Boltzmann, Philosopher

I have heard this quote from philosopher of science Paul Feyerabend before:

The withdrawal of philosophy into a “professional” shell of its own has had disastrous consequences. The younger generation of physicists, the Feynmans, the Schwingers, etc., may be very bright; they may be more intelligent than their predecessors, than Bohr, Einstein, Schrodinger, Boltzmann, Mach and so on. But they are uncivilized savages, they lack in philosophical depth — and this is the fault of the very same idea of professionalism which you are now defending.

I haven’t read much of the original works of “the predecessors” – most of my knowledge of their work comes filtered through textbooks and lecturers. I suspect this is true of most physicists. There are some good reasons for this – old papers aren’t easy to get a hold of, are awfully typeset, use archaic notation, and most of their content is purely of historical interest.

One exception is a paper I read recently by the great Ludwig Boltzmann, which is titled: On Certain Questions of the Theory of Gases. Its a three page Letter to Nature, a well-known publication which a lot of visitors to this site are trying to find when they Google its name. Here are a few quotes for you to mull over, to see if the “philosophical depth” comes through.

[Even if we had the ideal physical theory], we should still be a long way off what Faust’s famulus hoped to attain, viz, to know everything. But the difficulty of enumerating all the material points of the universe, and of determining the law of mutual force for each pair, would only be a quantitative one; nature would be a difficult problem, but not a mystery for the human mind.

Certainly, therefore, Hertz is right when when he says: “The rigour of science requires, that we distinguish well the undraped figure of nature itself from the gay-coloured vesture with which we clothe it for our pleasure.” But I think the prediliction for nudity would be carried too far if we were to forego every hypothesis. Only that we must not demand too much from hypothesis.

The theory of gases agrees in so many respects with the facts, that we can hardly doubt that in gases certain entities fly about pell mell. Can it seriously be expected that they will behave exactly as aggregates of Newtonian centres of force, or as the rigid bodies of our Mechanics? And how awkward is the human mind in divining the nature of things, when forsaken by the analogy of what we see and touch directly?

Assuming that the universe is great enough, the probability that such a  small part of it as our world should be in its present [low entropy] state, is no longer small. The summits of the [H = -1 x enthropy]curve would represent the worlds where visible motion and life exist.

The letter mostly addresses the objection to Boltzmann’s H-theorem that it appeals to time symmetric physical laws and thus the H-theorem must fail. Boltzmann argues that his proof only aims to show that the probability that H decreases (i.e. entropy increases) is always greater than that it increases. Along the way, we manages to comment on the proper goal of fundamental physics, the dangers of demanding too much from our theories, an anticipation of the problems that physics will face when analogies fail us (a few decades before quantum mechanics), and an attempt to solve the problem of the low entropy of the observable universe by appealing to a multiverse hypothesis. Not bad!

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