Lorentz Jr

That part is wrong. You need to go back and redo the inside integral in y.

-b < y < b

The y in the denominator changes sign. You're integrating over y, not x. Your inner integral is wrong. Try again. Start with [math]b^2 \equiv a^2 - x^2[/math].

Yep. That's what I did. (partial)

Hmmmmm... Not sure how that happened. 🤔 Maybe I should blame it on @Genady. He explained how to quote text selections, and I probably quoted the quotation in your post. 😶

Currently, the most successful theory of subatomic physics is quantum field theory, which models all matter and energy as wavelike disturbances in "fields". It doesn't specify what fields are, but they permeate all of space (and there are almost 20 of them), and the electromagnetic field is the basis of light.

Right. And local hidden variables means particles + hidden variables. So you can keep particles if you give up hidden variables, or you can keep hidden variables if you give up particles.

Bell's test refuted local hidden variables.

I was asking about the video. Given that time travel is one of the most unscientific concepts imaginable, at least from a classical point of view, I'm wondering what the justification is for invoking it. Not saying it's impossible in quantum mechanics, just wondering why it's in the video.

Substitute "explain" with "describe" if you like that word better.

No, my first suggestion was a number of long mirrored strips attached to each other to approximate a curve. Because I've seen those in home-improvement stores. Not strips exactly, but long and narrow. Oh, I see. But that has to be as tall as the wall.

Good point! I guess we need the mirrors to be dynamically programmed!

In what phenomena is the future necessarily "relevant to the present", i.e. nonlocality isn't sufficient to explain the weirdness?

To be perfectly honest, Alferd, if your goal is to light the wall evenly, this is a complicated optimization problem, so I doubt a circular mirror is ideal. Your best bet is probably to buy a bunch of long, skinny, flat mirrors and work out a way to hold them in place next to each other. Then you can adjust their angles experimentally to get whatever distribution of light you want, with no other restrictions on their overall shape. Flat mirrors will also be a lot cheaper than a custom-designed circular mirror. I'm sure people in the Engineering section of this forum will be able to help you. Another way to solve the problem would be to work it out geometrically and iteratively on a piece of paper. Draw a bunch of light beams, reflect them off an arbitrary curved surface, and then adjust the surface and the light beams until the beams have the correct spacing on the wall. Then you can mold your own support, if you know how to do that, and cover it with a reflective sheet. Generally speaking, the mirror will have to be flatter near the top and more curved near the bottom.

Is this a practical problem, Alferd? Do you really want to do it, or is it just a mathematical exercise?

Do you mean radius?

Radius/diameter = 0.5! 😁

How small (short and narrow) does the mirror have to be? If it can be 5 meters (the full height of the wall), it can just be flat (r = infinity) and the wall will be lit evenly. Radius?

That's a long season!

Until there's an earthquake, and then all of a sudden, knowing the answers to those "why" questions becomes VERY useful. 😉

Okay! So it looks like the consensus is as follows: I like @Genady's suggestion that the charge doesn't disappear because it never reaches the event horizon. That means it doesn't move inside the black hole, so there's no need to update the electromagnetic field outside of it. Even though electrostatic pressure obviously resists compression of the electrons, it's temporarily compensated for by external pressure from more incoming electrons. So the electrostatic energy of the electrons probably decreases the density required to form a black hole by increasing their total mass/energy. Electrostatic energy may also be the answer to charge-neutral Hawking radiation. As long as radiation reduces the electron density, it can get its energy from the resulting loss of potential energy. Thanks to @MigL for the link to info about charged black holes, and to everyone else for commenting.

Yes, and you're in the majority these days, so I should probably learn to keep my mouth shut about this subject. It's just that your phrasing seems to me to deny the existence of any ontology at all. Anyway, I think we've both made our points. Thanks for chatting. 🙂

Right, but no one has ever observed any experimental evidence to indicate what the correct "global" point of view is. The car may be traveling to the West relative to Earth's surface, but Earth's surface is traveling to the East. The car is probably moving relative to the rest of the visible universe, but for all we know the entire visible universe could be moving relative to some even more universal point of view. It's hard to say for sure who's moving and who isn't.

You said "purely a statistical phenomenon". "purely" means "with nothing else", and a causal explanation or physical basis would count as something else. You can define the word "entanglement" statistically if you want (although I'm not sure it was originally intended that way), but extending that description to the phenomenon itself implies a lack of causation. Right. That's the way the word "entanglement" is commonly used. I would say it's informally suggestive of some kind of interaction, but that's okay. It's commonly used to imply correlation, with no additional implications either way. Sure, but there's no correlation in temperature. No cause, no correlation. And entropy is one of the great mysteries of physics. No one understands how the universe can be in a state of such low entropy when thermodynamics tells us it shouldn't be. One would expect that it should have a cause. Anyway, I'm not criticizing your whole post, Markus. (And of course you didn't post it in this thread.) Most of it is very good. Just the combination of "purely statistical" and "phenomenon". Semantically speaking, I think it goes a little too far towards suggesting a lack of causation.

I'm sorry, but this is sheer nonsense. The first 99 percent of the post is a perfectly reasonable introduction to the subject, but then the last 1 percent literally says there's no physical basis for it at all (it's "purely statistical"). Math isn't a replacement for physics. Wave functions only describe physical systems, they don't explain why outcomes are correlated. Physics is not a purely a statistical phenomenon. Correlations may be caused by FTL communication, or they may be caused by what @joigus has called "beables" that were established when the particle was created, or they may be caused by something else. But they're caused by something. They don't happen by magic. Saying correlations in physical systems have no causal explanations is like saying human beings exist with no conscious thoughts. Math is not physics. @MigL The equation for the entangled state is something like [math]\displaystyle{|\psi> = \frac{1}{\sqrt{2}}\left(|01>+|10>\right>}[/math] [math]\displaystyle{|\psi> = \frac{1}{\sqrt{2}}\left(|01>+|10>\right>}[/math] You have to right-click the equation, copy the TeX, and paste it in as text surrounded by the math codes in your own post. EDIT: From Markus's post, the code is |\psi \rangle =\frac{1}{\sqrt{2}}\left(|01\rangle +|10\rangle \right)