Lies, Damned Lies, and Quantum Statistics

Lies, Damned Lies, and Quantum Statistics?
Posted on August 4, 2012 by Henning Dekant

Statistics has a bad reputation, and has had for a long time, as demonstrated by Mark Twain's famous quote that I paraphrased to use as the title of this blog post.

Of course physics is supposed to be above the fudging of statistical numbers to make a point. Well, on second thought, theoretical physics should be above fudging (in the experimental branch, things are not so clear cut).

Statistical physics is strictly about employing all mathematically sound methods to deal with uncertainty. This program turned out to be incredibly powerful, and gave a sound foundation to the thermodynamic laws. The latter were empirically derived previously, but only really started to make sense once statistical mechanics came into its own, and temperature was understood to be due to the Brownian motion. Incidentally, this was also the field that first attracted a young Einstein's attention. Among all his other accomplishments, his paper on the matter that finally settled the debate if atoms were for real or just a useful model is often overlooked. (It is mindboggling that within a short span 0f just 40 years ('05-'45) science went from completely accepting the reality of atoms, to splitting them and unleashing nuclear destruction).

Having early on cut his teeth on statistical mechanics, it shouldn't come as a surprise that Einstein's last great contribution to physics went back to this field. And it all started with fudging the numbers, in a far remote place, one that Einstein had probably never even heard of.

In the capital of Bangladesh, a brilliant but entirely unknown scholar named Satyendra Nath Bose made a mistake when trying to demonstrate to his students that the contemporary theory of radiation was inadequate and contradicted experimental evidence. It was a trivial mistake, simply a matter of not counting correctly. What added insult to injury, it lead to a result that was in accordance with the the correct electromagnetic radiation spectrum. A lesser person may have just erased the blackboard and dismissed the class, but Bose realized that there was some deeper truth lurking beneath the seemingly trivial oversight.

What Bose stumbled upon was a new way of counting quantum particles. Conventionally, if you have two particles that can only take on two states, you can model them as you would the probabilities for a coin toss. Lets say you toss two coins at the same time; the following table shows the possible outcomes:
Coin 1
Head Tail
Coin 2 Head HH HT
Tail TH TT

It is immediate obvious that if you throw to coins the combination head-head will have a likelihood of 25%. But if you have the kind of "quantum coins" that Bose stumbled upon then nature behaves rather different. Nature does not distinguish between the states tails-head and head-tails i.e. the two states marked green in the table. Rather it just treats these two states as one and the same.

In the quantum domain nature plays the ultimate shell game. If these shells were bosons the universe would not allow you to notice if they switch places.

This means, rather than four possible outcomes in the quantum world, we only have three, and the probability for them is evenly spread, i.e. assigning a one-third chance to our heads-heads quantum coin toss.

Bose found out the hard way that if you try to publish something that completely goes against the conventional wisdom, and you have to go through a peer review process, your chances of having your paper accepted are almost nil (some things never change).

That's where Einstein came into the picture. Bose penned a very respectful letter to Einstein, who at the time was already the most famous scie

Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/Sq2uVlGoBkg/lies-damned-lies-and-quantum-statistics

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