Day 132 – Quantum Mechanics and T-Shirts

Sunday May 30, 2021

I am reading George Greensein’s book entitled “Quantum Strangeness.”

I am taking my time, reading one chapter a day.

The chapters aren’t long, and so far the topics aren’t hard to understand.

What I am enjoying more than his trying to explain quantum physics is his describing how he didn’t understand it as a student in college, and nor did it seem did his professors.

It seemed they were all playing an elaborate game, a kabuki play of “The King has no Clothes.” Either it was “We’ll all pretend to understand,” or “We don’t talk about that (because we don’t understand, so please don’t ask).”

How refreshing!

Greenstein got by by learning how to answer the questions posed. But understanding eluded him.

There were the famous thought experiments posed by Einstein and answered by Bohr. 

Einstein was not convinced. Not sure about Bohr.

Einstein thought that quantum theory was only half a theory, because if it was complete some basic questions could and should be answerable.

Bohr said Einstein was asking the wrong question.

I’ve always had problems with the Theory of Relativity. What happens when the training traveling at the speed of light switches on its headlamp? 

Does the light not leave the lamp?

Does it matter where you are observing it from? (On the train or as a bystander on the hill beside the track?

I got a glimmer today when I read about spin.

Maybe, I’m asking the wrong question. Or maybe the question is irrelevant because the situation can not exist? If a train went the speed of light wouldn’t it become light and hence there is no train? Not at that speed at least.

So in the topic on spin Greenstein said that in the quantum world you can not think of spin as related to a horizontal and vertical axis but rather as a matrix of possibilities: of which there are two.

I dropped out of math classes at matrix algebra. I got it, but so what? 

Then came Cohl Furey and her lectures on Octagonal Algebra. Here’s a woman who was thinking about an abandoned part of mathematics. It was abandoned in the 80s when vectors came into popularity with big ass computing. Vectors can be used in weather mapping and boat design to tell the direction of a storm or the shape of a hull. However, what Furey pointed out in her lectures was that vectors don’t have enough descriptors to account for spin. In her wonderful recorded lectures she would stop and look at the camera and ask what something was that she had written. (“Look, lady, I”m hanging on by my fingernails. I got no idea.”) Then she’d answer the question. What she had written was an explanation of the Standard Model and the quarks with their spin! (Can’t do that with vectors. No, no. no… What’s Amy Winehouse doing here? Nevermind.)

I like Ms. Furey. I mean imagine being the journalist interviewing her and he’s looking at the bruises on her arms. “How did you get them?”, “Fighting. I like to do mixed martial arts. Especially karate.” 

“What would you be doing if you hadn’t gotten this professorship at Cambridge?”

“Playing accordion. Busking in New York.”

So here the thing I finally understood about matrix algebra. Order of operations is important. I mean I kind of got that in college but was left with a, “So what?” Felling (thought?)

It was follow up lectures on octagons and quadragons that I finally understood. 

It was a follow up lecture I watched where a guy was talking about quadragons and described taking your arm from a bent position to straight and then some other position. There were three steps. The order in which you did the steps determined whether the hand ended palm up or palm down.

So, how does this relate to tee shirts you ask? Good question.

Most tee shirts I own now have a tag on the inside left seam, near the bottom.

So what’s the likelihood that you will put the tee shirt on correctly, if you are in the dark and can’t see the tag?

This presupposes that what one would do in the light is look for the tag and orient the shirt such that when it slips on over your head that tag would be on the inside, left side.

I think the chances are one in four that you get it right. However, like the arm twisting experiment I think it takes three moves to correct an incorrect placement, and an incorrect placement is due to an incorrect order of operations. If you start with the tag to the outside you’re screwed. If you start with it on the inside you have a one in two chance of getting it right.

I’m not sure, but you can also put the shirt on backwards, either inside or out. Incorrect order of operations?

Doesn’t the orientation of the shirt front to back bring the odds to 8 to 1, not 1 in 4?

Or are certain situations in the 1 in 8 scenario not possible?

More to think about.

Gotta go.

But before I do, here’s a classic thought experiment by Einstein.

You have two hydrogen atoms. Let’s label them A1 and A2.

You have a box with two compartments: C1 and C2.

The atoms can be in either of the two compartments.

They can both be in the same compartment.

What are the odds of any situation?

Okay, here’s the classic solution:

What are the situations: A1&A2 in C1; A1&A2 in C2, A1 in C1 and A2 in C2, A2 in C1 and A1 in C2.

There are four situations. Therefore, there is a one in four chance of any situation happening.

Right?

Wrong.

It’s one in three.

What?

Reason. You can’t label an atom. One hydrogen atom looks like another. You have no way of knowing A1 from A2. Therefore the last two situations collapse into one situation and the situations are reduced to 3 possible. The odds are 1 in 3.

Want to try the Monte Hall Paradox? (Should you switch or not?)

Answer: always switch.

Now, I’m outta here.