We can easily forgive children who are afraid of the dark. The real tragedy is when men are afraid of the light...
No one can understand [quantum] theory until he is willing to think of "psi" as a real objective field rather than just a "probability amplitude", even
though it propagates not in 3-space but in 3N-space.
When I was a student I had much difficulty with quantum mechanics. It was comforting to find that even Einstein had had difficulties for a long time.
Indeed they had led him to the heretical conclusion that something was missing in the theory:
"I am, in fact, rather firmly convinced that the essentially statistical character of contemporary quantum theory is solely to be ascribed to the fact
that this theory operates with an incomplete description of physical systems". More explicitly,
"in a complete physical description, the statistical quantum theory would (...) take an approximately analogous position to the statistical mechanics
within the frame of classical mechanics".
Discussing how physics might develop, Born wrote: "If a future theory should be deterministic, it cannot be a modification of the present one (...)
How this could be possible (...) I leave to the determinists to worry about".
J. S. Bell, Speakable and unspeakable in quantum mechanics
Cambridge University Press (1987).
I think I can safely say that nobody understands quantum mechanics.
Richard Feynman. The Character of Physical Law. M.I.T. Press, Cambridge, 1965.
The more I think about the physical part of Schrödinger's theory, the more disgusting I find it: what Schrödinger writes about the Anschaulichkeit ( german for "clearness" )
of his theory I consider Mist ( german for "dung" ) (Heisenberg's letter to Pauli, 8 June 1926).
David Cassidy, Uncertainty: The Life and Science of Werner Heisenberg, W.H. Freeman and Co.(1992), pag.215.
Malgré la possibilité d'un échec final, il paraît donc utile de reprendre par sa base le problème très difficile de l'interprétation de la Mécanique
Ondulatoire, afin de voir si l'interprétation actuellement orthodoxe est vraiment la seule que l'on puisse adopter.
L. de Broglie, La Physique quantique restera-t-elle indéterministe? Gauthier-Villars, Paris (1953).
[La Mécanique Quantique], que je connais bien, puisque je l'ai longtemps enseignée, est très puissante et conduit à un très grand nombre de prévisions
exactes, mais elle ne donne pas, à mon avis, une vue exacte et satisfaisante des phénomènes qu'elle étudie. Cela est un peu comparable au rôle joué
naguère par la thermodinamique abstraite des principes qui permettait de prévoir exactement un gran nombre de phénomènes et était par suite d'une grande
utilité, mais qui ne donnait pas une idée exacte de la réalité moleculaire dont le lois de la thermodynamique des principes ne donnaient que les
L. de Broglie, "Un itinéraire scientifique", textes réunis et présentés par G. Lochak, Ed. La Découverte, Paris (1987).
Let me say at the outset that I am opposing not a few special statements of quantum mechanics held today (1952): I am opposing the whole of it, I am
opposing its basic views (...), shaped when Max Born put forward his probability interpretation, which was accepted by almost everybody.
E. Schrödinger, The Interpretation of Quantum Mechanics, Ox Bow Press (1995).
This relationship [group velocity = particle velocity] is very attractive: in particular it tempts us to interpret a particle of matter as a wave-packet
due to the superposition of a number of wave trains.This tentative interpretation, however, comes up against insurmountable difficulties, since a wave
packet of this kind is in general very soon dissipated.
M. Born, Atomic Physics, Blackie & Son Ltd (1935).
From Einstein's letter to Born of 12 May 1952:
"Have you noticed that Bohm believes (as de Broglie did, 25 years ago) that he is able to interpret the quantum theory in deterministic terms?
That way seems too cheap to me"!
M. Born, The Born-Einstein letters (Macmillan 1971, p. 192)
Our present quantum mechanical formalism is not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part
incomplete human information about Nature - all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble. Yet we
think that this unscrambling is a pre-requisite for any further advance in basic physical theory.
E. T. Jaynes, Proc. Workshop "Complexity, Entropy and the Physics of Information", Santa Fe (1989), ed. by W. H. Zurek. Addison-Wesley, 1990.
The mono-energetic de Broglie's waves - when considered as mutually independent, i.e. not scrambled
together (according to Jaynes's expression) by Born's wave-function - allow a non-probabilistic description in terms of exact point-particle trajectories,
providing a straightforward Wave-Mechanical extension of Classical Dynamics.
The Bohmian approach, in its turn, formally mimicking de Broglie's mono-energetic waves (whose objective reality is well-established by diffraction and
interference experiments), depicts Born's most general wave-function as a single physical object, hopefully sharing the same objective reality. It is indeed a strong attempt
to dress with plausibility the Born Rule, by presenting the wave-function as a generalized pilot wave (a "wave" for which no Davisson-Germer
experiment was ever contrived!) although it isn't even the solution of a wave equation.
A. Orefice, R. Giovanelli, D. Ditto, From Classical to Wave-Mechanical Dynamics, arXiv 1406.4968 v3 (2015).
According to the probabilistic interpretation these trajectories [given by the "guidance equations"] are the paths along which probability
flows. Clearly an explicit expression for the wave function is needed in this type of calculations. (...)
It is in this way that the wave "guides" the particles.
A. S.Sanz and F. Borondo, Causal trajectories description of atom diffraction by surfaces, Phys. Rev. B 61, 7743 (2000)
The Uncertainty Principle is not a result particular of quantum mechanics, but general of any wave theory, since dp and dx only measure the dispersion
associated with the wave, without specifying the physics described by such a wave.
A. S. Sanz and S. Miret-Artès, A Trajectory Description of Quantum Processes, Vol.I, Springer (2013).
In my view, de Broglie's pilot wave is a new kind of causal agent, a radically new kind of physical entity grounded in configuration space. To
understand it, it's helpful to examine the historical parallel with two other physical entities that seemed mysterious when first introduced: Newton's
concept of gravitational attraction-at-a-distance, and Faraday's concept of field.
A. Valentini, Quantum Interview, arxiv:1408.2836, (2014).
While Mathematics and Physics formed during centuries a single branch of the tree of knowledge (both were part of natural philosophy), physicists and mathematicians
started going different ways during the last century (one of the most recent culprits being the Bourbaki school). For instance, David Hilbert is reported to have said that Physics
is too difficult to leave to physicists, while Albert Einstein characterized Hilbert's physics (in a letter to Herman Weyl) as infantile.
To be fair, we must add that Einstein's theory was really based on physical principles, while Hilbert's travail in physics was an exercise in pure mathematics (we all know that even
today many mathematical texts, which claim to be of physical interest, are too often just pure mathematics dressed up in a phony physical language).
M. A. de Gosson, The Principles of Newtonian and Quantum Mechanics, Imperial College Press, London (2001).
Nonlocality is profoundly antirational, antiscientific. It violates common sense, logic and relativity all at once, not to mention its total lack of empirical
support. No previous "méprise" in the history of Physics, not the Ptolemaic solar system, phlogiston, cold fusion, or whatever, violates the fundamental precepts
of logic, the essential tool of scientific pursuit, to the extent that the concept of nonlocality does. Allowing something so violently antirational to be a
cornerstone of a fundamental science with little protest, or, what's worse, with wonderment, is beyond mind boggling. That nonlocality was not taken as a symptom
of error, but celebrated as a profoundity, from the distance of future times will earn scorn.
A. F. Kracklauer, Annales de la Fondation Louis de Broglie 25, 193 (2000).
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