Followup to:  Decoherence, Where Philosophy Meets Science

Once upon a time, there was an alien species, whose planet hovered in the void of a universe with laws almost like our own.  They would have been alien to us, but of course they did not think of themselves as alien.  They communicated via rapid flashes of light, rather than sound.  We'll call them the Ebborians.

Ebborians reproduce by fission, an adult dividing into two new individuals.  They share genetic material, but not through sexual recombination; Ebborian adults swap genetic material with each other.  They have two eyes, four legs, and two hands, letting a fissioned Ebborian survive long enough to regrow.

Human DNA is built in a double helix; unzipping the helix a little at a time produces two stretches of single strands of DNA.  Each single strand attracts complementary bases, producing a new double strand.  At the end of the operation, a DNA double helix has turned into two double helices.  Hence earthly life.

Ebborians fission their brains, as well as their bodies, by a process something like how human DNA divides.

Followup to:  The So-Called Heisenberg Uncertainty Principle

For decades, quantum physics was vehemently asserted to be nothing but a convenience of calculation.  The equations were not to be interpreted as describing reality, though they made good predictions for reasons that it was mere philosophy to question.  This being the case, any quantity you could define seemed as fundamentally real as any other quantity, which is to say, not real at all.

Physicists have invented, for convenience of calculation, something called a momentum basis of quantum mechanics.  Instead of having a complex amplitude distribution over the positions of particles, you had a complex amplitude distribution over their momenta.

The "momentum basis" contains all the information that is in the "position basis", and the "position basis" contains all the information that is in the "momentum basis".  Physicists use the word "basis" for both, suggesting that they are on the same footing: that positions are no better than momenta, or vice versa.

But, in my humble opinion, the two representations are not on an equal footing when it comes to being "fundamental".

Previously in series:  Decoherence

As touched upon earlier, Heisenberg's "Uncertainty Principle" is horribly misnamed.

Amplitude distributions in configuration space evolve over time.  When you specify an amplitude distribution over joint positions, you are also necessarily specifying how the distribution will evolve.  If there are blobs of position, you know where the blobs are going.

In classical physics, where a particle is, is a separate fact from how fast it is going.  In quantum physics this is not true.  If you perfectly know the amplitude distribution on position, you necessarily know the evolution of any blobs of position over time.

So there is a theorem which should have been called the Heisenberg Certainty Principle, or the Heisenberg Necessary Determination Principle; but what does this theorem actually say?

Previously in series:  Feynman Paths

To understand the quantum process called "decoherence", we first need to look at how the special case of quantum independence can be destroyed—how the evolution of a quantum system can produce entanglement where there was formerly independence.

Followup to:  Identity Isn't In Specific Atoms

It is widely said that some primitive tribe or other once feared that photographs could steal their souls.

Ha ha!  How embarrassing.  Silly tribespeople.

I shall now present three imaginary conversations along such lines—the common theme being frustration.

FADE IN around a serious-looking group of uniformed military officers.  At the head of the table, a senior, heavy-set man, GENERAL FRED, speaks.

GENERAL FRED:  The reports are confirmed.  New York has been overrun... by zombies.

COLONEL TODD:  Again?  But we just had a zombie invasion 28 days ago!

GENERAL FRED:  These zombies... are different.  They're... philosophical zombies.

CAPTAIN MUDD:  Are they filled with rage, causing them to bite people?

COLONEL TODD:  Do they lose all capacity for reason?

GENERAL FRED:  No.  They behave... exactly like we do... except that they're not conscious.

(Silence grips the table.)

COLONEL TODD:  Dear God.

Continuation of:  No Individual Particles
Followup to:  The Generalized Anti-Zombie Principle

Suppose I take two atoms of helium-4 in a balloon, and swap their locations via teleportation.  I don't move them through the intervening space; I just click my fingers and cause them to swap places.  Afterward, the balloon looks just the same, but two of the helium atoms have exchanged positions.

Now, did that scenario seem to make sense?  Can you imagine it happening?

Followup to:  Can You Prove Two Particles Are Identical?, Feynman Paths

Even babies think that objects have individual identities.  If you show an infant a ball rolling behind a screen, and then a moment later, two balls roll out, the infant looks longer at the expectation-violating event.  Long before we're old enough to talk, we have a parietal cortex that does spatial modeling: that models individual animals running or rocks flying through 3D space.

And this is just not the way the universe works.  The difference is experimentally knowable, and known.  Grasping this fact, being able to see it at a glance, is one of the fundamental bridges to cross in understanding quantum mechanics.

If you shouldn't start off by talking to your students about wave/particle duality, where should a quantum explanation start?  I would suggest taking, as your first goal in teaching, explaining how quantum physics implies that a simple experimental test can show that two electrons are entirely indistinguishable —not just indistinguishable according to known measurements of mass and electrical charge.

To grasp on a gut level how this is possible, it is necessary to move from thinking in billiard balls to thinking in configuration spaces; and then you have truly entered into the true and quantum realm.

Previously in series:  The Quantum Arena

At this point I would like to introduce another key idea in quantum mechanics.  Unfortunately, this idea was introduced so well in chapter 2 of QED: The Strange Theory of Light and Matter by Richard Feynman, that my mind goes blank when trying to imagine how to introduce it any other way.  As a compromise with just stealing his entire book, I stole one diagram—a diagram of how a mirror really works.

Previously in series:  Classical Configuration Spaces

Yesterday, we looked at configuration spaces in classical physics.  In classical physics, configuration spaces are a useful, but optional, point of view.

Today we look at quantum physics, which inherently takes place inside a configuration space, and cannot be taken out.