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

Dear Rafael,

thanks for having a look at my essay. I will try to find some time to read yours.

As for finiteness and extensibility, perhaps it helps to consider Spekkens' toy model, which demonstrates many of the features of quantum mechanics. The basic idea there is the 'knowledge balance principle': "the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge."

In other words, if your have one bit of information about the state of the system, you must also lack one bit of information that could be gained by additional measurement. But if you perform that measurement, then you'd have two bits of knowledge, and no further knowledge could be obtained; hence, to make things come out right with the knowledge balance principle, the state of the system must change so that the previous knowledge no longer applies.

It's similar with my model. You can think of this as trying to localize a system further within its state space: some amount of knowledge will allow you to perform this localization to a certain degree of precision. If only 'finiteness' were true, then well, that might just be it: you've localized the system as well as it's possible to localize it.

But 'extensibility' implies that you can obtain additional information. For instance, if the system (in state space) is localized to some degree along one axis, you can try to increase its localization along that axis by making a more highly fine-grained measurement; but to cope with the finiteness-requirement, its localization must consequently decrease along another axis. You can visualize this like squeezing a bubble, or a squishy ball: the volume (the total localization/total information you have) stays the same (equal to a power of Planck's constant), but the shape will deform, yielding information gain in one property, compensated by loss along another.

Does this make matters more clear?

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

Dear Tejinder,

thanks for the good wishes! Last I checked, I was in second place in the community voting, after Klaas Landsmann's essay---which I would've been more than happy with, it's definitely one of my favorites!---but it seems votes are up for review still, anyway.

I will definitely have to carve out some time to get more familiar with your approach, it seems intriguing. I have some vague familiarity with Adler's trace dynamics, because I was very interested in his quaternionic quantum mechanics at one time.

Cheers, and best of luck to you, too

Jochen

Dear Jeffrey,

thanks for your kind comment.

Your point about entropy and time resonates with something like Julian Barbour's approach---in a way, that the past is, well, the past is due to the fact that only higher-entropy states can 'remember' lower-entropy states, so if we view time just as a collection of moments, the ordering emerges just from the way records include that which they record.

Time is then 'non-local' in the sense that we start out with a certain foliation (a sequence of 'nows'), which however still can yield the dynamics of general relativity (as Barbour shows with his 'shape dynamics').

But this is basically just free association.

Cheers

Jochen

Dear Neil,

Lawvere's work is very well known in the category theory community, but perhaps not so much beyond it---perhaps less than it ought to be, given its breadth and depth.

I'm sorry to have missed your essay during the voting, it sounds very intriguing. Still, I will try and find some time to give it a read.

Cheers

Jochen