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December 17, 2009

"We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. [..]

We provide an extensive analysis of the lectures and discussions that took place, in the light of current debates about the meaning of quantum theory. The proceedings contain much unexpected material..."

December 8, 2009

This is a little problem which somebody (I forgot who it was) told me many years ago. It was wrapped in a story (I guess something about the physics of heads and tails), which I will not try to reconstruct.

Consider a random process x(t) which generates a series of 0s and 1s, but many more 0s because the probability for x(t) = 1 decreases with t as 1/2^t.

Now assume that we encounter this process not knowing 'how far we are already', in
other words we don't know the value of t.
The question is: "What is the probability to get a 1 ?"

Unfortunately there are two ways to answer this question. The first calculates
the 'expectation value', as a physicist would call it, or 'the mean' as a statistician would put it, which is zero.

In other words, we sum over all possible t with equal weight and have to consider
s = sum( 1/2^t ) with t = 1, 2, ... N; It is not difficult to see that
s = 1/2 + 1/4 + ... equals 1.

The answer is therefore prob(1) = s/N = 1/N and because N is infinite (the process never ends) we get prob(1) = 0.

The second answer simply looks at the definition of the process and points out that
prob(1) = 1/2^T, where T is the current value of t. Although we don't know T it must have some finite value and it is obvious that prob(1) > 0.

So which one is it, prob(1) = 0 or prob(1) > 0? And which one do you prefer, the 'equal weight' or the 'unknown T' answer?

added later: A Fatwa has just been issued, which should end this discussion: prob(1) > 0.

Of course, this would raise the heretic question "if prob(1) is greater than zero, what value does it actually have?" but we will not ask that question.

And it also leaves open my question about the lottery ticket (in the comments).

December 6, 2009

Three stories about quantum gravity ...

Steven Weinberg about asymptotic safety (again).

Chun-Yen Lin, a student of Steven Carlip, tries to find general relativity within 'loop quantum gravity'. (I don't understand enough about l.q.g. to know whether he succeeded.)

... but are they true stories?

In a completely unrelated article at PhysicsWorld Chad Orzel describes experiments which try to determine the electric dipole moment of the electron. These low-energy, high-precision experiments are indeed a search for physics beyond the standard model and so far they can already be used to rule out some 'naive' supersymmetric models.

Stories about atoms and simple molecules.

True stories.

December 5, 2009

"One of the great mysteries of our Solar System is why Uranus is tilted on its side. Surely, if the solar system formed from the same rotating cloud of dust and gas, then all the bodies within it should rotate in the same way. And yet Uranus' axis of rotation lies at 97 degrees to the plane of the solar system.

The standard explanation is that Uranus must have been involved in some kind of interplanetary collision with and earth-sized protoplanet in the early days of the solar system. That's a tempting idea but it has some shortcomings. For example, it doesn't explain why the orbits of the moons of Uranus are similarly tilted, not that of its rings.

Today, Gwenael Boue and Jacques Laskar at the Observatoire de Paris in France put forward another idea. [..]"

arXiv blog

added later: After reading the paper I have to confess that I still don't really understand how the trick works. I would have thought one needs to assume a multipole moment for the planet (Uranus is not a perfect sphere) and/or perhaps some tidal effects, but I don't really see a discussion of that in the paper. Of course, there are a lot of references to previous work...