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    Book with a good Introduction to Lagrangian Mechanics?

    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.
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    I Why are coordinates independent in GR?

    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.
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    I Why are coordinates independent in GR?

    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...
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    I Why are coordinates independent in GR?

    What about skew coordinates?
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    I Why are coordinates independent in GR?

    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 eachother. But is there a more straightforward and fundamental reason why we don’t consider dependent coordinates? Is it...
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    A Is it normal to forget most of your non-GR physics knowledge?

    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.
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    A Is it normal to forget most of your non-GR physics knowledge?

    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?
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    I Problem of time in quantum field theory?

    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...
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    I Problem of time in quantum field theory?

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

    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...
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    I Derivative operators in Galilean transformations

    And where I wrote ##x_0## originally I meant ##x’##.
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    I Derivative operators in Galilean transformations

    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...
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    I Derivative operators in Galilean transformations

    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...
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    I Invariance of timelike Killing vector of Schwarzschild sol.

    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...
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    I Invariance of timelike Killing vector of Schwarzschild sol.

    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...
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    A How much does peculiar velocity affect distance measurement?

    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...
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    Engineering Astrophysics going on to Aerospace Engineering

    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...
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    Other What level of knowledge should a new PhD graduate have?

    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?
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    Other What level of knowledge should a new PhD graduate have?

    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.
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    Other What level of knowledge should a new PhD graduate have?

    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...
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    Other What level of knowledge should a new PhD graduate have?

    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...
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    I Low quantum numbers, high energy, and distance scales.

    Okay, that's interesting, but how would I show that?
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    I Low quantum numbers, high energy, and distance scales.

    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...
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    A 5D relativity and stability

    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.
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    A 5D relativity and stability

    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...
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    Physics Thinking of dropping out of PhD program, need advice

    Isn't that different though because you would have taken QM?
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    Physics Thinking of dropping out of PhD program, need advice

    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).
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    Physics Thinking of dropping out of PhD program, need advice

    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...
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    Physics Thinking of dropping out of PhD program, need advice

    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...
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    Physics Thinking of dropping out of PhD program, need advice

    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...
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