Recent content by TomServo

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...