John Carlos Baez / is on Nostr

I'm a mathematical physicist who likes explaining stuff. Sometimes I work at the Topos Institute. Check out my blog! I'm also a member of the n-Category Café, a group blog on math with an emphasis on category theory. I also have a YouTube channel, full of talks about math, physics and the future.

homepage: http://math.ucr.edu/home/baez/
blog: https://johncarlosbaez.wordpress.com/
math blog: https://golem.ph.utexas.edu/category/
YouTube: https://www.youtube.com/channel/UCy9yxdnj0yfOiMWvMa47PNw

Last Notes

2024-09-14 17:54:51

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- the Beatles' "Norwegian Wood" is incredibly catchy, and the first Western pop song to use a sitar.

2024-09-13 23:53:21

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- they should repeat it with people who aren't Dutch. 🙃

2024-09-13 18:08:36

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- if you block the email address and/or journal/conference name for each one, does it help at all? Or are they mostly new instances?

2024-09-13 03:43:08

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- you meant to say rig.

2024-09-12 14:58:28

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One calculation argued that the vacuum we know and love will last about 10⁷⁹⁴ years before a bubble of 'true vacuum' forms and destroys our universe. But in June this year, a team of physicists claim to have found a small error in that calculation. Their new estimate is... drum roll, please... only 10⁷⁹⁰ years!
So we now have only 1/10,000 times as long to get stuff done. 🙃
Here's the paper:
https://arxiv.org/abs/2406.05180
and here is an explanation in simple terms:
https://www.quantamagazine.org/vacuum-of-space-to-decay-sooner-than-expected-but-still-not-soon-20240722/
Again, I can't stress too much that there are lots of potential sources of error in these calculations. The most obvious one is: new physics we don't know yet.

2024-09-09 15:29:21

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- if you haven't read it yet, you might enjoy the section in 𝑆𝑢𝑟𝑒𝑙𝑦 𝑌𝑜𝑢 𝑀𝑢𝑠𝑡 𝐵𝑒 𝐽𝑜𝑘𝑖𝑛𝑔, 𝑀𝑟. 𝐹𝑒𝑦𝑛𝑚𝑎𝑛 about Feynman's calculational methods - and how Hans Bethe was better.

2024-06-22 19:00:04

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- According to Wikipedia,
"A lengthy Nuclear Regulatory Commission investigation started in 1995, following allegations of safety problems at the plant. The NRC staff identified so many problems that Maine Yankee Atomic Power Co. decided "it would be too costly to correct these deficiences to the extent required by the NRC and decided to shut the plant down".
https://en.wikipedia.org/wiki/Maine_Yankee_Nuclear_Power_Plant

2024-06-19 18:26:15

When you have 3 helium atoms, they can stick together and form 'trihelium'. But even more impressively, the different energy states of trihelium are predicted to form an infinite sequence of molecules, each 22.6948 times larger than the previous one!
A while ago I talked about dihelium. This consists of 2 helium atoms held together, not by a chemical bond, but by the weak left-over remnants of the electrical forces holding each atom together. Trihelium works the same way, but it's more stable than dihelium. Indeed if you took one of the larger forms of trihelium and removed any one of the 3 atoms, the other two would fly apart.
This bizarre phenomenon was predicted by the Russian physicist Vitaly N. Efimov in the 1970s. He showed it should happen whenever you have 3 identical bosons attracting each other by a short-range force. As they come closer and closer to having enough energy to no longer be bound together, they form an infinite sequence of bound states, where the radius of the nth state is proportional to the nth power of some number λ. This number λ is close to 22.6948, but Efimov showed that it's actually
exp(π/s)
where s is the unique positive solution of
s cosh(π s/2) = 8 sinh(π s/6)/√3
Alas, I don't understand his calculation.
For a long time Efimov's work was just a theoretical prediction. In 2014 a team observed the first two 'Efimov states' in an ultracold gas of cesium. But trihelium is harder to work with, and it's only with great trouble that people have made it at all. So we have not verified that it has Efimov states... but the math and physics is solid.
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https://media.mathstodon.xyz/media_attachments/files/112/644/088/101/918/027/original/ba147bd5de56213a.mp4

2024-06-16 13:37:52

The last time a big galaxy crashed into ours was between 8 and 11 billion years ago. It added about 50 billion solar masses to our galaxy. And its remains, still visible today, are called the Sausage.
Why the funny name? It's the red thing in the picture! This picture shows orbits of various typical stars in the Milky Way. The z direction is at right angles to the galactic disk. There are 3 quite different kinds of stars:
• The green orbit is a star in the galactic disk, like our Sun.
• The blue orbit is a star in the galactic halo. These stars tend to be very old: over 12 billion years old.
• The red orbit is a star in the Sausage. It moves back and forth in a very narrow orbit!
We learned about the Sausage only after 2014, when an EU-run satellite called Gaia began carefully measuring the velocities of many stars in the Milky Way. Many dwarf galaxies that collided with the Milky Way were already known. But the Sausage was hard to detect until we got good at watching stars move by repeatedly measuring their position.
You see, redshifts are only good for telling if something is moving toward or away from you. Stars in the Sausage are moving back and forth from our point of view. Gaia accurately measured the position of a billion astronomical objects, measuring each 70 times in its five-year life! So it could actually see a bunch of stars slowly moving across the sky.
For more on the Sausage:
https://people.ast.cam.ac.uk/~vasily/gaia_sausage/info.html
https://media.mathstodon.xyz/media_attachments/files/112/625/255/739/022/466/original/9647f90ee430f7d2.png

2024-06-15 11:41:33

Even though helium is the least reactive of the noble gases, you can make a molecule of two helium atoms! Yes, He₂ is a thing! It's called 'dihelium' or the 'helium dimer'.
But the two helium atoms aren't held together by a bond. Instead, they're held together by a much weaker force: the van der Waals force. So this isn't an ordinary molecule. It's huge! The distance between nuclei is 70 times bigger than it is for H₂. And it's very loosely held together, so you'll only see it at extremely low temperatures.
It's called a 'van der Waals molecule'.
But what's the van der Waals force? It's actually a name for a few different forces that exist between electrically neutral objects. For dihelium, the most important one is shown in this gif.
Start with two neutral atoms. Each is a nucleus surrounded by electrons. If they start out spherically symmetric, like helium, and far enough apart that their electron clouds don't overlap, there will be no electrostatic force between them.
But wait - the electrons are randomly moving around! Sometimes they move to make each atom into a 'dipole', with the nucleus on one side, and the electrons over on the other side. If these two dipoles point the same way, this lowers the energy - so it will tend to happen. And now the two atoms attract... since two dipoles pointing the same way attract.
But this effect is small. The gif vastly exaggerates how much the electrons move to one side of each proton. And this van der Waals force dies off like 1/𝑟⁶. So we have two objects held together by a weak force... so they will orbit slowly, and far apart, so that the centrifugal force is equally small!
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https://media.mathstodon.xyz/media_attachments/files/112/619/849/994/096/209/original/5a618c066f0f34b2.mp4

2024-06-14 18:50:26

Whenever I see this on the bus it makes me think they're offering some sort of defective wifi access.
https://media.mathstodon.xyz/media_attachments/files/112/615/991/207/242/880/original/cf4f1a70317e2bf2.jpg

2024-06-10 11:54:59

I quit Twitter and moved to Mastodon in October 2022 when Elon Musk took over. Many other academics also came to Mastodon, and I was very happy - see my pinned posts. But most of them later became inactive.
I stick around because I've decided that corporate-owned social media are dangerous - especially now, when authoritarians are spreading their reach. Turns out it's unrealistic to expect that most academics feel this way - yet. They may get the idea when it's too late.
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https://arxiv.org/abs/2406.04005

2024-06-09 10:48:29

If you could watch an individual water molecule, about once in 10 hours you'd see it do this!
As it bounces around, every so often it hits another water molecule hard enough enough for one to steal a hydrogen nucleus - that is, a proton - from the other!
The water molecule with the missing proton is called a hydroxide ion, OH⁻. The one with an extra proton is called a hydronium ion, H₃O⁺.
This process is called the 'autoionization' of water. Thanks to this, roughly one in ten million molecules in a glass of water are actually OH⁻ or H₃O⁺, not the H₂O you expect.
And this explains why protons can move through water much more easily than larger ions can. Let's watch how it works.
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https://media.mathstodon.xyz/media_attachments/files/112/585/740/156/322/310/original/f4ec78e2d2ff1326.mp4

2024-05-21 15:13:59

When global warming gets bad enough to create millions of refugees, just imagine how nasty the EU and US will become. They may just ship people out to the desert to die.
Oh wait, you don't have to imagine! It's happening already:
"A year-long joint investigation by The Washington Post, Lighthouse Reports and a consortium of international media outlets shows how the European Union and individual European nations are supporting and financing aggressive operations by governments in North Africa to detain tens of thousands of migrants each year and dump them in remote areas, often barren deserts.
European funds have been used to train personnel and buy equipment for units implicated in desert dumps and human rights abuses, records and interviews show. Migrants have been pushed back into the most inhospitable parts of North Africa, exposing them to abandonment with no food or water, kidnapping, extortion, sale as human chattel, torture, sexual violence and, in the worst instances, death."
The full story is here: https://archive.is/1tEgl
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https://media.mathstodon.xyz/media_attachments/files/112/479/228/604/482/522/original/17d6aefa15d8fd61.jpg

2024-05-16 08:58:42

Chemistry is like physics where the particles have personalities - and chemists love talking about the really *nasty* ones. It makes for fun reading, like Derek Lowe's column "Things I Won't Work With". For example, bromine compounds:
"Most any working chemist will immediately recognize bromine because we don't commonly encounter too many opaque red liquids with a fog of corrosive orange fumes above them in the container. Which is good."
And that's just plain bromine. Then we get compounds like bromine fluorine dioxide.
"You have now prepared the colorless solid bromine fluorine dioxide. What to do with it? Well, what you don't do is let it warm up too far past +10C, because it's almost certainly going to explode. Keep that phrase in mind, it's going to come in handy in this sort of work. Prof. Seppelt, as the first person with a reliable supply of the pure stuff, set forth to react it with a whole list of things and has produced a whole string of weird compounds with brow-furrowing crystal structures. I don't even know what to call these beasts."
https://www.science.org/content/blog-post/higher-states-bromine

2024-04-14 10:30:40

It looks like they've found protonium in the decay of a heavy particle! 🎉
Protonium is made of a proton and an antiproton orbiting each other. It lasts a very short time before they annihilate each other.
It's a bit like a hydrogen atom where the electron has been replaced with an antiproton! But unlike a hydrogen atom, which is held together by the electric force, protonium is mainly held together by the strong nuclear force.
There are various ways to make protonium. One is to make a bunch of antiprotons and mix them with protons. This was done *accidentally* in 2002 during the first experiment that created antihydrogen. They only realized this upon carefully analyzing the data 4 years later.
This time, people were studying the decay of the J/psi particle. The J/psi is made of a heavy quark and its antiparticle. It's 3.3 times as heavy as a proton, so it's theoretically able to decay into protonium. And careful study showed that yes, it does this sometimes!
The new paper on this has over 550 authors, so I won't list them all. It also has a rather dry title - not "We found protonium!"
• Observation of the anomalous shape of X(1840) in J/ψ→γ3(π+π−), https://arxiv.org/abs/2310.17937
The idea here is that sometimes the J/ψ particle decays into a gamma ray and 3 pion-antipion pairs. When they examined this decay, they found evidence that an intermediate step involved a particle of mass 1880 GeV/c², a bit more than an already known intermediate of mass 1840 GeV/c².
This new particle is a bit lighter than twice the mass of a proton, 938 GeV/c². So, there's a good chance that it's protonium!
https://media.mathstodon.xyz/media_attachments/files/112/268/499/052/720/530/original/ab89c8eac9634b98.jpg