Heisenberg and the Copenhagen Interpretation
The Uncertainty Principle UP formulated in 1927 in the article On the physical content of quantum theoretical kinematics and mechanics by the 26 year old German physicist Werner Heisenberg, is the corner stone of the Copenhagen Interpretation of Quantum Mechanics with the wave function of a particle configuration supposedly representing the probability of the configuration in space and time. But Stanford Encyclopedia of Philosophy informs us that still after more than 80 years there is no consensus about the meaning of the UP:
- Does the Uncertainty Principle express restrictions on the experiments we can perform on quantum systems, and, therefore, restrictions on the information we can gather about such systems; or does it express restrictions on the meaning of the concepts we use to describe quantum systems; or is the restriction of an ontological nature, asserting that a quantum system simply does not possess a definite value for its position and momentum at the same time? The debate between these different views has been addressed by many authors, but it has never been settled completely.
How can this be? Do we live in an Age of Enlightenment or in a Dark Age? Let us seek answer connecting to
Many-Minds Quantum Mechanics Why Schrödinger Hated His Equation and The Microscopic World is Not a Casino in My Book of Knols.
The UP is a Triviality in Wave Mechanics
The commonly accepted model for the atomic world is the Schrödinger wave equation formulated by Schrödinger in 1926 and from wave mechanics point of view, the UP is a direct consequence or triviality:
- It is impossible to determine both the position and frequency of a wave precisely: Either the wave has a certain frequency but is spread out with uncertain position, or it is localized space with certain position but uncertain frequency.
The Mission of the UP: Copenhagen Interpretation
But if the UP is a triviality from wave mechanical point of view, why has it survived into our days as an independent principle? The answer is:
- The wave function of a system of N interacting particles as the solution of the Schrödinger equation, does not admit a physical interpretation, because it formally depends on 3N space coordinates, and physics lives in 3 space dimensions.
- Only the wave function of a one-particle system has a direct physical meaning.
- In the Copenhagen interpretation the dilemma is handled by considering the multi-dimensional wave function as a particle configuration probability, not as a physical wave.
The logic is:
- UP is a trivial aspect of a wave function
- UP is a trivial aspect of probability
- the wave function is a probability because they both have trivial aspects of UP.
This is like saying that a human being is a bird because the trivial property of having two legs is shared.
We recall that Heisenberg formulated the UP in 1925 in the setting of his matrix mechanics, which later showed to be mathematically equivalent to Schrödinger's wave equation mechanics, before Born's probabilistic interpretation of the wave function:
- At the instant of time when the position is determined, that is, at the instant when the photon is scattered by the electron, the electron undergoes a discontinuous change in momentum. This change is the greater the smaller the wavelength of the light employed, i.e., the more exact the determination of the position. At the instant at which the position of the electron is known, its momentum therefore can be known only up to magnitudes which correspond to that discontinuous change; thus, the more precisely the position is determined, the less precisely the momentum is known, and conversely.
Heisenberg thus suggested that an observation can influence the position/momentum of an electron being observed and thus can introduce an uncertainty. Heisenberg took a further bold step claiming that the uncertainty of observation reflected an intrinsic uncertainty of physical processes on atomic microscopic scales, which made quantum mechanics fundamentally different from classical macroscopic mechanics.
Heisenberg took an even further bold step and claimed that only physics which can be observed exists and the uncertainty of observation then suggested an intrinsic uncertainty of existence as a new phenomenon of atomic physics: Electrons are to be viewed as particles jumping around playing games of roulette and thus
have a different nature than both microscopic waves and macroscopic particles, which however is a weird world beyond scientific understanding.
The logic is thus to connect a (trivial) UP of wave mechanics to a (trivial) uncertainty of observation to obtain a (non-trivial) justification of the Copenhagen Interpretation. This logic was forcefully progagated by Bohr and Heisenberg, which made Schrödinger turn away from quantum mechanics in dismay.
The Dark Age of Modern Physics
The Enlightenment developed from a basis of classical mechanics expressing reason, rationality and certainty. The breakdown of European civilization with the 1st World War opened to modern physics based on
relativity theory and quantum mechanics embracing unreason, irrationality and uncertainty in a modern form of the Dark Ages. Physicists insist on informing us that modern physics cannot be understood:
- I think I can safely say that nobody understands quantum mechanics. (Richard Feynman)
- For those who are not shocked when they first come across quantum theory cannot possibly have understood it. (Niels Bohr)
- Shut up and calculate. (Dirac)
- Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that He does not play dice. (Einstein)
- Niels Bohr brainwashed a whole generation of theorists into thinking that the job of interpreting quantum theory was done 50 years ago. (1969 Nobel Laureate Murray Gell-Mann)
- Schrödinger was, to say the least, as stubborn as Einstein in his conservative attitude towards quantum mechanics; indeed, he not only rejected the statitical interpretation but insisted that his wave mechanics meant a return to a classical way of thinking. He would not accept any objection to it, not even the most weighty one, which is that a wave in 3N-dimensional space is not a classical classical concept and cannot be visualized. (Max Born)
- But maybe that is our mistake: maybe there are no particle positions and velocities, but only waves. It is just that we try to fit the waves to our preconceived ideas of positions and velocities. The resulting mismatch is the cause of the apparent unpredictability. (Stephen Hawking 1988)
- Therefore I feel that the Copenhagen Interpretation of quantum mechanics is dead. (H. D. Zeh)
The disappointing fact that quantum mechanics cannot be understood is turned around to become evidence that it is a masterpiece of human creativity and intellect:
- I call the UP bizar.
- No one understands quantum mechanics
- Things are made by littler things that jiggle (Feynman)
String theory is the ultimate expression of this form of (post)modern deconstruction:
The message to us in the audience is that we cannot understand, because nobody can understand,
except of course the expert physicist, who however is prevented from uncovering the mystery because nobody can understand, except of course the expert physicist, who however ....
It seems that we no longer live in an Age of Enlightenment, because we are no longer able to critically examine the message of physicists followed by politicians, scientists, doctors, teachers, financial advisors and personal coaches. Our role is to passively accept, swallow and consume, not to understand.
Enlightenment by Computational Simulation
In Many-Minds Quantum Mechanics we propose an interpretation of the wave function of a collection of electrons/kernels based on computing solutions of the Schrödinger equation using a Hartree method solving a system of one-electron/kernel three-dimensional wave equations, which can be given a direct physical deterministic interpretation.
The computational method thus suggests a physical interpretation of quantum mechanics, which can be grasped with experience from macroscopic wave mechanics and would have pleased Schrödinger since no reference is made to particle games of roulette.
Computational simulation does not interact with the system under study, and thus lacks the uncertainty possibly contributed by experimental observation. Computational simulation thus can be viewed as a form of non-intrusive observation or non-destructive testing, which can offer important insight into microscopic machinery inaccessible to direct experimental observation. It acts like computational medical tomography compared to classical dissection:
It is possible that computational quantum mechanics can be understood. More generally, it is possible that computational simulation can revive an Age of Enlightenment transcending from the blogosphere. A step in this direction is taken in My Book of Knols.
Spiros Kakos
Invite as author
Very good article
Best regards,
Claes
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