Recent content by jbergman

Paper is more relaxing. Something about screens annoys me. The only exception are Kindle Paperwhites.

Yes. In Lee's book, he defines a smooth functor with which you can lift constructions on vector spaces to vector bundles. https://en.wikipedia.org/wiki/Smooth_functor

The second doesn't look correct. It should be a multilinear function of sections of the tangent space, not the cotangent space. It's helpful to just look at a vector space since fields over a bundle don't really add that much. But for a vector space ##V## over the field ##\mathbb R##, ##V^*...

Not following all the arguments that closely but I think I agree with Martin. Once you learn some category theory, products are defined as something satisfying a specific universal property and are unique up to isomorphism. It's fairly easy to construct "different" products that satisfy the dame...

I think the context is that the book is from a mathematician who usually proves things. So, it's mostly just making the distinctions between QM, a physical theory, and say a mathematical theory.

I have said similarly before. Barandes' formulation appears to not guarantee properties like continuity and localism.

I don't understand. Why can't you just post your work on a blog or github or YouTube? I have done this before and have good results. What specifically are you looking for?

One other interesting point was that Barandes disputes the idea of a universal wave function for the entire universe. He also views his formalism as describing smaller systems so it seems like he is far from endorsing this as a fundamental ontology as many want to understand QM.

Some of your points are valid, but, he introduces an entirely new set of problems. - Violation of locality. Particle paths are not necessarily continuous. - As Carroll points out, particle behaviors violate expectations of theories like E&M. At this point, there are so many contradictions...

Yes. From the interview he still says he doesn't have much intuition for the theory or have a fundamental ontology. At this point it's just an alternative mathematical formulation of QM which is interesting in and of itself. But it's still a long ways from being an interpretation but maybe this...

Thought this might be of interest for those following Barandes nee interpretation. Carroll always has pretty good interviews. https://www.preposterousuniverse.com/podcast/2025/07/28/323-jacob-barandes-on-indivisible-stochastic-quantum-mechanics/

BTW, I found an old thread that mentions your Lie Derivative approach. https://www.physicsforums.com/threads/unraveling-diracs-general-relativity-equation.734239/ That's an interesting idea and seems correct. Still trying to wrap my head around it since we are dealing with a density induced...

Maybe, maybe not. I was aware of this part. Ok, this part, I was wondering whether ##b^r## was constant or not. I haven't read the book other than this section. Thanks for the clarification. That definitely renders my derivation invalid. I will see if I can salvage it. Look forward to it.

I read the passage around 27.4 and didn't understand Dirac's derivation either. I came up with the following. First we have an active transformation where we move each particle in the dust from $$z^{\mu} \rightarrow z^{\mu} + b^{\mu}$$ Then given this active transformation...

Can you say something about the key differences and benefits of the algebraic approach to quantum physics?