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Philosophers

Mortimer Adler
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Alexander of Aphrodisias
Samuel Alexander
William Alston
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Louise Antony
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Mark Balaguer
Jeffrey Barrett
William Barrett
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Henri Bergson
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Robert Bishop
Max Black
Susanne Bobzien
Emil du Bois-Reymond
Hilary Bok
Laurence BonJour
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Émile Boutroux
Daniel Boyd
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C.D.Broad
Michael Burke
Lawrence Cahoone
C.A.Campbell
Joseph Keim Campbell
Rudolf Carnap
Carneades
Nancy Cartwright
Gregg Caruso
Ernst Cassirer
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John Earman
Laura Waddell Ekstrom
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Herbert Feigl
Arthur Fine
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Frederic Fitch
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Philippa Foot
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Bas van Fraassen
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Alvin Goldman
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H.Paul Grice
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Ishtiyaque Haji
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Bernard Williams
Timothy Williamson
Ludwig Wittgenstein
Susan Wolf

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David Albert
Michael Arbib
Walter Baade
Bernard Baars
Jeffrey Bada
Leslie Ballentine
Marcello Barbieri
Gregory Bateson
John S. Bell
Mara Beller
Charles Bennett
Ludwig von Bertalanffy
Susan Blackmore
Margaret Boden
David Bohm
Niels Bohr
Ludwig Boltzmann
Emile Borel
Max Born
Satyendra Nath Bose
Walther Bothe
Jean Bricmont
Hans Briegel
Leon Brillouin
Stephen Brush
Henry Thomas Buckle
S. H. Burbury
Melvin Calvin
Donald Campbell
Sadi Carnot
Anthony Cashmore
Eric Chaisson
Gregory Chaitin
Jean-Pierre Changeux
Rudolf Clausius
Arthur Holly Compton
John Conway
Jerry Coyne
John Cramer
Francis Crick
E. P. Culverwell
Antonio Damasio
Olivier Darrigol
Charles Darwin
Richard Dawkins
Terrence Deacon
Lüder Deecke
Richard Dedekind
Louis de Broglie
Stanislas Dehaene
Max Delbrück
Abraham de Moivre
Bernard d'Espagnat
Paul Dirac
Hans Driesch
John Eccles
Arthur Stanley Eddington
Gerald Edelman
Paul Ehrenfest
Manfred Eigen
Albert Einstein
George F. R. Ellis
Hugh Everett, III
Franz Exner
Richard Feynman
R. A. Fisher
David Foster
Joseph Fourier
Philipp Frank
Steven Frautschi
Edward Fredkin
Benjamin Gal-Or
Lila Gatlin
Michael Gazzaniga
Nicholas Georgescu-Roegen
GianCarlo Ghirardi
J. Willard Gibbs
Nicolas Gisin
Paul Glimcher
Thomas Gold
A. O. Gomes
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Dirk ter Haar
Jacques Hadamard
Mark Hadley
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Ralph Hartley
Hyman Hartman
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Werner Heisenberg
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Basil Hiley
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Max Planck
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Jerome Rothstein
David Ruelle
Tilman Sauer
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Thomas Sebeok
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Francisco Varela
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John Wheeler
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Norbert Wiener
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H. Dieter Zeh
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Wojciech Zurek
Konrad Zuse
Fritz Zwicky

Presentations

Biosemiotics
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James Symposium
 
David Bohm

David Bohm is perhaps best known for new experimental methods to test Einstein’s supposed suggestion of “hidden variables” that would explain the EPR paradox by providing the information needed at the distant “entangled” particle, so it can coordinate its properties perfectly with the “local” particle.

Bohm wrote in 1952,

The usual interpretation of the quantum theory is based on an assumption having very far-reaching implications, ~i.e., that the physical state of an individual system is completely specified by a wave function that determines only the probabilities of actual results that can be obtained in a statistical ensemble of similar experiments. This assumption has been the object of severe criticisms, notably on the part of Einstein, who has always believed that, even at the quantum level, there must exist precisely definable elements or dynamical variables determining (as in classical physics) the actual behavior of each individual system, and not merely its probable behavior. Since these elements or variables are not now included in the quantum theory and have not yet been detected experimentally, Einstein has always regarded the present form of the quantum theory as incomplete, although he admits its internal consistency.

Einstein may have pressed Bohm to develop hidden variables as the source of nonlocal behavior. Einstein had heartily approved of Bohm’s textbook Quantum Theory and was initially supportive of Bohm’s new mechanics. Einstein thought Bohm was young enough and smart enough to produce the mathematical arguments that the older generation of “determinist” physicists like Erwin Schrödinger, Max Planck, and others had not been able to accomplish.

But when Bohm finished the work, based on Louis de Broglie’s 1924 “pilot-wave” idea (which Einstein had supported), Einstein rejected it as inconsistent with his theory of relativity.

Einstein wrote to Max Born on May 15, 1952,

Have you noticed that Bohm believes (as de Broglie did, by the way, 25 years ago) that he is able to interpret the quantum theory in deterministic terms? That way seems too cheap to me. But you, of course, can judge this better than I. 

Five years later, Bohm and his Israeli student Yakir Aharonov reformulated the original EPR argument in terms of electron spin. They said experimental tests with continuous variables would be much more difficult than tests with discrete quantities, such as the spin of electrons or polarization of photons. Bohm and Aharonov described the preparation of two particles, such that a measurement of one at a later time determines a measurement in the same direction of the other particle at any distance away.

We consider a molecule of total spin zero consisting of two atoms, each of spin one-half. The wave function of the system is therefore

ψ = (1/√2) [ ψ+ (1) ψ- (2) - ψ- (1) ψ+ (2) ]                 (1)

where ψ+ (1) refers to the wave function of the atomic state in which one particle (A) has spin +ℏ/2, etc. The two atoms are then separated by a method that does not influence the total spin. After they have separated enough so that they cease to interact, any desired component of the spin of the first particle (A) is measured. Then, because the total spin is still zero, it can immediately be concluded that the same component of the spin of the other particle (B) is opposite to that of A.

Conservation of Angular Momentum (and Spin)

Bohr and Aharonov gave a rare discussion of the role of conservation of angular momentum as explaining the fact (for the total spin zero state) that spin of the particle (B) will be found opposite to that of A. They also reacted to a hypothesis by Harvard professor Wendell Furry. Six years later Eugene Wigner also cited the conservation of angular momentum as explaining perfect correlations (or anti-correlations) in Bell-Bohm experiments.

Evidently, the foregoing interpretation is not satisfactory when applied to the experiment of ERP. It is of course acceptable for particle A alone (the particle whose spin is measured directly). But it does not explain why particle B (which does not interact with A or with the measuring apparatus) realizes its potentiality for a definite spin in precisely the same direction as that of A. Moreover, it cannot explain the fluctuations of the other two components of the spin of particle B as the result of disturbances due to the measuring apparatus.

One could perhaps suppose that there is some hidden interaction between B and A, or between B and the measuring apparatus, which explains the above behavior. Such an interaction would, at the very least, be outside the scope of the current quantum theory. Moreover, it would have to be instantaneous, because the orientation of the measuring apparatus could very quickly be changed, and the spin of B would have to respond immediately to the change. Such an immediate interaction between distant systems would not in general be consistent with the theory of relativity. This result constitutes the essence of the paradox of Einstein, Rosen, and Podolsky...

At first sight it would seem then that there exists at present no experimental proof that the paradoxical behavior described by ERP will really occur...

In fact, Einstein has (in a private communication) actually proposed such an idea; namely, that the current formulation of the many-body problem in quantum mechanics may break down when particles are far enough apart.

As Erwin Schrödinger explained to Einstein in 1935, reacting to EPR, the two-particle wave function will only separate (or decohere or decompose) into a product function when either particle is measured. For Bohm's case it will separate randomly into either ψ+ (1) ψ- (2) or ψ- (1) ψ+ (2)
The "definite" direction is created by the "free choice" of an experimenter measuring either A or B.
The consequences of such an idea have already been discussed by Furry.4 To illustrate Furry’s conclusions in terms of our problem, we may consider the possibility that after the molecule of spin zero decomposes, the wave function for the system is eventually no longer given by Eq. (1), which implies the puzzling correlations of the spins of the two atoms. Instead, we suppose that in any individual case, the spin of each atom becomes definite in some direction, while that of the other atom is opposite.

The molecule of spin zero is not yet in a single product. It is in a superposition of products
ψ+ (1) ψ- (2) and ψ- (1) ψ+ (2). It only decomposes (or "collapses") into one of these when a measurement is made.
The wave function will be the product

ψ = ψ+θ,φ (1) ψ-θ,φ (2)                 (2)

where ψ+θ,φ (1) is a wave function of particle A whose spin is positive in the direction given by θ and φ. In other words, each particle goes into a definite spin state, while the fluctuations of the other two components of the spin are uncorrelated to the fluctuations of these components of the spin of the other particle. In order to retain spherical symmetry in the statistical sense, we shall further suppose that in a large aggregate of similar cases, there is a uniform probability for any direction of θ and φ.

It is true that in any single case, the total angular momentum will not be conserved (just because the fluctuations of the two particles are now uncorrelated). However, thus far, there has not been given an experimental demonstration of the detailed conservation of every component of the angular momentum, for particles that are far apart and not interacting.

Conservation of angular momentum must be true at all times, not only on the average as Bohr-Kramers-Slater mistakenly argued for conservation of energy in 1924.
On the other hand, with the model that we have discussed here, the uniform probability of all directions will lead to the experimentally observed fact of conservation on the average. Thus, all evidence cited up to this point is equally consistent with either theory, but the model described above has the advantage of avoiding the paradox of ERP.
Thousands of Bell tests experimentally prove that measurement of particle A in a particular direction will show perfect correlations with particle B if (and only if) B is measured in the same direction. This is true after the measurement whether the product wave function becomes ψ+θ,φ (1) ψ-θ,φ (2) or ψ-θ,φ (1) ψ+θ,φ (2)
For if this model should be correct, there will be no precise correlation of an arbitrary component of the angular momentum of each particle in every individual case, and our decision to choose a certain direction for measuring the spin of particle A will have no influence whatever on the state of particle B [since the wave function is just the product (2)].

Bohm and Aharonov also gave a powerful explanation for the two-slit experiment. They wrote:

Bohmian mechanics provides a straightforward physical explanation.

First, close slit 1 and open slit 2.
The particle goes through slit 2.
It arrives at x on the plate with probability |ψ2(x)|2,
where ψ2 is the wave function which passed through slit 2.

Second, close slit 2 and open slit 1.
The particle goes through slit 1.
It arrives at x on the plate with probability |ψ1(x)|2,
where ψ1 is the wave function which passed through slit 1.

Third, open both slits.
The particle goes through slit 1 or slit 2.
It arrives at x with probability |ψ1(x)+ψ2(x)|2.

Now observe that in general,
1(x)+ψ2(x)|2 = |ψ1(x)+ψ2(x)|2= |ψ1(x)|2+|ψ2(x)|2 + 2ℜψ1(x) ψ2(x).

The last term comes from the interference of the wave packets ψ1 and ψ2 which passed through slit 1 and slit 2.

The probabilities of finding particles when both slits are open are different from the sum of slit 1 open and slit 2 open separately.

The wave function ψ(x) (squared), |ψ(x)|2, determines the probability of finding a particle at x, as Einstein first suggested and Max Born later described as his "statistical interpretation" (the so-called "Born Rule").

Now Richard Feynman's path integral formulation of quantum mechanics describes supraluminal paths and even some things moving backwards in time, so we must take a careful look at Bohm's work.

Bohm's search for "hidden variables" inspired John Bell to develop a theorem on "inequalities" that would need to be satisfied by hidden variables. To this date, every test of Bell's theorem has violated his inequalities and shown that the quantum theory cannot be replaced by one with "local" hidden variables. If they exist at all, "hidden variables" must also be "nonlocal."

The Measurement Process
Bohm was particularly clear on the process of measurement. He said it involves macroscopic irreversibility, which was a sign and a consequence of treating the measuring apparatus as a macroscopic system that could not itself be treated quantum mechanically. The macroscopic system could, in principle, be treated quantum mechanically, but Bohm said its many degrees of internal freedom would destroy any interference effects. This is the modern theory of quantum decoherence.

Bohm's view is consistent with the information-philosophy solution to the measurement problem. A measurement has only been made when new information has come into the world and adequate entropy has been carried away to insure the stability of the new information, long enough for it to be observed by the "conscious" observer.

In his 1951 textbook Quantum Theory, Bohm discusses measurement in chapter 22, section 12.

12. Irreversibility of Process of Measurement and Its Fundamental Role in Quantum Theory.
From the previous work it follows that a measurement process is irreversible in the sense that, after it has occurred, re-establishment of definite phase relations between the eigenfunctions of the measured variable is overwhelmingly unlikely. This irreversibility greatly resembles that which appears in thermodynamic processes, where a decrease of entropy is also an overwhelmingly unlikely possibility.*

* There is, in fact, a close connection between entropy and the process of measurement. See L. Szilard, , 53, 840, 1929. The necessity for such a connection can be seen by considering a box divided by a partition into two equal parts, containing an equal number of gas molecules in each part. Suppose that in this box is placed a device that can provide a rough measurement of the position of each atom as it approaches the partition. This device is coupled automatically to a gate in the partition in such a way that the gate will be opened if a molecule approaches the gate from the right, but closed if it approaches from the left. Thus, in time, all the molecules can be made to accumulate on the left-hand side. In this way, the entropy of the gas decreases. If there were no compensating increase of entropy of the mechanism, then the second law of thermodynamics would be violated. We have seen, however, that in practice, every process which can provide a definite measurement disclosing in which side of the box the molecule actually is, must also be attended by irreversible changes in the measuring apparatus. In fact, it can be shown that these changes must be at least large enough to compensate for the decrease in entropy of the gas. Thus, the second law of thermodynamics cannot actually be violated in this way. This means, of course, that Maxwell's famous "sorting demon " cannot operate, if he is made of matter obeying all of the laws of physics. (See L. Brillouin, American Scientist, 38, 594, 1950.)

Because the irreversible behavior of the measuring apparatus is essential for the destruction of definite phase relations and because, in turn, the destruction of definite phase relation's is essential for the consistency of the quantum theory as a whole, it follows that thermodynamic irreversibility enters into the quantum theory in an integral way. This is in remarkable contrast to classical theory, where the concept of thermodynamic irreversibility plays no fundamental role in the basic sciences of mechanics and electrodynamics. Thus, whereas in classical theory fundamental variables (such as position or momentum of an elementary particle) are regarded as having definite values independently of whether the measuring apparatus is reversible or not, in quantum theory we find that such a quantity can take on a well defined value only when the system is coupled indivisibly to a classically describable system undergoing irreversible processes. The very definition of the state of any one system at the microscopic level therefore requires that matter in the large shall undergo irreversible processes. There is a strong analogy here to the behavior of biological systems, where, likewise, the very existence of the fundamental elements (for example, the cells) depends on the maintenance of irreversible processes involving the oxidation of food throughout an organism as a whole. (A stoppage of these processes would result in the dissolution of the cell.)

But Bohm changed his mind about irreversibility when he developed his more realistic and deterministic theory. Now he became concerned with the classic "problem" of microscopic irreversibility, namely how can the increase of entropy involve macroscopic irreversibility if microscopic collisions of particles are reversible?

References
A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I

A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II

Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky

Causality and Chance in Modern Physics, U. Pennsylvania Press

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