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  2. The Quantum Postulate and the Recent Development of Atomic Theory | Niels BOHR | First edition
  3. A Farewell to Copenhagen?
  4. Copenhagen Interpretation of Quantum Mechanics

I have not read them all too many! So I leave it to Bohr scholars to tell us whether or not Bohr puts into his scientific work the Yin-Yang doctrine. It is hard to get any evidence for this.

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There is no mention of it. This is a polite way of Einstein saying that he cannot make much sense of it and when he does, he does not accept it. And many other scientists did, and still do, hold this view. But here goes. In the s Bohr began to think of the radiation emitted by atoms as having the dual features of a particle and of a wave. This is vague enough on what complementarity is, but it has to do.

An electron can have both momentum and position but any increase in accuracy of our knowledge of one of these has to be traded off with a decrease in our knowledge of the accuracy of the other.


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  6. Complementarity and the Copenhagen Interpretation of Quantum Mechanics.

Again an exclusive duality. This underlines the problem Einstein and many others had with formulating the principle of complementarity. Bohr first aired his views on complementarity in his autumn Como lecture. There we get further examples of complementarity. Whatever this is, it goes well beyond the issues in quantum mechanics which lead to complementarity in the first place. In later lectures Bohr got carried away by the wide application of complementarity which he found nearly everywhere.

Are there no limits to the application of complementarity? The last of these Bohr strongly resisted. So there are limits to its application but they are not easy to discern. What has this to do with Yin-Yang and its symbolism? Now did Bohr have prior knowledge of Yin-Yang and then apply it to his quantum mechanics? Or did his thinking about quantum mechanics, especially the problem of wave-particle duality, lead to the principle of complementarity of which Yin-Yang is a further example?

Bohr's emphasis on epistemological questions suggests he thought that the statistical uncertainty may only be in our knowledge. They may not describe nature itself. Or at least Bohr thought that we can not describe a "reality" for quantum objects, certainly not with classical concepts and language.

However, the new concept of an immaterial possibilities function pure information moving through space may make quantum phenomena "visualizable. But Einstein disliked this chance. He and most scientists appear to have what William James called an "antipathy to chance. Bohr and Heisenberg both thought we could never produce models of what is going on at the quantum level.

The Quantum Postulate and the Recent Development of Atomic Theory | Niels BOHR | First edition

Bohr thought that since the wave function cannot be observed we can't say anything about it. Heisenberg said probability is real and the basis for the statistical nature of quantum mechanics. Whenever we draw a diagram of the waves impinging on the two-slits , we are in fact visualizing the wave function as possible locations for a particle, with calculable probabilities for each possible location. Today we can visualize with animations many puzzles in physics, including the two-slit experiment, entanglement , and microscopic irreversibility.

No Path?


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  • Bohr, Heisenberg, Dirac and others said we cannot describe a particle as having a path. The path comes into existence when we observe it, Heisenberg maintained. Paul Dirac formalized quantum mechanics with these three fundamental concepts, all very familiar and accepted by Bohr, Heisenberg, and the other Copenhageners: Axiom of measurement. Bohr's stationary quantum states have eigenvalues with corresponding eigenfunctions the eigenvalue-eigenstate link.

    Werner Heisenberg on Quantum Mechanics

    Superposition principle. Projection postulate. Two-slit experiment.

    A "gedanken" experiment in the 's, but a real experiment today, exhibits the combination of wave and particle properties. Note that what two-slit experiment really shows is first, the wave function deterministically and continuously exploring all the possibilities for interaction, second, the particle randomly and discontinuously choosing one of those possibilities to become actual. There are many more elements that play lesser roles, some making the Copenhagen Interpretation very unpopular among philosophers of science and spawning new interpretations or even " formulations " of quantum mechanics.

    A Farewell to Copenhagen?

    Some of these are misreadings or later accretions. They include: The " conscious observer. Does the collapse only occur when an observer "looks at" the system? How exactly does the mind of the observer have causal power over the physical world? Einstein objected to the idea that his bed had diffused throughout the room and only gathered itself back together when he opened the bedroom door and looked in. John von Neumann and Eugene Wigner seemed to believe that the mind of the observer was essential, but it is not found in the original work of Bohr and Heisenberg, so should perhaps not be a part of the Copenhagen Interpretation?

    It has no place in standard quantum physics today The measurement problem , including the insistence that the measuring apparatus must be described classically when it is made of quantum particles.


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    There are actually at least three definitions of the measurement problem. They cannot both be true, it's claimed. The proper interpretation is simply that the two laws laws apply at different times in the evolution of a quantum object, one for possibilities, the other for actuality as Heisenberg knew : first, the unitary deterministic evolution moves through space exploring all the possibilities for interaction, second, the indeterministic collapse randomly acausally selects one of those possibilities to become actual.

    The original concern that the "collapse dynamics" von Neumann Process 1 is not a part of the formalism von Neumann Process 2 but is an ad hoc element, with no rules for when to apply it. If there was a deterministic law that predicted a collapse, or the decay of a radioactive nucleus, it would not be quantum mechanics! The many unreasonable philosophical claims for "complementarity:" e. It deals with epistemological knowledge of things, rather than the "things themselves.

    Copenhagen Interpretation of Quantum Mechanics

    Zeh and Wojciech Zurek deny the existence of particles and the collapse of the wave function , which is central to the Copenhagen Interpretation. Heisenberg had initially insisted on his own "matrix mechanics" of particles and their discrete, discontinuous, indeterministic behavior, the " quantum postulate " of unpredictable events that undermine the classical physics of causality.

    But Bohr told Heisenberg that his matrix mechanics was too narrow a view of the problem. This disappointed Heisenberg and almost ruptured their relationship. But Heisenberg came to accept the criticism and he eventually endorsed all of Bohr's deep philosophical view of quantum reality as unvisualizable. In his September Como Lecture , a month before the Solvay conference, Bohr introduced his theory of " complementarity " as a "complete" theory. It combines the contradictory notions of wave and particle. Since both are required, they complement and "complete" one another.

    Although Bohr is often credited with integrating the dualism of waves and particles, it was Einstein who predicted this would be necessary as early as But in doing so, Bohr obfuscated further what was already a mysterious picture. How could something possibly be both a discrete particle and a continuous wave? Bohr's Como Lecture astonished Heisenberg by actually deriving instead of Heisenberg's heuristic microscope argument the uncertainty principle from the space-time wave picture alone, with no reference to the acausal dynamics of Heisenberg's picture!

    After this, Heisenberg did the same derivation in his text and subsequently completely accepted complementarity. Heisenberg spent the next several years widely promoting Bohr's views to scientists and philosophers around the world, though he frequently lectured on his mistaken, but easily understood, argument that looking at particles disturbs them. This, which was later called the Copenhagen Interpretation, formed the foundation for the famous debates between Niels Bohr and Albert Einstein at the Solvay Conferences in and Of the 29 participants, 17 were or became Nobel Prize winners.

    Albert Einstein could not accept a theory of physics, which gave up classical causality.