Recent content by GRQFT

Interesting. Applying the Hodge dual in this way seems specific to EM given that it comprises two different yet equally important fields (E & B). Then again, I wonder if this can also be done for gravitational radiation (in the weak-field limit) to get 'homogeneous' and 'inhomogeneous'...

To be clear, that was not me talking about the 'realness' of E & B, but rather Viktor T. Toth's claim on this webpage (see last paragraph). I was referring to the 3-vector ##\vec{A}## (which I now realize is problematic given what you said about the 3-D classical view of ##\vec{E}##...

Thanks. I'll look into those... The size of my Zotero physics collection has grown considerably since I joined PF!

Excellent! I just learned that: 1. "...the theory of electromagnetism is really just the geometric theory of an arbitrary smooth vector field." 2. "...in the case of the electromagnetic field, both the equations used to define E and B and the field equations will automatically be satisfied in...

I'm interested in learning enough to understand relativity (and QFT). I studied physics in college (decades ago), so I guess I'm at a level where I I know enough to ask about stuff like the Hodge dual, but not really understand it. Thus far I've just been googling the terms I don't know, but...

Okay, thanks. There's clearly a lot that I need to learn about tensors! I was thinking of buying a copy of Sean Carroll's Spacetime and Geometry and reading the relevant sections. Would that be a good choice, or is there something better?

When you say "...that's dual to ##c_{k}##", are you talking about the Hodge dual?

Looking at what you wrote above makes me think that the notion that the magnetic field is really just an electric field viewed in the wrong frame of reference is actually false (I've read/heard this several times). Judging from the two matrices above, it seems that they are quite equal; i.e...

So, I'm guessing the black circle in the center of the photo on the RHS is the impact crater. But what's all that bright white stuff? Is it the ejected material from the impact? If so, why does it show-up as brighter white if it's just the same regolith as what it fell onto? Did the impact...

Thanks so much for taking the time to write all that out! So, to make sure I understand, you're saying that because Maxwells equations are Lorentz invariant (like SR which is foundationally Lorentz invariant), that's how we can see SR in Maxwells equations? And as a bonus question, Maxwells...

Are you sure this isn't a recording of one of his lectures or an interview?

For those of you who still have questions about the issues discussed in this thread, you should watch this (AI generated) video of Feynman. It's very informative!

Thanks. Your 2008 post on that subject is very useful in making these abstract concepts concrete. Cheers...

When I look at Maxwell's equations, the EM side is immediately obvious. However, until now, the SR side was not. Are you seeing it in the last equation where you have something spatial (the Laplacian of E) on the LHS and something temporal (a time derivative of E) on the RHS with 1/c^2 acting...

Well, you alluded to the fact that c could be differnent in what you wrote below (my emphasis). I did try to use a scenario involving a measurement, but you took issue with that. No problem. So that's when I switched to a scenario sans any measurement. Anyway, all of this was merely an...