Nostr notes by Bartosz Milewski

I am very sceptical. They provide a link to a paper by Tadeusz ...

2026-10-27T09:12:11Z

In reply to nevent1q…n8cd
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I am very sceptical. They provide a link to a paper by Tadeusz Bałaban about the nonlinear sigma model on a lattice. So I assume that they may have been able to prove that the lattice approximation to the YM theory is consistent.

This approximation uses a discrete grid of points in space-time and it breaks Poincare invariance. The actual YM theory is defined in a continuum. The Millenium Prize specifically talks about R^4, not a discretized lattice.

It's fascinating how a simple change of representation may ...

2026-10-18T15:16:18Z

In reply to nevent1q…xlup
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It's fascinating how a simple change of representation may lead to revolutionary progress. After all, these are the same numbers known to humans for thousands of years, since (or before?) the Sumerian civilization. We just write them differently.

In my mind, the closest parallel in recent history is the encoding of mathematical theorems and proofs using computer languages / proof assistants. Homotopy Type Theory is the first serious application of this new system.

For half a millenium Roman mathematicians were saying "We ...

2026-10-18T07:26:32Z

In reply to nevent1q…l5l9
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For half a millenium Roman mathematicians were saying "We need better notation for numbers," and their voices were ignored with "If it ain't broken, why fix it. Besides, we need backward compatibility."

Ah! 1/2 is semis. I was wondering what kind of fractions Romans ...

2026-10-16T22:58:25Z

In reply to nevent1q…mhg8
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Ah! 1/2 is semis. I was wondering what kind of fractions Romans used. I know that Egyptians only used fractions with the numerator 1, except for 2/3 and 3/4.

I was curious about the fraction 1/2 so I looked it up. I found ...

2026-10-15T23:09:22Z

In reply to nevent1q…yctv
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I was curious about the fraction 1/2 so I looked it up. I found the source that says it was 4,652 paces. Is this the same stone?
https://romaninscriptionsofbritain.org/inscriptions/2139

This is not a typical example. Idris is a language that's ...

2026-10-15T10:19:19Z

In reply to nevent1q…xmdd
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This is not a typical example. Idris is a language that's practically maintained by one person, Edwin Brady. I gave up on Idris long time ago. Cabal is a package manager from hell.

If I get an error message like this, I immediatly pass it to AI. As a human programmer, I'm not capable of processing it.

Duh! They could have asked me. Lasers will not work for fermions, ...

2026-10-07T17:59:30Z

In reply to nevent1q…v4lt
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Duh! They could have asked me. Lasers will not work for fermions, period. Neutrinos are fermions. I'm shocked that this was even proposed.

One could also argue that nuclear weapons damocletized the fate ...

2026-10-01T12:10:23Z

In reply to nevent1q…npav
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One could also argue that nuclear weapons damocletized the fate of humanity.

It has already spread to other wars: Iran, Houthis, Hezbollah are ...

2026-10-01T11:20:55Z

In reply to nevent1q…npav
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It has already spread to other wars: Iran, Houthis, Hezbollah are all using drones. And the US is forced to use Patriot missiles to shoot them down.

In modern times the same could be said about drones democritizing ...

2026-10-01T11:08:14Z

In reply to nevent1q…r47l
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In modern times the same could be said about drones democritizing warfare

One thing is sure, Putin will not call it a ...

2026-09-20T13:45:02Z

In reply to nevent1q…gc0k
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One thing is sure, Putin will not call it a "mobilization." Maybe a "special recruitment operation" or some such nonsense.

You do understand that bisons are us in this parallel?

2026-09-12T16:19:02Z

In reply to nevent1q…hc54
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You do understand that bisons are us in this parallel?

The invisible hand of the market will sort out the tension ...

2026-09-12T16:11:38Z

The invisible hand of the market will sort out the tension between AI and humanity. The same way it dealt with the bison problem in America... Sucks to be a bison, though.😟

That's a good idea. I will also sketch the main points and ...

2026-09-10T10:58:57Z

In reply to nevent1q…l34k
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That's a good idea. I will also sketch the main points and major obstacles in the beginning.

My problem is that there isn't a lot of literature. There is Street with 2-categorical approach, Paré whose conventions are opposite of mine, Shulman and Koudenburg with virtual categories. And I have to translate everything to string diagrams (and Haskell code).

Thanks. I'll try to rework it so it's more ...

2026-09-10T09:46:19Z

In reply to nevent1q…rn5j
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Thanks. I'll try to rework it so it's more self-contained. These universal constructions are not very intuitive.

I have a draft of a blog post about Yoneda structures in proarrow ...

2026-09-10T08:39:28Z

I have a draft of a blog post about Yoneda structures in proarrow equipments. Any feedback would be very welcome.
https://bartoszmilewski.com/?p=15072&preview=1&_ppp=7e33406e42

For me the connection between categorical limits and calculus ...

2026-09-09T16:33:26Z

In reply to nevent1q…a6dk
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For me the connection between categorical limits and calculus appears when you can define an iterative process, expecially if a category is a poset or is filtered.

For instance, you get a fixed point of an algebra by iterating the powers of a functor. Or you are defining smaller and smaller neighborhoods using sieves or sigma-algebras (hence integrals).

I realize this is handwaving, but categorical nomenclature evolved by generalizing concrete concepts from other areas of math.

Integral notation is preferred mostly because it's a ...

2026-09-09T15:11:05Z

In reply to nevent1q…5vyw
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Integral notation is preferred mostly because it's a (co-)limit. Just like the integral is a limit of a sum.

In category theory we have coends and ends. Coends are ...

2026-09-09T11:39:24Z

In category theory we have coends and ends. Coends are generalized sum types, so they corresponds to integrals in calculus and use integral notation.

Ends are generalized products. The main reason we don't use such things in calculus is that we can always convert a product into a sum by using a logarithm. Not so in category theory. The closest we get to logarithms is in representable functors.

Nostr event nevent1qqs0wq0nt5rc6gfl8mduwdl7s2zr9e8as5eh4z766xyc3h3xtjdxzdgzypraq6deyfcc9j28lf5hfsed0n0cwe84j9h0pekcsqghyzev78d4xq6gkh6

2026-08-28T15:18:12Z

In reply to nevent1q…0g4j
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I couldn't resist some back of the envelope calculations. ...

2026-08-25T18:57:48Z

In reply to nevent1q…tdt9
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I couldn't resist some back of the envelope calculations.
Schwarszchield radius: \[r = \frac{2GM}{c^2}\]
Newton's gravitational acceleration:
\[a = \frac{GM}{r^2}\]
Acceleration at the horizon:
\[a = \frac{GMc^4}{4G^2M^2} = \frac{c^4}{4GM}\]
Just looking at orders of magniture: \(c = 10^8\), \(G-10^{-11}\), \(M = 10^{41}\) gives the approximation \(a=10^2\), which is close enough.

Yes. "When the denser sima comes to the surface it forms ...

2026-08-25T12:45:16Z

In reply to nevent1q…3kn7
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Yes. "When the denser sima comes to the surface it forms mafic rocks."
https://en.wikipedia.org/wiki/Sima_(geology)

This was supposed to be a comment to @npub1nf4…nqe4 post about ...

2026-08-24T19:11:41Z

In reply to nevent1q…a8mw
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This was supposed to be a comment to John Carlos Baez (npub1nf4…nqe4) post about the mantle

In school I learned about sial and sima, which are now considered ...

2026-08-23T15:20:54Z

In school I learned about sial and sima, which are now considered antiquated terms.

The saddest thing is when people of some intelligence whom you ...

2026-08-22T11:34:54Z

In reply to nevent1q…ag24
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The saddest thing is when people of some intelligence whom you used to respect turn into rhinos. You suddenly remember wondering about the hoove-like shape of their shoes and some huffing and puffing you dismissed long time ago as the product of your imagination.

I had a whole blog post about this. ...

2026-08-20T20:22:32Z

In reply to nevent1q…5c6g
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I had a whole blog post about this.
https://bartoszmilewski.com/2019/03/27/promonads-arrows-and-einstein-notation-for-profunctors/

Or, if you're a physicist, think of a profunctor as a mixed ...

2026-08-20T10:38:58Z

In reply to nevent1q…dny3
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Or, if you're a physicist, think of a profunctor as a mixed variance tensor 𝑝ⁱₖ. Then a coend is just a trace of this tensor, 𝑝ⁱᵢ: \[ \int^i p i i \]

This might be more accessible: ...

2026-08-20T07:41:18Z

In reply to nevent1q…hrj5
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This might be more accessible:
https://bartoszmilewski.com/2017/03/29/ends-and-coends/

It's a very deep analogy. Just like an integral, a coend is a ...

2026-08-19T20:34:34Z

In reply to nevent1q…6snu
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It's a very deep analogy. Just like an integral, a coend is a sum: It's a coproduct modulo some identifications, taking account of the arrows in the category. The x occurs in positive and negative positions (covariant/contravariant) just like in a convolution or Einstein summation. A (co-)presheaf F is like a vector indexed by x, in which case the coend is like a trace, and C(x, a) is like a Kronecker delta. In fact it becomes a delta if the category is discrete. Should I go on... ?

Exactly! Under the coend, the hom-functor acts like a delta ...

2026-08-19T18:57:14Z

In reply to nevent1q…h5jc
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Exactly! Under the coend, the hom-functor acts like a delta function. I often say that we can "integrate over the hom-functor." The Australians call it the ninja Yoneda reduction.
∫ˣ𝐶(𝑥,𝑎)×𝐹𝑥≅𝐹𝑎

More precisely, the do notation would be used to create a ...

2026-08-19T08:23:13Z

In reply to nevent1q…7phr
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More precisely, the do notation would be used to create a distribution, and something like performDist would integrate it with a test function.

So an integral would play the role of the Haskell "do" ...

2026-08-19T07:35:32Z

In reply to nevent1q…hha6
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So an integral would play the role of the Haskell "do" notation?

Of course it all depends on the definition of ...

2026-08-16T12:59:32Z

In reply to nevent1q…6zf9
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Of course it all depends on the definition of "interesting." Yoneda lemma is definitely interesting as it's used, directly or indirectly, in almost every proof in category theory. So the level on interesting could be measured using an algorithm not unlike Google page rank.

Interesting problems might be the ones whose formulation and/or ...

2026-08-16T12:08:22Z

In reply to nevent1q…973f
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Interesting problems might be the ones whose formulation and/or proofs can be efficiently compressed. Famously, the Fermat's last theorem is very compact. So is Riemann's hypothesis. The Langland's program attempts to compress number theory and geometry into one package. And so on. So a good AI prompt might be to search for problems with low Kolmogorov's complexity.

"The magnetic field of a magnetar would be lethal..." I ...

2026-08-06T14:24:01Z

In reply to nevent1q…vwcf
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"The magnetic field of a magnetar would be lethal..." I don't doubt that it would be lethal, but I'm curious which physical effect of the static magnetic field would kill you first. There is a discussion about it:
https://www.reddit.com/r/AskPhysics/comments/1flxajv/could_a_strong_enough_magnetic_field_kill_someone/

A detective with high moral standard just seemed much less ...

2026-08-01T13:02:45Z

In reply to nevent1q…9c3n
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A detective with high moral standard just seemed much less plausible than him being a {spoiler}. So it's a deep reflection on human nature.

For context: ...

2026-07-31T12:34:54Z

In reply to nevent1q…ayrl
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For context:

They also mention the aplty named lokiarcheon

2026-07-26T10:36:23Z

In reply to nevent1q…hjwc
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They also mention the aplty named lokiarcheon

So it is a weird case of entanglement that involves mass. QM is ...

2026-06-13T21:42:53Z

In reply to nevent1q…p6ee
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So it is a weird case of entanglement that involves mass. QM is so weird!

I find this confusing: "If one could measure directly that ...

2026-06-13T17:38:14Z

In reply to nevent1q…dl6v
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I find this confusing: "If one could measure directly that neutrino's mass, it would be found to have mass \(m_i\) with probability ⁠\(|U_{\alpha i}|^2\)."

Consider a beta decay. We can measure the energies and momenta of the neutron, the proton, and the electron. From that we can calculate the energy (mass) of the neutrino. Do we always get one of the \(m_i\)? But we already know the flavor, so we can't! Notice that we are not performing a measurement on the neutrino itself, so there is no "wave function collapse."

I'm trying to think of mass/energy as analogous to spin/angular momentum. Is the mass of the neutrino entangled with the masses of other particles in beta decay?

Agreed. What I called \(E_i\) is the portion of E allotted to the ...

2026-06-13T13:58:47Z

In reply to nevent1q…0lgd
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Agreed. What I called \(E_i\) is the portion of E allotted to the i'th mass eigenvalue--your \(|\alpha_i|^2 E_i \). The question is, how \(|\alpha_i|\) are fixed. Does every electron neutrino start with the same mixture, or is it determined by the kinematics?

Here's my understanding: In a frame where the neutrino is ...

2026-06-12T19:40:05Z

In reply to nevent1q…3rjc
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Here's my understanding: In a frame where the neutrino is stationary, it has a fixed mass equal to its energy. This is its total energy. It is split into three parts \(E=E_1+ E_2+ E_3\), which remain fixed for the lifetime of the neutrino. If we were to weigh such a neutrino (e.g., in a gravitational field) we'd get a number that is somewhere between the lightest and the heaviest mass eigenstates (assuming they are positive). And this mass is different for each particular neutrino, depending on the kinetics of the process that produced it. Is that correct?

I wonder how this is reconciled with kinematics? The dispersion ...

2026-06-12T16:38:05Z

In reply to nevent1q…2dv8
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I wonder how this is reconciled with kinematics? The dispersion formula tells us that \[m_0^2 = E^2 - p^2\]
We can get E and p from conservation laws. Does it mean that a neutrino is produced and propagates with a particular fixed invariant mass \(m_0\) that depends purely on the kinematics of the creation process?

When you play a diminished seventh chord on a guitar, you can ...

2026-05-14T19:23:24Z

In reply to nevent1q…xuqc
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When you play a diminished seventh chord on a guitar, you can shift it in increments of 3 frets to get the same cord, but inverted. Red Hot Chili Peppers used this trick in Road Trippin'

Our worm-like ancestors were cyclops. When they decided to start ...

2026-05-07T11:17:01Z

In reply to nevent1q…9uxu
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Our worm-like ancestors were cyclops. When they decided to start swimming, the central eye squeezed out two side eyes and was itself reduced to the pineal gland that to this day regulates our circadian cycle.

https://theconversation.com/our-modern-vision-evolved-from-an-ancient-one-eyed-worm-creature-278120

I find it very telling that UAE decided to drop out of OPEC. ...

2026-05-04T18:05:06Z

In reply to nevent1q…yfax
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I find it very telling that UAE decided to drop out of OPEC. There seems to be a race to pump and sell as much oil before the demand disappears.

The side effect of the wars in Ukraine and in Iran is that countries are finally realizing that you cannot rely on uninterrupted supply of oil. The US is an outlier, as it can burn its own oil with abandon, stinking up the whole planet.

Unfortunately, this is offset by Citizens United, which gives ...

2026-04-16T07:48:37Z

In reply to nevent1q…8pdx
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Unfortunately, this is offset by Citizens United, which gives rights to corporations

On the other hand, humanity is a transient problem. We are ...

2026-04-15T18:40:45Z

In reply to nevent1q…ts0u
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On the other hand, humanity is a transient problem. We are nearing peak humanity, after which there will be exponential decay. As life gets more and more comfortable, the prospect of raising children becomes less and less atractive.

By coincidence, yesterday I asked Claude about the most common ...

2026-04-14T18:03:23Z

In reply to nevent1q…607w
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By coincidence, yesterday I asked Claude about the most common form of life.

By Number of Individuals: Bacteria (domain Prokaryota) dwarf everything else on Earth. Estimates put the total number of bacterial cells at around 10³⁰ (one nonillion) — that's more than the number of stars in the observable universe.

But viruses outnumber bacterial cells 10 to 1.

I think we are all hallucinating

2026-04-14T15:52:18Z

In reply to nevent1q…6773
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I think we are all hallucinating

A good source of information is ISW. ...

2026-04-14T08:35:53Z

In reply to nevent1q…nftk
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A good source of information is ISW. https://understandingwar.org/research/russia-ukraine/russian-offensive-campaign-assessment-april-13-2026/

This is how Claude explains the sudden change: The fall of ...

2026-04-14T08:34:01Z

In reply to nevent1q…t579
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This is how Claude explains the sudden change: The fall of Avdiivka triggered a phase where Russia, emboldened and pressing forward across open ground, ran headlong into a Ukraine that had massively scaled up cheap, lethal FPV drone warfare to compensate for its artillery shell shortage. The combination of Russian infantry-wave tactics and Ukrainian drone density proved catastrophically costly for Moscow.

I think Vance was sent to Hungary and to Pakistan as a punishment ...

2026-04-12T21:08:47Z

In reply to nevent1q…m8ev
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I think Vance was sent to Hungary and to Pakistan as a punishment for his opposition to the war in Iran. He's a despicable guy, but his IQ is slightly higher than Trump's, and that's a fatal flaw in Trump's eyes

You can also find microtonal influences in the Amercian blues. On ...

2026-04-10T18:18:14Z

In reply to nevent1q…stld
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You can also find microtonal influences in the Amercian blues. On a guitar you can do all kinds of bends, which gives the blues this emotional, longing quality.

Microtonality can be also heard in singing (before autotune). I think that's what gives me a lump in the throat every time I listen to Billie Holiday's Strange Fruit. Her voice matches perfectly the imagery.

I love their music. I was wondering when you'd mention them

2026-04-10T07:30:33Z

In reply to nevent1q…vkcx
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I love their music. I was wondering when you'd mention them

Maybe some republicans could be persuaded to join in the vote for ...

2026-04-07T18:43:09Z

In reply to nevent1q…dxl5
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Maybe some republicans could be persuaded to join in the vote for invoking the Twenty-fifth Amendment

The most surprising thing is that these virtual particles are ...

2026-03-25T22:12:55Z

In reply to nevent1q…el5n
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The most surprising thing is that these virtual particles are able to bend spacetime. 98% of the mass of any star is virtual quarks and that's what generates their gravitational field.

That reminds me of the lemur aye-aye that also has very long ...

2026-03-06T23:50:07Z

In reply to nevent1q…t29j
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That reminds me of the lemur aye-aye that also has very long fingers.

Unless the perfect fifth is a cultural artifact

2026-02-22T00:15:23Z

In reply to nevent1q…fq9d
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Unless the perfect fifth is a cultural artifact

I can confirm the Polish version: - jej psa (accusative case of ...

2026-02-20T19:44:18Z

In reply to nevent1q…k8rr
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I can confirm the Polish version:
- jej psa (accusative case of her dog)
- swojego psa (same but reflexive)

It made me wonder what other physical phenomena exhibit this kind ...

2026-02-17T09:06:44Z

In reply to nevent1q…8z63
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It made me wonder what other physical phenomena exhibit this kind of resonant behavior, and I thought of the Titius-Bode law of planets. Wouldn't it be cool if it was explained using the zeta function? (You also mentioned the rings of Saturn, which is a similar phenomenon.)
https://en.wikipedia.org/wiki/Titius%E2%80%93Bode_law

The piñata effect: At the final moment of a black hole ...

2026-01-28T13:48:40Z

The piñata effect: At the final moment of a black hole evaporation through Hawking radiation, all objects that were swallowed by it suddenly come back, thus restoring the conservation of information required by quantum mechanics.

This is even more obvious in constructive mathematics, where ...

2026-01-28T11:01:11Z

In reply to nevent1q…w79z
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This is even more obvious in constructive mathematics, where things are constructed rather than discovered. The ideas that are effective are kept alive by natural selection. Wigner was wrong-- the effectiveness of mathematics is very reasonable.

Maybe we are moving with the speed of light in the fourth ...

2026-01-15T11:41:45Z

In reply to nevent1q…cs58
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Maybe we are moving with the speed of light in the fourth dimension and it shrinks to zero.

In other words, the radius of curvature is a little more than one ...

2026-01-11T11:50:15Z

In reply to nevent1q…r2mn
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In other words, the radius of curvature is a little more than one AU, the distance between the Sun and the Earth

Omnipotent within limits

2026-01-07T14:02:14Z

In reply to nevent1q…7c8r
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Omnipotent within limits

I can imagine Stephen Wolfram's dilemma: Is the universe a ...

2025-12-24T10:24:40Z

In reply to nevent1q…35u3
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I can imagine Stephen Wolfram's dilemma: Is the universe a cellular automaton? Or was I wrong all along, and it's a billiard ball?

The dark archive reminds me of the Second Foundation as the ...

2025-12-22T13:02:45Z

In reply to nevent1q…4f5y
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The dark archive reminds me of the Second Foundation as the defense against the Mule

For scale: light travels 1.5 km (or about 1 mile) during that ...

2025-12-22T09:55:35Z

In reply to nevent1q…dpvu
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For scale: light travels 1.5 km (or about 1 mile) during that time

The US has a huge infrastructure debt. All those overhead power ...

2025-12-20T17:27:30Z

In reply to nevent1q…e8w2
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The US has a huge infrastructure debt. All those overhead power lines that snap every time the wind starts blowing. Not to mention the esthetic nightmare of tangles of sky-obscuring wires in every residential area. Most Americans don't even notice it.

I whould divide the two numbers and see if the result is less ...

2025-12-16T20:36:32Z

In reply to nevent1q…9u3h
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I whould divide the two numbers and see if the result is less than one. The advantage is that you can cancel the factor of 2⁴

What's fascinating about burds is that they have to be very ...

2025-12-06T12:06:39Z

In reply to nevent1q…pxc9
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What's fascinating about burds is that they have to be very thrifty with their brains, or they wouldn't be able to lift them into the air. And their brains have to deal with 3-d navigation and superior vision. Compared to birds, human brains are extremely wasteful.

I'm imagining a taffy machine running for billions of years, ...

2025-11-29T08:39:01Z

In reply to nevent1q…heda
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I'm imagining a taffy machine running for billions of years, with an emerging Taffian civilization discovering Taffian physics, when suddenly the movement is reversed.

I wonder if it could be undone. ...

2025-11-27T22:19:24Z

In reply to nevent1q…9utp
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I wonder if it could be undone.
https://www.youtube.com/watch?v=UpJ-kGII074

The centrifugal acceleration is the rate of change of velocity. ...

2025-11-06T14:03:47Z

In reply to nevent1q…yr7c
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The centrifugal acceleration is the rate of change of velocity. Velocity vector just rotates with the angular velocity \(\omega\). So its rate of change is the length \(v\) times the angular velocity: \(a = v \omega \). Since \(v = r \omega\), we get
\[a = r \omega^2 = v^2/r \]

Naively, the centrifugal force increases with distance, \(F = m ...

2025-11-06T13:46:00Z

In reply to nevent1q…nun7
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Naively, the centrifugal force increases with distance, \(F = m \omega^2 r\), but that is only true if you keep the angular velocity constant. In your case, you are keeping the angular momentum, \(L = m r^2 \omega \) constant. Thus \(\omega = \frac{L}{m r^2}\) and \(F=\frac{L^2}{m r^3}\)

Although gravity is not a Y-M field, you can formulate it as a ...

2025-11-03T17:04:04Z

In reply to nevent1q…gxus
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Although gravity is not a Y-M field, you can formulate it as a gauge theory of the local Poincare group. The "gauge potentials" for translations are vierbeins (tetrads) and spin connections correspond to local Lorentz transformations.

We used this trick when working with supergravity. The regular Y-M fields were just the components of gravitational fields in compactified dimensions, a la Kaluza-Klein.

I think its the Kolmogorov-Arnold theorem ...

2025-10-30T13:09:52Z

In reply to nevent1q…3g3k
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I think its the Kolmogorov-Arnold theorem
https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Arnold_representation_theorem

I know the pain. You want to simplify things but you don't ...

2025-10-22T19:45:56Z

In reply to nevent1q…qrqj
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I know the pain. You want to simplify things but you don't want to lie.

Since you mention that the simple Feynman diagram for ...

2025-10-22T14:06:16Z

In reply to nevent1q…0c9m
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Since you mention that the simple Feynman diagram for electron/positron annihilation is not physical, the same is true about the two others. You cannot satisfy the conservation of energy-momentum on-shell for these diagrams. And that's lucky, otherwise electrons in vacuum would spontaneously emit photons.

I voted for the bubble, but the technology behind AI will have ...

2025-10-09T10:01:51Z

In reply to nevent1q…n020
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I voted for the bubble, but the technology behind AI will have many useful applications. So it's just like the dotcom bubble: many companies went bankrupt, but the internet survived. It's a good bubble for the technology, bad for the investors.

Don't get me wrong, I don't doubt the reality of the AB ...

2025-10-06T20:25:40Z

In reply to nevent1q…02kr
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Don't get me wrong, I don't doubt the reality of the AB effect. I'm just sceptical about the arguments that it somehow proves that the magnetic potential is "real," and not a clever computational trick.

Since we're on the subject, I'm growing a bit sceptical ...

2025-10-06T18:42:23Z

In reply to nevent1q…jfpr
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Since we're on the subject, I'm growing a bit sceptical of the AB effect.

AFAIK, in the actual experiment we have an "infinite" string of electrons whose spins are aligned in one direction, so their magnetic fields cancel each other. We replace these electrons with a classical magnetic potential, and it looks like the passing electron can feel this potential, even though the (classical) field strength vanishes.

At what point can stacking N electrons on top of each other be described by a classical potential? It's not a phase transition. For any finite N, the system is just a bunch of electrons interacting by bouncing photons back and forth.

In physics, a conservative force is a force with the property ...

2025-10-06T16:37:51Z

In physics, a conservative force is a force with the property that the total work done by the force in moving a particle between two points is independent of the path taken.

In HoTT, the value of a mapping out of identity type does not depend on the path, only on its endpoints.

The tricky part is when the path is closed. The total work then is zero. In HoTT there are non-trivial paths that cannot be shrunk to a point. This reminds me of the Aharonov-Bohm effect. I wonder how far one can stretch this physics analogy.

On the bright side, they don't burn scientists at the stake ...

2025-10-06T08:35:18Z

In reply to nevent1q…2la7
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On the bright side, they don't burn scientists at the stake any more.

Great video! I think this is not just a physics problem, but a ...

2025-10-05T19:16:53Z

In reply to nevent1q…sz2f
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Great video! I think this is not just a physics problem, but a more general societal problem. We are living in times of unprecedented inequality. This is obvious when you look at the ownership of resources, with all these billionaires monopolizing financial wealth. But there is a similar divergence in the distribution of knowledge. Only the top one percent have the means, the dedication, and the ability to get basic understanding of the current knowledge in any given area of science. The physics-bashing or anti-vax propaganda is just a reflection of the rise of populism in politics. Uneducated people are easier to manipulate.

"True" chemical bond is the result of a (crude) ...

2025-10-04T11:05:12Z

In reply to nevent1q…r3j2
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"True" chemical bond is the result of a (crude) approximation, and as such it has its limitations.

For instance, we assume that the outer electron shell of the carbon atom has four lobes forming a tetrahedron (that's what the black blobs with four holes represent). It's a result of the hybridization of the S and P orbitals, which is an approximate solution of the Schroedinger equation.

Next we assume that when atoms form compounds, they essentially keep the shapes of their orbitals. This is the basis of stick models. Again, it's a crude approximation.

Theoretically, we could just solve the Schroedinger equation for all the electrons and nuclei and be done with it--no orbitals, no hybridization, no sticks. Just one glorious n-electron wave function. Since we can't do it, we use the crutches of valence, stick models, Hartree-Fock approximations, etc.

It makes sense. For a moment I thought that it would change ...

2025-10-02T11:45:41Z

In reply to nevent1q…czpv
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It makes sense. For a moment I thought that it would change chirality, but it doesn't.

There is one place in QFT where mass enters linearly: in the ...

2025-10-02T10:53:28Z

In reply to nevent1q…w8jh
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There is one place in QFT where mass enters linearly: in the Lagrangian and the propagator for fermions. I'm not sure if it only influences polarization, or dynamics as well.

I read the introduction, but unfortunately it doesn't talk ...

2025-10-01T11:43:53Z

In reply to nevent1q…n9h9
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I read the introduction, but unfortunately it doesn't talk about the mechanism for the production of heavy elements. You're right that beta decay is slow, but I can imagine that the merger could produce neutron rich isotopes of, say, mercury, which would then slowly decay into gold. Either way, a neutron star has an abundance of neutrons. Even the outer crust contains neutron-heavy isotopes. It's the protons that are hard to come by.

I'm trying to understand why neutrino oscillations would help ...

2025-09-30T23:09:43Z

In reply to nevent1q…3d0m
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I'm trying to understand why neutrino oscillations would help gold creation. Neutron stars are all neutrons, so in order to get gold you'd need to produce protons. These could come from beta decay, which also produces electron anti-neutrinos. These could oscillate into muon anti-neutrinos, which would prevent them from turning protons back to neutrons + positrons. Is that what's happening?

Make sure you have a good microphone. Sound quality is even more ...

2025-09-26T15:22:44Z

In reply to nevent1q…5cqh
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Make sure you have a good microphone. Sound quality is even more important than video quality.

So how exactly would you argue that the Universe doesn't have ...

2025-09-18T22:17:40Z

In reply to nevent1q…gjcd
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So how exactly would you argue that the Universe doesn't have an equator? Just curious.

My guess would be Compton scattering

2025-09-11T15:09:47Z

In reply to nevent1q…ymfm
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My guess would be Compton scattering

That makes sense. Inside a star, the accretion would be more ...

2025-09-11T13:10:28Z

In reply to nevent1q…6wr9
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That makes sense. Inside a star, the accretion would be more uniform, thus no fluctuations caused by chunky matter found in galaxies. And the outer layes of the star could absorb the resulting X-rays.

One argument against black holes is that LRDs don't emit ...

2025-09-11T12:22:42Z

In reply to nevent1q…0t0t
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One argument against black holes is that LRDs don't emit gamma rays, and don't fluctuate.

Here's another explanation of red dots by Nandal and Loeb. ...

2025-09-11T11:15:14Z

In reply to nevent1q…2zwj
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Here's another explanation of red dots by Nandal and Loeb.
https://arxiv.org/abs/2507.12618

I looked at the original paper and I'm confused. They are ...

2025-09-04T11:26:04Z

In reply to nevent1q…smdl
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I looked at the original paper and I'm confused. They are saying that the actual equations depend on the squares of masses, but the non-relativistic approximation becomes linear in the masses. That doesn't make sense.

If gravitational effects only depend on the square of the masses, ...

2025-09-04T11:15:12Z

In reply to nevent1q…4q5f
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If gravitational effects only depend on the square of the masses, I wonder why they are saying: "More gravitational lensing is also what you’d expect from neutrinos with negative masses."

"the Higgs boson of the Standard Model of particle physics, ...

2025-09-04T11:06:22Z

In reply to nevent1q…akez
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"the Higgs boson of the Standard Model of particle physics, which has an imaginary mass in its uncondensed phase". That's what makes it unstable, though.