1907 Crisis in Mathematical Physics According to Poincaré
With 2020 hindsight, we all agree that Einstein’s discoveries of 1905 revolutionized nearly every area of fundamental physics. But what did scientists think at the time? One telling source is Poincaré’s 1907 account of the “new crisis” in physics (available here, on the newly released Popular Science archive). Poincaré identifies five fundamental principles he thought were in danger of being overturned:
 Carnot’s principle of heat transfer. Brownian motion was thought to violate Carnot’s principle of heat transfer, since it apparently involved an unlimited source of motion. Poincaré wrote, “to see the world return backward, we no longer have need of the infinitely keen eye of Maxwell’s demon; our microscope suffices.”
 The principle of relativity. Although Einstein had recently defended this principle, Poincaré wasn’t convinced, and in particular worried about the prohibition on superluminal signaling. Anticipating a coming revolution in gravity, he wrote: “are such signals inconceivable, if we admit with Laplace that universal gravitation is transmitted a million times more rapidly than light?”
 Newton’s third law (of actionreaction). Electrodynamics seemed to be suggesting that not every action corresponds to an equal and opposite reaction. In particular, the action of one electric charge on another doesn’t necessarily give rise to a simultaneous reaction.
 Lavoisier’s principle of fixed mass. Alluding to Einstein, Poincaré wrote that electrodynamics suggests a body’s mass might increase with velocity, refuting principle of fixed mass: “And now certain persons think that it seems true to us only because in mechanics merely moderate velocities are considered.”

Mayer’s principle of energy conservation. Finally, the recent discovery of radiation by the Curies suggested to
LaplacePoincaré that radium might be a limitless source of energy, and hence that energy is not locally conserved.
What I find striking about this list is Poincaré’s recognition of the deep and difficult consequences of taking classical electrodynamics seriously — and in particular, of retaining the principle of relativity. Of course, only 3 and 4 were actually overturned, and a version of 4 may still be salvageable (by replacing “mass” with “rest mass”). And it’s somewhat surprising that as late as 1907, Poincaré isn’t mentioning Einstein by name.
But then, I suppose it’s never clear what the revolution will bring until well after it’s over.
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It may not have been unreasonable for Poincare to doubt Einstein’s conventional prohibition on superluminal signaling concerning universal gravitation. In some ways, this was partly why Einstein had to go onwards to General Relativity. Of course, this doesn’t take into consideration future concerns over fasterthanlight movement from the Quantum realm.
This is just such an interesting passage. Poincaré apparently didn’t understand that superluminal signaling is not prohibited by the postulates of special relativity. That’s an extra and unnecessary interpretive assumption (as was recently discussed). You actually can consistently formulate Newtonian gravity — and obviously quantum theory as well — on a relativistic background spacetime. Of course, such signaling is conceptually weird in relativity theory — for example, it means that in certain frames, a signal can propagate backwards in time. But it’s not incompatible, as Poincaré suggests.
I am not so sure what to make of the date of 1907. It could just be “fin de sciècle” crisis as well.
“La Valeuer des la Science” has been published in several editions, and it is not clear to me on which one the translation is based. So, one should be careful when trying to put the text into historical context. For example, it may mean nothing special that Einstein is not mentioned.
I have heard a few times that Poincaré did show that implementing retardation into Newtonian gravity is incompatible with the stability of planetary orbits – obviously relevant to crisis 2 – does anybody know some details about this?
Moreover, that electromagnetic fields may have inertia was proposed before Einstein (ask your favourite Einstein denier ;)…), so this fits well to the crises 4 and 5…
Thanks for the correction Stefan — the original publication seems to have been published in 1905, which explains the lack of Einstein references. (I suppose Popular Science readers were just a bit behind the times.)
Great point about the work of Poincaré on retarded Newtonian gravity. Poincaré published on this in 1905, the same year of this article — see Section 9 here (Springer PDF) or here. This is a more likely explanation of his beef with special relativity in crisis 2: If you replace the fixed mass terms in Newtonian gravitation with their relativistic counterparts, you don’t get an accurate description of planetary orbits. However, some still argue that a more sophisticated kind of relativistic Newtonian gravity is still possible, so the two theories may yet be compatible.
Bryan,
Is the reference to Laplace in point 5 supposed to be to Poincare? I thought Laplace died long before Madam Curie fiddled around with radium.
Haha — indeed, wires must have been crossed. Thanks. Corrected.
Hi Bryan,
thanks for digging out the Poincaré paper “Sur la dynamique de l’electron” It’s amazing that it is available online now, I have been looking for it for years!
No problem Stefan — thanks for the reminder about it!