elfmotat

The latter. You can just think of different particles as being excitations in different fields, and those fields can interact with each other according to some rules we call "laws of physics."

I don't think you understand what the word "homogeneous" means. The universe was still homogeneous when it was younger, it was just denser. It has nothing whatsoever to do with the scale factor. So you won't accept approximations because... you don't like approximations? Are you waiting around for an exact solution to the EFE's for our universe? Good luck with that. In the mean time, the rest of us will be making progress with our useful approximations. It's hard to respond to arguments that don't make sense. Why in the world would you think this? What led you to this thought?

Like a Rindler Horizon? Sure, but you'll never be able to interact with them because they're beyond the horizon. You'll probably get interesting effects from the horizon itself, like Hawking radiation. I am by no means an expert on this though, so I may not be as helpful as I'd like.

Because the FLRW metric is obviously just an idealization which makes for useful approximations, just like most anything else in physics. At large enough scales the universe is approximately homogeneous, meaning the FLRW metric approximates our universe at large scales. You also shouldn't take analogies too seriously: space isn't 2-dimensional either! I only provided the analogy because it makes visualization easier, which is sometimes helpful for people who aren't well-versed in this stuff.

Ah, okay, I understand. Our disagreement was coming from what we were using [math]d[/math] to represent. I was taking it to mean their separation when they are destroyed, while you were using it only as an initial separation so that initial P.E. can be calculated. That makes sense. I have no problems with this setup in terms of it violating any physical laws, but it is a bit fuzzy. In classical physics particles can never be created or destroyed -- you need QFT for that, with the introduction of creation/annihilation operators. The problem being, at this level all interactions consist of some sort of particle exchange. I.e. the charge doesn't really generate a classical EM field, it generates a bunch of virtual photons, a collection of which will act like a classical field at larger scales. As for where the energy goes, it can remain in that field or be transferred to other fields -- for example e⁺ e⁻ → γ γ converts all the mass/kinetic/whatever energy the electron/positron field had into two EM field excitations, called photons. Energy is conserved in all interactions like this because there is a 4-momentum conserving Dirac Delta Function in the Feynman rules for calculating amplitudes.

I'm certainly not trying to be dramatic, especially not overly so. If my bluntness offends then I apologize. The scenario makes for an inconsistent thought experiment because you are picking and choosing which physical laws you do/don't want to ignore, and some them can't be ignored in any meaningful or consistent way. The continuity equation for charge conservation is absolutely fundamental, and removing it means that the EM field is no longer a gauge field -- which means the entire theory of EM would have to be re-written for your question to make sense. You were also trying to remove locality, which is completely contrary to the point of using field theory in the first place. You changed the setup of your thought experiment. You originally said the charges would be destroyed while separated, and now you're saying they are brought together. The latter makes sense -- the former doesn't.

Say we're in a reference frame where the charges are separated by distance [math]d[/math] and both are destroyed simultaneously, i.e. [math]\Delta t = 0[/math]. If we boost to a frame moving at [math]v[/math] w.r.t. the charges, parallel to them, then the difference in time between when each charge was destroyed in this new frame will be: [math]|\Delta t'| = \frac{vd/c^2}{\sqrt{1-v^2/c^2}} \neq 0[/math] The scenario you propose violates physics, which is why I can't use physics to explain what happens.

Put a coin on a rubber sheet and stretch it. The space of the sheet is expanding, but it is not nearly enough to overcome the molecular bonds in the coin and rip it apart. This simulates galaxies, clusters, and other gravitationally bound objects. The force of expansion is not enough to overcome their gravity. If you put two coins on the sheet and stretch it, the coins will move apart from each other. This is because the coins are not bound to each other. It simulates two galaxies which are very far apart, such that their gravitational interaction is too small to overcome expansion. Also notice that the coins on the sheet reproduce Hubble's Law: if they are twice as far apart they will move twice as fast away from each other.

But I explained why this wouldn't work in my first reply. If the charges are separated by finite distance then they cannot be simultaneously destroyed in all reference frames. If the events are simultaneous in one frame then they necessarily won't be in other frames. That means one charge would be destroyed before the other, violating charge conservation. The only way for charges to be created/annihilated is with equal/opposite charges at interaction vertices, i.e. single points. All interactions must be local.

Those are theoretical models, some of which have problems, and none of which are accepted physics.

The most unusual thing about it is that the equations of motion are third-order. The closest thing I've seen would be a classical self-force, like the Abraham-Lorentz Force (and all the problems associated with it), which could be expressed in a Lagrangian like the following: [math]L= (\dot{x})^2-k(\ddot{x})^2[/math]

There's no problem, as long as all such interactions take place at a single point -- i.e. the distance d in your OP must be zero.

I don't know what your idea was or which thread you're talking about. I was just explaining why posts are usually moved to the trash can. Something along the lines of, "if my idea is correct then we should expect to see a value of X upon measuring such and such a quantity." Or, "this fits known data, as shown here." Something to tell us whether or not your idea is wrong, objectively.

Please read the Speculation section's rules. Rule #1: This is a science forum. If there is nothing objective to discuss then we aren't doing science.

The "speed" of the electron is not well-defined in atoms because they are not in eigenstates of the velocity operator. The best you can really do is an order-of-magnitude calculation: [math]\frac{mv^2}{2} \sim \frac{e^2}{4 \pi \epsilon_0 r}[/math] [math]mv \sim \hbar / r[/math] so: [math]v \sim \frac{e^2}{4 \pi \epsilon_0 \hbar c} \, c = \alpha c \approx \frac{c}{137}[/math] This is not a very large fraction of the speed of light. I.e. electrons do not really have "immense speed" in atoms, which is why non-relativistic quantum mechanics works so well. What field? What do you mean by "vortexes (sic)"? What do you mean by "probably"? That sounds very vague. Vague theories are not scientific. This is all rather vague as well. It's hard to comment on "theories" which are not well-defined or precise. This is why math is important. Beliefs should be based on evidence. Apparently you don't agree? I can't argue with someone who does not take seriously the scientific method. Except we know for a fact that it does. This was demonstrated in 1919 with the original Eddington experiment to test General Relativity.

I know that I, along with at least one other person (Strange I believe), already stated in this thread that nothing special happens at the event horizon. There is no "impact." You would pass right through without noticing a thing. Passing through the event horizon just means that you would have to move faster than light to escape. It's like a boater in a river approaching a waterfall -- the closer he gets to the edge, the faster the water flows. Eventually, when he gets close enough, the water flows faster than the boat's top speed -- he has passed a point of no return and will inevitably fall off the edge of the waterfall. Nothing special happens at this point, just like nothing special happens at the event horizon.

So you're intentionally wasting people's time?

Which breaks rule #1:

Total charge is indeed time-independent, but that doesn't mean charges can't be produced in interactions. γ + γ → e⁺ + e⁻, for example, produces two charged particles where previously there were none. Charge conservation requires equal and opposite charges be created/annihilated in any interaction. As for why there was more matter than antimatter created at the big bang, that remains a mystery .

Assertions made without evidence can be dismissed without evidence. Do you have any to support your claims or not? If not then there is no topic to focus on.

Good science starts with evidence, of which you have none. Thinking out of the box is fine as long as you don't bend facts to fit your ideas, instead of the reverse. Starting a topic based on an out-of-the-box idea is also fine, if you have evidence. What's not fine is starting a topic based on an out-of-the-box idea with zero supporting evidence, being too lazy to look for it yourself, and expecting others to do your work for you.

So let me get this straight: you post a thread based on a ludicrous proposition for which you have absolutely zero evidence, and you expect us to find the evidence for you? Sorry, but I think we all have better things to do with our time.

I don't think I agree. The point of a thought experiment is to gain insight by imagining a physical scenario which is, in principle, possible. I don't know how to answer this question meaningfully because it is simply not possible. You're proposing a different set of physical laws which are incompatible with the laws we know govern nature. I.e. this thought experiment is not self-consistent. The energy of any field is given by its stress-energy. If you know the field Lagrangian then you can find the stress-energy with a variational derivative w.r.t the metric: [math]T^{\mu\nu} \equiv \frac{2}{\sqrt{-g}} \frac{\delta ( \mathcal{L} \sqrt{-g})}{\delta g_{\mu \nu}}[/math] In particular, the stress-energy of the EM field in flat spacetime is (in appropriate units): [math]T^{\mu\nu} = F^{\mu \alpha}F^{\nu}_{~\alpha} - \frac{1}{4} \eta^{\mu \nu}F_{\alpha \beta} F^{\alpha \beta}[/math] where F is the electromagnetic field tensor. This gives you the stress-energy of the EM field at any point in spacetime. I.e. if you pick a point and plug in the value of the EM field at that point, the above equation will tell you the energy/momentum density of the field there. Energy can be found by integrating T00 over 3-volume. The dynamics of T are governed by the dynamics of F. The continuity equations [math]\partial_\mu j^\mu = 0[/math] and [math]\partial_\mu T^{\mu \nu} = 0[/math] explicitly forbid the scenario you suggest. The dynamics of the field energy in valid physical scenarios are given by the prescription above.

This scenario is not possible for a number of reasons: Pressing "nuke one" violates charge conservation. If the two charges are not exactly equal and opposite, pressing "nuke both" violates charge conservation. Even if they are equal and opposite it still violates local charge conservation. Say we press the "nuke both" button in a reference frame where both charges are at rest. The charges will be simultaneously destroyed. In another reference frame the events will not occur simultaneously, meaning for a finite period of time charge conservation was violated. The scenario violates both local and global energy/momentum conservation. It's hard to use physics to describe scenarios that violate physics. As for where the energy of a field is stored, it is stored locally. Every field has a stress-energy which can be easily calculated from the field Lagrangian.

Terms are not so important. Knowing the name of something is not the same as knowing something. (Another Feynman video.) You'll learn the terms over time, in their proper context, by reading textbooks or lecture notes -- the same way you learn interesting vocabulary words by reading books. Memorizing things is almost always a bad idea, as it does not really contribute to any meaningful understanding. What's important is understanding the math, what it means, and how to extract information from it. For example, the equation you posted above is a statement of local energy-momentum conservation. It means that energy/momentum cannot be locally created or destroyed.