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Morin, definitely. He also wrote a free chapter online about Hamiltonians. Includes valuable insights that I haven’t seen in other textbooks, even Goldstein. Highly recommended.

Okay, so my hypothesis at the end was correct? I don't like abuse of notations because of the confusion they cause, I'm grateful to you for point it out.

That's true, but perhaps you can help me to see something. Let's say I have the 1+1 Minkowski space, with coordinates x and t with basis vectors ##\hat{x}=(0,1)## and ##\hat{t}=(1,0)##. Now I define a new coordinate u=t+x to replace t, and so my coordinates are u and x with basis vectors...

What about skew coordinates?

I can see that by the tensor transformation law of the Kronecker delta that ##\frac{\partial x^a}{\partial x^b}=\delta^a_b## And thus coordinates must be independent of each other. But is there a more straightforward and fundamental reason why we don’t consider dependent coordinates? Is it...

Thanks for your answers everybody. I either have imposter syndrome or am not as knowledgeable as I should be and it causes a lot of anxiety.

I’m worried I’m going to get my PhD knowing GR but having a less-than-undergrad grasp on the other core topics like stat mech and QM. I feel like “forgetting” most of core physics makes me a bad physicist. Or is this normal when you specialize? How do y’all stay sharp on these topics?

Well today on arXiv was posted this pre-print: https://arxiv.org/abs/1905.09860 And that's what got me thinking, although it's a notion I've seen here and there before (often in the popular press, which of course doesn't explain it). The first ten references seem to be relevant to defining...

Well okay, but why do people say that there is a problem of time in QM if there isn't?

Summary: Does the "problem of time in quantum mechanics" go for Lorentz-invariant quantum mechanical theories like QED? Everything I read about "the problem of time in quantum mechanics," i.e. absolute time in QM clashing with relativity's relative time coordinate and relativity of...

And where I wrote ##x_0## originally I meant ##x’##.

Could you further explain what you mean here? I know what worldlines are, but it seems to me (just algebraically) that the ##t=\frac{x-x’}{v}## relation holds in general. After all, I’m just solving the transformation equation for t. I know this is wrong, but I’m trying to understand why the...

I'm studying how derivatives and partial derivatives transform under a Galilean transformation. On this page: http://www.physics.princeton.edu/~mcdonald/examples/wave_velocity.pdf Equation (16) relies on ##\frac{\partial t'}{\partial x}=0## but ##\frac{\partial x'}{\partial t}=-v## But this...

I wasn't exact enough with my question about invariance. I know that invariance of a scalar field refers to the invariance of the value of that scalar at that point in spacetime. What I see by plotting r vs. ##\rho## is that for ##0<\rho<\infty## we never go below ##2m##. It dips to the...

I use the ##(-,+,+,+)## signature. In the Schwarzschild solution $$ds^2=-\left(1-\frac{2m}{r}\right)dt^2+\left(1-\frac{2m}{r}\right)^{-1}dr^2+r^2d\Omega^2$$ with coordinates $$(t,r,\theta,\phi)$$ the timelike Killing vector $$K^a=\delta^a_0=\partial_0=(1,0,0,0)$$ has a norm squared of...

I'm a PhD student who's taken GR, so I have studied gravity and cosmology, and we have the underlying assumption of homogeneity and isotropy, but since this assumption comes from how we've calculated the distribution of galaxies in the visible universe I want to make sure I really understand it...

If you know you want to do aerospace, then maybe you should do that. There is a lot of fluid mechanics and stuff that they don't really teach to physics majors anymore but that aerospace jobs expect you to know. I could maybe see working on magnetohydrodynamics or some advanced kind of fluid...

Crap, I’m rusty on topics I haven’t seen in two years. How does one stay sharp in areas unrelated to their concentration throughout their PhD?

I should say I also learn by reading papers and trying to replicate them or go beyond them, so I am doing that as well.

Non-GR approaches to relativity, written a few papers being considered for publication so far. My problem is that I forget things if I go a long time without using them. I can usually get up to speed quickly with some study though. Thanks, I will get that book. This book...

Let's say I'm getting a PhD in an area of gravitational physics. Upon getting that diploma, what is expected of me in terms of knowledge of GR? I hope my question can be useful to other students in other concentrations, so substitute QFT, or condensed matter, or whatever. For example, is it...

Okay, that's interesting, but how would I show that?

I understand how we associate high energies with small wavelengths and thus small distance scales, but we also tend to associate small distance scales with ordinary quantum mechanics, and hence low quantum numbers (low energy). Also, many high-energy processes are active across large distance...

https://arxiv.org/abs/0808.2055 He directed my attention to the first paragraph on the second page. I also think references 74-77 are supposed to be about the fine tuning necessary in 5D models.

I tried a cursory search for this but couldn't find it. I was talking with my advisor about 5D theories such as those of Paul Wesson and Randall-Sundrum, and he said that I shouldn't spend too much time studying those theories because they are unstable, or require so many corrections to...

Isn't that different though because you would have taken QM?

I am still in good standing, do well at my TA duties and do well in my classes, especially GR and cosmology (which I'm taking now).

As I said in a reply above I was attending meetings and even running some, but I had to wait until I took GR (in my THIRD YEAR) before I could really start research, and even then I'm still taking a cosmology class now. Between doing the reading and homework for the class and TA duties and no...

He does get some grant money but none that covers an RA. I've been a TA the whole time. Classmates of mine with other experimentalist advisors have TA positions, go to CERN, present their research abroad, etc. One is even graduating soon. Meanwhile I was waiting to take GR before I could...

Let me explain what I mean when I say I haven't done any research. I've read papers, attended meetings, ran meetings, but I myself have not sat down and done any actual research. Most of my time was taken up with required classes (and we had a debacle my first year that made things much more...

I loved it actually, and I would like more of it. I worry however that TA duties will just slow things down even more even if the research side really picks up.

Grad school is *not* what I was hoping it would be. I wanted to study GR and was fortunate enough to get accepted in a program with an advisor who is a gravity theorist. I have the best fellowship awarded to grad students at my school. I passed all my prelims on my first try. My grades...

I'm in gravity (cosmology, GWs, etc.) and starting my fourth year and only just recently took GR for the first time. I'm wondering what standard I should set for myself WRT GR. It feels like you'd need to be an expert in GR just to identify worthwhile problems to work on, and I'm expected to...

Well actually my advisor is not the researcher in question, nor is my advisor the professor I mentioned. I'm getting my advisor's opinion as well.

I'm a grad student working on a PhD in physics at an accredited university in the US. I have the opportunity this Summer of doing a side research project or two under the auspices of a physicist who works at a private research outfit funded by another physicist who was involved in "paranormal"...

I'm not quite following, do you think you can provide examples of these two paragraphs?

"Ho"?

Oh, okay. I thought that might be the point you were making, but it also seemed like maybe you were trashing industry, I couldn't tell.

Well my adviser is building a collaboration with a university in China where a former post-doc of his works and where the dean has tons of research grant money (can't be spent in my country, the US, darn). It's using things like atomic interferometry and optical clocks to measure gravitational...

I only applied to one school that would be considered elite (in physics), and did not get it. I attribute this to two things, one is that I was going for theory and got a 50th percentile on the PGRE (I had serious health issues that kept me from studying for it, alas), the other is that I...

I'm...a little unclear on your point. Would you mind elaborating?

Yes :biggrin:

I hope my question doesn't sound bitter, it's not meant to be, I'm just a grad student wanting to get some opinions on how things are. I'm especially interested in hearing from people outside academia as well, since I assume people *within* academia might have an unrealistic view of what the...

NM, I found out what I was doing wrong. Thanks for confirming that my initial hunch on what was going on was correct, even if I botched the execution.

I think that is what I first considered and wound up with a factor that had its numerator and denominator opposite of what the paper had.

t'=t+r/c-(r/c)cos(theta)

I am studying a paper and a math step like this was used: dt'=(1+\frac{h}{2}sin^2(\theta))dr \\ \int^{t1}_t dt'=\int^d_0 (1+\frac{h}{2}sin^2(\theta))dr \\ where\\ h=h(t-\frac{r}{c}-\frac{r}{c}cos(\theta)) This seems wrong because it seems to me that you're not doing the same thing to both...

Darn. Can you recommend another one then?

BTW I recommend the book Head First Design Patterns as an intro to the subject.

Yes, but in practice isn't QFT used relativistically? I'm just describing it as I've heard other, much more knowledgeable people describe QFT. I took a class in it and still don't understand any of it, clearly.