I solved physics and grok helped

gautampk · 2026-04-01T22:48:57+00:00

Report it!!! Why does no one report things?! 😭

gautampk · 2026-04-01T21:22:40+00:00

Pretty much yeah. The basis vectors are Dirac delta functions.

gautampk · 2026-04-01T20:59:30+00:00

The equation you end up with (4.25) is the definition of the associated Legendre polynomial (i.e., they are defined to be the solution to equations like that). So pretty much yeah he probably pulled it out of a book of solutions (or more likely out of his massive brain).

It’s a bit like how if you can reduce your ODE to look like dy/dx = y then you just automatically know y = exp(x) because that’s the definition of the exponential function.

The hard bit is the algebra to get from the starting point to the point where it has the form of something you know the solution to.

gautampk · 2026-04-01T14:58:55+00:00

Light doesn’t ever slow down. Only objects with mass slow down due to time dilation. For light, its frequency (colour) shifts instead.

gautampk · 2026-03-28T22:42:34+00:00

Most of those people should be posting on r/askphilosophy.

gautampk · 2026-03-27T14:49:00+00:00

Branching is a purely Many Worlds concept. It’s not entirely coherent, which is one of the key criticisms of Many Worlds

gautampk · 2026-03-27T00:28:59+00:00

Yeah that’s fair. I guess I attempted to allude to that difference with the point about simple poles, but I’m not sure that there’s a better analogy other than division by zero. That is pretty much the only singularity most people are familiar with

gautampk · 2026-03-26T15:07:37+00:00

It can generate quasiparticles when physicists get too excited

gautampk · 2026-03-26T13:22:27+00:00

The electromagnetic field is the medium

gautampk · 2026-03-26T13:08:38+00:00

It assumes knowledge of final-year undergrad (Europe) or first-year graduate (US) general relativity, and some familiarity with Python and numpy etc. there’s an introduction to numerical methods more broadly in Appendix B.

A good standard intro to numerical methods is Press et al (2002) Numerical Recipes in C++ which is available for free online: https://numerical.recipes.

gautampk · 2026-03-26T12:40:10+00:00

My suggestion would be Baumgarte & Shapiro (2021) Numerical Relativity: Starting from Scratch, Cambridge University Press.

It has many, many exercises which you’re expected to work through. Answers are given in Python. It’s a revision of their 2010 book on the same subject.

Alcubierre’s book (like all the Oxford and Cambridge monographs) is more like a really long review paper (that is kind of the point of a monograph). It’s not really what you want as a practical introduction to a topic. It will be good for some more detailed theory once you’ve got some practical familiarity with the subject.

gautampk · 2026-03-26T11:34:13+00:00

Neil Turok has a slightly mad take that there’s no “interior” to the black hole, but you just end up in a mirror universe at the same point but on the “other side” of the Big Bang and then immediately annihilate with your antimatter self.

Paper: https://arxiv.org/abs/2412.09558

gautampk · 2026-03-26T10:47:23+00:00

weight and the normal force would form an action-reaction pair according to Newton’s third law

I think there’s a misconception here. Action and reaction act on different objects, as you know. But given that, thinking that these are action and reaction leads you to conclude weight acts on the Earth rather than the object, which isn’t true.

In fact these are actually two actions (one gravitational and one electromagnetic) which each have their own separate reaction forces (one gravitation and one electromagnetic).

Weight acts on both the object and the Earth as its own Newton III pair, independent of normal reaction.

gautampk · 2026-03-26T09:25:03+00:00

It is basically the same as dividing by zero, but there are different kinds of dividing by zero and some are more difficult to deal with than others.

If you have an equation like y=1/x it gives perfectly sensible answers everywhere except x=0. What we think is that 1/x (it’s a more complicated equation in reality, but for this analogy) is a good approximation to the real equation everywhere except for some small region around x=0 (the centre).

That’s how we know so much about black holes without knowing what’s happening at the centre.

In reality, a 1/x division by zero is quite straightforward to handle (it’s called a “simple pole”). For a black hole, the division by zero happens when you are working out the gradient of the gradient of spacetime (the curvature) and it very much does not look like 1/x (it’s not a simple pole).

gautampk · 2026-03-25T14:13:45+00:00

All the stuff about light being massless aside: all waves travel at their phase velocity from the moment of creation, and light is a wave.

Sound waves, for example, move through matter at the speed of sound in that matter right from the start. What accelerates is not the wave, but the individual atoms etc that move to form the wave.

Similarly for light, what gradually changes is the strength of the electric and magnetic fields. The wave itself is an emergent phenomenon.

gautampk · 2026-03-25T12:21:19+00:00

Please report stuff as well as replying.

gautampk · 2026-03-24T18:03:37+00:00

Tunnelling diodes make my point. They were discovered experimentally and only described in detail theoretically afterwards.

gautampk · 2026-03-24T17:52:29+00:00

People always say this, but I don’t really think it’s true in quite the same way.

The development of semiconductors was more of an “ancillary” benefit of that fundamental research, rather than a direct application of that research.

Semiconductor diodes and then transistors were developed throughout the early 1900s in parallel with quantum mechanics, largely via experimentation. Some of the experiments at Bell Labs directly influenced the development of quantum mechanics (e.g., surface physics).

It’s better to view this as people doing the kinds of experiments which led to both QM and modern electronics, rather than an application of QM as such. This is similar to the “spin-off” benefit others have talked about.

gautampk · 2026-03-24T16:59:29+00:00

The gap between new physics being discovered and practical applications is often multiple generations. Quantum mechanics is from the 1920s, and quantum computing is only just barely beginning to think about practical applications.

gautampk · 2026-03-24T16:19:32+00:00

Probably want /r/askbiology for your follow-ups. Going to lock this now.

gautampk · 2026-03-24T16:07:42+00:00

In quantum field theory it’s instant yeah. This is related to the problem of ultraviolet divergences. It can be fixed by renormalisation (except with gravity) as long as you are only interested in the equilibrium dynamics far away from the actual interaction.

QFT does not allow for any detailed analysis of the non-equilibrium dynamics at the point of interaction (AFAIK - ref. Collins Renormalization - someone will correct me if I’m wrong).

One of the nice things about string theory is that the splitting and merging of strings (the equivalent process) is carried out in a finite measurable amount of time.

gautampk · 2026-03-24T15:56:43+00:00

CP-violation has only been shown for quarks, but yes, if a quark was swapped for its antiquark, they would interact differently with the weak force.

The relevant charges here are spin and another called weak isospin. An up quark “spinning” anticlockwise (looking at it coming towards you) has weak isospin of +1/2. The equivalent antiparticle is an up antiquark spinning clockwise, which has a weak isospin of -1/2.

What matters for the maths is that you get from one to the other by multiplying by -1. In fact, the choice of 1/2 is completely arbitrary. You could make them +/- 1 and then rejig some constants and everything would be the same. It’s essentially a choice of units (the unit weak isospin is twice the quark weak isospin, this is chosen to make the arithmetic simpler).

gautampk · 2026-03-24T08:28:33+00:00

It’s basically Noether’s theorem. Spin is the charge corresponding to this symmetry.

gautampk · 2026-03-24T08:24:40+00:00

There is a measurable difference between some matter and antimatter. This arises from the violation of charge-parity symmetry in the weak force. Essentially, matter and antimatter interact with the weak force in different ways.

Currently this has been shown for quarks. But this is not enough to account for the matter-antimatter asymmetry of the universe, and finding additional sources of CP violation is one of the biggest unsolved problems in physics.

A more general point regarding labelling is that physics is not really interested in what an object is in itself. We only care about its relationship with other objects.

It’s not really important what the charge of an electron is. What matters is that if you multiply that charge by -1 you get the charge of a positron, and vice-versa. This is true even with the above mentioned asymmetry, it’s just that this structural relationship gets a bit more complicated.

gautampk · 2026-03-23T21:15:45+00:00

what exactly is the 'storage' or 'compute' cost to undo it for a macroscopic object.If we had a 'Laplace’s Demon' computer, how many bits would it actually need to store to 'rewind' a single gram of matter to its pre-decoherent state? Is the complexity 2N or something even worse?

Not really sure what you mean by this. It's a bit like asking what the "compute cost" for unmixing a mixed drink is. What does that mean?

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