Gin And The Art of Quantum Mechanics

“Fancy a card game, Johnny?”
“Sure, Jennie, deal me in.  Wot’re we playin’?”
“Gin rummy sound good?”


Great idea, and it fits right in with our current Entanglement theme.  The aspect of Entanglement that so bothered Einstein, “spooky action at a distance,” can be just as spooky close-up.  Check out this magic example — go ahead, it’s a fun trick to figure out.

Spooky, hey?  And it all has to do with cards being two-dimensional.  I know, as objects they’ve got three dimensions same as anyone (four, if you count time), but functionally they have only two dimensions — rank and suit.gin rummy hand

When you’re looking at a gin rummy hand you need to consider each dimension separately.  The queens in this hand form a set — three cards of the same rank.  So do the three nines.  In the suit dimension, the 4-5-6-7 run is a sequence of ranks all in the same suit.Gin rummy chart

A physicist might say that evaluating a gin rummy hand is a separable problem, because you can consider each dimension on its own. <Hmm … three queens, that’s a set, and three nines, another set.  The rest are hearts.  Hey, the hearts are in sequence, woo-hoo!> 

“Gin!”

If you chart the hand, the run and sets and their separated dimensions show up clearly even if you don’t know cards.

A standard strategy for working a complex physics problem is to look for a way to split one kind of motion out from what else is going on.  If the whole shebang is moving in the z-direction, you can address  the z-positions, z-velocities and z-forces as an isolated sub-problem and treat the x and y stuff separately.  Then, if everything is rotating in the xy plane you may be able to separate the angular motion from the in-and-out (radial) motion.

But sometimes things don’t break out so readily.  One nasty example would be several massive stars flying toward each other at odd angles as they all dive into a black hole.  Each of the stars is moving in the black hole’s weirdly twisted space, but it’s also tugged at by every other star.  An astrophysicist would call the problem non-separable and probably try simulating it in a computer instead of setting up a series of ugly calculus problems.Trick chart

The card trick video uses a little sleight-of-eye to fake a non-separable situation.  Here’s the chart, with green dots for the original set of cards and purple dots for the final hand after “I’ve removed the card you thought of.”  The kings are different, and so are the queens and jacks.  As you see, the reason the trick works is that the performer removed all the cards from the original hand.

The goal of the illusion is to confuse you by muddling ranks with suits.  What had been a king of diamonds in the first position became a king of spades, whereas the other king became a queen.  You were left with an entangled perception of each card’s two dimensions.

In quantum mechanics that kind of entanglement crops up any time you’ve got two particles with a common history.  It’s built into the math — the two particles evolve together and the model gives you no way to tell which is which.

Suppose for instance that an electron pair has zero net spin  (spin direction is a dimension in QM like suit is a dimension in cards).  If the electron going to the left is spinning clockwise, the other one must be spinning counterclockwise.  Or the clockwise one may be the one going to the right — we just can’t tell from the math which is which until we test one of them.  The single test settles the matter for both.

Einstein didn’t like that ambiguity.  His intuition told him that QM’s statistics only summarize deeper happenings.  Bohr opposed that idea, holding that QM tells us all we can know about a system and that it’s nonsense to even speak of properties that cannot be measured.  Einstein called the deeper phenomena “elements of reality” though they’re currently referred to as “hidden variables.”  Bohr won the battle but maybe not the war — Einstein had such good intuition.

~~ Rich Olcott

Advertisements

2 thoughts on “Gin And The Art of Quantum Mechanics

  1. I just discovered your HardSAHard site and I love it! I think it is a wonderful way into Science in a most accessible way!

    I poked around your site looking for the right communications hook so I ended up here. Sorry if I am a bit out of context, but I wasn’t able to find another way to reach you.

    I would love to see a discussion about quantum computers that sorted out some of the facts from the hype. I’m only a dilettante with strong untested, unproven opinions, but here is one of my posted comments that will clarify the quantum topic that I think it would be a lot of fun to go in your kind of discussion.

    This is my posted reply in comment discussion of the MIT Tech Review article:
    https://www.technologyreview.com/s/604242/googles-new-chip-is-a-stepping-stone-to-quantum-computing-supremacy/?set=604243#comment-3271907059

    “….Do you really think that will be enough? 99% is nothing.

    If you talk about superimpositions of 10^100 or larger, which is the sort of thing you need to break encryption.

    If in such a large superimposition, 10^50 errors mean an error rate of 1 part in 10^50. Which in my lights would be an incredibly good error reduction. So again, what good does it do to reduce 10^50 errors to 10^48 errors, which is what 99% reduction would do.

    Even if you compound the fault talerence, 99% at a time. Modern conventional fault talerence is usable on gigahertz machines, but that means an error reduction near the order of magnitude of 10^10,

    But with our minimal encryption scenario , that reduces your errors from 10^50 errors to 10^40 errors. (Just now added: Our entanglement is holistic and can be looked at only from a view of the whole, because the individual states don’t have their own isolated existence seperate from the whole. So we can’t simply address a particular individual state in isolation. I think this puts great demand on the statistics we have at our didposal, statistics being the only tool we have to narrow down the answer.)

    Don’t forget that to break prime number encryption you have to identify the exact prime number used as key, and up to now that as far as we know would require brute force exhaustive analysis of prime numbers of more than 100 digits with no error.

    You still have a long way to go. Again, I’m not going to hold my breath until I see someone demonstrate proof of concept.”

    Like

    • Thanks for the encouragement, John, and the ideas, There’s enough there for a series if I can do it justice. I’ll have to mull that for a while. Meanwhile, keep coming back, I try to have a fresh post every Monday morning.

      Like

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s