joigus

The singularity of a BH lies in the future, rather than at the centre. So it's a time, not a position, from what I know. Now, you can call that the centre, for convenience, but it's a time, not a radius. Time and radius change roles when you cross the event horizon. That's what the maths says. What does that mean? I don't know. There are many things about black holes that I would like to understand better. Is the Schwarzschild black hole anything to go by, or is it just a freak of the equations of relativity for being so unrealistically simple? The only thing I can say is that theorists keep discussing them and the role they play in physics, including giant ones, microscopic ones that may exist, etc. There is no unanimous agreement about them. That's all I can say. The best thing about black holes is probably that they create conflict in our theories. I hope that means that research in black holes will usher in the next revolution in physics, but not much is certain about them except one thing: astrophysical black holes do exist.

I like this sentence. We should never underestimate the power of rephrasing the basics.

Love these tunes... There's something about waltz. And there's something about folk songs... Nightmarish tho.

Loved it.

It is not strictly necessary to excel at maths in order to have a good idea. Historically, Faraday was a perfect example of this.. Although it helps knowing your maths. But you need to understand how the ideas of physics relate to each other.

There is absolutely no significance whatsoever in the ratio between a kilo and a Coulomb. Same reason why the length of my nose divided by the mass of my head has no significance whatsoever. But I can define units o mass, length and time so that aforementioned ratio happens to be 9×109 or whatever other value I find convenient. Such is the nature of \( \varepsilon_0 \).

Bound state? You do have Yukawa couplings in the SM. Are you changing the SM? Your question isn't focused on what the Higgs field does? Can you 'hear' yourself? The Higgs field was summoned into physics because of what it does. Why else would we have a Higgs field? To make physics more spicy?

Saw it a couple of days ago. Almost spooky!

Force is related to momentum, and KE is a function of momentum: essentially (momentum)2/mass.

Really, really strange animal. Pink fairy armadillo, culotapado (hidden ass) or pichiciego (which I dare not translate). It has unique features among mammals, can use its tail and legs as a tripod, and its muscles reach the end of its extremities. https://en.wikipedia.org/wiki/Pink_fairy_armadillo

Maybe you don't see it this way, but everything I've seen so far upstream of this thread is help. You first need to understand what the Higgs field does in the standard model. The job description of the Higgs field is to provide mass for particles that, for some fundamental reason, shouldn't have one. The first class is gauge bosons that are found to be massive (W+, W-, and Z0 of the weak interaction). The other (quite important class) is charged fermions (not Majorana fermions, provided they exist). That includes quarks, and all leptons (electron, tau, muon...). It's not through strong coupling, as you've been told; it's through spontaneous symmetry breaking. In a manner of speaking, the particles get 'dressed' with a mass term. It's not at all like a coupling. How does your Gauss-law-based 'Higgs' do that? How does the symmetry get broken? How does it even work as a Higgs field? The Higgs field enters the physics through a potential, but it's a potential in the Higgs-field variable itself, not the space variable, as in Gauss' law. Etc. You need to understand basic physics. Let alone quantum field theory, and how the vacuum operates in that theory.

(my emphasis) SOL* * Smirking out loud

That's not how thermodynamics or heat transfer works. A process is exo or endothermic irrespective of what the temperature of the thermal bath is. Also wrong that high-energy states 'naturally transition' to lower energy states. That depends on the temperature. And force has very little, if anything, to do with heat transfer. Starting with the fact that equations of heat transfer are irreversible, while mechanics equations are reversible --except when friction is involved. There's nothing about what you've said so far that shows any understanding of how physics works, IMO.

That is incorrect. It's the Aristotelian mistake. Aristotle thought that in order to have something move you need a force. That's now how Nature operates. You need a force in order to have something change its motion.

Gauss' law has nothing in the way of spontaneous symmetry breaking, which is what the whole idea of the Higgs mechanism is based on. You need an equation with a continuous symmetry with particular solutions that break that symmetry. I haven't thought about it, but I don't think Gauss' law can accomplish that, nor have I seen it discussed anywhere.

What is c? The speed of light? Oh, OK. No, that math doesn't even start to talk about speed of light. As said by Studiot, the quantum wave function is a very different thing. For starters, it's a function, while \( \varepsilon_{0} \) and \( c \) are constants. Another thing is that \( \varepsilon_{0} \) is not really a constant of Nature. Rather, just an artifice in the choice of units for electric charge. Stick to Heaviside-Lorentz units and there's no \( \varepsilon_{0} \). It disappears!

You could call it an error. I prefer to see it as a limitation of the ideas of electrostatics when you consider charges smaller than one electron's charge, and --directly related to that-- the fact that, at some point, you need to replace classical electrodynamics with quantum electrodynamics. You cannot consider an electron as made up of elementary charges smaller than e. Capacitance is perhaps not the best way to see it, because it's not a fundamental quantity. It doesn't make a lot of sense considering an electron as infinitely many infinitesimally-small charges adding up to give an electron. You would have, I guess, to assume what the capacity of an 'incremental electron of charge dq' is. For a point-like electron (you haven't specified what spatial distribution of charge you're thinking of) it's best to use the expression, \[ \frac{\varepsilon_{0}}{2}\int\left|\boldsymbol{E}\right|^{2}dV=\int_{0}^{\infty}\frac{e^{2}}{32\pi^{2}\varepsilon_{0}r^{4}}4\pi r^{2}dr \] which gives you nonsense, \[ U=-\frac{e^{2}}{8\pi\varepsilon_{0}}\left(\frac{1}{\infty}-\frac{1}{0}\right)=\infty \] So, considering an electron as being made up of infinitely many (smaller) incremental charges doesn't make sense. You would like to consider a finite electron. In that case you're going to have to face even worse problems --mostly having to do with the fact that this electron cannot consistently be considered as a rigid object, nor has anybody found a way to make it elastic and be consistent with relativity --Poincaré and others tried very hard. That's why we use quantum mechanics when things get so small. And also forget about capacitance, which is a highly-derived concept. I hope that was helpful. Sorry, I misread this.I thought you meant dq<=e, which is what you need. If you integrate from zero you should add smaller charges than e, which is what Studiot is pointing out, in a way.

No, that must have been before I 1st came here. Teaching methods interest me a lot.

Lame joke on my part. I know how much you love books. You actually mentioned the human factor. I couldn't agree more.

No. You need to say what these things are.

Wonderful complement to what I was saying

Now I know @studiot is going to hit me hard. What I mean is: Look out for teachers that are putting out their material online, a lot of them for free. When the drive to learn synchs with the drive to teach, something wonderful happens, and knowledge is passed on. If the teacher does well, and the student does well, elements of criticism and analysis of how ideas are built and corrected/improved are also transferred in the process. Khan Academy --that @Phi for All already mentioned--, Stanford, MIT courseware, and a long etc. You've got plenty of university material out there. And my all-time favourite, PI (Perimeter Institute): Psi Online

Probably just a rhetorical question, but interesting nonetheless. The answer, very much having to do with the excellent points made, is all about symmetry groups --from a mathematical physics perspective. In economics, eg., you have graphs representing marginal utility --dimensionless, if I remember correctly-- plotted against number of units of goods --again, dimensionless. In electrical engineering tho, you have graphs plotting intensity against voltage --both dimensionful. But the subtle mathematical point is that in neither of those cases is there a group of symmetry relating different, but equaly valid, observational stances --classes of valid observers. In the physics of space-time, there is such class of valid observations, and the measurements of time and space of one observer are mixed up with the measurements of time and space of another, so it is natural to define the parameters of the transformation as dimensionless numbers. You could insist that (I,V) (intensity and voltage) be a 'vector', but it doesn't make much sense unless you can define transformations that take one stance to another and relate them in a linear way: I'=aI+bV V'=cI+dV with a,b,c,d being the dimensionless parameters that mix them up. That's the reason why in mathematical physics you tend to be more careful and say: Such and such quantities are a vector under SO(3) (rotations); or a vector under O(3) (rotations and inversions-reflections), etc. In the case of Minkowski vectors, it's all about inertial observers. It's what we call the 'Lorentz group'.

Ok. I'm sorry if I missed a particularly subtle point you made. The OP seems to be under the impression that special relativity demands us to admit that space 'deforms'. I was just trying to be helpful, because I think that's an unfortunate misconception. (my emphasis.) Wrong!!! That's what I'm trying to address. And believe me, we've all been there at some point. Even though I'm under heavy workload, believe me; I wanna be helpful. So I've made a little drawing that explains why that's wrong based on my analogy with foreshortening in space. Nothing is deformed. Space is not deformed. The object is not deformed. Yet, foreshortening is real enough that, if you don't take it into account, you're going to damage the paint from the frame of your garage's door, and the ladder, or worse. The explanation that special relativity gives of this is just common sense. Common sense gets you a long way. One must study special relativity and there comes a moment when you naturally understand it, and there's no looking back. That's what I meant.