Lorentz Jr

Mathematical models can be a lot simpler than the systems they approximate. (Economics is another good example.) It's hard to include exceptions in them without sacrificing their simplicity, which is useful for analysis. Sort of like trying to indicate a point on a map when you're wearing a boxing glove. 😋 Being formally trained in mathematical modeling, I call both statements God's honest truth! 😄 Hi Genady! Nice to meet you. 🙂

Dark skin contains more melanin (I almost wrote "melatonin"! 😲), which protects the skin against UV, but I would imagine it must be warmer. Even in cold weather, it can be better to wear light-colored clothing with extra insulation, because dark clothing will heat up and cool down as you go between sunlit areas and shaded areas. With light colors, your temperature will be more even.

Good job! 🙂 They're not. Okay, my friend. Suit yourself. 🙂

No, but it's still a spectacularly useful expression. One of the few in English that are more or less impossible to misinterpret.

You can look up the Millikan oil drop experiment if you're interested. Read up on particle accelerators. They've been doing it for decades. Equality is implied by the fact that normal objects don't react to electric charges.

Right. Experimental evidence. Of course. The net force is the sum of the two forces, so it would be nonzero if one force were stronger than the other.

Correct. No, that one works either way. Once one statement is known to be false, the question of whether or not both statements are allowed to be true becomes moot.

That's exclusive, not inclusive. In the geekier circles, it's sometimes written "xor". The word "either" strongly suggests the exclusive meaning, but it doesn't absolutely imply it, at least not in casual conversation. If the condition for being admitted to an animal-lover's club is that you "either" like dogs or like cats, they probably won't mind if you like both dogs and cats. It's just people using the terminology informally. If they really want you to understand that they mean the exclusive version, they may say something like "... but not both". Or they might not say anything because they don't know any better. 🤷‍♂️

Actually, I think the light must have the same frequency in the coordinate frame along the whole path, just as a matter of boundary conditions. It would seem faster to time-dilated observers in the gravity well, and that should also apply to their perception of the light (that its frequency is constant) before and after it's in the gravity well, for the same reasons. 🤔

Right, of course. That was my point. Sorry. I thought you were talking about electrons and protons interacting with each other in individual atoms.

Sorry @swansont! It's not my fault! 😲 @tmdarkmatter: the mass of all the objects of our solar system should combine and increase the effect. Any masses that are spread out in a solar system or a galaxy can only contribute to lensing of light from other solar systems or galaxies. And that happens. I'm not sure where to look for decent links, but there are photos of lensing around galaxies and galaxy clusters. Concerning the Einstein radius, I would like to know what happens to this light being deviated. Does it travel through the lens galaxy? No, it travels around it. It has to stay moderately far away from the galaxy to reach Earth, which is along an almost straight path if the source is directly behind the galaxy. shouldn´t the light coming from stars or galaxies that are not exactly behind a lens galaxy also be manipulated/bended, even if we do not see Einstein rings? Yes, that happens. They can even be seen closer to the galaxy, but on the other side, because the light had to be deflected through a larger angle. There should be some 1000 galaxies between Earth and the furthest galaxies we can see, so shouldn´t their light be extremely deviated? No, not extremely. Only concentrated mass can generate extreme lensing. The galaxies surrounding the light's path will tend to bend it in the opposite direction, so the overall effect tends to be a wash. Imagine light coming from a galaxy and passing by the galaxies in between, always on the same side next to the lens galaxies. The angles of the Einstein ring effect should combine and completely deviate the light. It does. Some of the light from distant sources gets deflected in other directions so we don't see it. But as the light does not travel exactly in a way creating an Einstein ring, we just see a normal galaxy and think that the light of this galaxy was never manipulated. Distortion and displacement of the source go hand-in-hand. It's pretty hard for a professional astronomer to miss the distortion. And of course a greater deflection angle means the light got closer to the lens, so there would be even more distortion. Is it possible that the light of our milky way travels to the border of our universe and, due to an extensive combination of these Einstein radii, it comes back? What if background radiation is actually light from galaxies coming back home? I'm sure that happens a little bit, but it's not enough to explain the cosmic microwave background. The intensity of light turning all the way around and going in the opposite direction is really low. Maybe there will be a point where we cannot see any more galaxies because the light is just getting deviated too much in order to arrive at Earth Maybe someday. That would be a lot of light. shouldn´t this effect also be responsible for the observed red shifting? No. The frequency of the light speeds up again once the light is out of the gravity well. if light has a tiny mass, it should be able to "attract" objects, and this attraction force might be responsible for the tiny "loss of energy" resulting in red shifting. Red shift has been studied to death. It's not caused by gravitational attraction by the light. Overall, we should say that what we see in the sky might be totally different to what is actually going on out there. Maybe so. I'm sure astronomers will consider that possibility if they ever think they have observational evidence for it.

Is that really significant? They're attracted electrostatically, and they're kept apart because of the Pauli exclusion principle. How does quantum mechanics contribute to their mutual attraction in a way that differs significantly from Coulomb's law?

That's the question I answered. The net force is from two equal and opposite forces that have joined together to make another force that adds up to zero. F + (-F) = F - F = 0. There can be nonzero net forces between atoms if they're right next to each other in the same solid or liquid. For instance, the Van der Waals force is caused by separations of the charges in each atom so opposite charges in the two atoms get closer to each other and attract each other. Hydrogen bonding is a similar phenomenon that occurs in water because the charge is already distributed unevenly between the hydrogen and oxygen atoms. That's why water isn't as volatile as gasoline.

It can be tricky. There are different kinds of problems, there are different kinds of things that can cause them, and there are different things you can do to deal with them. If you're not sure what to do, you might want to consult with someone you trust and see what they recommend.

Do you want to know the force between the proton and the electron, or the total force they exert together on other charges? I told you the answer to the first question (it's zero because the charges are equal and opposite), and @joigus told you the answer to the first one: Quantum mechanics prevents the electron from getting any closer to the proton than it does in its atomic orbital, because of the Heisenberg uncertainty principle.

I just started "Fashion, Faith, and Fantasy". Maybe I'll try "100 Roads" sometime.

The net force exerted by the atom on an external charge Q is [math]F = \frac{kQ(q-q)}{r^2} = \frac{kQ(0)}{r^2} = \frac{0}{r^2} = 0[/math]

Coulomb's law No, the general expression for the classical electrostatic force is [math]F = \frac{kQq}{r^2}[/math], where q is the net charge on the atom, which is zero.

They're not. The electron and the proton both contribute to the net electric field created by the atom. The electron's charge and center of mass are exactly the same (and opposite for charge) as the proton's. So the total force exerted by a hydrogen atom on a distant charge Q is [math]F = k_e Q(\frac{(+q) + (-q)}{r^2}) = k_e Q(\frac{q-q}{r^2}) = k_e Q(\frac{0}{r^2}) = 0[/math]

I don't know how many of the people saying that were physicists, but they've learned their lesson now and they don't say it anymore! 😄 What if it is? What do you think? Einstein radius This is an interesting question for me. I know the Lorentz transformations are symmetric, so even an observer moving WRT the fixed stars views other objects as time-dilated. But I'm not sure what general relativity says about how observers in gravity wells see things. My short answer would be that the subject has been thoroughly researched, so I'm sure theorists are well aware of any effects that we might experience because of being in a galactic gravity well. Except for that whole "dark matter" thing, of course. They're still working on that one. 😋

I think by "neither homogeneous nor isotropic" he just means "not flat". Those are properties. I could have sworn I saw a video of him giving one of his talks, where he says the ether can't be made of "atoms", but I can't seem to find it anymore. And I don't think he meant atoms of normal matter (although I could be wrong about that). I think he was saying that the vacuum/ether somehow exists without being made of any kind of cells or particles that can have a state of motion.

It's similar to what Maxwell worked on back in the late 1800s, except it's more complicated because there are almost 20 known fields now. Maxell's model had little mechanical things of some kind spinning inside cells with rollers around them to allow the spinning. I'm still reading about Penrose's ideas, but I have to guess that they're based on the [math]e^{i\omega t}[/math] terms in quantum wave functions, since they obviously at least suggest some kind of spinning activity.

Thanks. 🙂

Page 169 in Volume 7: The Berlin Years: Writings, 1918-1921 (English translation supplement):

In my opinion, the simplest explanation of fields is that they're all oscillatory modes or other properties of the vacuum/ether. Roger Penrose has modeled the vacuum as a "spin network". Physicists talk about fields as being "fundamental", or "liquids", but I would say they're too complicated to be fundamental "building blocks of nature", and real liquids don't overlap each other.