Recent content by aliens123

Yes. Well, mostly, I think that the problem just needs to be stated more precisely. "Show that if we average out any physical quantity, whose dependence on ##p_\theta## and ##p_\phi## comes only through the kinetic energy of the particle." However, a function ##R(r, \theta...

Sure, but this type of substitution could be done for any F We would still get the factor of $$r^2 \sin \theta$$ if we do this substitution, regardless of what F looks like.

For part A: We need to look at the Jacobian, which is the matrix of partial's: $$J=\frac{\partial(x,y,z,p_x,p_y,p_z)}{\partial(r,\theta,\phi,p_r,p_\theta,p_\phi)}.$$ \begin{align*} x&=r\sin \theta \cos \phi \\ y&=r\sin \theta \sin \phi \\ z&=r\cos \theta \\ p_x = m\dot{x} &= m\dot{r} \sin \theta...

I believe that the following transformation (as in the article): Is obtained by making the identifications $$E' = F'_{i 0}, E = F_{j 0}, i, j \in \{1, 2, 3\}$$

I am not saying that these should be equal. The use of the term "Lorentz transformation" perhaps should not have been used. But the formula in the link considers the following "transformation": $$F_{\mu 0} \mapsto F'_{\mu 0}$$ I should note that the author does not use the term "Lorentz...

This doesn't seem to agree with PeterDonis. He is saying the Lorentz transformation relates the components of \uE according to u^a with the components of \uE according to v^a .

If this is the case, then why isn't the Lorentz transformation given in this link: https://webhome.phy.duke.edu/~rgb/Class/phy319/phy319/node136.html Related by a "simple" Lorentz transformation? That is, ##(E_G)_\mu \mapsto (E_G)'_\mu## Is just $$(E_G)_\mu = (E_G)'_\alpha \Lambda_{\mu}^{\ \...

Okay, so the transformation given in this link: https://webhome.phy.duke.edu/~rgb/Class/phy319/phy319/node136.html Does not answer the question: "If I am at rest in frame G, then boost to frame H, what will be the new electric field I measure?"

Let me try to be more clear. Suppose we have two observers G and H. Let observer G be at rest in the unprimed frame, and let H be at rest in the primed frame. There are two different covariant quantities: the electric field measured by observer G, and the electric field measured by observer H...

What does the Lorentz transformation equation for the E field tell you, if not the components of the E field in the observer's frame?

The statement which you are saying is not correct is literally what Wald said.

When I first read this I didn't understand what you were trying to see but it appears crystal clear in hindsight

Oh okay I think I see. So would it be correct to say that Is the electric field seen by an observer with 4-velocity ##v^a##. And Is also the electric field seen by an observer with 4-velocity ##v^a##, but they appear to be different because they have different components because they have a...

Well, yes; I'm aware that there is no conflict. As I interpret Wald's statement there is a conflict. I know that there is no conflict. So I know that I am misinterpreting Wald's statement. Hence my question.

The second part of my post is the random internet post. How can that be both correct and not correct? In the first part of my post I do not try to transform the EM field tensor.