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Wave Function

by Miles Mathis

This paper was originally written as the introduction to my paper on superposition.  It was so long I decided to scrap it and publish my analysis of superposition with minimal commentary.  This introduction has been sitting in my WORD file collecting dust until I tripped over it today.  A re-reading encouraged me to publish it, for a laugh if nothing else.

Let me begin this paper with a little parable.  There was once a man and this man was hired by the Coca Cola bottling company to study how quarters fall through their machines.  These machines have a collection tray at the bottom that collects the quarters in stacks.  The president of Coca Cola, having a bit too much time on his hands, was curious to know why the coins stacked up as they did.  This president was a very priggish man and he wanted all the coins to land face-up.  So he hired the man to build a complex coin drop that would guarantee that no matter how the coins are fed into the machine, they would fall face-up at the bottom.

The man studied the problem for a while and decided that the best thing to do was to develop an algorithm that explained why the coins fell in the way they did, with the coin drop like it was.  He hoped that this would provide him with a clue as to how to proceed from there.  After several years he succeeded in developing a complex set of equations that gave him probabilities at the end.  In these equations he expressed the odds as a combination of two factors: the basic factor of heads/tails and the additional factor of the effect of the coin-drop.  At last he met with the president and made his report:

“Sir,” he said, “I have found that these two factors superimpose in a very strange way that is not expressible in normal language.  But my math is of such extreme importance and beauty, as you can see, that I am sure that all must love me for it.  Besides, I have spent almost a decade developing this math, and your company has invested several billion dollars to discover why coins fall like they do.  There is no going back now, Sir.”

The president saw the logic of this and begged him to proceed.

“Sir, I will not bore you with the details of the math, which concerns many terms and procedures I have invented just for the occasion, such as eigenvectors and Hermitian operators (don’t you just love the look of them, Sir?).  But, as you can see, I have a final equation right here that gives us what we want.  The odds of landing heads-up is 1/√2.”

The president studied the charts for a while, mostly bewildered (which gave the man great satisfaction).  But then he noticed a final chart where the man had counted the coins in the drop box, finding ½ of them heads-up.   So he asked the man about that.

“Well, Sir, that is one of the amazing things about the math.  The math gives me absolutely perfect numbers, numbers which cannot be doubted except by the most mathematically naïve, and I think we all know that my equations will go down in history as the most important work of the century.  But, Sir, the most beautiful part of the math is that last part, which I call the collapse of the coin function.  Once the coins are actually counted in the drop box, my equations collapse into the number ½.  What is more, my equations collapse in this way like clockwork.  Sir, I can guarantee you that 100% of the time, my equations will collapse into the percentage indicated by the coins—provided that someone actually counts the coins.”

The president looked at the man dumbly for a few moments and then said, “Wouldn’t it be easier just to count the coins from the start?”

“Sir, Sir!” the man said, “Counting coins is such a pedestrian operation.  I am a physicist and a mathematician.  I have developed the greatest set of equations known to man and you want to talk of counting coins?”

“I still don’t understand,” the president answered.  “Is ½ the right answer or 1/√2?”

The man looked at the president in some exasperation before continuing: “Up until the moment of measurement, 1/√2 is the right answer.  I can absolutely guarantee you that until someone looks at the coins, the odds of finding a heads facing up is 1/√2.  I have put everything I know into these equations and they simply cannot be wrong.  Did I show you the Hermitian operator?  Just look at this matrix!”

“Hmmm,” the president said, “There still seems to be some lack of agreement between the math and the measurement.  I don’t know which to trust.”

“Yes, I call that ‘decoherence.’  The two don’t cohere due to the fact that until the measurement is made, the number is just a probability.  In fact, the coins themselves don’t exist until they are looked at by the guy counting them.  The number 1/√2  flawlessly describes the state the coins are in as they are falling through the machine.  The number ½ describes the coins in the mind of the guy counting them.  So you see, Sir, we can’t really directly compare the two.”

“The coins don’t exist until they are counted?  But what about the person who fed them into the machine?  Didn’t they exist for him or her?”

“Sir, this is all very esoteric.  Do you really want to talk about philosophy or metaphysics?  I just calculate.   My math shows the facts and you can’t argue with facts.”

“But are you saying the coins existed as real things until they disappeared into the machine, then they were probabilities in the machine, and then when they were counted they became physical objects again?”

“Well, Sir, since you won’t drop it, the truth is that there are ‘many minds’ and ‘many worlds.’   The person buying the drink and the person counting the coins are different people, with vastly different brains and desires and hobbies.  We cannot know what they think or believe, and probably would not want to.  Outside the brain of such a person, a coin is an infinity of things, an undefinable and unknowable object.  All the greatest philosophers in history have told us this—Kant, Hume, Timothy Leary.  It exists simultaneously in an infinity of dimensions and worlds, and only my math can begin to put a number on these infinities and worlds.   This number is a probability, and that probability is the surest of all possible knowledge for a human being, supposing one exists.  When the coins are counted at the end, that probability collapses into a much lower form of knowledge, which laymen call ‘data’.  That data is as fleeting and illusory as a passing cloud or a dream of a kiss.  It depends on that least dependable and least quantifiable object in the universe, the human mind.  Whereas my probabilities depend only on my math, which is, as I have assured you, flawless.   You can argue with people, but you can’t argue with vectors, Sir.”

“So the coins don’t exist as they are dropping?”

“Well, Sir, I ask you one simple question.  Can you see them?  If you can’t see them, they can’t exist.”

“Might it be that they are hidden by the metal door of the machine?”

“Exactly, Sir.  Hidden in obscurity.  Untouchable and unknowable.  Everything and nothing.”

Ok, so that was not really a parable.  It was a pretty transparent lampoon.  The sad part is that it is also now state-of-the-art in physics.  Most physicists would not even see the humor in it.  They have accepted the joke or the delusion as gospel and would not even recognize the implication of a problem.  They would say the only problem is mine.  I expect things to make sense.  Physics does not make sense.   Nature does not make sense.  I must accept this or go into another field.

My first answer to this is that I will go into any field I like and not ask their permission.   My second answer to this is that once physics begins to accept paranormal answers, physics is over.  Hawking was wrong: physics will not be over in a decade because all will be known; physics will be over because it will be indistinguishable from astrology or tarot or the reading of entrails.  In truth, physics has been dead since Bohr’s quantum leap.  The fact that an entire field would accept that an electron travels from point A to point B without traversing the space in between was a sure sign that the field was already completely corrupt.  Those physicists were already so ill-trained in logic that they could accept any math or any postulate that gave them the results they wanted.   They wanted an answer at any cost, even if that cost was rationality.  Who cares about rationality when you have a Nobel Prize in hand?

This whole problem is based on an absolute ignorance of what math is and what it represents. The wave function is a piece of mathematics. It is a probability. It doesn't have to "collapse" into reality or into data, since no kind of math does that. Math is one thing, reality is another. The math represents reality, but is not the reality itself, just like the letter "A" represents a certain sound, but is not that sound itself. We do not expect the letter "A" to collapse into a sound, because we understand what representation means. The wave function gives us a ballpark for a value, and then experiment gives us a firm number. Where is the mystery? Where is the great philosophical problem that needs to be solved? The collapse of the wave function does not describe any real mathematical or physical problem: what it describes is the conceptual retardation of modern physicists, buried in their equations, absolutely incapable of seeing beyond their math. When Pauli and Gell-Mann talk about Mars as a probability, we are not seeing the airing of an esoteric problem, we are seeing the airing of a fundamental stupidity.

Every time I read that QED is the most successful physical theory in history, I have to laugh.  If it is so successful at making predictions, then why does it require a collapse of the wave function?  The collapse is necessary precisely because QED cannot predict reality.  It not only cannot predict individual outcomes, it can’t even predict probabilities, as I showed above.  If the probabilities of the wave equations matched the probabilities of experiments, then you wouldn’t need a collapse of the wave function, even as it is defined now.

The collapse of the wave function is an almost unbelievably bold attempt to contain the failure of the theory within the theory.  QED, with infinite disregard for the intelligence of the reader, tries to take the fact that the math fails and incorporate that into the math.  QED hides all within a very clever terminology.  It does not call the failure to match measurement “the collapse of the math”, which it is.   It instead calls it the collapse of the wave function, as if the equations themselves resolve into reality by the working of some mysterious mathematical operator.  But the equations don’t collapse into anything.  The final answer of the wave equations doesn’t become the real answer of experiment by any operation whatsoever.  We just give the gap a fancy name.  “The wrong answer is beaten into the right answer by main force”: that would be the honest name for the collapse of the wave function.

A logical person can see what levels of intellectual trauma a physicist must suffer under not to see this.  I showed in my paper on string theory that string theory was invented because physicists had become bored with QED.   It was finished.  It was so nearly perfect that there was nothing left to do.  This despite the fact that no one living can rationally explain superposition, entanglement, the two-slit experiment, the spooky force, the origin of the strong force, renormalization, the mechanics of the E/M field at the quantum level, gravity at the quantum level, the quantum leap, the cause of quantization, the collapse of the wave function or wave packet, the wave/particle duality, the propagation of light, diffraction, interference, mass limits in accelerators, and so on.  Sure, we have partial and usually irrational answers for all these things.  If you believe in goblins and black-magic, then physics has answers you will love.

What is most amazing is that physicists are satisfied with this.  We might expect that the public would pay handsomely for mysticism, but scientists often profess to a keener regard for the truth and for rigor and for reason.  We are constantly reminded of the scientific method, which supposedly sets scientists apart from the gullible and the credulous, the faithful and the ignorant, the facile and the slipshod.   And yet physicists are satisfied with magic within their “highest achievement.”  They are satisfied by exhortions to faith and by unveiled indoctrination.  Most terribly, they are satisfied by unscientific answers. They have brought QED to a very partial state, a state where they have some equations that begin to work in some situations, and they are ready to move on.  They can ram some particles together in accelerators and not be shocked by what happens everytime, and so they are gods.  Time to move on.

The real reason that physicists have moved on is that it is generally believed that all the Nobel Prizes in QED have been given out already.  The future of Nobel Prizes in QED is only a future of applied math, as we saw this year with the prize given in laser technology.   Explaining superposition rationally instead of irrationally will not win anyone any prizes, and everyone knows it.  There is no Nobel Prize for metaphysics or logic.  You get noticed for big equations or for technology, not for explaining things sensibly.

It used to be that physics was “explaining things sensibly.”   For thousands of years, the definition of physics was making strange things not-so-strange, paranormal things normal.   Now the definition of physics is just the opposite.  QED and QCD created little worlds where everything was curiouser and curiouser.   String theory is attempting to follow them by creating a world that is strangeness itself, irrationality made god.  It may be that in the near-future, the Nobel Committee can save itself a bit of money by combining physics and fiction.  About the time that Arnold Schwartzenegger’s son becomes President, the scriptwriters for Star Trek: Generation Z  will win the Nobel Prize for “physiction.”

We see this on the cover of every book jacket: “Read about the strange theory of QED!”   Discover the realm where all our ideas break down, where nothing makes sense and nothing can be understood by the mind.   Of course the same might be said by a book on canine shakras or on people who live at the center of the Earth or on curing cancer with a drum machine.

Science as a consistent and logical explanation has been replaced by science as hypnosis and bullying.  Heisenberg and Bohr were the original masters of this neo-science, and Feynman was the last great guru in this line.    The string theorists had hoped to inherit this mantle, and they certainly have the right materials for a first-class irrational dogma.  Unfortunately they don’t have the charm.  A religion requires a front-man and string theory has never found the right dashing person—someone who cracks safes or bangs cocktail waitresses between feats on the blackboard.   Primarily, they need someone with really good hair.

We constantly see articles now asking why there aren’t any geniuses these days in physics.  I have a very simple answer for you, although you won’t like it.  There aren’t any geniuses in physics because geniuses have a very low tolerance for mystification, hypnosis, bullying, arguments based on faith or on prestige, and so on.  What use would a genius be in physics right now?  Geniuses don’t follow the status quo in lockstep.  Geniuses aren’t sheep.  Geniuses don’t just accept what you tell them and go on, since it is easier that way.  Geniuses are goddamned difficult, and a genius wouldn’t last a day in academia.  That is why they go into other fields.

If you show a genius an equation or a sentence that doesn’t make sense, he is smart enough to know it.  What is more, it bothers him.  If he is a true genius, he would rather live on the street and eat cold potatoes at the Salvation Army than be caught repeating a false equation or sentence.

Conversely, if you want to make it in physics your road is clear.  You accept superposition and renormalization and all the other dippy processes and maths and ideas, since if you don’t you will be nothing more than a pariah.   You might as well sit in the corner and recite the Questions of King Milinda or lie under a table eating your own shoes as imply, in the least offensive way possible, that Heisenberg might have been a phony.

As proof that physics has become a strange and corrupt field, I point you to Alan Lightman’s book Great Ideas in Physics.   The book is basically one more copy-job on a bunch of flawed theories, just like Feynman’s Six Not-so-Easy Pieces, or a couple hundred other books.   Lightman, like all the other top lecturers in physics at MIT, Cal Tech, and so on, has nothing to add to the history of physics.  It all looks good to him.  Brilliant, glowing, and perfect, it only needs a continuous cheer from the bleachers, and he has his pompoms puffed.

Although Lightman is almost 60, we get a picture of him on the back cover from his 30’s, if that.  Why?  Well, I offer one possibility.  Go to chapter IV, the chapter on Quantum Mechanics, the longest chapter in the book.  Lightman leads with a picture and short bio of Heisenberg.   The bio contains four short paragraphs and the last paragraph is limited to one subject.  The Nobel Prize.  Heisenberg won at age 31, and Lightman finds this fact very important.  He goes on to tell us that the youngest winner for physics was W. L. Bragg, at age 25.  The next youngest were all 31, like Heisenberg.   And then we get an average age: late 40’s.

How is that pertinent to physics or to QED?   It’s not, of course.  Only a boor or a climber (or someone in midlife crisis) could possibly be interested in how old people were when they won prizes.  But the rest of the book exists on this same plane.  We get all the sad tie-ins to culture of these theories, like Thomas Pynchon’s mention of the Second Law of Thermodynamics, or Annie Dillard’s mention of the same. We get Richard Serra and Robert Morris and Athena Tacha weighing in on Relativity.    We get the Second Law tied to evolution, and so on.

Lightman might counter that this is the market.  He is writing pop science and this is what people want.  He has to compete with Paul Davies and the rest, and he can’t do that by bringing up real questions or implying that physics is not near-perfect.  Laymen buy books like this because they have stars in their eyes, and you don’t win book awards by destroying people’s false preconceptions.

Possibly, but it seems to me that the false preconceptions are had mainly by the physicists themselves.  For them, physics is learning the equations and ideas in the books.  If you can learn these things very quickly and very thoroughly, then you graduate at the top of your class and earn the right to lecture and write bestsellers.  It never occurs to them to actually analyze any of the equations and ideas they have learned.  They never once entertain the idea that any of these ideas in the books might be wrong.  If they don’t do that, then they can’t truly understand them.  I know that they haven’t done that, because if they had they would be forced to be more honest about the shortcomings of all their equations and ideas.  Someone who had pulled apart all his knowledge and put it back together would realize how partial that knowledge was.  He would be aware of how much there was left to do.  He might still be proud of the achievements of physicists in the past, but he would not irrationally idolize them.  He might be proud of his own achievements as a student of science and of the world, but he would ultimately be quite humble in the face of what his field had yet to learn.

Contemporary physicists don’t seem aware of this at all.  They think they have an answer for everything, and they take questions with a poor grace.  This is probably most true in Quantum Mechanics.   Quantum Mechanics is the most fortified of all fields, except maybe Relativity.  Relativity is quite simply closed.  It is finished.  It was Einstein’s baby, and his alone.  He created it and he is the only one who understood it.  Best leave it be.  But Quantum Mechanics has been the great class project of 20th century physics.  Almost everyone’s fame and career depends on it.  It therefore must be protected with the utmost security.   Any real threat to QED would set off loud alarms all over the country, and physicists would rush to the trenches.   But such an event is highly unlikely.  The possibility has been defused long since, while the young physicists were in school.  All revolution was weeded out then, all signs of discord, all malcontent, all variance.  Outside academe, everyone has been predefined as a crank, so the spotlight only needs to scan within the walls.  We don’t have to worry about anyone getting in, we only have to worry about anyone breaking out.

But where would a breakout go?  What molepeople would he join?  More to the point, who would publish him, who read him?  Science is our savior: no one wants to hear that physics, the last refuge of the purist, is just as corrupt as the rest of the world.  No one wants the idols to fall.  God may be dead, but we cannot watch the demise of Heisenberg and Bohr.   The statues of Newton and Aristotle have become tarnished; we cannot let the same happen to Einstein and Feynman.   In whom would we trust?

The reason I have mentioned this is not to vent (or not only to vent).  I have mentioned it because physics claims to want to solve some of the thornier problems still admitted to remain.  String theory is the vanguard of this claim.  But it is my contention that the few problems admitted to exist cannot be solved without digging out and solving many, many of the problems not admitted to exist.  Physics cannot continue to keep its secrets secret any longer.  It cannot proceed with the very thin boards covering the chasms, as it has so far proceeded.  That is, no matter how interested physics is in the future, it must return to the past.  Only by shoring up the foundation can physics hope to climb any higher.  The current planking simply will not hold any more weight.

Now that I have allowed myself that long diversion, I intend to concentrate on some specific problems. Lightman begins his chapter on QED by saying this: “Like the relativity of time, the wave-particle duality of nature violates common sense.”  He admits that QED violates it with much more gusto that relativity, but there is more to it than that.  The difficulties of relativity and QED are not only different in size, they are different in kind.  Strictly speaking, the relativity of time does not violate common sense.  What it violates is the old way of thinking.  Relativity is not irrational or unexplainable in logical terms.  It is revolutionary, without a doubt, but not everything that is revolutionary is irrational.   It is possible to explain the relativity of time such that a normal person can understand it.  He or she may not accept it, even then.  But he or she will understand the concept.  The same cannot be said of QED.  The Quantum Leap, the spooky forces, and all the other things I listed above, cannot be explained rationally.  They can be explained only if you accept inconsistency in definitions and terminology.  No matter how smart you are, in order to accept QED you must accept a contradiction.  QED uses all the old words, which have certain definitions, words like point, motion, time, future, past, exist, and so on, and then makes statements that contradict those definitions.

Relativity never does that.  It asks you to accept something that you did not accept before, but it does not ask you to accept something that is unacceptable, as a matter of logic.

Go to my paper on Superposition

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