In December 1925, a 24 year old Grete Hermann declared to her doctoral advisor - the great Emmy Noether - that she would become private assistant to Leonard Nelson, the controversial Frisean neo-Kantian socialist. Noether, who had made sure there was a university position waiting for Hermann, responded
‘She studies mathematics for four years and suddenly discovers philosophy in her heart!’
Nelson’s ISK promoted an “ethical socialism” distinct from the democratic socialism of the SPD and the Marxist socialism of the KPD. Members - including Hermann - were expected to live up to the ethical standard which the ISK derived from Kantian philosophy: vegetarianism, non-smoking, atheism, membership in trade unions and - that most Kantian of virtues - punctuality. With this and her pioneering work in computational algebra she is, except for the bit about punctuality, the precursor to a certain part of Twitter.
At the same time, the third paper on matrix mechanics by Heisenberg, Born & Jordan was emerging from the German press. This marked the first time that a mathematical theory which consistently applied the physical principles of quantum theory - called by Bohr ‘complementarity’ and ‘correspondence1’. By consistently applied, I mean “applied not only to the final set of equations, but to each step of derivation”.
From a classical mechanics point of view, the remarkable thing about ‘the quantum algorithm’ as it was called, is that the output depends on partial input of two states rather total input of one state. In Dirac’s notation, the values of each component of an operator depend on both the ‘ket’ and the ‘bra’.
How you understand this fact not only determines your interpretation of quantum mechanics but essentially is your interpretation.
Why does every German do that pose? Anyway, Kant had placed what he called the ‘limits of reason’ at the center of science. The most obvious limit of reason is the inability to reasonably derive a contradictory statement from a true statement. Therefore we may say that any premise which leads reasonably to a contradiction is false (so called ‘intuitionistic negation’).
There are many ways to understand this. For instance, one could, with Sellars, see this as a semantic constraint on the word ‘reasonably’. One can then understand ‘reasonably’ as a modal operator that works like ‘necessarily’ or ‘really’, whose meaning like all other words is historically determined. This is how Brandom gets Hegel out of Kant & Wittgenstein.
Kant went further to describe less obvious, more positive limits of reason. For example, in the critical B130s of Critique Of Pure Reason
‘If (in another example) I perceive the freezing of water, I apprehend two states (of fluidity and solidity) as ones standing in a relation of time to each other. But in time, on which I ground the appearance as inner intuition, I represent necessary synthetic unity of the manifold, with out which that relatione could not be determinately given in an intuition (with regard to the temporal sequence). But now this synthetic unity, as the a priori condition under which I combine the manifold of an intuition in general, if I abstract from the constant form of my inner intuition, time, is the category of cause, through which, if I apply it to my sensibility, I determine everything that happens in time in general as far as its relation is concerned. Thus the apprehension in such an occurrence, hence the occurrence itself, as far as possible perception is concerned, stands under the concept of the relation of effects and causes, and so in all other cases.’
Cause relieves the tension between the apparent continuity of perception and its actual coarse graining. That is to say: the system at one microact of attention is in one state, at another in another and we save the appearance of continuous attention by the concept of a cause.
Non-Kantians - like me - tend to read the use of ‘I’ in the translated paragraph as entailing that Kant has a subjective notion of reason. It is important to remember that Kantians in general do not.
Kantians - like Grete Hermann - would, of course and correctly, say this passage doesn’t need a classical mechanics notion of cause. Kant’s account applies equally well to a perception of freezing in a dream. Kant’s connection to mechanics comes in after a long logical, empirical and social process of objectification which maintains its stability through many redundant moving parts. The dang ol’ Copernican Revolution.
Let’s put a sharp end on this by an example: Bohr’s wonderful one-slit experiment. Alice2 stands to the left of an experimental apparatus, a rigid screen with a single slit in it. The screen is attached to a piezoelectric which allows Alice to measure either the momentum of the screen by the instantaneous value of charge or the distance from neutral by an accumulator. Meanwhile in the distance, Bob has a large photographic plate. He can either keep the plate open, determining the position of the particle, or use a prism, which would tell him the momentum.
Now let a gamma ray pass through the system. Bob can measure a precise position if and only if Alice decided to turn on the accumulator.
At least one of the directions of this ‘if and only if’ is deeply odd. Bob has measured a fact about Alice, despite the fact that - by the Pythagorean theorem - Bob and Alice are spacelike separated. They can’t be physically interacting and yet knowledge has been gained.
Notice incidentally, there is no indeterminism here: Bob and Alice are both getting sharp position measurements. The issue is the two state input nature of quantum algorithm.
One can start the walk back to Kant by presuming that Alice freezes liquid water iff she sees a sharp position. Bob’s notion of the water goes from liquid to solid without the possibility of a cause between himself and the water.
To get all the way back into my pseudo-Kantian terms, the notion of cause (at least, not physical cause) can’t possibly be relieving the tension between Bob’s subjectively continuous attention to the water and his actual coarse grained microattentions.
One can phrase this more intuitively but less sharply without relativity. In exactly the same sense that Alice causes Bob’s sharp measurement, Bob causes Alice’s sharp measurement despite the fact that Alice’s measurement came first.
Finally back to Hermann as a philosopher of physics. Hermann began publishing serious philosophy of physics in 1935. As the below articles leapt from the press, the Nuremberg Laws were oozing out of the Reichstag.
With respect to quantum mechanics, Hermann was a Bohrist. She consistently described quantum mechanics as a theory through an interplay of complementarity, correspondence and the discreteness implied by Planck’s quantum of action.
Hermann is increasingly, and deservedly, famous for her warpath against subjectivist interpretations of quantum mechanics - in particular, von Neumann’s mental interpretation. The following quote from The Foundations Of Quantum Mechanics In The Philosophy of Nature is typical:
‘This subjective interpretation is incompatible with the derivation of these relations from the dualism of wave and particle pictures: by also subjecting each atomic process to the characteristics of the wave picture, one restricts the application of the corpuscular picture in such a way that not all characteristics of moving point masses - in the classical sense - can be properties of the moving electron as well.’
Hermann also had no truck with hidden variable theories. The following, from Determinism And Quantum Mechanics, sums up her attitude
So how did Hermann rescue causality from Bohr and Heisenberg? I can do no better than her own summary:
‘Even for events which cannot be calculated in advance, quantum mechanics provides a causal explanation and verifies it via predictions. But this verification is achieved in a roundabout way: from events which cannot be calculated predictively their cause is inferred retrodictively; and assuming this cause existed, one can then in turn derive predictions of coming events whose occurrence can be verified empirically.’
Reading this outside the context of Kantian philosophy one can see the reason that Hermann didn’t make it into the textbooks. Heroic retrodictive causality just parses too easily into villainous retrocausality to be of more than peripheral interest to the physicist.
She also had the disadvantage of her time consuming hobby of being a leading anti-Nazi resistance agent.
The difference between retrodictive causality and retrocausality can be illustrated by walking back over our bridge to relativity. Nothing about Bob or Alice’s sharp measurements are mysterious, perfectly normal causation by the gamma ray. Only their relation to each other is mysterious. Bob’s local attention to his film has taught him that Alice turned the accumulator on.
Bob has, in essence, paid insufficient attention to Alice. He has to think of her in her own proper time in order to transfer his attention properly. He doesn’t know what her proper time is like until he gets that information, but once he knows causality works as normal. For instance, he knows that she will now freeze the water.
Anyway, do I think that Hermann is successful in rescuing Kant from the jaws of Bohr? Yes, as I argued just a second ago retrodictive causality is a disguised version of local causality - a real physical principle.
I do think that Kant believed that global causality would turn out to be an objective empirical truth in his sense. I agree with the neo-Kantians that he doesn’t need it to be true even if he thought it was true.
The crucial distinction in Kant is between acting for a reason - which leaves you free - and acting from a cause - which does not. Siting down versus being chained down. Crawling down the mountain versus tumbling down.
The fragment ‘which leaves you free’ seems to require ‘could have done otherwise’. But this is a poor excuse for analysis. As Dennett has emphasized, we often say about a woman who acts for her own reasons ‘She is so determined!’. As Ernst Cassirer put it in 1935
In other words, the two input nature of the quantum algorithm is so distant from the unity (or perhaps emptiness, but certainly less than two) of I that one can only pass between them through the loosest of relations.
This two pronged attack by Hermann and Cassirer (on the sides of science and ethics respectively) does, I think, successfully defend Kant - or a neo-Kantianism - as a viable philosophy.
Oh my goodness, Hermann is doing the Kant portrait pose in the first photo I posted. That’s hilarious, all Kantians should have to do that.
Not to get to deep into Bohr exegesis at this point, but I want to warn against ‘correspondence’ meaning a “limit connecting classical and quantum theory”.
In Bohr’s original presentation he doesn’t personify, but talks about the screen and optical far field themselves. This is in many ways superior, but lacks charm and goes a long way to the widespread perception of coldness.