## fredag 12 juni 2015

### Tragedy of Modern Physics: Born's Statistical Interpretation of Quantum Mechanics

Max Born in 1926 just after violating principles of classical physics of reality and causality:

Max Born was awarded the Nobel Prize in physics in 1954 for his statistical interpretation of solutions of Schrödinger's wave equation named wave functions. Schrödinger formulated his equation, which has come to serve as the basic mathematical model of the modern physics of quantum mechanics, in a moment of heavenly inspiration in the Alps in 1926 (together with one of his many girl friends), with the objective of interpreting the modulus squared $\vert\psi\vert^2$ of a wave function $\psi$ as charge distribution.

But there was a problem with this interpretation: For an atom with $N$ electrons, Schrödinger's wave function depends on $3N$ space coordinates, which allows a direct physical meaning only in the case of Hydrogen with $N=1$. Schrödinger could not get around this obstacle and his equation was instead hi-jacked by Heisenberg and Born supported by Bohr and was then twisted into the so-called Copenhagen Interpretation with the wave function a probability distribution of particle positions viewed to represent wave-particle duality as the incarnation of the new physics.

Schrödinger could not accept this probabilistic destruction of causality, but was effectively marginalized (together with Einstein and Planck and Lorentz and others) by the Bohr Copenhagen school leading the world into a new modern physics of wave-particle duality and complementarity outside classical rationality.

It did not help that grandfather Lorentz joined Schrödinger's protest:
•  I care little for the conception of  $\vert\psi^2\vert$  as a probability...In the case of an H-atom there is for a given energy E, also a non-vanishing probability outside the sphere which electrons of energy E cannot leave.
The Copenhagen interpretation took the lead and today we can see the result as a tragedy of modern physics dominated by string theory and multiversa beyond any rationality.

Born describes in his Nobel lecture the sacrifice of classical ideals (or crime) which a modern physicist must be willing to commit:
• It is necessary to drop completely the physical pictures of Schrödinger which aim at a revitalization of the classical continuum theory, to retain only the formalism and to fill that with new physical content.
To commit a crime requires a motivation and to commit a big crime requires a strong motivation. The first step on this road of modern physics was taken by Planck in 1900:
• The whole procedure was an act of despair because a theoretical interpretation (of black-body radiation) had to be found at any price, no matter how high that might beI was ready to sacrifice any of my previous convictions about physics...For this reason, on the very first day when I formulated this law, I began to devote myself to the task of investing it with true physical meaning.
Einstein followed up in 1905 with his special relativity asking humanity to sacrifice classical concepts of space and time.  In both cases, the grandness of the sacrifice supported credibility.

In describing his crime Born first gives credit to scientists following the law:
• Planck, himself, belonged to the sceptics until he died. Einstein, De Broglie, and Schrödinger have unceasingly stressed the unsatisfactory features of quantum mechanics and called for a return to the concepts of classical, Newtonian physics while proposing ways in which this could be done without contradicting experimental facts. Such weighty views cannot be ignored.
Born then recalls the historic fact that Bohr was stronger, adding an excuse that the crime rather concerns philosophy than physics:
• Niels Bohr has gone to a great deal of trouble to refute the objections. I, too, have ruminated upon them and believe I can make some contribution to the clarification of the position. The matter concerns the borderland between physics and philosophy, and so my physics lecture  will partake of both history and philosophy, for which I must crave your indulgence.
• The work, for which I have had the honour to be awarded the Nobel Prize for 1954, contains no discovery of a fresh natural phenomenon, but rather the basis for a new mode of thought in regard to natural phenomena.
Next follows an excuse with reference to "intellectual crisis":
• The first point is this: the work at the Göttingen school, which I directed at that time (1926-I927), contributed to the solution of an intellectual crisis into which our science had fallen as a result of Planck’s discovery of the quantum of action in 1900.
• At the beginning of the twenties, every physicist, I think, was convinced that Planck’s quantum hypothesis was correct. According to this theory energy appears in finite quanta of magnitude $h\nu$ in oscillatory processes having a specific frequency $\nu$ (e.g. in light waves). Countless experiments could be explained in this way and always gave the same value of Planck’s constant .
Then Born puts the blame on Heisenberg, his assistant:

• Heisenberg, who at that time was my assistant, brought this period to a sudden end. He cut the Gordian knot by means of a philosophical principle and replaced guess-work by a mathematical rule. The principle states that concepts and representations that do not correspond to physically observable facts are not to be used in theoretical description.
• I was as excited by this result as a sailor would be who, after a long voyage, sees from afar, the longed-for land...I was convinced from the start that we had stumbled on the right path.

Next, the success in the case $N=1$ is taken as evidence that the theory is correct for $N>1$:
• The first non-trivial and physically important application of quantum mechanics was made shortly afterwards by W. Pauli who calculated the stationary energy values of the hydrogen atom by means of the matrix method and found complete agreement with Bohr’s formulae. From this moment onwards there could no longer be any doubt about the correctness of the theory .
But some doubts presented themselves:
• What this formalism really signified was, however, by no means clear. Mathematics, as often happens, was cleverer than interpretative thought.
In any case, Schrödinger's wave equation was accepted as the right thing, but not Schrödinger's interpretation of $\vert\psi\vert^2$ as charge density:
• Wave mechanics enjoyed a very great deal more popularity than the Göttingen or Cambridge version of quantum mechanics. It operates with a wave function $\psi$, which in the case of one particle at least, can be pictured in space, and it uses the mathematical methods of partial differential equations which are in current use by physicists. Schrödinger thought that his wave theory made it possible to return to deterministic classical physics. He proposed (and he has recently emphasized his proposal anew’s), to dispense with the particle representation entirely, and instead of speaking of electrons as particles, to consider them as a continuous density distributions.
And then Born's commits the crime:
• I immediately took up Schrödinger's method and an idea of Einstein’s gave me the lead. He had tried to make the duality of particle-light quanta or photons and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons.
• This concept could at once be carried over to the $\psi$-function: it ought to represent the probability density for electrons (or other particles).
• It was easy to assert this, but how could it be proved?
Here is Born's justification of the crime:
• To us in Göttingen Schrödinger's interpretation seemed unacceptable in face of well established experimental facts. At that time it was already possible to count particles by means of scintillations or with a Geiger counter, and to photograph their tracks with the aid of a Wilson cloud chamber.
with more "proof" from Heisenberg's Uncertainty Principle:
• However, a paper by Heisenberg containing his celebrated uncertainty relationship, contributed more than the above-mentioned successes to the swift acceptance of the statistical interpretation of the $\psi$-function.
• It showed that not only the determinism of classical physics must be abandonded, but also the naive concept of reality which looked upon the particles of atomic physics as if they were very small grains of sand.
But Born still struggled with the skeptics of atoms as dice-games:
• How does it come about then, that great scientists such as Einstein, Schrödinger, and De Broglie are nevertheless dissatisfied with the situation? Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation. Two closely knitted points of view are to be distinguished: the question of determinism and the question of reality.
arguing that everything including classical physics is a dice-game,:
• The determinism of classical physics turns out to be an illusion, created by overrating mathematico-logical concepts....and cannot, therefore, be used as an objection to the essentially indeterministic statistical interpretation of quantum mechanics.
But finally the self-doubts take over and Born's Nobel lecture given 28 year after the commitment of the crime, ends with questions:
• Are we still justified in applying to the electron the concept of particle and therefore the ideas associated with it?
• Somewhere in our doctrine is hidden a concept, unjustified by experience, which we must elim- inate to open up the road.
• To come now to the last point: can we call something with which the concepts of position and motion cannot be associated in the usual way, a thing, or a particle? And if not, what is the reality which our theory has been invented to describe?
To sum up we see that Born's justification of giving up the basic principles of classical physics, boils down to the following shaky weak arguments:
• A perceived need to make the duality of particle-light quanta or photons and waves comprehensible.
• Because a Geiger counter gives a "click", what caused the "click" must be a "particle".
We understand following Schrödinger as inventor of the basic mathematical model of quantum mechanics, if the particle idea is given up, then there is no need to make wave-particle duality "comprehensible", since then waves are enough. What remains is to reformulate Schrödinger's multidimensional wave equation into a system of three-dimensional wave functions representing charge distribution. This is what I now explore as (Computational) Physical Quantum Mechanics.

But the sad truth today is that nobody cares if the fundamentals of physics make sense or not: Quantum mechanics and relativity, although incompatible, is "settled modern physics" with all questions answered once and for all by now dead and gone physicists, who took the answers along into the grave.

PS Note that Heisenberg received the Nobel Prize in physics in 1932 and Schrödinger shared the Prize with Dirac in 1933, while Born had to wait 20 years until the coining of the Copenhagen Interpretation by Heisenberg in the early 1950s as the official formulation of quantum mechanics.
Today, only a few hard core extremist like Lubos Motl claim that this is the final word to which nothing can be added. The historical dimension of this view is described by A. Pais in the opening of his Address to the Annual Meeting of the Optical Society in 1982 entitled Max Born and the Statistical Interpretation of Quantum Mechanics as follows:
• The introduction of probability in the sense of quantum mechanics, probability as an inherent feature of physical law, may well be the most drastic scientific change yet effected in the twentieth century.
In other words: A Big Lie is more credible than a small one, so if you are going to cheat, make it Big. CO2 global warming alarmism gives an example of this tactic, which is now threatening to throw Western civilization back to Stone Age: This is "settled science" which is so Big that it cannot be  questioned!

#### 5 kommentarer:

1. Hi!

Since you seem to like the use of rhetoric of words as crime and such I guess you wouldn't mind me pointing out one of your own crimes here. It would be really nice of you if you could give some kind of rationalization for the crimes you here commit.

Your crime consists of a logical fallacy. Simply in that you assume that the behavior of physical systems must correspond to processes that agrees with the way our brains process and filters the world.

It is not controversial to clam that it is shown beyond any reasonable doubt that the information that our brains process ends up biased to how the macroscopic world around us behave. But that says nothing on how the microscopic world behave. There is a logical fallacy in assuming that there must be a direct connection.

Think about the averaged quantities that constitutes a classical behavior. There is no way that you can say anything about the microscopic processes that average up to a net effect from the averaged quantities alone.

Crime number two.

You assume that statistics isn't real mathematics. A statistical model of a physical phenomena can be just as good as an analytic model. Many times allot better since the analytic model isn't feasible to solve.

One really good example is molecular dynamics (MD). MD is a classical model that with certainty do not give a correct direct solution to the problem. The initial conditions is not known, that is problem one. When solved, instability in precision will result in a quick deviation from the "true" path the classical system takes. This is problem two.

But these problems isn't important for the final use since the result are interpreted statistically. The evolution is 100% wrong but the statistical averages are not and can be used to compare to experimental data and making further predictions. All this given that the force fields used are good enough.

This shows that statistical models are fundamental even in the event of classical physics.

For me it feels like a really strange thing to get hung up on. This with the statistical element of quantum mechanics. Quantum mechanics is the most fundamental theory we know of. It is possible that there may be a more fundamental theory. But until one is known, there is no way to really make a meta analysis of quantum mechanics.

There is not really any possibility to evaluate the physical meaning of quantum mechanics in this perspective because quantum mechanics is then the fundamental physical meaning. Fundamental reasonable means that there is no deeper way to explain. Or do you disagree?

With that said. Unfortunately, based on quantum mechanics there is some limitation in what we can know about the outcome of certain experiments. One of best experiments to easy understand this is different variations of the Stern-Gerlach experiment. If you haven't done so already you should really try and understand the importance of the results from these kind of experiments. If you don't do that, and from what you write I'm quite certain that you don't, the recommendation is to look at the first lecture here (Lecture 1: Introduction to Superposition)

http://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/lecture-videos/

The whole concept is beautifully demonstrated in that lecture. That lecture and the following one gives a very solid ground for understanding quantum mechanics so that is my warm recommendation to you. If you want edge of your aversion towards modern physics a nudge, here is a good way to start.

Enjoy the sun, and take care!

2. Superposition is superstition. Why must atoms subject to linearity? Classical mechanics is non-linear. It is inconcievable that microscopic mechanics sudddenly should become linear.

3. You seem to have missunderstood what superposition means in this context and why it is necessary to describe correct physics. By physics is meant a process that shows a real experienceable effect.

Did you watch the lecture?

4. I prefer to read books.

5. You say it is inconceivable that mechanics 'suddenly becomes linear'. But, the difference between a linear and a nonlinear theory is not so clear. If x(t) is the solution to, say, Hamilton's equations (that are non linear), we can consider the induced flow on functions f on phase space, and get F(t,x)= f(x(t)). Then F satisfies the equation

dF/dt={H,F}.

This is a linear equation that is equivalent to Hamiltons equations.