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So, I prompt the LLMs a certain way before I asked your questions (hence why you see think, act, observe), and this one has access to wolfram, and it did 2 calculations through the process. I'll just post the response so you can be the judge of them, and maybe it'll inspire you to take a closer...

I attended a conference on quantum spacetimes this week, and I think there are two relevant things I'd like to add. One day, the focus was on singularities, and if they needed to be resolved, and if quantum gravity would solve it. Naively, I assumed the field would be split into 2 distinct...

One of the greats! Relativity became a much better field thanks to his contributions, and when I first learned about ADM I was instantly hooked.

Section 4 of this paper might be useful: https://arxiv.org/pdf/1606.08756.pdf

Interesting update (still reading myself): https://writings.stephenwolfram.com/2023/03/chatgpt-gets-its-wolfram-superpowers/

Exactly the issue I ran into. One of his own papers (that he references a lot to justify the relation in the boltzmann entropy) comes from "D. Fiscaletti, “Perspectives of Bohm’s quantum potential towards a geometrodynamic interpretation of quantum physics. A critical survey”, Reviews in...

So, I'm hesitant to post this because I get a somewhat crack potty feeling to the book (however, he actually does reference some of your papers in the more "normal" section [i.e section 1.5.2 he references https://arxiv.org/abs/quant-ph/0305131]), but I'm not sure if that's because my Bohmian...

The moral thing is to contact them with exactly what you told us here. But it's hard to say no to a free vacation!

I think this is a very interesting question and depends on which field of physics you're in. I like how fresh_42 put it where math is more akin to philosophy, and physics is more akin to nature. In the 60s-80s, some fields saw those who could philosophize nature succeed the most. Wheeler...

Following your format in OP, I wanted to start with some random topic, and keep asking questions... (but will put answers in spoilers since quite long) and give my take away at the end. Me: Write a lecture on the Baltrami identity (wanted to see if it could see that I meant Beltrami) ChatGPT...

You should get this book: https://www.amazon.com/dp/1108928250/?tag=pfamazon01-20 and eventually: https://www.amazon.com/dp/052151407X/?tag=pfamazon01-20 and lastly, a paper that you might find interesting: https://arxiv.org/pdf/1805.00813.pdf They also have some code on...

Bryce DeWitt has a piece called "Why Physics" which you can read for free in the preview here: https://www.amazon.com/dp/3642142699/?tag=pfamazon01-20 I enjoy the whole book, but it may not be what you're looking for.

It sounds like you're living too far in the future and that is causing some anxiety. You have to talk to your advisor. Once you do that you will ACTUALLY know what options you have available to you. Only good can come from this conversation, which you might not be able to recognize due to your...

Of course not, but would I write down ##\frac{1}{\sqrt{2}}## on a math exam? Nope. In a similar vein, would you stop at ##\sqrt{80}##, or would you write ##4\sqrt{5}##? ##\frac{7\sqrt{10}}{\sqrt{2}}## or ##7\sqrt{5}##? Let's make it more algebraic, ##\frac{1}{i-\sqrt{3}}## or...

I would always use this following explanation to high schoolers when I tutored for why they "have" to rationalize their denominators. I personally didn't care, but a lot of teachers would take off points if they don't. In human history, people first started counting things, like how many cows...

Got 3 books recently, 2 by T.D. Lee: Particle Physics and Introduction to Field Theory (an oldie, but hoping for some random insights on topics I'm looking at again) and Symmetries , Asymmetries, and the World of Particles. Also got Speakable and Unspeakable in Quantum Mechanics by Bell, which...

An interesting paper i found today that might be relevant: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.040101 (https://arxiv.org/abs/1110.6169) and a reply to the above paper: https://arxiv.org/abs/1604.05748

Here are 2 metrics you can use as examples: http://sites.science.oregonstate.edu/physics/coursewikis/GGR/book/ggr/schwcurv.html (Schwarzschild) http://sites.science.oregonstate.edu/physics/coursewikis/GGR/book/ggr/rw.html (Robertson-Walker) If you're interested in differential forms, you can...

This seems like a fun book, I will probably be getting it. Thanks for mentioning it!

In essence, this is a bad starting point because if we can't see or detect it, what's the point of thinking about it? Modern science is based on this principle: I can take your theory and predictions and put it to a test and see if it's wrong. I can't say you're correct, I can just say it wasn't...

It sounds like you have issues staying on task and a potential attention disorder. You had a task to do, and instead of finishing it, you pretend that you're doing something more fruitful that garners a "better" understanding of the world. Cool, then if that was the case, why would you be...

This is called getting a doctorate. Getting a doctorate isn't "more coursework" or "reading papers", you are being trained by a professional to do exactly this: formulate ideas rigorously in the attempts to advance your field in a given direction. So no, don't expect a book to spell out ABC...

Yes, but you have to start with one, and complete a project within a time frame. You have to understand, to stay in academia, you have to produce some work. Before you can develop that "special taste" you have to showcase you have a tongue that can taste to begin with. In other words, while you...

Yes, and no. If you're asking if, you, the student can do both at once? Of course, it's just abstract lines we draw to differentiate the fields. Study whatever you want in your free time. The no comes from doing both on a research stint. I would be lying if I never envisioned myself doing it...

I would recommend this then: https://www.amazon.com/dp/0198748566/?tag=pfamazon01-20

Is there a physical significance to logarithm bases in GR? Why not just change the base using basic log properties?

Would you consider the addition of the Gibbons-Hawking-York term a solution to doing GR on manifolds with boundaries?

You don't need lagrange, you need Newton+hamilton+idea of test particle. We, as physicists, use test particles to learn about the behavior and motion about the world around us. Newton's first law is basically "test particles, when left alone, will move in a straight line at a constant speed"...

Another idea: Find papers that cite this paper, and contact those authors to see if they have a copy.

The only other book I knew that did E+M in this formulation was written like 30 years ago: https://www.amazon.com/dp/0387964355/?tag=pfamazon01-20 And... it left me wanting more to say the least! I'm currently reading this, and wow, I'm hooked. Thanks for sharing!

This was the right approach, but your u-sub is too fancy. Use a different u-sub from the expression ##\sqrt{x(16-x^7)}##. It falls into place after that. In this problem you'll have to bring something back from outside the square root (which you'll see once you use the right U-sub), a complete...

I didn't have to self study it, luckily, so I can't comment on a book that would help. However, having self studied other things, the textbook isn't going to make or break you anymore. The most important part of learning, imo, is feedback. Find an author who you can understand and derive the...

If you enjoy analysis, then I'd go for topology, specifically "point-set topology". However, I'm not a mathematician, and I haven't studied that book from Abbott, so I'm not sure how deep he goes in analysis, and the overlapping proof styles. If you're tired of analysis, then go for group...

I guess it depends on "really famous", in relativity, a well known woman is: https://en.wikipedia.org/wiki/Yvonne_Choquet-Bruhat In relativity (she may be classified as a mathematician, but at her time I don't know what the difference really was) as well...

Some interesting lecture notes I found on these theorems, chapter 4 is where you should start, but lecture 21 onward seems the most fruitful if looking for a global application: https://stanford.edu/~sfh/257A.pdf I'll take a look at them deeper in the future, but maybe this can help.

Even times odd is always even, so it would be what I said it was. ##\omega## is one form, ##d\omega## is a two form, thus ##\omega \wedge d\omega = (-1)^{1*2} d\omega \wedge \omega = d\omega \wedge \omega##, but that's besides the point, I didn't think this problem through. I was sloppy with...

##\omega \wedge d\omega = 0##, seems kind of trivially true, no? If ##\omega## is a one form, then it is in the form of ##\omega = h dx## where ##h,dx## are just place holders. By product rule, i get that ##d\omega = dh \wedge dx + h d^2x## since d^2 = 0, the 2nd term vanishes. thus, we're left...

https://www.amazon.com/dp/0486493423/?tag=pfamazon01-20 Another good book IMO

You got a definition backwards, it is said that under an inversion (also known as a parity transformation), that ##\vec{x} \rightarrow -\vec{x}## and as you just said, the cross product remains the same. So, it can't be a polar vector (aka "real vector"), so historically they called it a...

It depends on what your daughter is feeling. I sympathize with her because I've never, not once, went into an exam not nervous/anxious. But that's because they're exams, and their point is to judge our knowledge, and being judged usually invokes an emotional response. Since she has time until...

https://arxiv.org/pdf/1505.06390.pdf Section 4/5 may be what you're looking for, but the paper gives a good historical perspective as well.

I think you're underestimating how competitive physics programs are at top tier unis in most countries if you think 3.8+ is crazy. They're top tier for a reason!

I used this book by Burke to help my dad (former EE) understand some relativistic/cosmological ideas he has seen on the science channel shows (looks like they updated it! I have a copy made back in the 80s): https://www.amazon.com/dp/0486845583/?tag=pfamazon01-20 Looks like it is on sale too.

Top tier schools will want 3.8+, and great letters of recommendations from professors you've done research with.

Well, he is doing a PhD in molecular biology, while I'm doing one in physics. My thesis is dealing with gravitational waves/binary black holes, and I'm not the best relativist in the world, so getting perspectives from multiple books has helped me. I prefer tangible books over digital, so I had...

The Indian/Biology books are mainly my roommate's. Excuse the lamp placement, our apartment is small!

I'll just be blunt: Unless your research resulted in a few papers in top tier journals (and they're relevant enough to get citations), you won't get into a top tier school with that GPA.

http://home.uchicago.edu/~geroch/Course%20Notes End of page 4, 5 of his general relativity notes cover this for me, very simple and easy explanation.

PreoK's answer is very good, so read it a few times. He mentioned energy, but if you've taken chemistry before, you might remember Pauli's exclusion principle talking about electron spin. Particle spin is also formulated as a superposition before measurement. But, a quick answer is: it's just...

The only thing that really springs to mind is the concept of "gradient descent" and example 1 in this link uses some geodesic stuff: https://agustinus.kristia.de/techblog/2019/02/22/optimization-riemannian-manifolds/