Experimental Support for de Broglie-Bohm QM

[dennislmay]

Quantum Physics First: Physicists Measure Without Distorting

http://www.sciencedaily.com/releases/2011/06/110602143159.htm

"Our measured trajectories are consistent, as Wiseman had predicted, with the realistic but unconventional interpretation of quantum mechanics of such influential thinkers as David Bohm and Louis de Broglie," said Steinberg."

Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer.

http://www.sciencemag.org/content/332/6034/1170

Abstract

A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or “trajectory” that a quantum particle takes,

because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the

result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the

propagation of subensembles of quantum particles in a two-slit interferometer.

[Guyau]

.

Additional Information

On one level, the experiment appears to violate a central rule of quantum mechanics, but Professor Steinberg said this was not the case.

He explained to BBC News that "while the uncertainty principle does indeed forbid one from knowing the position and momentum of a particle exactly at the same time, it turns out that it is possible to ask 'what was the average momentum of the particles which reached this position?'".

"You can't know the exact value for any single particle, but you can talk about the average."

[BaalChatzaf]

.

Additional Information

On one level, the experiment appears to violate a central rule of quantum mechanics, but Professor Steinberg said this was not the case.

He explained to BBC News that "while the uncertainty principle does indeed forbid one from knowing the position and momentum of a particle exactly at the same time, it turns out that it is possible to ask 'what was the average momentum of the particles which reached this position?'".

"You can't know the exact value for any single particle, but you can talk about the average."

Interesting article. But it remains still that for an individual particle one cannot know both its position and velocity with indefinite precision. For aggregates it is both interesting and important that one can recover -the average momentum- of a set of particles that reach a given position. Heisenberg's principle still holds.

Ba'al Chatzaf

[Guyau]

Some Interpretations of Quantum Mechanics

Feynman v. Bell

Goldstein, Tumulka, and Zanghi on Bohmian Trajectories

Kramer’s Transactional Interpretation and Rand

Kastner on TI as One-World Interpretation

Origins

From Fifth Section of “Volitional Synapses”

(1995 – Objectivity V2N2)

Three Chances

. . .

Similarly, we initially describe radioactive alpha emissions as instances of a Poisson distribution having a certain blank constant (expected number of events per unit of time) in the argument of its exponential function. When we look further into the physics, we are able to express that constant in terms of physical constants such as electric charge of nuclei, size of nuclei, and Plank’s constant. The Poisson distribution does not get dissolved, or repudiated, by our assimilation of deeper physics into the decay constant. The assimilation does tell us, however, some of the physical factors constraining the overall rate of alpha emissions. One of these physical factors, Planck’s constant, is the telltale of quantum indeterminacy.

Let us now open the lid on the sort of chance distinctive to quantum mechanics. This is our second sort. . . .

At the turn of the [twentieth] century, Planck succeeded in deriving the correct distribution of electromagnetic radiation, according to wavelength, for blackbody emissions. The correct distribution had been known empirically, but theories to account for it in terms of electronic oscillations in the cavity walls and in terms of Maxwell’s theory of radiation had failed. Planck succeeded by supposing energies exchanged between oscillators and radiation to be only in discrete quantities directly proportional to the oscillator-radiation frequencies: E = hf, where the proportionality constant h is what came to be called Planck’s constant. Einstein, in 1905, saw that this discreteness was not consistent with Maxwell’s theory (1864) of electromagnetic radiation. Einstein proposed holding on to the discreteness and reforming Maxwell’s theory: light comes in quanta (Jammer 1966, 26–30). The existence of photons was strikingly confirmed in experiments between 1908 and 1922. Einstein was investigating the statistical character of photons by 1909 and even glimpsed the statistical linkage of photon to light wave (ibid., 37–39). By 1911 Planck had realized that the quantization of energy in the blackbody oscillators was the result of a much more general principle: h is a quantum of action [action is the physical quantity having the units of angular momentum, which is the units (mass x velocity x length), which is also (mass x velocity-squared x time)], a finite minimum area in the phase space of a mechanical system (ibid., 53–54). Also by 1911, Sommerfeld realized that Planck’s quantum of action should be related to the action function in Hamilton’s classical dynamics (ibid., 55–56). In 1916 Einstein showed that Planck’s blackbody-radiation law could be derived on the supposition that the energy exchanges are governed by Poisson probabilities, as had been implicated in radioactivity (ibid., 112). However, in 1916 the chance seen in radioactivity was still considered to be mitigable by further as yet unknown factors (ibid., 113).

By the early 1920’s, there was considerable experimental evidence that electromagnetic radiation possessed both a particle aspect and a wave aspect (ibid., 236–40). The old debate whether light is fundamentally particle (ray) or undulation of a continuum had been well settled in favor of the latter by mid-nineteenth century, according to the report of William Whewell (Butts 1989, 154, 157–58). The wave model could explain all that the particle model could explain and more. In the latter half of last [before last] century, Maxwell and Hertz would demonstrate that light waves are undulations of electromagnetic fields. The particle model was dead and buried. Then came Planck and Einstein, as we have seen.

We should notice that already at mid-nineteenth century the polarization of light was being studied extensively. This character of light was then without any theoretical explanation. The fact of polarity was grafted smoothly onto the wave model; likewise for Maxwell’s later electromagnetic wave model. In our century [20th], it was discovered that polarization, under the Einsteinian particle nature of light, is intrinsic spin (Frauenfelder and Henley 1974, 80–82). That has units of angular momentum, specifically, simple multiples of Planck’s constant. Intrinsic spin is a quality of matter not known until the quantum revolution. I stress that it is evidently a quite primary quality of matter, in the league of momentum, mass, and charge. Not all of the really basic items in the world are available for apprehension at the beginning of inquiry; we sometimes arrive at the most basic only after much investigation. Intrinsic spin was such an item (see also Penrose 1990).

Electromagnetic radiations, including X-rays, were stubbornly particle-like and wave-like by 1923 (and are even more stubbornly so today; Braginsky and Khalili 1992, 4–17). The velocity of those waves or particles was, of course, simply the velocity of light. The concept of rest mass does not apply to such particles; we say their rest mass is zero. This zero has been confirmed experimentally down to 10exp(-48) grams (Jackson 1975, 5–9). 1923 was the year de Broglie issued his theory that matter with nonzero rest mass has not only particle character, but wave character. He said essentially that if we were to associate with any material particle of nonzero rest mass m a certain periodicity given by h/(mc·c), where h is Planck’s constant and (mc·c) is the internal energy of the particle, then applying Einstein’s relativity of duration (French 1968, 92–109; Itano and Ramsey 1993), we are led to conclude that any moving particle, from the perspective of an outside rest frame, is accompanied by a train of propagating waves. The internal periodicity remains always in phase with that wave train. (These are phase waves, waves of constant action moving in the abstract phase space [or configuration space] of the particle [Goldstein 1950, 305–14]; though abstract, the relation of phase space to concrete space of the particle is real and definite [Krips 1987, 39–47].) The velocity of the particle will be inversely proportional to its wave’s phase velocity. The constant of inverse proportionality is c·c, the velocity of light squared (Jammer 1966, 243–45; Messiah 1958, 50–53). Louis de Broglie, merci beaucoup.

Clearly, since the velocities of massive particles (nonzero mass) must be less than c, their associated phase velocities must be greater than c. This is not in conflict with relativity since no mass nor momentum is being transported in concrete space at phase velocities. It may be helpful to think of phase velocities as geometrical velocities; like the velocity the spot of a laser beam would have tracing across the moon, the laser being rotated at high speed here on earth. Geometrical velocities can exceed c, consistent with relativity (Chiao, Kwait, and Steinberg 1993).

Einstein received a manuscript from India in the summer of 1924. Satyandra Nath Bose had deduced Planck’s radiation law independently of classical electrodynamics, assuming only a gas of photons whose phase space is divided into elementary cells of volume h·h·h. Einstein joined the effort of Bose and showed by early 1925 that the statistics of the photon gas are not entirely Boltzmannian (Pathria 1972, 187–89, 145–47, 132–34, 24–29). The mean-square energy fluctuations are given by a term reflecting Boltzmann statistics, but an additional term reflecting interference fluctuations, associated with wave character, is also present. We now have experimental confirmation of this distinctive statistical clustering of photons and other bosons (Kittel 1969, 260–62; Braginsky and Khalili 1992, 172–85). Einstein had gotten hold of de Broglie’s papers in December 1924, and he suspected the interference statistical fluctuations he was finding in the mathematics of the photon gas were related to de Broglie’s vast hypothesis.

Einstein spoke of de Broglie’s thesis with Max Born, together with James Franck and Walther Elasser. They began to think of experimentally testing the thesis by diffraction of free electrons (not because electrons are bosons, which they are not, but because they have nonzero rest mass). Franck informed them there had in fact already been positive results obtained in the research lab of the American phone company in New York. More definitive confirmation of de Broglie’s matter waves followed in the next few years (Jammer 1966, 248–54).

In 1926 Schrodinger divined the wave equation for de Broglie’s waves. Schrodinger invented a new mechanics—a wave mechanics—that was quickly adopted as the broad approach for calculating quantum characteristics (Jammer 1966, 255–80). Schrodinger’s physical interpretation of his equation’s wave function was dubious. (I should say “ditto” for the approach of Sachs 1988, 249–59.) He could not account very well for particle character of quantum entities. He could superpose wave functions, thereby forming a wave packet that naturally vanishes everywhere outside some local zone. The packet could then move along en masse, a nice semblance to an ordinary moving body. For macroscopic, classical bodies, all is well. There is wonderful harmony between quantum mechanics (whether Schrodinger’s wave mechanics or Heisenberg’s matrix mechanics) and classical mechanics (Nauenberg, Stroud, and Yeazell 1994). Schrodinger’s wave packet, it was soon discovered, spreads out spontaneously with the advance of time. A packet for a macroscopic object having a mass of 1 gram would follow a very precise trajectory without any significant spreading of the packet during the age of the universe. This is good enough. But an electron is a terribly tiny thing. If we require the packet for an electron to be localized to within 10exp(-8) centimeters, the packet will spread out significantly in 10exp(-16) seconds (Saxon 1968, 60).

Enter Max Born 1926. He applied Schrodinger’s wave equation to the scattering of a beam of electrons off atoms and obtained the deflection distribution among the scattered electrons that are found in experiment. Einstein had already shown that the intensity of light waves was a measure of the concentration of light quanta. Born generalized, proposing we regard the intensity (amplitude squared) of Schrodinger’s wave function as a probability density of particles in general (Jammer 1966, 283–93). De Broglie waves, then, are probability waves.

Born’s was a new genre of probability because of its wave-like interference bands. The mathematical theory of probability did not encompass such a thing as interference of probabilities. The mathematical theory, of course, had been made for a world of Boltzmann chance, not quantum chance. The mathematical theory of probability, from Pascal in the seventeenth century through Kolmogorov in the 1930’s, assumes straight additivity of probabilities for mutually exclusive events. The notion of quantum probability waves seems still today to be in tension with the mathematical additivity assumption, and at any rate, the interference of probabilities does not issue from the mathematical theory of probability.

We earlier observed that the Maxwell-Boltzmann sort of statistical mechanics had explained certain macroscopic thermodynamic principles by starting with Boltzmann chance and classical mechanics at the micro level. Between 1922 and 1924, some theoretical physicists proposed that energy and momentum conservation might be only true in statistical aggregation. They thought these conservations might not hold rigorously all the way down to individual photon or atom. Within two years, experimentalists thoroughly devastated that proposal (Jammer 1966, 181–87). Conservation of energy and momentum go all the way down. Born’s statistical interpretation of the quantum mechanical wave function is consistent with that fact (cf. debate between Renouvier and Delboef in 1882–83; ibid., 177–78). That is to say, Born’s statistical interpretation is consistent with some general form of material and efficient causation at the micro level (see Boydstun 1991, 30, 25).

Born’s quantum chance might go all the way down, without abridgement of energy-momentum conservation, and I think that indeed is the way quantum chance is. I do not mean to say we cannot discover more about the nature of probability waves in the future, but I do not expect the sort of chance they modulate to be diluted to sheer Boltzmann chance. I should distance this view of quantum phenomena from certain views of Niels Bohr. Many today reject the Bohrian view that probability waves are meaningfully attached only to collections of particles. We should rather attach the wave to the individual particle (individual quantum entity, such as a photon or electron). That is one thing we may conclude from the exquisite experimental manipulations of single quantum entities that became possible in the 1980’s (Ruhla 1992, 152–203; Haroche and Raimond 1993; Krips 1987, 59–62). We evidently should also reject the Bohrian idea that the Heisenberg indeterminacies (which I surely do accept) are the source of interference effects (Englert, Scully, and Walther 1994; Krips 1987, 69, 84). We should reject also the Bohrian view that “collapse (or reduction) of the wave packet” depends essentially on observation, or the presence of consciousness. Schrodinger’s cat dies if and when the vial of poison is broken by the radioactive decay. Our opening the box and finding out the result has nothing to do with the collapse (Krips 1987, 113–15).

. . .

[dennislmay]

Some Interpretations of Quantum Mechanics

Feynman v. Bell

Goldstein, Tumulka, and Zanghi on Bohmian Trajectories

Kramer’s Transactional Interpretation and Rand

Kastner on TI as One-World Interpretation

Origins

From Fifth Section of “Volitional Synapses”

(1995 – Objectivity V2N2)

Three Chances

. . .

Similarly, we initially describe radioactive alpha emissions as instances of a Poisson distribution having a certain blank constant (expected number of events per unit of time) in the argument of its exponential function. When we look further into the physics, we are able to express that constant in terms of physical constants such as electric charge of nuclei, size of nuclei, and Plank’s constant. The Poisson distribution does not get dissolved, or repudiated, by our assimilation of deeper physics into the decay constant. The assimilation does tell us, however, some of the physical factors constraining the overall rate of alpha emissions. One of these physical factors, Planck’s constant, is the telltale of quantum indeterminacy.

Let us now open the lid on the sort of chance distinctive to quantum mechanics. This is our second sort. . . .

At the turn of the [twentieth] century, Planck succeeded in deriving the correct distribution of electromagnetic radiation, according to wavelength, for blackbody emissions. The correct distribution had been known empirically, but theories to account for it in terms of electronic oscillations in the cavity walls and in terms of Maxwell’s theory of radiation had failed. Planck succeeded by supposing energies exchanged between oscillators and radiation to be only in discrete quantities directly proportional to the oscillator-radiation frequencies: E = hf, where the proportionality constant h is what came to be called Planck’s constant. Einstein, in 1905, saw that this discreteness was not consistent with Maxwell’s theory (1864) of electromagnetic radiation. Einstein proposed holding on to the discreteness and reforming Maxwell’s theory: light comes in quanta (Jammer 1966, 26–30). The existence of photons was strikingly confirmed in experiments between 1908 and 1922. Einstein was investigating the statistical character of photons by 1909 and even glimpsed the statistical linkage of photon to light wave (ibid., 37–39). By 1911 Planck had realized that the quantization of energy in the blackbody oscillators was the result of a much more general principle: h is a quantum of action [action is the physical quantity having the units of angular momentum, which is the units (mass x velocity x length), which is also (mass x velocity-squared x time)], a finite minimum area in the phase space of a mechanical system (ibid., 53–54). Also by 1911, Sommerfeld realized that Planck’s quantum of action should be related to the action function in Hamilton’s classical dynamics (ibid., 55–56). In 1916 Einstein showed that Planck’s blackbody-radiation law could be derived on the supposition that the energy exchanges are governed by Poisson probabilities, as had been implicated in radioactivity (ibid., 112). However, in 1916 the chance seen in radioactivity was still considered to be mitigable by further as yet unknown factors (ibid., 113).

By the early 1920’s, there was considerable experimental evidence that electromagnetic radiation possessed both a particle aspect and a wave aspect (ibid., 236–40). The old debate whether light is fundamentally particle (ray) or undulation of a continuum had been well settled in favor of the latter by mid-nineteenth century, according to the report of William Whewell (Butts 1989, 154, 157–58). The wave model could explain all that the particle model could explain and more. In the latter half of last [before last] century, Maxwell and Hertz would demonstrate that light waves are undulations of electromagnetic fields. The particle model was dead and buried. Then came Planck and Einstein, as we have seen.

We should notice that already at mid-nineteenth century the polarization of light was being studied extensively. This character of light was then without any theoretical explanation. The fact of polarity was grafted smoothly onto the wave model; likewise for Maxwell’s later electromagnetic wave model. In our century [20th], it was discovered that polarization, under the Einsteinian particle nature of light, is intrinsic spin (Frauenfelder and Henley 1974, 80–82). That has units of angular momentum, specifically, simple multiples of Planck’s constant. Intrinsic spin is a quality of matter not known until the quantum revolution. I stress that it is evidently a quite primary quality of matter, in the league of momentum, mass, and charge. Not all of the really basic items in the world are available for apprehension at the beginning of inquiry; we sometimes arrive at the most basic only after much investigation. Intrinsic spin was such an item (see also Penrose 1990).

Electromagnetic radiations, including X-rays, were stubbornly particle-like and wave-like by 1923 (and are even more stubbornly so today; Braginsky and Khalili 1992, 4–17). The velocity of those waves or particles was, of course, simply the velocity of light. The concept of rest mass does not apply to such particles; we say their rest mass is zero. This zero has been confirmed experimentally down to 10exp(-48) grams (Jackson 1975, 5–9). 1923 was the year de Broglie issued his theory that matter with nonzero rest mass has not only particle character, but wave character. He said essentially that if we were to associate with any material particle of nonzero rest mass m a certain periodicity given by h/(mc·c), where h is Planck’s constant and (mc·c) is the internal energy of the particle, then applying Einstein’s relativity of duration (French 1968, 92–109; Itano and Ramsey 1993), we are led to conclude that any moving particle, from the perspective of an outside rest frame, is accompanied by a train of propagating waves. The internal periodicity remains always in phase with that wave train. (These are phase waves, waves of constant action moving in the abstract phase space [or configuration space] of the particle [Goldstein 1950, 305–14]; though abstract, the relation of phase space to concrete space of the particle is real and definite [Krips 1987, 39–47].) The velocity of the particle will be inversely proportional to its wave’s phase velocity. The constant of inverse proportionality is c·c, the velocity of light squared (Jammer 1966, 243–45; Messiah 1958, 50–53). Louis de Broglie, merci beaucoup.

Clearly, since the velocities of massive particles (nonzero mass) must be less than c, their associated phase velocities must be greater than c. This is not in conflict with relativity since no mass nor momentum is being transported in concrete space at phase velocities. It may be helpful to think of phase velocities as geometrical velocities; like the velocity the spot of a laser beam would have tracing across the moon, the laser being rotated at high speed here on earth. Geometrical velocities can exceed c, consistent with relativity (Chiao, Kwait, and Steinberg 1993).

Einstein received a manuscript from India in the summer of 1924. Satyandra Nath Bose had deduced Planck’s radiation law independently of classical electrodynamics, assuming only a gas of photons whose phase space is divided into elementary cells of volume h·h·h. Einstein joined the effort of Bose and showed by early 1925 that the statistics of the photon gas are not entirely Boltzmannian (Pathria 1972, 187–89, 145–47, 132–34, 24–29). The mean-square energy fluctuations are given by a term reflecting Boltzmann statistics, but an additional term reflecting interference fluctuations, associated with wave character, is also present. We now have experimental confirmation of this distinctive statistical clustering of photons and other bosons (Kittel 1969, 260–62; Braginsky and Khalili 1992, 172–85). Einstein had gotten hold of de Broglie’s papers in December 1924, and he suspected the interference statistical fluctuations he was finding in the mathematics of the photon gas were related to de Broglie’s vast hypothesis.

Einstein spoke of de Broglie’s thesis with Max Born, together with James Franck and Walther Elasser. They began to think of experimentally testing the thesis by diffraction of free electrons (not because electrons are bosons, which they are not, but because they have nonzero rest mass). Franck informed them there had in fact already been positive results obtained in the research lab of the American phone company in New York. More definitive confirmation of de Broglie’s matter waves followed in the next few years (Jammer 1966, 248–54).

In 1926 Schrodinger divined the wave equation for de Broglie’s waves. Schrodinger invented a new mechanics—a wave mechanics—that was quickly adopted as the broad approach for calculating quantum characteristics (Jammer 1966, 255–80). Schrodinger’s physical interpretation of his equation’s wave function was dubious. (I should say “ditto” for the approach of Sachs 1988, 249–59.) He could not account very well for particle character of quantum entities. He could superpose wave functions, thereby forming a wave packet that naturally vanishes everywhere outside some local zone. The packet could then move along en masse, a nice semblance to an ordinary moving body. For macroscopic, classical bodies, all is well. There is wonderful harmony between quantum mechanics (whether Schrodinger’s wave mechanics or Heisenberg’s matrix mechanics) and classical mechanics (Nauenberg, Stroud, and Yeazell 1994). Schrodinger’s wave packet, it was soon discovered, spreads out spontaneously with the advance of time. A packet for a macroscopic object having a mass of 1 gram would follow a very precise trajectory without any significant spreading of the packet during the age of the universe. This is good enough. But an electron is a terribly tiny thing. If we require the packet for an electron to be localized to within 10exp(-8) centimeters, the packet will spread out significantly in 10exp(-16) seconds (Saxon 1968, 60).

Enter Max Born 1926. He applied Schrodinger’s wave equation to the scattering of a beam of electrons off atoms and obtained the deflection distribution among the scattered electrons that are found in experiment. Einstein had already shown that the intensity of light waves was a measure of the concentration of light quanta. Born generalized, proposing we regard the intensity (amplitude squared) of Schrodinger’s wave function as a probability density of particles in general (Jammer 1966, 283–93). De Broglie waves, then, are probability waves.

Born’s was a new genre of probability because of its wave-like interference bands. The mathematical theory of probability did not encompass such a thing as interference of probabilities. The mathematical theory, of course, had been made for a world of Boltzmann chance, not quantum chance. The mathematical theory of probability, from Pascal in the seventeenth century through Kolmogorov in the 1930’s, assumes straight additivity of probabilities for mutually exclusive events. The notion of quantum probability waves seems still today to be in tension with the mathematical additivity assumption, and at any rate, the interference of probabilities does not issue from the mathematical theory of probability.

We earlier observed that the Maxwell-Boltzmann sort of statistical mechanics had explained certain macroscopic thermodynamic principles by starting with Boltzmann chance and classical mechanics at the micro level. Between 1922 and 1924, some theoretical physicists proposed that energy and momentum conservation might be only true in statistical aggregation. They thought these conservations might not hold rigorously all the way down to individual photon or atom. Within two years, experimentalists thoroughly devastated that proposal (Jammer 1966, 181–87). Conservation of energy and momentum go all the way down. Born’s statistical interpretation of the quantum mechanical wave function is consistent with that fact (cf. debate between Renouvier and Delboef in 1882–83; ibid., 177–78). That is to say, Born’s statistical interpretation is consistent with some general form of material and efficient causation at the micro level (see Boydstun 1991, 30, 25).

Born’s quantum chance might go all the way down, without abridgement of energy-momentum conservation, and I think that indeed is the way quantum chance is. I do not mean to say we cannot discover more about the nature of probability waves in the future, but I do not expect the sort of chance they modulate to be diluted to sheer Boltzmann chance. I should distance this view of quantum phenomena from certain views of Niels Bohr. Many today reject the Bohrian view that probability waves are meaningfully attached only to collections of particles. We should rather attach the wave to the individual particle (individual quantum entity, such as a photon or electron). That is one thing we may conclude from the exquisite experimental manipulations of single quantum entities that became possible in the 1980’s (Ruhla 1992, 152–203; Haroche and Raimond 1993; Krips 1987, 59–62). We evidently should also reject the Bohrian idea that the Heisenberg indeterminacies (which I surely do accept) are the source of interference effects (Englert, Scully, and Walther 1994; Krips 1987, 69, 84). We should reject also the Bohrian view that “collapse (or reduction) of the wave packet” depends essentially on observation, or the presence of consciousness. Schrodinger’s cat dies if and when the vial of poison is broken by the radioactive decay. Our opening the box and finding out the result has nothing to do with the collapse (Krips 1987, 113–15).

. . .

Another link on the original topic:

http://physicsworld....icle/news/46193

Has some graphics similar to those associated

with de Broglie-Bohm mechanics.

Dennis

[dennislmay]

Some Interpretations of Quantum Mechanics

Feynman v. Bell

Goldstein, Tumulka, and Zanghi on Bohmian Trajectories

Kramer’s Transactional Interpretation and Rand

Kastner on TI as One-World Interpretation

Origins

From Fifth Section of “Volitional Synapses”

(1995 – Objectivity V2N2)

Three Chances

. . .

Similarly, we initially describe radioactive alpha emissions as instances of a Poisson distribution having a certain blank constant (expected number of events per unit of time) in the argument of its exponential function. When we look further into the physics, we are able to express that constant in terms of physical constants such as electric charge of nuclei, size of nuclei, and Plank’s constant. The Poisson distribution does not get dissolved, or repudiated, by our assimilation of deeper physics into the decay constant. The assimilation does tell us, however, some of the physical factors constraining the overall rate of alpha emissions. One of these physical factors, Planck’s constant, is the telltale of quantum indeterminacy.

Let us now open the lid on the sort of chance distinctive to quantum mechanics. This is our second sort. . . .

At the turn of the [twentieth] century, Planck succeeded in deriving the correct distribution of electromagnetic radiation, according to wavelength, for blackbody emissions. The correct distribution had been known empirically, but theories to account for it in terms of electronic oscillations in the cavity walls and in terms of Maxwell’s theory of radiation had failed. Planck succeeded by supposing energies exchanged between oscillators and radiation to be only in discrete quantities directly proportional to the oscillator-radiation frequencies: E = hf, where the proportionality constant h is what came to be called Planck’s constant. Einstein, in 1905, saw that this discreteness was not consistent with Maxwell’s theory (1864) of electromagnetic radiation. Einstein proposed holding on to the discreteness and reforming Maxwell’s theory: light comes in quanta (Jammer 1966, 26–30). The existence of photons was strikingly confirmed in experiments between 1908 and 1922. Einstein was investigating the statistical character of photons by 1909 and even glimpsed the statistical linkage of photon to light wave (ibid., 37–39). By 1911 Planck had realized that the quantization of energy in the blackbody oscillators was the result of a much more general principle: h is a quantum of action [action is the physical quantity having the units of angular momentum, which is the units (mass x velocity x length), which is also (mass x velocity-squared x time)], a finite minimum area in the phase space of a mechanical system (ibid., 53–54). Also by 1911, Sommerfeld realized that Planck’s quantum of action should be related to the action function in Hamilton’s classical dynamics (ibid., 55–56). In 1916 Einstein showed that Planck’s blackbody-radiation law could be derived on the supposition that the energy exchanges are governed by Poisson probabilities, as had been implicated in radioactivity (ibid., 112). However, in 1916 the chance seen in radioactivity was still considered to be mitigable by further as yet unknown factors (ibid., 113).

By the early 1920’s, there was considerable experimental evidence that electromagnetic radiation possessed both a particle aspect and a wave aspect (ibid., 236–40). The old debate whether light is fundamentally particle (ray) or undulation of a continuum had been well settled in favor of the latter by mid-nineteenth century, according to the report of William Whewell (Butts 1989, 154, 157–58). The wave model could explain all that the particle model could explain and more. In the latter half of last [before last] century, Maxwell and Hertz would demonstrate that light waves are undulations of electromagnetic fields. The particle model was dead and buried. Then came Planck and Einstein, as we have seen.

We should notice that already at mid-nineteenth century the polarization of light was being studied extensively. This character of light was then without any theoretical explanation. The fact of polarity was grafted smoothly onto the wave model; likewise for Maxwell’s later electromagnetic wave model. In our century [20th], it was discovered that polarization, under the Einsteinian particle nature of light, is intrinsic spin (Frauenfelder and Henley 1974, 80–82). That has units of angular momentum, specifically, simple multiples of Planck’s constant. Intrinsic spin is a quality of matter not known until the quantum revolution. I stress that it is evidently a quite primary quality of matter, in the league of momentum, mass, and charge. Not all of the really basic items in the world are available for apprehension at the beginning of inquiry; we sometimes arrive at the most basic only after much investigation. Intrinsic spin was such an item (see also Penrose 1990).

Electromagnetic radiations, including X-rays, were stubbornly particle-like and wave-like by 1923 (and are even more stubbornly so today; Braginsky and Khalili 1992, 4–17). The velocity of those waves or particles was, of course, simply the velocity of light. The concept of rest mass does not apply to such particles; we say their rest mass is zero. This zero has been confirmed experimentally down to 10exp(-48) grams (Jackson 1975, 5–9). 1923 was the year de Broglie issued his theory that matter with nonzero rest mass has not only particle character, but wave character. He said essentially that if we were to associate with any material particle of nonzero rest mass m a certain periodicity given by h/(mc·c), where h is Planck’s constant and (mc·c) is the internal energy of the particle, then applying Einstein’s relativity of duration (French 1968, 92–109; Itano and Ramsey 1993), we are led to conclude that any moving particle, from the perspective of an outside rest frame, is accompanied by a train of propagating waves. The internal periodicity remains always in phase with that wave train. (These are phase waves, waves of constant action moving in the abstract phase space [or configuration space] of the particle [Goldstein 1950, 305–14]; though abstract, the relation of phase space to concrete space of the particle is real and definite [Krips 1987, 39–47].) The velocity of the particle will be inversely proportional to its wave’s phase velocity. The constant of inverse proportionality is c·c, the velocity of light squared (Jammer 1966, 243–45; Messiah 1958, 50–53). Louis de Broglie, merci beaucoup.

Clearly, since the velocities of massive particles (nonzero mass) must be less than c, their associated phase velocities must be greater than c. This is not in conflict with relativity since no mass nor momentum is being transported in concrete space at phase velocities. It may be helpful to think of phase velocities as geometrical velocities; like the velocity the spot of a laser beam would have tracing across the moon, the laser being rotated at high speed here on earth. Geometrical velocities can exceed c, consistent with relativity (Chiao, Kwait, and Steinberg 1993).

Einstein received a manuscript from India in the summer of 1924. Satyandra Nath Bose had deduced Planck’s radiation law independently of classical electrodynamics, assuming only a gas of photons whose phase space is divided into elementary cells of volume h·h·h. Einstein joined the effort of Bose and showed by early 1925 that the statistics of the photon gas are not entirely Boltzmannian (Pathria 1972, 187–89, 145–47, 132–34, 24–29). The mean-square energy fluctuations are given by a term reflecting Boltzmann statistics, but an additional term reflecting interference fluctuations, associated with wave character, is also present. We now have experimental confirmation of this distinctive statistical clustering of photons and other bosons (Kittel 1969, 260–62; Braginsky and Khalili 1992, 172–85). Einstein had gotten hold of de Broglie’s papers in December 1924, and he suspected the interference statistical fluctuations he was finding in the mathematics of the photon gas were related to de Broglie’s vast hypothesis.

Einstein spoke of de Broglie’s thesis with Max Born, together with James Franck and Walther Elasser. They began to think of experimentally testing the thesis by diffraction of free electrons (not because electrons are bosons, which they are not, but because they have nonzero rest mass). Franck informed them there had in fact already been positive results obtained in the research lab of the American phone company in New York. More definitive confirmation of de Broglie’s matter waves followed in the next few years (Jammer 1966, 248–54).

In 1926 Schrodinger divined the wave equation for de Broglie’s waves. Schrodinger invented a new mechanics—a wave mechanics—that was quickly adopted as the broad approach for calculating quantum characteristics (Jammer 1966, 255–80). Schrodinger’s physical interpretation of his equation’s wave function was dubious. (I should say “ditto” for the approach of Sachs 1988, 249–59.) He could not account very well for particle character of quantum entities. He could superpose wave functions, thereby forming a wave packet that naturally vanishes everywhere outside some local zone. The packet could then move along en masse, a nice semblance to an ordinary moving body. For macroscopic, classical bodies, all is well. There is wonderful harmony between quantum mechanics (whether Schrodinger’s wave mechanics or Heisenberg’s matrix mechanics) and classical mechanics (Nauenberg, Stroud, and Yeazell 1994). Schrodinger’s wave packet, it was soon discovered, spreads out spontaneously with the advance of time. A packet for a macroscopic object having a mass of 1 gram would follow a very precise trajectory without any significant spreading of the packet during the age of the universe. This is good enough. But an electron is a terribly tiny thing. If we require the packet for an electron to be localized to within 10exp(-8) centimeters, the packet will spread out significantly in 10exp(-16) seconds (Saxon 1968, 60).

Enter Max Born 1926. He applied Schrodinger’s wave equation to the scattering of a beam of electrons off atoms and obtained the deflection distribution among the scattered electrons that are found in experiment. Einstein had already shown that the intensity of light waves was a measure of the concentration of light quanta. Born generalized, proposing we regard the intensity (amplitude squared) of Schrodinger’s wave function as a probability density of particles in general (Jammer 1966, 283–93). De Broglie waves, then, are probability waves.

Born’s was a new genre of probability because of its wave-like interference bands. The mathematical theory of probability did not encompass such a thing as interference of probabilities. The mathematical theory, of course, had been made for a world of Boltzmann chance, not quantum chance. The mathematical theory of probability, from Pascal in the seventeenth century through Kolmogorov in the 1930’s, assumes straight additivity of probabilities for mutually exclusive events. The notion of quantum probability waves seems still today to be in tension with the mathematical additivity assumption, and at any rate, the interference of probabilities does not issue from the mathematical theory of probability.

We earlier observed that the Maxwell-Boltzmann sort of statistical mechanics had explained certain macroscopic thermodynamic principles by starting with Boltzmann chance and classical mechanics at the micro level. Between 1922 and 1924, some theoretical physicists proposed that energy and momentum conservation might be only true in statistical aggregation. They thought these conservations might not hold rigorously all the way down to individual photon or atom. Within two years, experimentalists thoroughly devastated that proposal (Jammer 1966, 181–87). Conservation of energy and momentum go all the way down. Born’s statistical interpretation of the quantum mechanical wave function is consistent with that fact (cf. debate between Renouvier and Delboef in 1882–83; ibid., 177–78). That is to say, Born’s statistical interpretation is consistent with some general form of material and efficient causation at the micro level (see Boydstun 1991, 30, 25).

Born’s quantum chance might go all the way down, without abridgement of energy-momentum conservation, and I think that indeed is the way quantum chance is. I do not mean to say we cannot discover more about the nature of probability waves in the future, but I do not expect the sort of chance they modulate to be diluted to sheer Boltzmann chance. I should distance this view of quantum phenomena from certain views of Niels Bohr. Many today reject the Bohrian view that probability waves are meaningfully attached only to collections of particles. We should rather attach the wave to the individual particle (individual quantum entity, such as a photon or electron). That is one thing we may conclude from the exquisite experimental manipulations of single quantum entities that became possible in the 1980’s (Ruhla 1992, 152–203; Haroche and Raimond 1993; Krips 1987, 59–62). We evidently should also reject the Bohrian idea that the Heisenberg indeterminacies (which I surely do accept) are the source of interference effects (Englert, Scully, and Walther 1994; Krips 1987, 69, 84). We should reject also the Bohrian view that “collapse (or reduction) of the wave packet” depends essentially on observation, or the presence of consciousness. Schrodinger’s cat dies if and when the vial of poison is broken by the radioactive decay. Our opening the box and finding out the result has nothing to do with the collapse (Krips 1987, 113–15).

. . .

Another link on the original topic:

http://physicsworld....icle/news/46193

Has some graphics similar to those associated

with de Broglie-Bohm mechanics.

Dennis

[dennislmay]

Some Interpretations of Quantum Mechanics

Feynman v. Bell

Goldstein, Tumulka, and Zanghi on Bohmian Trajectories

Kramer’s Transactional Interpretation and Rand

Kastner on TI as One-World Interpretation

Origins

From Fifth Section of “Volitional Synapses”

(1995 – Objectivity V2N2)

Three Chances

. . .

Similarly, we initially describe radioactive alpha emissions as instances of a Poisson distribution having a certain blank constant (expected number of events per unit of time) in the argument of its exponential function. When we look further into the physics, we are able to express that constant in terms of physical constants such as electric charge of nuclei, size of nuclei, and Plank’s constant. The Poisson distribution does not get dissolved, or repudiated, by our assimilation of deeper physics into the decay constant. The assimilation does tell us, however, some of the physical factors constraining the overall rate of alpha emissions. One of these physical factors, Planck’s constant, is the telltale of quantum indeterminacy.

Let us now open the lid on the sort of chance distinctive to quantum mechanics. This is our second sort. . . .

At the turn of the [twentieth] century, Planck succeeded in deriving the correct distribution of electromagnetic radiation, according to wavelength, for blackbody emissions. The correct distribution had been known empirically, but theories to account for it in terms of electronic oscillations in the cavity walls and in terms of Maxwell’s theory of radiation had failed. Planck succeeded by supposing energies exchanged between oscillators and radiation to be only in discrete quantities directly proportional to the oscillator-radiation frequencies: E = hf, where the proportionality constant h is what came to be called Planck’s constant. Einstein, in 1905, saw that this discreteness was not consistent with Maxwell’s theory (1864) of electromagnetic radiation. Einstein proposed holding on to the discreteness and reforming Maxwell’s theory: light comes in quanta (Jammer 1966, 26–30). The existence of photons was strikingly confirmed in experiments between 1908 and 1922. Einstein was investigating the statistical character of photons by 1909 and even glimpsed the statistical linkage of photon to light wave (ibid., 37–39). By 1911 Planck had realized that the quantization of energy in the blackbody oscillators was the result of a much more general principle: h is a quantum of action [action is the physical quantity having the units of angular momentum, which is the units (mass x velocity x length), which is also (mass x velocity-squared x time)], a finite minimum area in the phase space of a mechanical system (ibid., 53–54). Also by 1911, Sommerfeld realized that Planck’s quantum of action should be related to the action function in Hamilton’s classical dynamics (ibid., 55–56). In 1916 Einstein showed that Planck’s blackbody-radiation law could be derived on the supposition that the energy exchanges are governed by Poisson probabilities, as had been implicated in radioactivity (ibid., 112). However, in 1916 the chance seen in radioactivity was still considered to be mitigable by further as yet unknown factors (ibid., 113).

By the early 1920’s, there was considerable experimental evidence that electromagnetic radiation possessed both a particle aspect and a wave aspect (ibid., 236–40). The old debate whether light is fundamentally particle (ray) or undulation of a continuum had been well settled in favor of the latter by mid-nineteenth century, according to the report of William Whewell (Butts 1989, 154, 157–58). The wave model could explain all that the particle model could explain and more. In the latter half of last [before last] century, Maxwell and Hertz would demonstrate that light waves are undulations of electromagnetic fields. The particle model was dead and buried. Then came Planck and Einstein, as we have seen.

We should notice that already at mid-nineteenth century the polarization of light was being studied extensively. This character of light was then without any theoretical explanation. The fact of polarity was grafted smoothly onto the wave model; likewise for Maxwell’s later electromagnetic wave model. In our century [20th], it was discovered that polarization, under the Einsteinian particle nature of light, is intrinsic spin (Frauenfelder and Henley 1974, 80–82). That has units of angular momentum, specifically, simple multiples of Planck’s constant. Intrinsic spin is a quality of matter not known until the quantum revolution. I stress that it is evidently a quite primary quality of matter, in the league of momentum, mass, and charge. Not all of the really basic items in the world are available for apprehension at the beginning of inquiry; we sometimes arrive at the most basic only after much investigation. Intrinsic spin was such an item (see also Penrose 1990).

Electromagnetic radiations, including X-rays, were stubbornly particle-like and wave-like by 1923 (and are even more stubbornly so today; Braginsky and Khalili 1992, 4–17). The velocity of those waves or particles was, of course, simply the velocity of light. The concept of rest mass does not apply to such particles; we say their rest mass is zero. This zero has been confirmed experimentally down to 10exp(-48) grams (Jackson 1975, 5–9). 1923 was the year de Broglie issued his theory that matter with nonzero rest mass has not only particle character, but wave character. He said essentially that if we were to associate with any material particle of nonzero rest mass m a certain periodicity given by h/(mc·c), where h is Planck’s constant and (mc·c) is the internal energy of the particle, then applying Einstein’s relativity of duration (French 1968, 92–109; Itano and Ramsey 1993), we are led to conclude that any moving particle, from the perspective of an outside rest frame, is accompanied by a train of propagating waves. The internal periodicity remains always in phase with that wave train. (These are phase waves, waves of constant action moving in the abstract phase space [or configuration space] of the particle [Goldstein 1950, 305–14]; though abstract, the relation of phase space to concrete space of the particle is real and definite [Krips 1987, 39–47].) The velocity of the particle will be inversely proportional to its wave’s phase velocity. The constant of inverse proportionality is c·c, the velocity of light squared (Jammer 1966, 243–45; Messiah 1958, 50–53). Louis de Broglie, merci beaucoup.

Clearly, since the velocities of massive particles (nonzero mass) must be less than c, their associated phase velocities must be greater than c. This is not in conflict with relativity since no mass nor momentum is being transported in concrete space at phase velocities. It may be helpful to think of phase velocities as geometrical velocities; like the velocity the spot of a laser beam would have tracing across the moon, the laser being rotated at high speed here on earth. Geometrical velocities can exceed c, consistent with relativity (Chiao, Kwait, and Steinberg 1993).

Einstein received a manuscript from India in the summer of 1924. Satyandra Nath Bose had deduced Planck’s radiation law independently of classical electrodynamics, assuming only a gas of photons whose phase space is divided into elementary cells of volume h·h·h. Einstein joined the effort of Bose and showed by early 1925 that the statistics of the photon gas are not entirely Boltzmannian (Pathria 1972, 187–89, 145–47, 132–34, 24–29). The mean-square energy fluctuations are given by a term reflecting Boltzmann statistics, but an additional term reflecting interference fluctuations, associated with wave character, is also present. We now have experimental confirmation of this distinctive statistical clustering of photons and other bosons (Kittel 1969, 260–62; Braginsky and Khalili 1992, 172–85). Einstein had gotten hold of de Broglie’s papers in December 1924, and he suspected the interference statistical fluctuations he was finding in the mathematics of the photon gas were related to de Broglie’s vast hypothesis.

Einstein spoke of de Broglie’s thesis with Max Born, together with James Franck and Walther Elasser. They began to think of experimentally testing the thesis by diffraction of free electrons (not because electrons are bosons, which they are not, but because they have nonzero rest mass). Franck informed them there had in fact already been positive results obtained in the research lab of the American phone company in New York. More definitive confirmation of de Broglie’s matter waves followed in the next few years (Jammer 1966, 248–54).

In 1926 Schrodinger divined the wave equation for de Broglie’s waves. Schrodinger invented a new mechanics—a wave mechanics—that was quickly adopted as the broad approach for calculating quantum characteristics (Jammer 1966, 255–80). Schrodinger’s physical interpretation of his equation’s wave function was dubious. (I should say “ditto” for the approach of Sachs 1988, 249–59.) He could not account very well for particle character of quantum entities. He could superpose wave functions, thereby forming a wave packet that naturally vanishes everywhere outside some local zone. The packet could then move along en masse, a nice semblance to an ordinary moving body. For macroscopic, classical bodies, all is well. There is wonderful harmony between quantum mechanics (whether Schrodinger’s wave mechanics or Heisenberg’s matrix mechanics) and classical mechanics (Nauenberg, Stroud, and Yeazell 1994). Schrodinger’s wave packet, it was soon discovered, spreads out spontaneously with the advance of time. A packet for a macroscopic object having a mass of 1 gram would follow a very precise trajectory without any significant spreading of the packet during the age of the universe. This is good enough. But an electron is a terribly tiny thing. If we require the packet for an electron to be localized to within 10exp(-8) centimeters, the packet will spread out significantly in 10exp(-16) seconds (Saxon 1968, 60).

Enter Max Born 1926. He applied Schrodinger’s wave equation to the scattering of a beam of electrons off atoms and obtained the deflection distribution among the scattered electrons that are found in experiment. Einstein had already shown that the intensity of light waves was a measure of the concentration of light quanta. Born generalized, proposing we regard the intensity (amplitude squared) of Schrodinger’s wave function as a probability density of particles in general (Jammer 1966, 283–93). De Broglie waves, then, are probability waves.

Born’s was a new genre of probability because of its wave-like interference bands. The mathematical theory of probability did not encompass such a thing as interference of probabilities. The mathematical theory, of course, had been made for a world of Boltzmann chance, not quantum chance. The mathematical theory of probability, from Pascal in the seventeenth century through Kolmogorov in the 1930’s, assumes straight additivity of probabilities for mutually exclusive events. The notion of quantum probability waves seems still today to be in tension with the mathematical additivity assumption, and at any rate, the interference of probabilities does not issue from the mathematical theory of probability.

We earlier observed that the Maxwell-Boltzmann sort of statistical mechanics had explained certain macroscopic thermodynamic principles by starting with Boltzmann chance and classical mechanics at the micro level. Between 1922 and 1924, some theoretical physicists proposed that energy and momentum conservation might be only true in statistical aggregation. They thought these conservations might not hold rigorously all the way down to individual photon or atom. Within two years, experimentalists thoroughly devastated that proposal (Jammer 1966, 181–87). Conservation of energy and momentum go all the way down. Born’s statistical interpretation of the quantum mechanical wave function is consistent with that fact (cf. debate between Renouvier and Delboef in 1882–83; ibid., 177–78). That is to say, Born’s statistical interpretation is consistent with some general form of material and efficient causation at the micro level (see Boydstun 1991, 30, 25).

Born’s quantum chance might go all the way down, without abridgement of energy-momentum conservation, and I think that indeed is the way quantum chance is. I do not mean to say we cannot discover more about the nature of probability waves in the future, but I do not expect the sort of chance they modulate to be diluted to sheer Boltzmann chance. I should distance this view of quantum phenomena from certain views of Niels Bohr. Many today reject the Bohrian view that probability waves are meaningfully attached only to collections of particles. We should rather attach the wave to the individual particle (individual quantum entity, such as a photon or electron). That is one thing we may conclude from the exquisite experimental manipulations of single quantum entities that became possible in the 1980’s (Ruhla 1992, 152–203; Haroche and Raimond 1993; Krips 1987, 59–62). We evidently should also reject the Bohrian idea that the Heisenberg indeterminacies (which I surely do accept) are the source of interference effects (Englert, Scully, and Walther 1994; Krips 1987, 69, 84). We should reject also the Bohrian view that “collapse (or reduction) of the wave packet” depends essentially on observation, or the presence of consciousness. Schrodinger’s cat dies if and when the vial of poison is broken by the radioactive decay. Our opening the box and finding out the result has nothing to do with the collapse (Krips 1987, 113–15).

. . .

Another link on the original topic:

http://physicsworld....icle/news/46193

Has some graphics similar to those associated

with de Broglie-Bohm mechanics.

Dennis

[BaalChatzaf]

Another link on the original topic:

http://physicsworld....icle/news/46193

Has some graphics similar to those associated

with de Broglie-Bohm mechanics.

Dennis

This link does not work for me.

Ba'al Chatzaf

[dennislmay]

Another link on the original topic:

http://physicsworld....icle/news/46193

Has some graphics similar to those associated

with de Broglie-Bohm mechanics.

Dennis

This link does not work for me.

Ba'al Chatzaf

http://tinyurl.com/3gaut4z

It didn't work for me either. Here is

a tinyurl version instead.

Dennis

[dennislmay]

Another link on the original topic:

http://physicsworld....icle/news/46193

Has some graphics similar to those associated

with de Broglie-Bohm mechanics.

Dennis

This link does not work for me.

Ba'al Chatzaf

http://tinyurl.com/3gaut4z

It didn't work for me either. Here is

a tinyurl version instead.

Dennis

Another link about the subject:

http://tinyurl.com/3px5jfr

Dennis