sgdpk

What are the dubious assumptions in your opinion?

The GHZ/Mermin experiment refined the Bell argument into an "all-or-nothing" experiment with three parties. In that scenario, there are no probabilistic tests. Alice, Bob and Charlie each receive one particle (entangled, of course) and make a local decision to measure one of two quantities of that particle: x or y, each with a binary outcome. The decision to measure x or y is local and beyond the light cone of influence of each.

No matter what they chose to measure, the results are strongly correlated. So much so, that it is clear that you cannot predict every outcome of what the three parties measure. There just isn't a single pre-determined logically consistent assignment of outcomes before the actual measurement (there is a parity restriction of the outcomes).

But the measurements are consistent anyway. So, either there is faster-than-light communication which enforces the consistency, or indeed the outcomes cannot be decided until one of them measures something. It just isn't mathematically possible.

This is also independent of the physical theory by the way. You don't need Schroedinger, Dirac, or anything. Any physical theory that predicts measurements just like QM would will have this restriction. So hidden variables are incompatible with locality (no faster-than-light communication).

Very cool presentation. I loved how he says that they improved dict so much that they basically rediscovered database tables with indices.

Second Axler's book! (probably as a second exposure after a first course, to really understand what's going on in Linear Algebra)

We have been pretty well informed of Musk's shenanigans in Portugal. His sieg heil spread pretty quickly.

Cool :) I am a scientist, so having an easier way to parse the abstracts would be most welcome. Keep up the good work.

It looks great. But it's missing one critical feature of "fast-food" apps like TikTok: the content is not easily digestible. Which is understandable, because scientific papers are dense.

Maybe a good idea would be to parse the abstract through an LLM to make it more understandable (maybe caching the results so it's not expensive)? Maybe also using some standard style, like starting with a couple of "dumbed-down" sentences of the article for the non-expert, and progressively explaining better.

Good read. It is also refreshing to read how Schrödinger came up with his equation even if it was not clear how to interpret it.

He was attempting to formalize de Broglie's "particles as waves" concept, which, according to the article, "could obtain the quantization rules of Niels Bohr and Sommerfeld by demanding that an integer number of waves should be fitted along a stationary orbit."

Schrödinger's equation put that claim on firm mathematical grounds. It gave correct predictions. But just what this new "wave function" was remained up to interpretation.

I don't know about this book, but I highly recommend "Linear Algebra Done Right" by the same author. It is a very clear presentation of Linear Algebra. Although I would recommend it for someone who already took a first course on it.

Thank you for replying! The project seems promising, I'll follow with interest. Hope it goes well :)

Does this handle elimination of variables in a polynomial system (using an eliminating order for Groebner basis)?

This is a visualization of what the states of a qubit can look like in two different physical systems (particle spin / photon polarization). Despite their differences, they can be described using the same mathematical object: a unit vector, here represented on the famous Bloch sphere.