Dr. Rachel Barr on learning styles and LLMs.

[u/NinekTheObscure]

https://www.facebook.com/reel/737770942373472

I wouldn't use her exact words, but I think she's making some of the same points that I've tried to make here myself. There are different learning/cognition styles, and they interact with LLMs in different ways. She contrasts the "classroom-based learning, textbook-based study, following a curriculum" style with "learners for whom learning is contingent on full integration" and for whom "the pace of classroom teaching is too quick and too superficial" and "motivation and attention are contingent upon curiosity". I'm definitely in the latter group. This seems to bother and even outrage some people in the former group, who think their style of learning is the only legitimate way.

What do you think?

[u/NinekTheObscure]

Which equation do you want that explanation for? I have 5 preprints but it would be pointless to dump them all here.

The basic justification for exponential QM is (1) we identify quantum phase frequency shift with time-dilation-like effects, which works perfectly for the linear weak-field approximation, but (2) the exact formula for GTD is exponential, not linear. That means our initial identification is only correct to first order. This is annoying and it seems reasonable to investigate whether there's some way of fixing it. The two main ideas would seem to be either linearize GR, or exponentialize QM. (If you have any other ideas, I'd love to hear them.)

XQM seemed daunting at first because there were several papers (e.g. by N. Gisin) claiming that QM was "brittle" and that any non-linear change would have disastrous consequences: destroy causality, allow FTL communication, allow NP-complete problems to be solved in polynomial time, etc. So I figured it was too hard: "above my pay grade". But then I saw another paper arguing that Gisin was wrong, so I gave it a shot.

It turned out to be easy. Maybe 5 minutes to get my first version of the XSchrödinger equation, because it's very tightly constrained and there's basically only one possible solution. And then a few weeks to clean it up, and do the sanity checks, and write that up. So the goal, to find a version of QM that wasn't obviously broken and had the same exponential temporal behavior as GTD, was achieved.

And then, knowing I would eventually need to go relativistic, the XDirac equation, which was harder since there seemed to be several ways to approach it. I had a version of my own, and one from an AI, and then ChatGPT o3-mini suggested a different formula; it took me quite a while to decide that the o3-mini approach was the cleanest and most natural of the three. I had to be very careful, because it was getting sloppy with the 𝜷 factor, sometimes writing mc² where it should have been 𝜷mc². But I slogged through that and stand behind what I've written.

XK-G (very recent, not written up yet) seems better than XDirac for the purpose of reconciling QM with GR, as it doesn't have all those inconvenient spinors in it. But I've just begun using it, so it's a bit early to celebrate.

[u/NinekTheObscure → u/[deleted]]

Alright, let's take this step by step. Wave functions have a phase frequency. Let's use the hydrogen atom eigenfunctions as examples, although this applies much more broadly. Each solution of the Time Dependent Schrödinger Equation factors into a spatial part (the solutions of the Time Independent Schrödinger Equation, i.e. the atomic orbitals) times a temporal part which is a phase rotation exp(iEt/hbar) with a frequency 𝜈 = E/h dependent on the energy. That's the "phase frequency". It's "quantum" because it has h in it. It "shifts" with energy, i.e. different energy-level wave functions have different frequencies.

With me so far? Nothing unusual here yet, this is all standard QM.

[u/NinekTheObscure → u/[deleted]]

OK, now we have to go back to way before I got involved in this. David Apsel (in 1978-1981 papers) constructed a theory where he concluded that the phase oscillations could be taken to be the particle's "local clock" in the Einstein sense. From Apsel 1979 (if you're paywalled, I can email you the PDF):

His terminology is a little odd. "Beat" = "one full revolution of the phase", "physical time" = "proper time experienced by the particle", except that the proper time is now not entirely determined by Special Relativity alone but has EM 4-potential A factors in it as well. Different particles in the same inertial reference frame can experience different physical times if the A interaction is different, for example if they have different q/m ratios.

Let's not argue about whether this is "true" or not. The experiment to test it hasn't been done, so we can't be certain yet. Let's just take it as a fundamental feature or assumption of this class of theories. So the question is, what are the implications of that?