Recent content by TomServo

1. 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.
2. 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.
3. 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...

5. 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...
6. 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.
7. 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?
8. 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...
9. 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?
10. 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...
11. I Derivative operators in Galilean transformations

And where I wrote ##x_0## originally I meant ##x’##.
12. 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...
13. 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...
14. 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...
15. 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...