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 solid 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 city that is now 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 led 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:
It is immediate obvious that if you throw two coins the combination head-head will have a likelihood of one in four. 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.
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 scientist of all time, and well on his way to becoming a pop icon (think Lady Gaga of Science). Yet, against all odds, Einstein read his paper and immediately recognized its merits. The rest is history.
In his subsequent paper on Quantum Theory of Ideal Monoatomic Gases, Einstein clearly delineated these new statistics, and highlighted the contrast to the classical one that produces unphysical results in the form of an ultraviolet catastrophe. He then applied it to the ideal gas model, uncovering a new quantum state of matter that would only become apparent at extremely low temperatures.
His audacious work set the state for the discovery of yet another fundamental quantum statistic that governs fermions, and set experimental physics on the track to achieving ever lower temperature records in order to find the elusive Bose-Einstein condensate.
This in turn gave additional motivation to the development of better particle traps and laser cooling. Key technologies that are still at the heart of the NIST quantum simulator.
All because of one lousy counting mistake ...
 Actually the source of the quote is somewhat murky - yet clearly inducted into popular culture thanks to Twain (h/t to my fact checking commenters).
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