Thanks!

]]>Apparently, one reason Einstein did not get the Nobel prize for general relativity was because Gullstrand was on the Nobel committee. Gullstrand thought Einstein was wrong. Ironically, the Gullstrand Painleve coordinates that were intended to prove this, are now known to be an equivalent formulation of the Schwarzschild solution.

]]>Hmm, I hadn’t known the jury was still out! It’s a pretty big question.

]]>I know, Popper’s star has faded. He’s generally thought to have come second in the long-running debate with Kuhn. But Popper, to my mind, better captures the process of discovery. He offers the metaphor of a net: your hypothesis is a net which you cast into the future, to see what it will catch.

I love this and I think it’s a model of problem-solving that is followed by people in many practical fields: plumbers, electricians, car mechanics. The vital point is to distinguish the hypothesis, or theory, from the discovery (or observation), which is a fact.

My original proposition, perhaps crudely advanced, was that “proof” needn’t have the same meaning in science as in mathematics (or, say, law or history). The methods and criteria are different. I think it’s fair to trace this error to Plato; call it over-reliance on verbal categories.

I don’t fully subscribe to Hersh’s attempt at a ‘humanist’ compromise between Platonism and anti-Platonism. But his book at least has the merit of pointing up the contrast in an accessible way.

Quine (to oversimplify no doubt) took on board the 19th century elaboration of the real number line, and held that such a conception of number was indispensable to physics. Again, this seems to me a step too far.

]]>I also recommend this, which is short and free:

• Helge Kragh, Max Planck: the reluctant revolutionary, *Physics World*, 1 December 2000.

A quote about Planck’s 1900 paper:

Quantum theory was born. Or was it? Surely Planck’s constant had appeared, with the same symbol and roughly the same value as used today. But the essence of quantum theory is energy quantization, and it is far from evident that this is what Planck had in mind. As he explained in a letter written in 1931, the introduction of energy quanta in 1900 was “a purely formal assumption and I really did not give it much thought except that no matter what the cost, I must bring about a positive result”. Planck did not emphasize the discrete nature of energy processes and was unconcerned with the detailed behaviour of his abstract oscillators. Far more interesting than the quantum discontinuity (whatever it meant) was the impressive accuracy of the new radiation law and the constants of nature that appeared in it.

Another:

]]>If Planck did not introduce the hypothesis of energy quanta in 1900, who did? Lorentz and even Boltzmann have been mentioned as candidates, but a far stronger case can be made that it was Einstein who first recognized the essence of quantum theory. Einstein’s remarkable contributions to the early phase of quantum theory are well known and beyond dispute. Most famous is his 1905 theory of light quanta (or photons), but he also made important contributions in 1907 on the quantum theory of the specific heats of solids and in 1909 on energy fluctuations.

There is no doubt that the young Einstein saw deeper than Planck, and that Einstein alone recognized that the quantum discontinuity was an essential part of Planck’s theory of black-body radiation.

Well, one might argue that Quine did a pretty good job “rubbishing” Popper. And when it comes to the history of science, Popper’s “one counterexample disproves a theory” has turned out to be a rather useless viewpoint.

Hirsch’s philosophy of mathematics is definitely off-the-beaten track. Intriguing, but hardly Holy Writ.

]]>pwmiles:

Einstein was following up on Max Planck’s 1900 work on quantisation.

You should read Kuhn’s *Black-Body Theory and the Quantum Discontinuity, 1894–1912*. He argues that Planck did not believe in the quantized emission or absorbtion of light-energy until *after* Einstein’s work. Of course, not everyone agrees with Kuhn’s conclusions, but the issue isn’t as cut-and-dried as your comment suggests.

For a more recent evaluation, see Revisiting the Quantum Discontinuity.

]]>I’m just using “prove” in the everyday sense like: “if you sit down on your chair and it breaks, that proves it wasn’t strong enough to support you”. (Yes, maybe there was some other cause… ).

John, Plato started this line of thought. Paraphrasing a bit >>Surely in the words of our own language (Classical Greek in his case) can be found all the ideas that are necessary<<

It doesn’t work. My hero Popper devoted the entire first volume of ‘The Open Society and its Enemies’ to rubbishing Plato. Another great book on this topic is “What is Mathematics Really” by Reuben Hirsch, sometime emeritus professor at the U of Albuquerque NM.

]]>Tomate wrote:

Do you mean that the integral along a geodesic from any spacetime point to the singularity of the interval is finite?

Yes. This is the time that would be ticked out by your watch as you fell into the black hole—the ‘proper time’.

Do you know where I can find this calculation?

It’s in any decent textbook on general relativity. (We can use this as a definition of “decent textbook”, making the statement tautologously true.) I’m having trouble finding the calculation online, but the result is here:

• Geraint F. Lewis and Juliana Kwan, No way back: maximizing survival time below the Schwarzschild event horizon.

This studies how to maximize the time it takes to hit the singularity by firing your rocket as it falls into a black hole. Once you cross the event horizon there’s a finite upper bound!

]]>Interesting, I was not familiar with that rule! So maybe, morbid as it seems, they had to wait for Hawking to die before they could award a prize for this topic. It's strange that they would have this rule and still feel able to divide the prize in such a way that half is for the theoretical work (to go to Penrose alone) and half is for the experimental work (split between two people). That made it seem like they really wanted to split it evenly between all four people and Penrose only got Hawking's quarter because Hawking had died.

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