Weekly update
Classical limit paper published, Relatorium seminar, ongoing collaborations and GitHub actions
Here are the news from this week.
Paper on classical limit published. Our paper on the classical limit has finally been published. This was our first paper that came out of a collaboration born on YouTube. Michele Landini saw my video presenting the conjecture and helped us get to the finish line. Quantum mechanics at high entropy looks classical: no mechanism is required. Next step is to prove the converse: quantum mechanics is just classical mechanics with a floor for the entropy. Looking for mathematicians expert in group theory and, in particular, group contractions…
Potential new collaboration in philosophy. We may have found a philosophers interested in working with us on non-additive approaches to probability and state counting in physical theories. Moderately optimist, but we’ll see out it goes!
Moved draft build to GitHub actions. For a long time, we used https://latexonline.cc/ to provide a build for the latest draft of all our work. It’s a fantastic tool! And the author has been super responsive when the service was down. However, the book is getting big, and the build take more than 30 seconds. Since the build is on demand, not really responsive at this point. So, I figured out how to use GitHub actions, found one for LaTex and a new version is built and made available with every push. And now that I know how to use GitHub actions, lots of potential ideas are coming. If any software engineer want to help out, shoot me an e-mail! 😁
Preliminary results for quantum moment problem. We have been meeting with David Carfì, a mathematician expert in both quantum mechanics and functional analysis, to solve crucial technical details about representing quantum states with wavefunctions. One crucial question is: can the state be reconstructed from the expectations of all polynomials of positions and momentum? From that questions, and lots of others we looked at in the past couple of month, David came up with a couple of theorems that are really interesting. So, what started as just a consultation, likely will turn into publications! At some point we’ll have David do a mini-course on our research channel on functional analysis as applied to quantum mechanics.
Online presentation at the Relatorioum. Ted Theodosopoulos kindly invited me to present at the Relatorium, which is available online. We talked about the goals of Assumptions of Physics and some of the open problems. They have a lot of other interesting recorded talks, which you may want to check out.
The weekly YouTube reading group will take a pause next week as I have a conflict. Will resume the following week. Thanks to Negative Entropy for reporting a typo in our open access book.
Congrats on the paper! I got distracted by something else.
What is the status of the project? Also, I must advise taking longer than six months to understand small-scale thermodynamics for safety reasons.
https://www.reddit.com/r/physicsmemes/comments/dx9y72/the_opening_paragraph_to_goodsteins_textbook/?rdt=63905
I believe your premise is that quantum is thermodynamics at small scales. I have a soft spot in my heart for anyone who says to themselves, "This is just thermo, right? This looks like an entropy argument.”
The Schrödinger equation is the classical diffusion equation, the classical heat equation, and we do probability theory with imaginary numbers because pure imaginary numbers lack an order. This order property is useful when there is not enough entropy to define an arrow of time, so everything happens at once in a nonlocal (linear equation) superposition until a measurement increases entropy and provides an order to events. Alternatively, we could use ordered lists for the number of microstates and unordered lists for the number of macrostates from combinatorics. Then use permutation groups to derive the special unitary groups of Lie algebras.
We do want a mechanism for a wavefunction collapse, and that mechanism is an increase in entropy. Specifically, an increase in entropy during a measurement to collapse the wavefunction and produce an overwhelmingly likely macrostate, an observable eigenstate.
The Schrödinger, Klein-Gordon, and Dirac equations are all linear differential equations that are better suited to solving quantum problems in different circumstances. We do not have many methods for solving differential equations. Therefore, linear differential equations and the methods used to solve them are incredibly useful for analyzing linear quantum superpositions. It is immediately obvious that the Einstein field equations are non-linear and incompatible with quantum mechanics.
As the number of elements in a set increases, the number of permutations increases nonlinearly. As the number of atoms increases, so does the system's entropy; the number of microstates increases nonlinearly.
Nonlinear differential equations are even harder to solve than linear differential equations. But luckily, the solutions can converge to an average due to the law of large numbers. In quantum mechanics, we have to apply Ehrenfest's theorem during the transition from a linear superposition to a nonlinear average.
This is all extremely difficult. It would be helpful to have those frictionless elephants and spherical chickens to simplify the assumptions and make these problems algebraic.
If I had to pick one physics axiom, it would be F = m · a. However, it should always be written as F = dP/dt, because if mass is not constant, we must use the chain rule and obtain a non-linear advective term like the one that is present in the Navier-Stokes equation. What is interesting about the Navier-Stokes equation is that it states that, for a fluid, F = (m A + nonlinear) = pressure gradient - frictional forces (viscosity) + external forces (gravity). But the nonlinear advective term comes from the chain rule. In most cases, the volume of a hard particle and its mass density are constant, which means F = dP/dt simplifies to F = mA because dm/dt = 0.
As modern physicists, we know the uncertainty principle is a law of nature. Now, suppose I have a particle with a nuclear cross-section, and it travels through space, carving out a volume of probability space given by its cross-section, projected along a length L. This space it carves out overlaps with the uncertainty in the position of another quantum particle. By decreasing the uncertainty in position by a volume, does this measuring particle increase the volume of uncertainty in the momentum of the quantum particle by the same amount of volume?
According to F = dP/dt, a change in momentum is a force. Does a particle that reduces another particle’s position uncertainty by briefly occupying that position change the momentum uncertainty? Is that change in momentum a force? In this interaction, momentum is not a constant, but is the mass density a constant?
Is there a better way to understand atoms, like maybe spherical harmonics for atomic orbitals, as standing waves produced by coupled oscillations in changing position and momentum uncertainties? Similar to standing waves on a two-dimensional speaker.
https://imgur.com/gallery/science-hkp0u
Can we understand why a massive proton occupying a small volume of the electron's position-space uncertainty creates a force between the particles using the uncertainty principle?
https://m.youtube.com/watch?v=6IWhRffFRc8&t=7m43s
One way to think of the uncertainty principle is to treat entropy as a measure of uncertainty. We can never reduce entropy without increasing it by equal amounts elsewhere.