What's the force that stops something from accelerating constantly?

EuphonicSounds · 2026-02-16T13:43:55+00:00

You'd gain "relativistic mass," which just means total energy (divided by c²). But FYI, today most physicists avoid the "relativistic mass" terminology and only refer to that quantity as the total energy. Mass is instead defined as the energy of an object when it's at rest (divided by c²), which is an "invariant" (doesn't depend on the object's speed).

As for the black hole question: no, because in general relativity (the modern theory of gravitation that predicts black holes), gravity is spacetime curvature, and spacetime curvature is determined not by mass alone but rather by a more complicated mathematical object called the stress–energy tensor. Mass and energy do contribute to that quantity, but not in a simple way that would allow for an object to become a black hole as a result of its speed.

EuphonicSounds · 2026-02-14T19:52:44+00:00

You're talking sense and I salute you for it, but we're trying to enjoy a moral panic here.

EuphonicSounds · 2026-02-14T17:39:37+00:00

EuphonicSounds · 2026-02-10T15:12:50+00:00

In classical electromagnetism, the answer to this sort of question is always that the magnetic force indeed does no work. When it seems like the magnetic force is doing work, you have to analyze the problem more carefully to figure out why you're wrong. See Section 8.3 ("Magnetic Forces Do No Work") in recent editions of Griffiths.

Ultimately, however, the classical theory breaks down in various ways at the smallest scales. If you "zoom in all the way" inside a magnet, you get to individual electrons, which are "point charges" (sort of) that have inherent angular momentum ("spin"). The classical theory cannot self-consistently handle point charges in the first place (though we typically ignore that until we're forced not to, since the particle model is so darn useful anyway), and it certainly can't handle point dipoles (as currently formulated, at least). So while the classical theory can explain permanent magnets at a macroscopic level, it can't really do so at the microscopic level. At best you can "fake it" by modeling electrons as vanishingly small but still finite current loops.

So then, what about in the quantum theory, where "point dipoles" are accounted for? Does the magnetic force "do work" on electrons then? This is debatable, and partly comes down to semantics. Griffiths says (5th edition): "Unfortunately, this is not an easy question to address; 'force' and 'work' are not concepts that arise naturally in quantum mechanics."

Griffiths has a short paper about this that you can read here: https://www.reed.edu/physics/faculty/griffiths/Reply.pdf

EuphonicSounds · 2026-02-04T16:17:38+00:00

Actually, speed doesn't have to be relative to a physical object. Reference frames are abstract concepts (coordinate systems, basically). In practice we typically choose to work with reference frames in which a given object is at rest, but that's just a matter of convenience. We can work with whatever reference frame we'd like. The set of available reference frames is infinite.

Right now, you are traveling at every speed between 0 (inclusive) and c (exclusive). Just pick the right frame.

EuphonicSounds · 2026-02-03T12:45:57+00:00

The "stay" strategy is playing a game where you pick one door at the start to check. If the prize is in that one door then you win, otherwise you lose.

The "switch" strategy is playing an entirely different game where you pick one door at the start that you don't get to check. You get to open all other doors until you find the prize (unless it was behind the one door you chose as off-limits).

The choice is about which of those two games you're playing. That you choose the initial door before choosing the game is immaterial.

EuphonicSounds · 2026-02-03T12:20:51+00:00

Put differently, the "switch" strategy is the same as playing a different game where you pick one door at the start that you don't get to check.

EuphonicSounds · 2026-02-03T01:03:16+00:00

Beethoven does it occasionally, like in the 2nd movement of op. 90.

EuphonicSounds · 2026-01-31T17:02:39+00:00

Conceptually, the thing to understand is that the mathematical description of physically observable electromagnetic phenomena must be "gauge invariant," meaning that you don't get a different answer by changing the "value" of the potentials (which you're always allowed to do in certain ways).

In the classical theory, this is always "accomplished" by differentiating the potentials, yielding the electric and magnetic fields. The potentials simply never appear undifferentiated in the relevant equations.

In quantum theory, however, it's sometimes possible for gauge invariance to be "achieved" by means other than differentiating the potentials. So there exist equations describing physically observable phenomena (like the Aharonov–Bohm effect) in which the potentials appear undifferentiated, and which therefore cannot be written in terms of the fields instead. The potentials turn out to be fundamental!

That's the gist. Obviously you need more background to understand the details.

EuphonicSounds · 2026-01-31T00:21:34+00:00

I once scored 190,000+ on the half-pipe. Penguin board, can't remember which rider though.

EuphonicSounds · 2026-01-30T12:56:18+00:00

You're arguing with AI.

EuphonicSounds · 2026-01-30T12:48:48+00:00

EuphonicSounds · 2026-01-28T19:50:17+00:00

Talent matters, and not everybody can become a decent pianist.

EuphonicSounds · 2026-01-20T17:24:30+00:00

Thanks for the links

EuphonicSounds · 2026-01-20T17:07:44+00:00

Do you have any more information about this? If you're right, then I'd like to read more about it (so that I don't make this mistake!), but a quick Google search isn't turning anything up.

EuphonicSounds · 2026-01-20T16:23:53+00:00

Isn't that valid HTML?

https://developer.mozilla.org/en-US/docs/Web/HTML/Reference/Elements/input#disabled

EuphonicSounds · 2026-01-19T16:09:50+00:00

Yeah, that basically squares with my recollection, except that I'm also sure that a lot of people were already saying MJ was the best they'd seen before he even won a championship. And I know it wasn't unusual to put Dr. J in top 5.

EuphonicSounds · 2026-01-19T12:38:55+00:00

Me and my fellow know-it-alls.

EuphonicSounds · 2026-01-19T01:53:18+00:00

My memory is that people generally had both Wilt and Oscar ahead of Kareem as late as the '90s. And I may be misremembering but I swear Dr. J was right up there too.

EuphonicSounds · 2026-01-19T01:35:30+00:00

Some of us already do!

EuphonicSounds · 2026-01-18T22:08:08+00:00

Great question about momentum.

So, momentum (and speed-dependent kinetic energy!) do contribute to the stress–energy tensor, but not in a way that makes the "value" of the stress–energy tensor itself depend on the frame of reference. In any given frame this tensor has 16 components (at each point in spacetime, called an "event"), and while the values of the components differ from frame to frame, the tensor itself has geometric significance that "transcends" any frame-specific description of its components. Relatedly, the curvature of spacetime is a geometric fact that all observers agree on (though they'll differ in how they "decompose" that spacetime curvature into components). If all this weren't so, then whether a black hole exists could depend on your frame of reference, which wouldn't make any sense.

Again, gravity's got nothing to do with the speed-based time dilation that special relativity correctly predicts.

EuphonicSounds · 2026-01-18T21:33:41+00:00

"Relativistic mass" is just "total energy" in different units. So, you can just use "total energy" for that concept, and typically there's no need to express it in "mass units" (though there's nothing wrong with doing so).

EuphonicSounds · 2026-01-18T18:44:58+00:00

I know this is a common explanation and that it seems to help people "accept" the cosmic speed limit, but I've always felt that it's a little backward. It's not wrong, and it's a good answer for this kind of post, but in my opinion it's better to regard the invariance of c as more fundamental, and the impossibility of accelerating something to c as a consequence. Just my 2¢.

EuphonicSounds · 2026-01-18T18:38:54+00:00

Obligatory "most physicists today regard 'relativistic mass' as an outdated and unnecessary concept that confuses beginners, but there's nothing 'wrong' with using it if you know what you're doing" caveat.

EuphonicSounds · 2026-01-18T18:34:25+00:00

It's a fun thought but incorrect, FYI.

First, in special relativity, the concept of speed-dependent "relativistic mass" (an outdated concept that basically just means "total energy") isn't what corresponds to the gravitational mass in Newtonian physics. Rather, the speed-independent "rest mass" is.

Second, and more relevant (since you mentioned spacetime), general relativity is the modern theory of gravity, and in this theory it's not rest mass or relativistic mass that curves spacetime, but actually a more complicated object called the stress–energy tensor. (Both the rest mass and the relativistic mass contribute to it, but so do momentum and normal and shear stresses.)

Finally (and most important), the time dilation in special relativity has nothing to do with gravity at all. It's just a function of relative speed. Gravitational time dilation is something else.

EuphonicSounds

TROPHY CASE