Epistemic Horizons: This Sentence is 1/√2(|True> + |False>) by Jochen Szangolies

Dear Luca,

if I understand you correctly, I think you've gotten something a little mixed up---Finiteness and Extensibility are the starting points for the reconstruction of quantum mechanics in many recent attempts to justify the formalism from first principles (the way the invariance of the speed of light and the relativity principle are for special relativity). However, that just invites the question---but why are we limited in the amount of information we can obtain about a physical system?

That's the question I'm trying to answer---in other words, Finiteness and Extensibility are the output of my approach, they're what I'm arguing must hold, due to the application of Lawvere's theorem to the notion of measurement. That these principles hold is then equivalent to Assumption 1 being false---there isn't a function f(n,k) such that it yields a value for every state and measurement. There are some measurements on certain states such that it doesn't yield a value (Finiteness, although not quite---you need the argument from the Foundations paper based on Chaitin's theorem for that), and for these, we will learn new information upon measurement (Extensibility).

This doesn't really impinge on the objectivity of quantum phenomena, by the way. My proposal of a relative realism---which I don't really develop in the essay, admittedly---assigns values only to those measurements where f(n,k) yields a value, but that's a perfectly objective statement: in a given state, only those properties where the measurement outcomes can be predicted with certainty actually have definite values.

You can, of course, also interpret this as a subjectivist stance---i. e. claim that there's some real values out there, but our descriptions can't include them. But that's an additional interpretational commitment, nothing that's forced on us by my argument.

Cheers

Jochen

Dear Michael,

thanks for your comment! I'm glad you found my intuitive approach to deriving the Heisenberg uncertainty relation approachable. It can be made more rigorous---for a start in that direction, I refer to the Found. Phys.-paper---but I think this is a virtue of this particular approach: it makes an otherwise 'mysterious' phenomenon somewhat more easily palatable, by connecting it with statements that have a readily appreciable intuitive import.

Thinking about the energy needed to extract the information is an interesting direction. In some sense, there ought to be a relation there---thinking about this in terms of energy and time, rather than momentum and position. But I don't have a clear intuition there yet.

You're right to note that this sort of picture sort of straddles the epistemic/ontic divide. In a way, I'm not so sure it's good to think of these as rigidly distinct---certainly, in some sense at least, what we know about something is not something removed, off in some Cartesian realm of 'thinking stuff', from the physical world: the stuff in our brains is ultimately physical, itself. Hence, what we can know, and how we know it, is in the end also a question of what there is, i. e. what sort of stuff supports our knowledge. There's too much of the old 'detached observer' still lingering in this picture.

Regardless, if you're so inclined, I think it's perfectly well possible to interpret my proposal in epistemic as well as ontic ways. This is, to my way of thinking, an issue that only further argument will be able to settle. So, perhaps it's a topic for another contest!

Cheers, and thanks again for your kind words

Jochen

Dear Branko,

thanks for your comment. I think that your proposal for entanglement would run into trouble with established quantum mechanics, however: for one, quantum particles must be exactly identical---otherwise, quantum statistics would come out wrong, which would lead to easily detectable disagreement with experiment.

But the more important part is that your proposal is essentially a local hidden variable theory---particles have additional properties, not obvious to ordinary measurements, that are responsible for their correlations. But this is just the sort of thing Bell's theorem shows not to be possible---the argument in my essay tells you why: there would then be a probability distribution (whether we know it, or not) for the hidden variables to take on specific values; but this, alone, is enough for all Bell inequalities to be perfectly obeyed. Hence, violation of Bell inequalities tells you that such a picture won't work.

Does this make sense to you?

Cheers

Jochen

Dear Dean,

thanks for your very kind words! I'm happy you got some enjoyment out of my essay.

As for the epistemic vs. ontic question, I'm kinda torn about that. I'm not sure the issue is best framed in these terms---after all, what we know, and can know, depends always on what there is---items of knowledge are, in whatever oblique a way, elements of reality, and even at least supervenient on physical matters of fact, provided one tends towards a materialist metaphysics. So what we call 'epistemic' in that sense is really just a particular way of looking at what's there.

In the other direction, we have of course no unvarnished access to what's out there in the world---whether it's behind the veils of Maya or lurking in Kantian noumena, we (re-)construct the world by means of the phenomena, which are all we can directly access. So what we can know depends on what there is; and what we consider there to be depends on how it is present to us. I'm not sure, then, there's really a hard-and-fast dividing line to be drawn---it may, perhaps, be rather a matter of method: we study the world in an epistemic or ontological way.

So maybe it should not come as too much of a surprise that nobody has yet managed to unscramble the quantum omelette---and perhaps, it's a mistake to try, because the world itself is a mixture of the objective and the subjective. So quantum theory, in my view, can tell us something about what is---for whatever that is, it's something that admits a quantum description at least in some sense---and about what we can know---what information we can hope to obtain about the world.

Hence, I'm not sure if whether the wave function is out there in the world, or in our heads, ultimately makes much of a difference; what's in our heads is in the world, too, after all.

I appreciate the disambiguation regarding Wheeler's 'quantum principle'---but I'd like a bit of elaboration (or perhaps, a pointer to the relevant literature). I don't really know about the connection Wheeler drew between undecidability and space-time (vaguely, in the back of my head, it seems I remember something about building space-time out of a logical calculus, or something along those lines), so I'd love to understand this better!

Cheers

Jochen

Dear Pavel and Dmitry,

thanks for the kind comment! I have taken a look at your essay, and have left a few comments of my own.

I'm glad you've found something of interest in my arguments!

Cheers

Jochen

Dear Del,

thank you for your kind words! I'm glad you liked my offering.

You're also pretty much on point with how I plan to advance my 'program'---a study of Kochen-Specker and Leggett-Garg inequalities will be on my agenda sometime soon. I think the precise conditions for co-measurability of observable need to be thrown into sharper relief---fellow contestant Hippolyte Dourdent, in his essay, has pointed out an analogy between non-simultaneously measurable observables and 'chains' of mutually co-referential, incoherent sets of propositions. I am curious whether I can understand this sort of thing from the perspective of Lawvere's theorem/diagonal arguments.

I've also been thinking about the Frauchiger-Renner 'extended Wigner's friend' in this connection. Let's see whether anything will come out of this!

Cheers, and thanks again for your kind comment,

Jochen

Dear Tejinder,

thanks for reading my essay, and for your kind comment! Your paper looks fascinating, I will have to carve out some time to delve deeper into it. A 'geometrization' of quantum theory (albeit with some algebraic input, it seems) would certainly have been something of great interest to Einstein!

I wonder if you've seen the recent proposal deriving quantum mechanics from special relativity due to Dragan and Ekert: essentially, they take the (usually discarded) superluminal solutions to the defining equations of the Lorentz transformation, and show that keeping them leads to very quantum-like behavior.

I sometimes wonder: with such proposals to get the quantum from relativity, coupled with the proposals to get relativity from the quantum (as in the recent spacetime-from-entanglement program), perhaps we've been talking about the same thing all along! Maybe, in their own sense, both Bohr and Einstein had it right---after all, as the former is supposed to have said, the opposite of a deep truth may also be a deep truth.

Cheers

Jochen