Recent content by Matterwave

This helped me visualize different geodesics between two points one which maximizes and one which only extremizes. Thanks! It was crucial to clearing up my confusion.

I reread the sections carefully. I *think* I have resolved my confusion. The core confusion indeed came from my reading of "extremal" as "maximal" and my inherent intuition to keep that around in my head. Wald states several theorems (e.g. 9.3.5 and 9.4.2/9.4.3 as pointed out by Peter) which...

Let me digest and reread the section when I get a chance. I'll be back if I have more questions! :)

My (very) rough sketch of the set up of the time-like singularity theorems as presented by Wald: 1. Get Raychaduri eqns and find that caustics form within finite proper time (given SEC and initially negative expansion). 2. Find conjugate points corresponding to those caustics between points in...

I would like to hear more about this :) I'm just now getting to the section in Khinchin where he makes the formal analogy/conversion between phase space measures and probability measure. I think he will set up the CLT soon to handle the N->inf limit explicitly without invoking general ergodicity.

Maybe the closest way I know how to steer this towards physics and not philosophy: If I knew everything there is to know about a microcanonical ensemble (i.e. the trajectories of every particle) does that ensemble have 0 entropy or the same entropy as it has if I knew only ##N,V,E##? If the...

Yeah, I don't really have many calculational questions arising from the musings as I am no longer being asked by homework assignments to calculate something. 😂

Note that in non of my discussion w/Peter did either of us try to find the "energy momentum tensor of the gravitational field". We were always talking about the stress-energy-momentum tensor of the matter fields. The SET of the "gravitational field" is subtle. As a tensor, the SET must be well...

Beyond the "are these different definitions the same", this part of just the Boltzmann entropy also bothers me a decent amount.

Link to the video for those interested

My knowledge on the topic, I must admit, come from like watching 2 YouTube videos of Barandeis describing the subject. (From the Robertson Podcast). In one, he debates Tim Maudlin, and Tim's argument that this indivisible interpretation (Tim would certainly call this a theory and not an...

Well it might be true for Boltzmann Entropy and Claussius. Though, I still think the connection is much more tenuous than the work example and especially the "ontological status" is quite different in the entropy sense (is it purely phenomenological? Is it fundamental?) but not so different in...

Yeah I asked my question because, even in the case of Bohmian mechanics, even 60 years later and with "some decent subset of physicists working on it" there are still debates about whether it makes any predictions that are not congruous with QM (here's a recent one on whether arrival time...

I think this discussion is a little "above my pay grade". As I have not read the paper in detail, a lot of these arguments are going over my head haha. It seems I probably need to "go read the paper" to even have anything intelligent to say here. 😂

Yes indeed, but the situation for Entropy somehow feels more pronounced. For in your example, at least when we consider piston-like objects doing work, the PdV work is at least very similar formally to Fdx work. And for me, this seems intuitive. But in the case of Entropy, I am aware of various...