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John C. Baez

@johncarlosbaez.bsky.social

400 followers 130 following 190 posts

Mathematical physicist

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John C. Baez @johncarlosbaez.bsky.social · 9d

I'm trying to lose weight. I was so happy when I saw my local pastry shop sold negative-mass doughnuts. But what happened next really freaked me out.

(Negative mass in Newtonian mechanics, special relativity and relativistic quantum mechanics.)

www.youtube.com/watch?v=THT8...

Negative mass

YouTube video by John Baez

www.youtube.com

John C. Baez @johncarlosbaez.bsky.social · 13h

In the old days, when I first visited Hong Kong, they had illegal bus services! Slowly they became legalized....

trippin.world/feature/red-...

Why You Need to Take a Red Mini Bus in Hong Kong

You may think hailing one of the many taxis off the road is the right way to get around in Hong Kong, but locals might disagree.

trippin.world

John C. Baez @johncarlosbaez.bsky.social · 17h

Swirl: a swirling piece of music from my album Treq Lila, made by "breeding" cellular automata in Steve Wolfram's WolframTones system:

soundcloud.com/john-c-baez/...

Art by Greg Egan.

Swirl

From my album Treq Lila, made by

soundcloud.com

John C. Baez @johncarlosbaez.bsky.social · 17h

If anyone can give me Vinberg's

The theory of convex homogeneous cones, Trans. Moscow Math. Soc., 12 (1965) 340–403.

please do! The best source I have now is Chua's paper on T-algebras and convex homogeneous cones:

dr.ntu.edu.sg/server/api/c...

(2/2)

dr.ntu.edu.sg

John C. Baez @johncarlosbaez.bsky.social · 18h

The exceptional Jordan algebra 𝔥₃(𝕆) is connected to quantum logic and perhaps also the Standard Model (see below). More complicated algebras like 𝔥₃(𝕆⊗ℍ) aren't Jordan algebras, but they're Vinberg T-algebras and still connected to quantum logic!

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golem.ph.utexas.edu/category/202...

A Complex Qutrit Inside an Octonionic One | The n-Category Café

golem.ph.utexas.edu

John C. Baez @johncarlosbaez.bsky.social · 20h

My crazy new hope about quantum logic is that it's been inconsequential for "real-world physics" mainly because we haven't gone far enough down the rabbit-hole. I am now going down the rabbit-hole.

(Vinberg's special T-algebras, here I come!)

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John C. Baez @johncarlosbaez.bsky.social · 2d

More like a tsunami, as far as students see it.

John C. Baez @johncarlosbaez.bsky.social · 2d

Grothendieck wrote of how the gradual buildup of results in algebraic geometry is like a slowly rising sea.

But from the student's perspective, it looks like this. 😆

Hokusai's famous print "The Great Wave off Kanagawa", showing three boats moving through a storm-tossed sea, with a large, cresting wave forming a spiral in the centre over the boats and Mount Fuji in the background.

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John C. Baez @johncarlosbaez.bsky.social · 2d

Grothendieck talked about how the sea of results slowly rises, almost imperceptibly. This book cover makes it look pretty threatening. Which is how students perceive Grothendieck's work. 😆

John C. Baez @johncarlosbaez.bsky.social · 2d

So someone thinks science isn't creative work? I'm confused.

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John C. Baez @johncarlosbaez.bsky.social · 3d

I don't understand it, but this article claims to explain it.

"This article outlines the use of the Brunauer-Emmett-Teller (BET) method and Barrett-Joyner-Halenda (BJH) method for the calculation of surface area and pore volume, respectively...."

app.jove.com/t/65716/dete...

Determining Surface Areas and Pore Volumes of Metal-Organic Frameworks

Georgia Institute of Technology. This article describes the use of nitrogen porosimetry to characterize metal-organic frameworks, using UiO-66 as a representative material.

app.jove.com

John C. Baez @johncarlosbaez.bsky.social · 3d

In principle yes, but it seems they haven't reached the goals people want for them.

chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/...

Metal‐Organic Frameworks (MOFs) As Hydrogen Storage Materials At Near‐Ambient Temperature

Hydrogen as is difficult to store in significant quantities via physical methods especially at near-ambient temperatures (248–373 K). Metal-organic frameworks (MOFs) have the potential to increase hy...

chemistry-europe.onlinelibrary.wiley.com

John C. Baez @johncarlosbaez.bsky.social · 3d

So I wrote a few blog articles. But I decided, unsurprisingly, that they wouldn't scale up enough to do any good for climate change. So I quit, and never got paid for the articles I wrote.

Still, they are a cool technology and have lots of potential uses.

Synthesis of the MIL-101 metal-organic framework. Each green octahedron consists of one Cr atom in the center and six oxygen atoms (red balls) at the corners.

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John C. Baez @johncarlosbaez.bsky.social · 3d

In 2019, someone offered to pay me to publicize their business involving metal-organic frameworks. The idea proposed to me was that these could be used to soak up greenhouse gases, and that I should blog about this.

johncarlosbaez.wordpress.com/2019/03/11/m...

Metal-Organic Frameworks

I’ve been talking about new technologies for fighting climate change, with an emphasis on negative carbon emissions. Now let’s begin looking at one technology in more detail. This will …

johncarlosbaez.wordpress.com

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John C. Baez @johncarlosbaez.bsky.social · 3d

Gas molecules like to sit inside these holes. So, perhaps surprisingly at first, you can pack a lot more gas in a cylinder containing a metal organic framework than you can in an empty cylinder at the same pressure!

A large yellow sphere representing a hole where gas molecules can go, surrounded by blue tetaherad and struts connecting small red and blue dots.

John C. Baez @johncarlosbaez.bsky.social · 3d

Susumu Kitagawa, Richard Robson and Omar M. Yaghi won the Nobel prize in chemistry for metal-organic-frameworks!

These are molecular structures built from metal atoms and organic compounds, full of microscopic holes. One gram can have a surface area of more than 12,000 square meters!

Yellow and orange balls between a complex lattice-work of blue tetrahedra.

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John C. Baez @johncarlosbaez.bsky.social · 3d

If you look at my book, which seems like a big project, start by looking at just the pictures.

John C. Baez @johncarlosbaez.bsky.social · 3d

You don't really need to know physics to understand some of the key tensors in general relativity, like the metric tensor and Riemann tensor. Those are about geometry, and Einstein needed his old college pal Marcel Grossman to explain them to him. But other tensors are about physics.

John C. Baez @johncarlosbaez.bsky.social · 3d

"How do you visualize something wild like a rank (5, 5) (contravariant, covariant) tensor?"

Have you ever needed to do that in a physics course? In my physics courses the worst thing I've met is the Riemann tensor, which is rank (1, 3). And that's perfectly visualizable.

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John C. Baez @johncarlosbaez.bsky.social · 3d

Yes, Penrose introduced a lot of these ideas:

math.ucr.edu/home/baez/pe...

Penrose on Spin Networks

math.ucr.edu

John C. Baez @johncarlosbaez.bsky.social · 3d

"Maybe it's a good thing to learn how to model physical processes/phenomena without being able to "get a picture of" the thing."

I think most physicists rely heavily on getting a picture of the thing. What they do is increase their visualization powers.

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John C. Baez @johncarlosbaez.bsky.social · 4d

It's a fascinating process, getting from the math to the physical intuition.

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John C. Baez @johncarlosbaez.bsky.social · 4d

In reality this is what we do: compare clocks and rulers to each other and throw out the ones that disagree too much. It's a fascinating process, especially in this regard: how in the world do we create "more accurate" clocks and rulers and know they are more accurate?

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John C. Baez @johncarlosbaez.bsky.social · 4d

The good things is that I'm working on that now so it's on my mind.

Varadarajan wrote a good book "The Geometry of Quantum Mechanics", but I'd take a much more light-weight approach.

John C. Baez @johncarlosbaez.bsky.social · 4d

I would never talk about string theory. Someday I might do QFT for mathematicians. But for now I'm choosing from the list of topics I listed, because those are the topics where I already have notes written up.

John C. Baez @johncarlosbaez.bsky.social · 4d

You have to choose from the list, because I won't make a series of videos on a topic where I don't already have notes prepared! At least not at first.