Elementary (school) Quantum Mechanics

Here's the second essay.  See previous post for Chapter One.

Elementary Quantum Mechanics:  Chapter 2   The Pauli Exclusion Principle

 According to the Pauli Exclusion Principle no two fermions (particles like electrons, protons and neutrons) can occupy the same state at the same time.  One of them must move to another energy level or space, or switch from positive to negative spin or vice-versa. This is one of the most important principles in elementary particle physics.  This effect can be observed any day in any elementary school.  The set-up for the experiment is simple:  Ask a class of children to line up.  Here are some typical results which affirm the exclusion principle.

           As twenty-five 8-year-olds leave their desks (seats, spots on the floor, rug, bleachers) and head for ‘the line’ they begin to judge their distance from a particular point (not point-particles—I’ll tie that in to string theory later), and their maximum speed towards it.  Like electrons seeking the lowest energy level possible, over 60% of the students are headed for the point which they perceive as the front of the line.  An observer who is a futbol (soccer) lover may notice the various high elbows, stepovers, and hip-swinging shielding tactics employed.  One who loves the gridiron will surely notice the twists, leaps, and head-down motion of a running back. Wrestling fans will surely see a few take-downs, reverses, and even an occasional pin. 

            The students who pile up at the ‘first’ spot in line, like electrons piling up in energy shells, obey the exclusion principle.  That is why as the never-static line begins to snake out of the room, those students still in the same ‘spots’ must acquire opposite spin (so they are not the same).  Spin is easy for second graders, and is only ever interrupted by an adjacent student stepping on the spinner’s untied shoestring which often causes a domino effect   (The odds of one untied shoe in a line of 25 students has been proven to be 16:50.  Such a high percentage may surprise a layman, but teachers realize that it is only lower than 25:50 because some students wear sandals.)

            As the line moves towards its destination it is likely to encounter other lines which may proceed in the same direction or move in an opposite one, but students in any one line have a predicted effect on another line.  Any encounter with another line may induce ferromagnetism, “in which the exclusion effect results in exchange energy that induces neighboring electron spins to align,” (Wikipedia.org).  This effect is best observed outside multi-purpose rooms when classes are backed up waiting for an assembly or other attraction.

 Because, as the teacher, I am in charge, I have tried many different initial line-up conditions; but, in a bizarre, reverse ‘butterfly effect’ (the butterfly effect is from chaos theory, not physics—yes, some people actually study chaos), they all end with the inevitable pile-up and spins.  If I understood elementary quantum mechanics better, I might be better able to deal with line-ups, but when it comes to things like the Pauli Exclusion Principle, societal expectations of self-esteem curriculum induce me to just make sure I don’t leave anyone out. 

 Facts:  The Pauli Exclusion Principle is real, as are chaos theory, domino effect, butterfly effect and side effects of reading this.  As to the statistics quoted, 35% of statistics are made up.

Elementary (school) Particle Physics

As an elementary teacher who enjoys reading about (but never really understanding) astrophysics, I'm sharing a series of essays I wrote a few years ago with apologies for any mistakes in matters of science.

Elementary Quantum Mechanics:  Chapter 1   The Heisenberg Uncertainty Principle

 According to the Heisenberg uncertainty principle you cannot know both where an object is and its velocity at the same time.  In fact, the more precisely you try to fix its position the less certain is its velocity.  This is a principle of elementary quantum particles.  Every primary teacher, for example, has experienced this strangely disconnected, surreal feeling when a hat or pair of gloves is left in the back of the room.

   Only the students who belong to my classroom bring their coats and things into the room in the morning.  No one else.  No one else brings coats, hats, gloves, book bags into my classroom except my students whose names are on the roster and who sit in the desks in our room.  They are the only ones.  They are the only ones who bring these items to the room, so, if, for instance, a hat is left in the back of our room at dismissal time when everyone is putting on coats and packing book bags, one could be certain that the hat must belong to someone in our room.  But it does not. 

            First, the student whose job it is to check the coat rack, holds the hat aloft and bellows, “Whose hat?  Somebody left their hat here.” 

            Several students definitively identify several other students as the owner.

             “That’s Jeremy’s,” or “That’s Eric’s.”

             I motion for the coat rack helper to bring the hat to me, and, because I am in charge, I quickly quiet the room, commanding attention, and say, “Whose hat? Somebody left his hat here.”          No, no one.

             “Jeremy, is this yours?”  No, not his.

             “Eric, is this yours?”  No, not his.

             “Are you sure?  Look at it.  Boys and girls!  I want everyone’s attention.  Stop what you are doing.  Look at this hat.  Maybe you wore it yesterday.  Did anyone wear a hat like this yesterday?”  No, no one.

             “Look, again, please.  Stop and look here.  Does anyone have a green hat like this?”  No, no one.

             “Wait a minute.  Does anyone have a brother or sister who has a hat like this?  Maybe it was stuck on your coat or book bag and was brought to school by mistake.”  No, no one. 

            Since they weren’t really paying attention, I decide to visit each desk (trying to more accurately fix the position of the hat.  Part of me says to do this, but I’m starting to feel that physicsly speaking, this is wrong on a quantum level).

             I stand in front of each of my 25 students.  I establish eye contact.  I animate the hat.  I set it on each one’s desk.  I point to it. I say each one’s name.

             “Alyssa, is this your hat?”  No, it is not.  No.  No.  No.

            As I move along, now, I try to sell the hat, noting its good points.

             “Kevin, is this your hat?  Are you sure, because it really goes well with your coat, and this is the kind of hat the big boys are wearing, so I thought maybe your mom got one like this for you since you seem to wear grown-up clothes.”  No. Not his. 

            As I try harder to identify the hat’s owner, I know that quantum mechanics and old Heisenberg’s uncertainty principle is kicking into high gear.  Although I try to disguise it, by now the students can sense the frustration in my voice.

             “Jenna, is this your hat?  It has to be someone’s.  It has to belong to someone in our room.” 

            Now, it becomes clear that if the owner does finally realize that the hat is his, he will never claim it, because to do so might invoke the wrath of the teacher who wasted 15 minutes of bus-waiting time that she could have been using to read another chapter of Charlotte’s Web. 

  Elementary quantum mechanics is so hard to understand, but after 28 years, I’ve finally decided I understand the uncertainty principle—at least relatively well.  The next time a hat is left, I intend to calmly read aloud a chapter from The Elegant Universe, and string along until some day when the hat goes home with someone in our room, who by some quark of nature recognizes it that day.  After all, you can’t spend 15 minutes trying to identify a hat.  You’ve got to mμ(v)on.

Facts:  The Heisenberg Uncertainty Principle is real, as are quarks, mμons, and string theory (which is Chapter 3 in Elementary Quantum Mechanics—‘String Theory and Primary Prepositional Phrases’ due out in recycled paper in November).  Opus Dei is real, too. The Illuminati used to be real.  I’m no longer sure about the Priory of Sion.