David Quintero

Physicist in atmospheric sciences, but mainly Jack of all trades and master of none. Canary Islands, Spain.

Blog: https://mundosmultiples.wordpress.com

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Last Notes

2026-09-13 10:49:51 GMT

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I love them, too. Ferns are part of the laurel forests (laurisilva), typical from the Macaronesia region, and they were present in the Gondwana supercontinent.

2026-09-10 12:31:51 GMT

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thanks for sharing. These two guys really deserve recognition. They also show that there's much more in Spain than football. Science is not very popular here, nor well paid. These guys are worth a lot.

2026-08-26 11:50:12 GMT

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there's a hard ethical question here: is it morally justified/ethic for a young mathematician to use AI if it's going to be great for his/her career, but if at the same time is supporting these companies and damaging the environment?
(It can be applied to other people, too, not only mathematicians).
@npub1juz…njnt

2026-08-23 15:27:35 GMT

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interested in your opinion once you finish it.

2026-08-16 16:05:03 GMT

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thank you very much 👍👍

2026-08-16 15:17:57 GMT

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could you please further explain or point out to a resource about the "true by chance" and its relation to Gregory Chaitin?

2026-05-30 22:33:43 GMT

Something I learnt recently in the online course on quantum foundations I'm following is that, in the double slit experiment, you can put in one slit a vertical polarizer, in the other an horizontal. You'll get two bands, as expected, since you're measuring.
But you can introduce, after the two slits with polarizers, diagonal polarizers, and you'll get the interference pattern! With the diagonal polarizers you don't know where the photons come from, you lose information, you have "undone" your measurement, so to say.
Curiously, you can explain everything with classical physics: a vertical and horizontal rays of light can't interfere, so two bands on the screen. And the diagonal polarizer allows interference again.

2026-05-18 07:39:49 GMT

TIL: there's a museum of broken relationships in Zagreb, Croatia. The two creators had a 4 years love relationship that ended, and decided to store their personal and common objects in a museum. The collection grew fast with donations from many people and their failed relationships.
(Via: @npub1cu7…4j9j).
Museum of Broken Relationships - Wikipedia
https://en.wikipedia.org/wiki/Museum_of_Broken_Relationships

2026-04-23 22:10:31 GMT

"The Royale" is the Star Trek TNG episode where Picard is (how not) trying to solve Fermat's Last Theorem. Because in that world, supposedly, the theorem was in the XXIII th century still unsolved.
And there's a book by Arthur C. Clarke where Fermat's original proof is found and it turns to be much more elegant and simpler than Wiles' proof. Even Clarke shows his dislike for the complexity of the proof.

2026-01-27 23:56:11 GMT

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BTW, another source of surprise could be the fact that even being described by mathematics, we can understand that them. The rules could be unreachable for us (they could still be, I guess), but it's a surprise that we have been able to go so far.

2026-01-27 23:42:35 GMT

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I was thinking not in total randomness, but yes, these universes (understood as containers) would probably not be able to have life. But I don't think their existence is _necessarily_ forbidden.

2026-01-27 22:33:58 GMT

Greg Chaitin on famous physicist John Wheeler asking Gödel about uncertainty: 'Well, one day I was at the Institute for Advanced Study, and I went to Gödel's office, and there was Gödel. I said "Professor Gödel, what connection do you see between your incompleteness theorem and Heisenberg's uncertainty principle?" And Gödel got angry and threw me out of his office!'
Whiteson and Warner tell this in their book. Others say that Gödel just changed the topic of the conversation (which it seems more plausible to me). Anyway, W & W explain that in physics you look for the axioms instead of building from them, which "sidesteps incompleteness". You are constantly adding extra axioms whenever you need them, which is something that is not seen as elegant, mathematically speaking.

2026-01-13 22:51:03 GMT

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I wonder if the Gell-Mann matrices of SU(3) can be deduced, too, or they are found just from the commutation relations of SU(3).

2026-01-11 12:11:56 GMT

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very interesting. This reminds me of the anecdote (perhaps apocryphal) that Gauss tried to evaluate Earth's curvature with a geodesic triangle constructed by rays of light.
BTW, I didn't know the \(\pi+KA\) formula. I have studied differential geometry, but mostly oriented quickly to GR. Where does it come from?

2026-01-03 11:14:47 GMT

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the website is fun. It has a great collection of mathematical fiction "classified" by mathematical content and literary quality. It can give ideas for future readings.

2026-01-03 10:47:02 GMT

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Stephen Baxter, the sf writer, used Dante's universe as a 3-sphere in a story: https://www.kasmana.people.charleston.edu/MATHFICT/mfview.php?callnumber=mf910
(The website gave me a warning advice, but it seems to be secure).

2025-12-31 00:19:46 GMT

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impressive, thanks.

2025-12-31 00:04:15 GMT

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that painting definitely has something.

2025-12-27 11:52:27 GMT

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now I'm interested in them, too. I'll keep my fingers crossed that they broadcast them here in the Canary Islands.

2025-12-27 00:04:40 GMT

Sometimes you don't like a book that is considered a classic or that most people consider good. It may happen. It has even happened to scholars. You approached the book in a neutral way and you didn't like it.
But sometimes you actually *want* to like a book, but you can't! It happened to me with Kim Stanley Robinson Mars trilogy. I really wanted to like it, but I couldn't: overwritten, excessive. I read Red Mars, was able to finish Green Mars skipping many parts and didn't have energy to grab Blue Mars. (I emjoyed a lot KSR Aurora, though).
Has this happened to you and with what book?

2025-12-19 13:54:43 GMT

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yes, I think he was a very practical man. It's curious that he, being a theoretical physicist, was more "practical" than Aspect, being an experimental, and intrigued by the true meaning of QM. I guess in this context practical and experimental doesn't overlap.

2025-12-18 22:29:50 GMT

Alain Aspect tells that Feynman considered the EPR paradox in his famous "Lectures on Physics". Feynman said that the EPR could be explained as the case of the interference of just one particle was explained. But not.
Decades later, Feynman changed his mind, as he stated in a famous article, pioneer in quantum information. And when Aspect gave a conference about EPR in Caltech in 1984, an old Feynman attended to the conference.

2025-12-16 12:12:37 GMT

Rainer Maria Rilke, the great German poet, said that the purpose of life was being defeated by greater and greater things.
But I have been defeated just trying to hide the warning messages in a jupyter notebook...

2025-12-10 15:45:53 GMT

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Regarding "QFT for the Gifted Amateur" explains a little bit its motivation, but I don't remember it exactly. A bit I didn't like is that when explaining the SM, they expressed the non-abelian field strength with a cross product,
\[G_{\mu\nu}=\partial_{\mu}W_{\nu} - \partial_{\nu}W_{\mu} +g(W_{\mu}\times W_{\nu}\]
I know it's a minor detail, but somehow I found it annoying. I would have left the cross product restricted to classical physics, chained there for all the eternity.

2025-12-10 15:35:37 GMT

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if you consider a textbook as good, then it's *definitely* a textbook to consider. And your paper goes to my to read list.
When I heard about Zee, I think people said it was good but it didn't do canonical quantization, that it went directly with the path integral (if I remember correctly). So we students, always worried by the exams, left it apart.
BTW, once you have a solid grasp of the SM, is understanding Great Unification easier than the extension of SM with SUSY?

2025-12-10 11:12:12 GMT

Although I took QFT courses, most of it is forgotten, so some years ago I bought "Quantum Field Theory for the Gifted Amateur" (which I'm probably not).
I should revisit it, but I remember it as a good introduction, with more solid state applications than it is usual.
About extensions beyond the SM there's almost nothing. It's a pity but I guess that they don't fit in an introductory text.

2025-12-09 20:47:46 GMT

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regarding the mysteries by Jessica Fletcher, an uncle of mine said that the coincidences of her presence and the murders were so striking that the only explanation was the she was committing the crimes.

2025-12-06 12:44:26 GMT

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Mistral, the European LLM, also chooses the octopus as first option. Amazing. The novelty is that as second option it chooses the elephant:
"I’d go with the elephant for my second pick. Their social bonds, memory, and sheer presence are awe-inspiring. What’s yours—any runners-up?"

2025-12-05 00:06:41 GMT

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incredibly intriguing. Mass hysteria in some violent form?

2025-12-01 08:15:25 GMT

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thank you very much!

2025-11-27 00:03:35 GMT

I learnt some new stuff in Daniel and Kelly's Extraordinary Universe episode "Relativistic beaming". For instance, it's a mystery how super massive black holes in the center of galaxies form (it doesn't seem that they're the result of collapsing stars). And it's a mystery how they accumulated such mass so early in the universe.

2025-11-23 23:52:30 GMT

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following you here, in your blog, is a source of wonderful stuff. Thanks for everything.

2025-11-22 16:28:10 GMT

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indeed I appreciate them a lot! Thank you very much for your time and corrections👍

2025-11-22 14:17:05 GMT

Last thing happening in Spain now, with the crazy prices of houses and flats: ask for loan in a bank, then in another bank, then another... buy as many flats as possible and rent them, mostly to foreigners, with a higher purchasing power.
The "human factor", as Graham Greene put it, plus capitalism is an incredibly dangerous combination.

2025-11-18 13:29:36 GMT

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thank you! My English improves asymptotically as of lately.

2025-11-17 23:02:20 GMT

I bought a copy of "Explorations in Mathematical Physics", by Don Koks. It includes a wide variety of topics: random walks, discrete Fourier transform, geometric algebra, tensors (how not!), a bit of cosmology...
Of course, it's not a treatise on any of these topics, and I think I know some of them. But the mixed approach called my attention, it's good to revisit material and many stuff are certainly new for me. So I hope buying it was a correct decision.

2025-11-16 13:53:37 GMT

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but that begs the question of why is that? In theory, there has been more than enough time for advanced civilisations in the galaxy.

2025-11-16 12:53:05 GMT

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I hope so as well. Indeed, in the podcast they claim two possible solutions (among others) to the inexistence of self-replicant probes. One would be a pessimistic one, the dark forest hypothesis: being silent is the best option to survive because otherwise other civilisations would destroy you to avoid you developing self-replicant probes that storm the galaxy. A more optimistic one they would call it "transcendence", that you refrain from creating this probes because you respect other forms of life and want to watch their development instead of stealing their resources.

2025-11-16 11:36:19 GMT

In his episode on October 2nd, the podcast "Daniel and Kelly's Extraordinary Universe" interviews Phil Metzger, who mentioned something curious, he thinks there will never be an upper limit of the demand of intelligence, so AI servers would eventually need to go to the space, and hopefully as soon as possible, for the good of the planet.
He also mentioned that the concept of Von Neumann probe (self-replicant probes) would be more like an ecosphere of robots with different activities each one, that just one probe doing everything seems too much.

2025-11-10 18:57:43 GMT

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I haven't read anything by McLeod yet. Perhaps that one could be a nice way to begin.

2025-11-07 10:52:22 GMT

"These and other threats, including tariffs, sanctions and the revocation of diplomats’ U.S. visas, effectively killed the deal, according to the nine American, European and developing-nation diplomats directly involved in the negotiations. They spoke on the condition of anonymity out of fear of retribution from the Trump administration."
Trump Officials Accused of Bullying Tactics to Kill a Climate Measure - The New York Times
https://www.nytimes.com/2025/11/06/climate/trump-climate-international-bullying.html

2025-11-04 13:24:25 GMT

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I liked Slow Horses a lot, but yes, there seems to be handicaps with this new one. Thanks, I'll give it a thought.

2025-11-04 12:01:23 GMT

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do you recommend the series?

2025-11-04 11:57:52 GMT

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her writing saying how alone she felt and her attempt not to be alone on Christmas 1938 really touch my heart.

2025-11-03 19:46:58 GMT

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eager for the next ones, when you'll go more into the details!

2025-10-31 00:28:24 GMT

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I saw the quote and thought it was curious. That's why I shared it, not with the idea of showing any deep thought or arcane wisdom. As you suggests, Dostoievsky can't give you the same that Gauss can give. I think the quote only shows the passion Einstein had for Dostoievsky, and how intensely he felt that. That's why I shared it.

2025-10-30 23:39:46 GMT

"Dostoevsky gives me more than any scientist, more than Gauss!"
Einstein, as told by his friend Alexander Moszkowski.

2025-10-25 12:27:51 GMT

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👏👏👏

2025-10-22 20:41:48 GMT

I managed to watch 30 minutes of a YouTube video. I mean 30 minutes entangled with 30 interruptions for commercials.

2025-10-21 10:43:10 GMT

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quite interesting channel, by the way.

2025-10-17 23:25:20 GMT

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ah, yes, you're right! I think the most accurate answer is that I don't like going out late in the night, not because it's late (I read many days until late), but because I don't like the atmosphere of the night: noisy places that barely allow a conversation, the superficialiaty, the posturing. I had been there sometimes, and I had felt very out of place.

2025-10-17 22:40:50 GMT

When my mother was correcting exams and she saw the same mistake over and over again, sometimes she had to go to the dictionary because she began to doubt herself.
I went to a dancing lesson. It finished at 22.00. I'm among the youngest. Once it finished, colleagues at least 15 years older than me went to a pub to listen to music. I didn't want to go. This has happened to me so many times that, as in the example before, sometimes I wonder if everything's ok with me.

2025-10-15 14:11:19 GMT

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perhaps you can find it less expensive and in good shape here: https://www.abebooks.com/servlet/SearchResults?cm_sp=SearchF-_-home-_-Results&ref_=search_f_hp&sts=t&tn=ellipsoidal%20figures%20of%20equilibrium%20
For a moment, I thought it dealt with the model of the ellipsoidal Earth and the calculations derived from there, until I read your comment to the image saying that it was about the hydrodynamics of stars.

2025-10-15 13:47:05 GMT

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it looks interesting, especially being from that author. Have you read (or partially read) his text on black holes?

2025-10-07 15:59:31 GMT

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I vote for SM, GUT and Clifford algebras, in this order of preference, but I'm a not very theoretical physicist, and perhaps you're thinking in a more mathematical audience.

2025-09-20 16:39:19 GMT

TIL: with an estimated lifetime of 1000 years, acid-free paper (pH neutral) is almost surely more reliable than any digital storage device we currently have.

2025-09-19 17:08:15 GMT

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curiously, I have heard nowadays of a line of research that is the opposite of what Wheeler said: instead of all being features of the space-time, the space-time is an emergent property, perhaps from quantum entanglement. (I don't know how promising or solid is this).

2025-09-05 09:40:42 GMT

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, thanks, I understand it now. So, the tachyon without any QFT analysis, using only special relativity, is the one I was used to, and the one mentioned in classic sf stories like Benford's Timescape. I didn't know of the QFT analysis.

2025-09-04 22:08:25 GMT

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but the same Wikipedia article mentions in the "special relativity" section that the tachyons could break causality. It mentions the "tachyonic antitelephone experiment." Or are these tachyons different to those that Feinberg mentions?

2025-09-02 11:44:04 GMT

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you're welcome! I remember the hypothesis of the supernova from the documentary series, but I checked on Wikipedia before telling you, to be sure.

2025-09-02 11:12:37 GMT

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I didn't know that there were so many alternatives for the Siberian Traps. The Ordovician extinction seems very mysterious, Wikipedia days there's no evidence of impact or vulcanism, and the favorite hypothesis seems to be a near supernova.
I watched some time ago a documentary series about the extinctions named "Animal Armaggedon." It was a little bit dramatic, but it was entertaining. Peter Ward (of the Rare Earth hypothesis appeared there).

2025-08-27 22:04:10 GMT

"A Geometrical Introduction to Tensor Calculus," by Jeroen Tromp, teaches you differential geometry with a focus on continuum mechanics and materials, not relativity (although examples for relativity are given). This has been surprising for me in many ways.
For instance, in continuum mechanics, you may need to account for deformations. For instance, dislocations and disclinations are 2-forms (vector valued form and tensor valued form). They are the equivalent of torsion and curvature in relativity, respectively. They obey Bianchi identities, too.
In General Relativity, you can have torsion, then you have the Einstein-Cartan gravitation. But it seems that the universe doesn't need torsion. We're lucky because the field equations with torsion are (even more) horrible to solve!
But in materials science (continuum mechanics), you can have these deformations. So, you need more sophisticated differential geometry than for gravitation. But although you could need all that sophistication to _describe_ your continuum media, I'm not sure if people are actually using it. (I mean, if it's practical).

2025-08-26 09:46:55 GMT

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the fact that someone like Hofstadter couldn't understand the theorems his colleagues were proving somehow soothes me.

2025-08-26 00:07:16 GMT

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thanks for the beautiful personal story. It makes me a little envious. I also want interesting ladies to give me books as gifts.

2025-08-24 10:30:30 GMT

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I have that book as much next to read. Are you enjoying it? It seems that, for some critics, it is the most important work in German literature in the XXth century.

2025-07-29 23:01:42 GMT

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now I want to read that one, too! I read a little bit about her story in Philip Ball's book on science under nazism.

2025-07-29 22:40:42 GMT

"Life need not be easy, provided only that it is not empty." Lise Meitner.

2025-07-25 12:02:27 GMT

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if the very early steps of life seem so "easily" reachable, then, to comply with the Fermi Paradox, the later steps should be the hard ones. I wonder if there's something similar to the proposed "Great Filter" or if it's more a combination of many relatively unlikely factors that multiplied give a very low probability.

2025-07-06 19:51:58 GMT

TIL: perhaps you have heard that black holes are something detected (Cygnus X-1) and well established, while white holes are a mathematical solution, but probably they don't exist.
But the theoretical physicist Carlo Rovelli thinks the opposite! He suggests that there're essentially no black holes in the universe, only stars collapsing more and more slowly due to time dilation. His proposal is that the singularity never forms because of the effects of quantum gravity and that these effects somehow spit out all the matter, creating a white hole.
I guess the community is very sceptical of all this, and rightly so. I wonder how Rovelli explains the detection of gravitational waves via black holes merging. (I'm not discussing his height as a physicist, though. I'm sure he has developed an explanation).

2025-06-30 22:32:28 GMT

I'm in the middle of this video, and I'm astonished by the clarity of the explanations. It's about parallel transport, both from the perspective of Relativity and gauges theories.
Javier García is a physics professor with online courses on mechanics, QFT, General Relativity and more. Yes, it's in Spanish, but it's so good that I think his presentation can be followed and I dare to recommend it.
Transporte paralelo y DERIVADA COVARIANTE: la piedra angular de las teor...
https://youtube.com/watch?v=fqj9pjhZ7CU&si=ndA6cXP-StpNddMD

2025-06-10 23:16:46 GMT

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I guess this comes from the expression for the Schwarzschild radius: more mass means bigger radius. What I'm not sure of is if the mass of the black hole takes into account only the interior of the event horizon or exterior parts as well.

2025-06-10 14:33:37 GMT

TIL: the claim that says that you'll never see a probe you sent towards a black hole crossing the event horizon is correct, but it assumes that the probe is the last object entering into the black hole. If more objects go into the black hole, the event horizon expands and "absorbs" the probe, hiding it from you, forever.
(Learnt in the podcast Daniel and Kelly's Extraordinary Universe"). #physics

2025-06-01 12:28:58 GMT

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More in this vein: he also answers the question of why in the double slit experiment, the electron doesn't get entangled with the slits. The reason is that you can assume that the slits are big and solid, and there's no entanglement because there's barely any interaction. (Actually, there's a little bit of entanglement, but you can safely ignore it).
Indeed, Carroll mentions the book "Quantum Paradoxes" by Aharonov and Rohrlich, where the double slit is set over wheels, so the electron passing through the slits can transmit momentum. Then, the degree of entanglement depends on the lightness of the structure with the two slits.
I would certainly love to see that calculation, but the book has an incredibly funny price, and it is only reasonable to buy it second hand.

2025-05-30 12:14:31 GMT

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I liked it a lot, Bryan.

2025-05-29 17:18:46 GMT

Something cool I learnt in the video of the chapter 8, Entanglement, Q&A, by Sean M. Carroll: not every interaction creates an entanglement. You need each part of the superposition to act differently in the interaction.
For instance, an electron in a superposition of spin up and down states falling in a gravitational field doesn't get entangled with the environment (the field) because both spins act equally under the gravitational field; whereas if instead of a gravitational field you have a magnetic field then spin down and up interact differently, so there you have entanglement with the field.
I guess I should have known this, but in my defense I should say that my QM classes were solving the Schrödinger equation under different circumstances and diagonalising hamiltonians, and almost nothing regarding more conceptual ideas...🤷‍♂️

2025-05-10 16:32:49 GMT

Geographiclib solves both geodesic problems: the direct problem (given initial problem and a distance, find a point), and the inverse problem (given initial and final point, find the distance). It also gives angles with respect to meridians.
They claim to have an ellipsoid model of the Earth with a maximum error of the order of nanometers (!!). The Vincenty approximation for the Earth is at around 0.1 mm of maximum error. One of the authors they cite is Bessel, the mathematician of the XIX century.
Geodesics on an ellipsoid — geographiclib 2.0 documentation
https://geographiclib.sourceforge.io/html/python/geodesics.html

2025-05-05 12:01:19 GMT

Interesting bit about Sean Carroll's April AMA. He says he assumes that brute facts exist (although he says other people think differently). But that for him it's clear.
He mentions the work of the philosopher David Lewis, who wrote about the plurality of the worlds: there're many possible worlds (for instance a world with a different charge for the electron, or different initial conditions...) but we happen to live in this one. That's a brute fact. We can't explain why we live in this particular world.
Anthropic considerations allow you to leave out worlds where it would be impossible for us to exist, but you still have a plethora of possible worlds. Even if you have a principle that selects the world (the best or the simplest world), Carroll says, that principle would be a brute fact, because it could have been another one.
Some people have even claimed that the universe is the greatest brute fact ever.

2025-04-27 11:26:28 GMT

Interesting comment on Sean Carroll's last AMA: he says that Steven Weinberg's book "Gravitation and Cosmology" was a way to teach General Relativity in a very anti-geometric way.
Carroll says that Weinberg wasn't interested in curvature or the geometry of spacetime. Weinberg saw things like, we have a field (the metric), and it has this dynamic, it obeys these differential equations and we solve them. That how we think about the spacetime, the curvature or the geometry wasn't relevant at all. That the only relevant stuff were dots in photographic plates. A very particle physicist point of view, Carroll says.
Carroll says that, while being humble and acknowledging that Weinberg was a much more important physicist than him, he thinks Weinberg was wrong. Carroll thinks that the metaphors and terms we use to understand science are essential to improve and go beyond of our present knowledge, and that they offer understanding.

2025-04-14 14:40:05 GMT

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perhaps Élie Cartan? Although the idea could be in the air before.

2025-02-26 21:38:13 GMT

Since loneliness is high in our societies, I guess someone should have thought that LLMs can keep to those alone some company.

2025-01-29 22:53:05 GMT

A colleague, but above all a friend has created his own YouTube channel to teach Special Relativity with a different point of view.
Another way to introduce Einstein's Special Relativity based on Minkowsk...
https://youtube.com/watch?v=QHAt8vrQ5LE&si=35zxr7oGFLqnRMJ2

2025-01-27 17:02:47 GMT

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For instance, here he comments that electricity was thought to be a fluid time ago. And more recently, some people tried to connect the continuum equations of materials with Maxwell's equations.

2025-01-27 17:00:15 GMT

If you understand Spanish, I recommend this channel, where the author speaks about books on mathematics and physics.
El átomo vorticoso, el rayo globular, los campos de Beltrami y la topolo...
https://youtube.com/watch?v=p91i4ICyPcQ&si=N3SlD2K1mQeQDQ6o

2025-01-17 16:42:35 GMT

I'm reading "The Best of All Possible Worlds," a kind of biography of Leibniz. The author, Michael Kempe, is a world expert on the work and life of Leibniz.
At some moment in 1696, after his 50th birthday, it seemed that Leibniz, always very active and hard worker, was tired, felt uneasy, distracted, and had some apathy. He didn't feel well. He thought that beginning a diary could help him.
In the diary it can be appreciated that Leibniz decided to redouble his efforts, doing even more stuff than before ("actionism", in the words of Kempe); and that, combined with the self-reflection that the diary offered, helped him to surpass that moment he was experiencing.

2025-01-05 20:22:54 GMT

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ah, that perspective I didn't know, perhaps it's one of the ideas that appear in the debate after Norton's paper. I found interesting what @npub1hnp…26ht said that after the physics of the XXth century, what happens in a set of zero measure is not so disturbing (although yes, it's a quite interesting result).

2025-01-05 11:54:48 GMT

Philosopher of #physics John Norton found a solution to Newtonian physics that seems to show that indeterminism is indeed at the heart of the previously thought deterministic Newton laws.
This video does a *great* job explaining it. Except for a few math details regarding the exact building of the dome, everything's in the video!
As you can guess, there has been a lot of heated debate around this problem, but in my humble opinion, what Norton has found seems entirely valid. #philosophy
https://youtube.com/watch?v=EjZB81jCGj4&si=rss7mvG2BU3d4HRq

2024-12-23 13:11:00 GMT

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I'm far from being an expert, but I think that part of the problem with Copenhagen is that even the supporters had different views. Bohr, Pauli and Heisenberg didn't say exactly the same.
Physicists like Sean Carroll say that the Copenhagen interpretation is not very well established, but Carroll is a strong MWI supporter, one has to say.

2024-12-22 14:33:02 GMT

Kurt Gödel found a solution to Einstein's equations that depicted a rotating universe, where all the space-time rotates. This universe would have closed timeline curves, that is, time travel would be possible.
Gödel presented this result in a conference. John Wheeler was there and wrote that in such a universe you could live your life over and over again. In his book on Gödel, Palle Yourgrau says that Wheeler misunderstood Gödel (!).
What Gödel was trying to show was that if time travel is possible, then time, as a subjective experience, can't exist, it's just an illusion. It's not that you repeat your life. Yourgrau says that such closed timelike curves are like circles: points in a circle aren't moving around forever. They just stay there.
Gödel was a platonic mathematician, so if in one possible universe the subjective passing of time is an illusion, then the concept itself is not reliable, not something that universally exists, just an artifact, an illusion just convenient for our universe.
Yourgrau says that these results by Gödel regarding the illusory nature of time haven't been widely accepted.
(More details in "A World Without Time", by Palle Yourgrau). #physics #philosophy

2024-12-18 17:02:07 GMT

Is "perhaps" more American English and "maybe" more British?

2024-12-16 17:33:27 GMT

I'm reading these days "Reflections on Kurt Gödel", by Hao Wang. One of the things that surprised me considerably is that it seems Gödel was as much a philosopher as a mathematician. Perhaps even more a philosopher than a mathematician! At least if you count the time dedicated to each activity. He felt close to Leibniz. #philosophy

2024-12-01 22:31:47 GMT

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is this a generic declaration (very reasonable, by the way), or has the context been lost?

2024-11-24 00:36:22 GMT

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have you ever read Chandrasekhar? Wald seems much more succinct: few calculations in detail for a dense material. Chandrasekhar looks like exactly the opposite: lots of calculations in detail. (Well, and Chandrasekhar deals only with the subtopic of black holes).

2024-11-23 13:08:09 GMT

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a little bit off topic: I've always found that textbooks on GR arrive to black holes after such a long way behind that they're like exhausted, and deal with the topic lightly. Perhaps this is not the case with an specific book, like the one by Chandrasekhar.

2024-11-22 18:18:42 GMT

David Lewis was a philosopher proponent of Humeanism. He was famous for his support of the plurality of possible worlds, which have resonated with those who sympathize with the many worlds interpretation of quantum mechanics. He said once: "anything can coexist with anything else, at least provided they occupy distinct spatiotemporal positions. Likewise, anything can fail to coexist with anything else". That's his so called _principle of recombination_.
From his entry in Wikipedia: "Combined with the assumption that reality consists on the most fundamental level of nothing but a spatio-temporal distribution of local natural properties, this thesis is known as 'Humean supervenience'. It states that laws of nature and causal relations merely supervene on this distribution of local natural properties".
Curiously, for some people, this last definition (Humean supervenience)
seems to be in conflict with quantum entanglement (QE)! Thay argue that
QE precisely says that laws of nature don't just supervene (are a consequence) from the distribution of local natural properties in spacetime, because QE seems to "break" the notion of locality. For others, Humean supervenience can still be saved. There's debate around.
#philosophy #physics

2024-11-22 18:12:54 GMT

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I would have taken one, too!

2024-11-21 17:54:06 GMT

In his October AMA, Sean Carroll explained (at around the beginning of
the third hour) why he supports Humeanism as a philosophy of science. Summing up a lot, he says it's what gives more from less.
Humeanism is big, it deals with many issues, and I wonder if Hume
himself would have subscribed everything. Perhaps the two main points are the "bundle theory of the self", i.e., that there's no such thing as
a self contained in the brain, but a continuous flux of states and
conceptions. I think this idea detaches you from taking yourself too
seriously, and it could bring some peace of mind to people who tends to
worry or be nervous a lot.
Regarding the philosophy of science, Humeanism rejects the independent
reality of the laws of nature. This collides with Platonism, a way of
thinking that many mathematicians (perhaps most of them?) support. A
humeanist would say that the laws of nature explain the regularities
observed, but, following Hume, you can never be absolutely, 100 % sure
that tomorrow the Sun will rise. I don't know what to think here. My
sympathies lie toward Platonism, but I can't say Humeanism is not
reasonable. #philosophy #physics

2024-10-27 11:00:13 GMT

"The condition of being good is that it should always be possible for you to be morally destroyed by something you couldn’t prevent. To be a good human being is to have a kind of openness to the world, an ability to trust uncertain things beyond your own control, that can lead you to be shattered in very extreme circumstances for which you were not to blame."
Martha Nussbaum #philosophy

2024-10-23 22:54:29 GMT

I have a doubt (actually, I have many doubts, but let's go step by step beginning with a #physics doubt):
Every equation written with classical vector calculus can be translated into tensorial form (and many times, it's desirable). But can every equation of physics written with vectors (or tensors) be also expressed with differential forms?
I always see differential forms in the context of electromagnetism, classical mechanics, and (rarely) thermodynamics. But differential forms are essentially absent in areas like fluid dynamics (how many times have you seen the Navier-Stokes equations written with differential forms?), optics, and other areas of physics.

2024-10-20 14:50:41 GMT

#silentsunday
https://media.mathstodon.xyz/media_attachments/files/113/340/301/885/353/999/original/ee727b2d35024e5c.jpg

2024-09-28 17:38:02 GMT

Due to analysing the movement in a rotating frame, the famous Coriolis term appears: \(\boldsymbol{a}_C=-2\boldsymbol{\omega}\times\boldsymbol{v}\), with \(\boldsymbol{v}\) your velocity in the rotating frame and \(\boldsymbol{\omega}\) the angular rotation velocity of the Earth (or another rotating system).
One of the consequences of this term is that, depending on your velocity, a vertical acceleration with respect to the surface of the Earth can appear. It's called the Eötvös effect. If you're moving eastwards, the Eötvös effect pulls you upwards, and if you're moving westwards, the effect pulls you downwards.
It's a certainly small effect for typical velocities in comparison with gravity, but it's there. #physics