Hard Tweets Explained: Amplituhedron

This is a pretty rich trove of quantum physics references. Hang on.

Amplituhedron theory is a relatively new development in quantum physics. It is a way of computing various properties of the interactions of particles at the quantum level. You represent the things that might bump into each other using a geometric structure, and then measure its volume to find out what would happen. There is a very readable article about the theory here:

Wired: Scientists Discover a Jewel at the Heart of Quantum Physics

The shape of an amplituhedron is like a jewel, so if there was one in your shoe, it would probably hurt. That’s the first joke. Pretty obvious.

The key thing that amplituhedron theory changes are the notions of locality and unitarity. Locality is the notion that interactions happen between particles that are next to each other. This new theory seems to say that isn’t necessarily always the case.

So there is our second joke. It hurt, but it hurt the foot that was in the other shoe. That would be non-locality of particle interaction.

The other thing that amplituhedron theory changes is unitarity. In quantum physics, particles exist in what they call a “superposition” of states. It isn’t in one state or another. It’s probably in one and probably in the other. The cat in Schrodinger’s box is probably both alive and dead. The probability of each of these states has been assumed to add up to 1. But the amplituhedron changes that rule.

So that’s the third joke. It probably hurt. Maybe it didn’t.

Homework: Go read that Wired article, and then blather on to your friends about non-locality and see how long it takes them to get non-local to where you are standing. It probably won’t take long.


Hard Tweets Explained: Paradox

There is a very obvious joke in this tweet, but there is also a much more subtle one. The obvious joke is about sex. You can figure that one out on your own.

The subtle joke has to do with the way physicists describe electromagnetic radiation. You know – light, radio waves, that sort of thing. Those are waves, and you can think of them moving through space at a constant speed (the speed of light). Being waves, they bounce up and down. Like a sports bra on a jogger.

The rate at which they bounce up and down (I’m not letting that image go), is called the frequency. Typically described in how many times per second they do it, for which we use the unit Hertz (Hz). A jogger bounces about once per second, so the frequency of that sports bra is 1Hz. AM radio waves, in contrast, bounce up and down thousands of times a second (ouch, that hertz), so we use KHz (K means kilo, which means 1000) to describe them.

Another way to describe the same wave is by how much distance it travels between each up/down cycle. This distance is called the wavelength. The typical stride length of a jogger is 30 inches, so the typical wavelength of our sports bra is 30″. Suppose you had two joggers going exactly the same speed. One has long legs and the other has short legs. Ms Long Legs is going to be bouncing a lot slower than Ms Short Legs.

If the overall speed is constant, as it is with our two joggers (and light and radio waves), a low frequency covers a big distance on each bounce. And a high frequency only covers a short distance on each bounce.

Low frequency -> large wavelength; High frequency -> small wavelength. Mathematicians call this opposite relationship “inversely proportional.” So wavelength is inversely proportional to frequency.

A really low frequency wave will take a long time to reach its next peak. But a high frequency wave will reach its next peak in a short time. The duration of that wavelength, at constant speed, is proportional to the wavelength. And it is therefore also inversely proportional to frequency.

Hence the paradox. Physics tells us that duration is inversely proportional to frequency. But our own experience in the bedroom yields the opposite result.

Further study is clearly warranted.

Homework: For the sake of science, try convincing your partner to increase your frequency and see whether duration also increases. It’s really a win/win. Happy bouncing.