If we give Mars an atmosphere, it'll slowly get knocked away by the solar wind unless we also give Mars a magnetic field.

Ruth Bamford's plan: create a torus of plasma around the orbit of Mars' moon Phobos, carrying electric current!

The electric current, going around a loop, could create a magnetic field that protects Mars from the solar wind... just as Earth's magnetic field protects us!

The solar wind hitting Mars now creates radiation 12,000 times that on Earth - not good for your health.

Plasma could be created from the material of Phobos itself, which has low escape velocity. "Kicker" stations would be needed to keep the loop going, and the whole enterprise would require a LOT of energy. But Bamford and coauthors argue it's better than the alternatives.

Their paper in the journal 𝘈𝘤𝘵𝘢 𝘈𝘴𝘵𝘳𝘰𝘯𝘢𝘶𝘵𝘪𝘤𝘢 is open-access. Please check it out before you propose alternative schemes!

First, of course, we should terraform the Earth. COP26 discussed some plans for how to do that.

(4/n, n = 4)

I was way off: the radiation on Mars is not 10,000 times that on Earth - it's at most 50 times that on Earth. I misread some figures.

Thanks for @AlaskaLawlor for catching this.

(5/n, n was 4) 🥴


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More from @johncarlosbaez

23 Nov
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.

By attaching another photon line to those pictures, Stefano Laporta found all 891 diagrams with 4 loops where an electron absorbs a photon. Here are examples.

An electron is a little magnet. He computed the effect of all 891 diagrams on the strength of that magnet.

He showed the effect of these 891 diagrams on the magnetism of the electron is about -1.912 times the (fine structure constant over π) to the 4th power.

But since he's a bit obsessive, he computed this number to 1100 digits of accuracy!

Read 5 tweets
22 Nov
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.

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


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

(2/n) Image
@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.


Read 4 tweets
19 Nov
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.

If benzene looks like Kekulé first thought, there would be 4 ways to replace two hydrogens with chlorine! You could have two chlorines next to each other with a single bond between them as shown here... or a double bond.

But there aren't 4, just 3.

In 1872 Kekulé tried to solve this problem by saying benzene rapidly oscillates between two forms!

This is his original picture of those two forms. The single bonds and double bonds trade places.

Read 6 tweets
18 Nov
What's a "topos", and why do people care? I wrote a short answer here:


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)
Topos theory arose from the collision of Lawvere and Grothendieck, two great mathematicians with very different goals. Lawvere wanted to find foundations of mathematics more closely connected to actual practice, with the help of category theory. (2/n)
Grothendieck was trying to unify algebra and geometry, in order to solve some hard problems connected to number theory. He invented a concept of "topos" so he could easily talk, not just about *whether* equations are true, but *where* they are true. (3/n)
Read 6 tweets
11 Nov
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.

The bacterium lives in bubbling hot mud in a volcano. It survives by metabolizing methane.

It can use any of the 4 lightest lanthanides to do this: lanthanum (Ln), cerium (Ce), praseodymium (Pr) and neodymium (Nd). These are chemically very similar.

The next lanthanide, prometheum (Pm), is not found naturally on earth. Why? That's another story - a story about nuclear physics. The next three are also used by life, very slightly: samarium (Sa), europeum (Eu) and gadolinium (Gd). The rest, apparently not.

Read 6 tweets
10 Nov
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)
But "fundamental" physics - which I try to quickly define in my talk - is not necessarily the most important or best kind! Other kinds of physics are doing well now. Condensed matter physics is full of amazing new ideas *testable by experiment*. (2/n)
For my talk go here:

In the second half I ask how physicists should respond to the Anthropocene. This is the really big, hard question. I suggest a few answers, but I don't feel I have a handle on it.

Read 4 tweets

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