New video. Released a new, more complete, video on the classical limit. It’s also a way to participate in Curt Jaimungal's #CORE1 initiative, which I think it's a brilliant idea!
New brief. Wrote a new brief that tries to formalize the argument that I had already showed in a previous video. This is an attempt to “dress up” Reverse Physics, and make it look more like the type of things one does in mathematical logic and Reverse Mathematics. It will probably evolve, but it’s a decent first try.
More work on Reverse Quantum. Related to the above, I have started to work more on the Reverse Physics of Quantum Mechanics. I finally have a list of conditions with their likely logical relationships… now I have to “untangle the web” into a sequence that works for the linear exposition of the written word. It’s going to be a pain!
I am finally starting to understand more of infinite dimensional function spaces! It’s funny how you can hold things in your head, but not see the connections… Something clicked on Friday. While I was hoping that the entropy would give us not just a distance function, but it would, in a way, generate the topology of the space, decide what ensemble converges to what ensembles, I have now realized that that can’t be… In fact, I was able to create a sequence of ensembles for which the entropy converges, but the observables do not converge in a meaningful way. The same problem applies in Hilbert spaces… So, I have now another reason as to why Hilbert spaces don’t work, and I think the way one gets the right topology is how one does it in analysis: via the dual space. This is consistent with the idea that topology is experimental verifiability: all measurable statistical quantities (i.e. affine linear functional of ensembles) define the topology.
As other odds and ends, we still have to decide what to do for live-streams. Hopefully we’ll make a decision tomorrow. Thanks for the attention!
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