.