Tuesday, August 28, 2007

Auto Mechanics and Quantum Mechanics -- Really

This has never happened before, I actually got questions about auto mechanics and quantum mechanics. Wow.

Ben asks:

Are the rotors on your car attached at all once you remove the calipers or will they just slide off? Seriously though, the auto-mechanics thing made me think about it and I really need to do my brakes (been trying to learn how to do these things myself instead of getting robbed).
Yup, once you get the calipers and the caliper bridge off (this may have been put on with the impact gun by the mechanic who last worked on the brakes and so may be a bear to get the bolts loose), the rotor should just slide off (unless, of course, it's rusted in place).

Hanno asks:
What is the weirdest implication of Quantum Mechanics? What tortures our everyday intuitions the most?
Depends upon whose intuitions you are talking about.

For the average person, probably the strangest is what we call "quantum tunneling." The idea is that if a particle is trapped in a box, generally to get out of the box it needs enough energy to break through the wall. However, quantum mechanics shows us that there is a small, but finite possibility that, with any given interaction between the particle and the wall, the particle will simply leak through the wall. Imagine playing pool and every once in a while, you try to make a bank shot and the ball simply shoots through the rail leaving no hole in the side of the table.

If you are Albert Einstein, the strangest aspect is the spooky action at a distance. When unobserved particles will not be in particular well defined property states, but in "superposed states" that is combinations of all possible states. As soon as an observation is performed, it instantly "collapses" into one and only one of these property states. We can never observe the superposed states, but we can do experiments that prove the particle didn't have a specific value for the thing we measure until we measured it. As if this wasn't bad enough, it is impossible to predict which of values the particle will have.

To make this a little clearer consider a particle that has what we call spin. The spin could be up or down, those are the only two choices. Until we observe a particle it is in the superposed state of spin up and spin down, but the instant we look it is either up or down.

Now, let's create two particles that have to have opposite spins (it's easy enough to do). We don't look at either one, so they are both in superposed states of spin up and spin down. Now, send one through a wire to New York and the other through a wire to Los Angeles. Look at the one in New York. As soon as you look, it will collapse from its superposed state into one of its property states (up or down) randomly. But remember that the two particles have to have opposite spins, so that means the very instant the particle in New York assumed its randomly determined spin value, the particle in Los Angeles also left its superposed state and assumed the opposite value.

Here's the punchline: how did the particle in LA know? It has to assume it's value the instant that the NY particle takes the other value, but a signal from the NY to LA particle saying, "I've been measured. I'm now spin up, so you must be spin down" would have to go faster than the speed of light. That bothered Einstein to no end.