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There are infinitely many ways an electron (straight line) can emit virtual photons (wiggly lines), which in turn split into virtual electron-positron pairs, and so on. All these affect the electron's mass.

There 104 ways where the picture has 4 loops.

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There 104 ways where the picture has 4 loops.

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Owen Lynch, @Joe_DoesMath and I have combined classical thermodynamics, classical statistical mechanics and quantum stat mech in a unified framework based on entropy maximization! The key trick is the operad of convex spaces.

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johncarlosbaez.wordpress.com/2021/11/22/com…

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johncarlosbaez.wordpress.com/2021/11/22/com…

@Joe_DoesMath Owen blogged about this project early on, and this post explains the physics intuitions behind our work:

topos.site/blog/2021/09/c…

It's all about equilibrium thermodynamics, or "thermostatics". Thermostatic systems maximize entropy. Entropy is a concave function.

(2/n)

topos.site/blog/2021/09/c…

It's all about equilibrium thermodynamics, or "thermostatics". Thermostatic systems maximize entropy. Entropy is a concave function.

(2/n)

@Joe_DoesMath We define a "thermostatic system" to be a convex space of states together with a concave function assigning each state an entropy. Whenever you combine several thermostatic systems, they maximize entropy subject to the constraints you impose.

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arxiv.org/abs/2111.10315

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arxiv.org/abs/2111.10315

The structure of benzene is fascinating. In 1865 Kekulé guessed it has a ring of 6 carbons with alternating single and double bonds. But this led to big problems, which were only solved with quantum mechanics.

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What's a "topos", and why do people care? I wrote a short answer here:

math.ucr.edu/home/baez/topo…

But since this is twitter let me say it even shorter... and more vaguely. A topos is a mathematical universe kinda like the one you grew up in, but maybe different. (1/n)

math.ucr.edu/home/baez/topo…

But since this is twitter let me say it even shorter... and more vaguely. A topos is a mathematical universe kinda like the one you grew up in, but maybe different. (1/n)

Wow! Rare earth elements, or 'lanthanides', aren't really very rare. But only in 2011 was a bacterium found that requires rare earths to live. It even has a special protein for dealing with them, called 'lanmodulin'. And now scientists have used it to make a sensor.

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Progress in so-called "fundamental" physics slowed to a crawl after about 1980, at least if you only count theories that get confirmation from experiment. I saw this clearly when I made a timeline of fundamental physics from 1900 to 2020. (1/n)