Eugene Commins died on Saturday.

Eugene Commins

I only knew Prof. Commins as a professor whose courses had to be taken. They were not formally required for astronomy students, but the word was that if you were a Berkeley grad student and didn’t take is courses, you would regret having missed an amazing opportunity, and if you did take them you would always remember them.

He had a brilliant career, too. Read about it here:
http://physics.berkeley.edu/news-events/news/20150915/a-scholar-a-gentleman-and-an-esteemed-colleague

Something only touched on there, though, were how his courses changed the students. I still remember many of the problems he assigned. Some of them totally changed the way I think about the world and physics. Here’s one (by fellow Berkeley grads can correct my memory):

This calculation is purely classical, but the quantum analog yields the same result.

Consider the paths of the gas particles in this room. Now, consider their future motions if an electron on the surface of a star at the edge of the observable universe is instantaneously displaced by 1 cm. How long until their paths are qualitatively different as a result of that displacement?

Path to solution:

• For this rough, order-of-magnitude calculation, treat them as a set of identical hard spheres traveling ballistically and undergoing elastic collisions.
• Calculate the particles’ typical speed
• Calculate the particles’ typical masses
• Calculate the particles’ typical sizes
• Calculate the particles’ typical separation
• Calculate the change in acceleration from that electron’s displacement on a particle
• Calculate the differential acceleration (tides) from the electron’s displacement on neighboring particles
• Calculate the relative change in lateral position the particle will experience during its travel between particles
• Calculate the change in the angle the particle will experience upon scattering due to the electron’s displacement
• Calculate the number of scatterings until the change in lateral displacement is equal to the size of a particle
• Calculate the time it takes to experience this number of scatterings.

I don’t remember the quantitative answer, but it’s absurdly small. The reason is that the change in angle grows geometrically with each scattering (i.e. it grows by a constant factor each time). As a result, it takes something like dozens or hundreds of scatterings before two particles that would have collided miss each other instead. Because particles collide many times per second, the time it takes for this to happen is far less than a second.

The lesson is that the idea of calculating the future of the universe, or even a tabletop experiment that is sensitive to small perturbations, is impossible. In order to get the paths of the gas particles in this room correct for less than a second, one needs to know the position of every particle in the universe to much better than a cm.

So if the universe (or even just this room) is a simulation (if we are in a Matrix), then either the physics is being faked, or the computer doing the simulating is, itself, a super-universe-sized affair.

Professor Emeritus Commins was 85.

Update: Marshall Perrin found the problem:

I was pretty close!  I had the point of the problem wrong (though not its implications) and the distance to the star (off by 10⁹, but that hardly changes the answer at all!)