Monday, October 13, 2014

Lumo Confuses Himself About Probability - Again

Unfortunately I must report that the Blogfather has once again gotten himself dizzy while chasing his tail in yet another futile attempt to make his version of Statistical Mechanics make sense. This time he decides that suitable mutilation of the concept of probability will do the trick:

But what's important to notice is that the meaning of the probability always refers to the situation

a property is unknown/blurred at t=1−ϵ it is well-known/sharp at t=1+ϵ

The two signs simply cannot be interchanged. The very meaning i.e. the right interpretation of the wave function or the phase space probability distribution is in terms of probabilities so the time-reversal-breaking quote above is inevitably understood in every and any discussion about probability distributions and wave functions.

He is trying to tell us that probability only applies to prediction of the future - though the stuff about wave functions and quantum mechanics is thrown in mostly for obfuscation. Oddly enough, he forgets one of the more familiar roles of probability in particle physics - his subdiscipline - is in retrodiction. Suppose one is measuring the cross section for a particular type of event as a function of energy and one notices more events at one energy than the rest. The question one then wants to answer is what is the probability that the current state resulted from the various possible or imaginable states in the past - is the bump in your curve a fluctuation or does it indicate resonance producing a real change in cross section.

Probability is a more versatile concept than is imagined in the Lumonator's world. We use it in a for more time symmetric fashion than he imagines. Of course all these ideas, including the unitary evolution of the quantum state, have been discussed by more subtle minds than mine or Lumos. He really ought to read some of them.