Green astronomy Saturday, Jun 28 2008

In matters relating to the Mother Star, Core77 point out a company claiming to build higher-efficiency solar collectors: instead of a flat photo-voltaic cell across the entire collection area, a small-but-more-apparently-more-efficient cell is placed at the focus of a curved mirror:

Now wait just a minute, there. Photons, check. Primary and secondary mirrors, check. CCD-analogue, check. Yes, it’s the world’s smallest, single-band, optical telescope. I for one welcome the prospect of roofs lined with arrays of Solar observatories.

Not to step lightly over the glorious history of start-ups in Mountain View, CA, I am sure that SolFocus have the semi-conductor physics well in hand, though their website contains jargon commensurate with the field of solid-state physics an ambitious new-energy company, and I am not able to understand properly how the cell in the middle is different from regular photo-voltaic cells. Upon reflection, I think we are supposed to conclude that it is exactly the same, but because the cells are the expensive part of the collector and mirrors are cheap, the design provides the same energy as a larger collector at a smaller cost.

In any event, it’s interesting and exciting, like spintronics, about which more needs to be written, and with more clarity.

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Did the universe just get less weird? Friday, Nov 23 2007

At the beginning of this month, New Scientist’s cover story detailed the work of Oxford physicist Joy Christian. He recently released a paper on quant-ph (apparently its a cheap copy of of astro-ph) with the provocative title:

Disproof of Bell’s Theorem by Clifford Algebra Valued Local Variables.

Here’s the idea. Quantum mechanics doesn’t predict deterministic quantities - it only gives the probability of measuring various outcomes. If quantum mechanics is the final word in microscopic physics, then it suggests that, at its most fundamental, the universe is really quite weird - it has a ghostly, fuzzy existence, only making up its mind when observed.

But what if quantum mechanics is just an approximation to a better theory? What if the reason that quantum mechanics only gives us probabilities is that it is ignoring hidden variables?

Enter Bell’s theorem, which states that “no physical theory which is realistic as well as local in a specified sense can reproduce all of the statistical predictions of quantum mechanics.” Roughly, realistic means that reality exists independently of being observed; local means that no physical influence can travel faster than the speed of light. In other words, we either get spooky particles that pop into existence when they are observed, or we mess with causality via ’spooky action at a distance’, as Einstein said.

Enter Christian. He claims that Bell’s reasoning is correct, but relies on an unjustified assumption. Bell assumed that the hidden variables would commute under multiplication: like ordinary numbers, a x b = b x a. Christian claims that if we instead consider non-commutative variables then Bell’s theorem fails. Such variables are provided by Clifford algebras. (Consult Wikipedia and references therein. I know practically nothing about Clifford algebras, other than that they are particularly useful for dealing with rotations).

There have been critics, replies and further work so the debate is not over. This is either the first step in a major revision and extension of quantum mechanics, or the mathematical equivalent of cold fusion. The whole thing thing almost makes me want to go learn Clifford algebras.

Almost.

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Hans Bethe Lectures Saturday, Feb 10 2007

I can’t recall from where I learned of these; thought it was CV but I couldn’t find the link there. Cornell has made available three lectures on quantum physics given by the 93-year old Bethe to folks at his retirement home.

They’re a wonderful overview of the whole of quantum theory, rather than just the quantum mechanics that undergraduates in Australia encounter in rigorous detail. The lack of mathematics means that one gains no facility with calculation whatsoever from watching them, but the concepts are lucid. Also noteworthy is Salpeter and Schweber’s introduction - the latter’s writing on the development of the quantum theory is particularly good.

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Refraction: it’s so hot right now. Friday, Jan 5 2007

Happy New Year!

A pair of interesting results on the common theme of refraction, or more specifically, refractive index, have been published in the last month. The first, reported in last year’s penultimate Nature (subscription required) is a good example of a simple physical question for which an answer is still elusive. The problem is this: what is the momentum of light in media other than the vacuum?

I think questions like these are wonderful for their simplicity, but on the other hand it’s embarrassing to realise modern physics can’t answer them. To see why this is the case, let’s examine some possible responses. We can take as given that light slows down in a non-vacuous media of refractive index n, to have speed c/n. There are two ways to proceed, the first due to Minkowski¹, the second to Abraham².

• The wave equation inside a medium of index n is λν = c/n. The Planck relation for light is E = hν, so that E(λ/h) = n/c, and as the de Broglie momentum is p = h/λ, the result is simple and even requires no Greek letters: p = (nE)/c.
• The postulates of relativity necessitate, after some thought, that E=mc². While it isn’t sensible to talk of light having mass per se, no-one would frown if you wrote out the momentum as ‘mass’ times velocity, and this is just what Abraham did: p = (E/c²)(c/n) = E/nc.

Oh no! The two expressions differ by a factor of n². They are only equivalent for the vacuum case, which is no help at all. For everyday transparent substances, we expect n to be just a bit larger than 1, but enough so n² is a measurable factor. The arbiter is of course experiment, and these have been carried out. Minkowski predicts that the momentum goes up, Abraham that it goes down. Place your bets now.

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