Those of you who know my writing will know that I don't use many analogies. Analogies have a very useful place in helping people understand difficult concepts, but they also have a tendency to be a end up strained beyond their limits. Now, imagine how I would react to a whole new field of physics that might be best described as "physics by analogy."
The whole field is based on the premise that, when two physically very different situations can be described using the same mathematical model, the conclusions drawn from one situation can be applied to the other. Unfortunately, this is usually applied in situations where the physics in one situation—black holes, for instance—are so extreme that it is difficult, if not impossible, to test any of the conclusions.
It appears I must adjust my attitude and admit that the field as a whole is not useless. I reached this conclusion after reading a paper that uses sound propagation in Bose Einstein condensates (BEC) to throw light on the origin of the largest discrepancy between two calculations ever seen.
You are out by how much?
The Nobel prize in physics for 2011 was awarded to three astronomers who discovered that the rate of our Universe's expansion was increasing. This came as a surprise, because it meant that there was some sort of previously unknown, long-range repulsive force permeating the Universe. A force, however, requires energy, which earned this the moniker dark energy. Using the data obtained from observations, cosmologists calculated the amount of energy required to produce the Universe we observe.
This number only tells us something if we can match it to something else—that is, we need to match the energy in the field with that of some energy source. Unfortunately, this calculation is likely to require a quantum theory of gravity so, although we know how much dark energy is out there, we don't know where it comes from. This, however, does not stop a good theorist. Even without a complete theory, you can often figure out the correct result, even if it doesn't sit on sound foundations.
The best candidate source for dark energy is the energy contained in vacuum fluctuations (otherwise known as zero point energy). These are described very well by quantum mechanics in the absence of gravity. So, cosmologists toted up the amount of energy in the vacuum, and they came to a result that is 10120 times larger than amount of dark energy required for accelerating the expansion of our Universe. The zero point energy contribution to dark energy has been labelled the worst prediction in the history of physics.
Can we learn anything from physics by analogy?
A trio of physicists noted that the physics of sound waves in an expanding BEC appear to be analogous to the physics of the accelerating expansion of the Universe. And, in this case, we know the microscopic source of the energy driving the BEC expansion—acoustic waves—and how much energy they contain. So, the waves can act as a pretend cosmological constant (the cosmological constant is the simplest description of dark energy) and possibly tell us something about the amount of energy in the real one.
They actually found that the energy and the expansion simply cannot match. Now, the analogy between the two is not perfect and it's an analogy, which means we must be cautious in drawing conclusions anyway. Nevertheless, we already know that the two numbers don't match in cosmology, so, what we are interested in here are potential reasons for the mismatch.
There are some interesting hints contained within the work. In this model, the cosmological constant is independent of most of the zero point energy fluctuations. In the BEC, this is a direct result of an energy gap that arises from the presence of a phase transition between a normal gas and a BEC. The authors point out that some attempts to combine quantum mechanics and gravity have such a phase transition, which may provide a similar decoupling between zero point energy modes and the cosmological constant.
The authors also point out that, in their model, gravity seems to be an emergent, collective phenomena. This will warm the heart of Erik Verlinde, one of the leading proponents of such an idea.
So, what makes this work different to other physics by analogy papers. Well, it is not an experimental paper, so it isn't trying to tell us something new about, say, black holes, by studying light in optical fibers. In fact, its main redeeming feature is that it isn't trying to tell us anything new about gravity and the cosmological constant at all. Instead it highlights a potential reason for why something we already know doesn't work, doesn't work. And, in doing so, offers fruitful directions for exploration in cosmology rather than in the field of atomic physics.
Under these conditions, physics by analogy is useful. My hat: consider it eaten.
Physical Review Letters, 2012, DOI: 10.1103/PhysRevLett.108.071101