Dear Jochen,
I have enjoyed reading your deep essay. Thank you for the insights.
From my side, I tend to agree with Einstein that qm is incomplete. But it turns out that to make it complete one has to also modify relativity and spacetime-structure. I explain this in my recent paper
Nature does not play dice at thePlanck scale
I will value your critique of these ideas.
Many thanks,
Tejinder
Hi Jochen,
My May 6 response to your question -- "Your notions regarding---if I interpret you correctly---an inherent thermal 'noise' making the acquiring of perfect information about a system impossible remind me of Nelsonian stochastic mechanics. Is there a connection?" -- was at best misleading.
Thermal randomness applies to random fluctuations in energy levels, as defined by Boltzmann's partition function at a given temperature. In my dissipative dynamics conceptual model, thermal randomness is contextually defined at the system's positive ambient temperature(*). The randomness of ground-state energy is "irreducible," meaning its statistical description is complete and reflects perfect information. There are no hidden variables. So--I do not see any connection with Nelson's stochastic mechanics. Further discussion can be found in my Medium essay, Reinventing Time.
Harrison
(*) Conventional interpretations (conceptual models) define thermal randomness either at absolute zero (deterministic mechanics) or at the system temperature (thermodynamics) in order to avoid contextuality.
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 Jochen,
Thank you so much for your clear answer.
This was made clear. This open question will be solved in your future research.
Best wishes,
Yutaka
Hi Jochen,
A clear explanation of a complex topic to a broad audience. Very good.
If we view time as a function of entropy with entropy only having meaning for a collection of particles then time becomes the non-local.
All the best,
Jeff Schmitz
Dear Jochen,
This is a very sophisticated and impressive work. I had not heard of Lawvere, now I see I should have. I reference related issues of quantum mechanics to the correlations you address, in particular the inability of realistic "signaling" models to explain the strong correlations of entanglement. (https://fqxi.org/community/forum/topic/3548)
Dear Jochen,
It is great that you finished at the top in community rankings! Wonderful All the best for the next round too :-)
I have seen the paper by Dragan and Ekert and like it a lot [I was one of their referees for the journal!] : It would be great if someone explored the connection of their idea with Adler's trace dynamics, and my approach.
Indeed I think both relativity and quantum theory have to give in, and be replaced by an underlying theory from which they both emerge. Yes, that would make both Bohr and Einstein right, in a way. I agree :-)
Best,
Tejinder
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
Jochen,
Entropy is meaningless for a single particle. Entropy only exists for a collection of particles, the larger the better (to a point). A sound wave is another example of a collective mode. If time is not fundamental, but a function of entropy then time only has a clear meaning for a collection of particles making it non-local.
All the best,
Jeff