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Proceedings of the National Academy of Sciences

The Nature of Light

Gilbert Newton Lewis

Published Jan 1, 1926• 106 citations
Publisher

Abstract

The following views regarding the mode of transmission of light are of so unorthodox a character that I set them down with some reluctance; but it seems to be generally admitted that the paradox of quantum theory cannot be resolved without doing violence to one or more of our cherished common notions.Some of the consequences of the theory that I am going to advance are repugnant to common sense, yet, searching in vain for an alternative and finding no physical fact of optics or of thermodynamics in opposition to the theory, I have come to regard it as a natural and indeed inevitable extension of Einstein's principle of relativity.Let me start with two statemefits which seem now to be well supported by experiment, although perhaps not entirely demonstrated.They are, however, the postulates upon which the following theory is built.

DOI
10.1073/pnas.12.1.22

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More them any other topic in the foundations of physics, the problem of the arrow (or arrows!) of time seems to be characterized by a unique ‘slipperiness’: it is not only difficult to find answers to the questions once posed, but difficult to find meaningful questions to ask in the first place. Perhaps this is because an asymmetry with respect to the sense of time is built into us at an even deeper level than other ‘synthetic a priori’ conceptions about the world such as the continued existence of unknown objects. However that may be, in this situation, rather than trying to pose general questions which may turn out in the end to be ill-defined, there may be something to be said for trying to formulate much less speculative, indeed perhaps in retrospect trivial questions to which at least we have a hope of finding a definite answer. This is what I shall do in this essay: to be specific, I shall ask whether a test which is currently being designed concerning the validity of a certain ‘common-sense’ view of the macroscopic world (‘macrorealism’) would be affected if we were to relax our common-sense assumptions about the direction of causality in time. Let me start with a very brief review of established ideas concerning the formal (a)symmetry of the quantum theory with respect to the direction of time. The classic works on this subject are the paper of Aharonov et al. (‘ABL’) and the book by Belinfante. In these discussions the notion of ‘measurement’ is taken as primitive and undefined.

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On the Nature of Light

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In a recent article in these Proceedings (1) Professor G. N. Lewis has suggested that the conflict between the quantum theory of light and the known facts of interference might be resolved by assuming that an atom never emits a quantum of light except to another atom, the possibility of transmission of the quantum being determined by the nature of the paths connecting the two atoms in such a manner that the transmission will not occur if forbidden by the known laws of interference. The idea is made more plausible by describing such transmissions with the help of Minkowski's four-dimensional geometry of relativity.

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Readers offer their own magic moments with John Bell

N. Bykovetz

I greatly enjoyed reading Reinhold Bertlmann’s article “Magic moments with John Bell.” Sprinkled with levity, it discussed Bell’s life, work, and outstanding insights and achievements in the foundations of quantum mechanics (QM). In my view, the reading should also make one acutely aware that scientists, despite our expectations of them, are sometimes still prone to the same failings that beset the rest of humanity.Bertlmann outlines very nicely Bell’s theorem and inequalities and the consequences of their violation; that work led to the subsequent startling experimental results on “entangled” quantum mechanical states, which, Bertlmann writes, showed “that nature contains a nonlocality in its structure.” Nonlocality, in Bell’s conception of it, is clearly a violation of special relativity (SR), so we have a problem. The startling thing for me is that Bell actually does appear to solve the problem, at least in principle, but at the same time he seems afraid to say so and, in fact, distances himself from the proposed solution.The essence of his ambivalence is conveyed in the following paragraph, quoted by Bertlmann:It may be that we have to admit that causal influences do go faster than light. The role of Lorentz invariance in the completed theory would then be very problematic. An “ether” would be the cheapest solution. But the unobservability of this ether would be disturbing. So would be the impossibility of “messages” faster than light.Clearly, faster-than-light propagation is not possible in SR. But it is permissible in the approximately 100-year-old ether-based Lorentzian theory of relativity (LR), developed by Joseph Larmor, Hendrik Lorentz, Henri Poincaré, and others. Bell was explicitly cognizant of LR and discussed it in his book Speakable and Unspeakable in Quantum Mechanics (2nd edition, Cambridge University Press, 2004). It is well known that LR and SR are totally congruent in their kinematics and dynamics, for speeds equal to or less than c. All predictions are identical. However—though one cannot find this in any standard textbooks—the LR ether theory differs from SR by allowing, without contradiction, speeds greater than c.Historically, Einstein’s SR gained ascendancy, and LR was relegated to the scrap heap of history for many reasons, but I think predominantly for the following. SR was viewed as being far more elegant and simple to develop—from the perspective of theory formation—because it followed deductively from Einstein’s two simple axioms. On the other hand, LR theory was developed from a realism perspective, where waves were thought to need a medium to wave in (the luminiferous ether).Considering that Bell was clearly aware of LR and was entertaining the idea, albeit reluctantly, of “causal influences [going] faster than light”—that is, being consonant with LR—I find it difficult to understand his expressions in the quote above about cheap solutions and disturbing features. It seems to be part of human psychology that once a set of ideas or a theory is accepted as valid for a long enough time by a community of people, as has been the case for SR, it gets transformed into belief, psychologically not unlike religious belief. Once that happens, those who would question the established dogma are treated as if the questioning was ill-intentioned, if not downright sacrilegious.© 2015 American Institute of Physics.

Physics Today•Nov 30, 2015•0 citations

A proposal to get some common-sense intuition for the paradox of the double-slit experiment

G. Coddens

We argue that the double-slit experiment can be understood much better by considering it as an experiment whereby one uses electrons to study the set-up rather than an experiment whereby we use a set-up to study the behaviour of electrons. We also show that the concept of undecidability (like e.g. occurs in G\odel's theorem) can be used in an intuitive way to make sense of the double-slit experiment and the quantum rules for calculating coherent and incoherent probabilities. We meet here a situation where the electrons always behave in a fully deterministic way, while the detailed design of the set-up may render the question about the way they move through the set-up experimentally undecidable. It is very important to make a distinction in quantum mechanics between the determinism of nature (Einstein) and the decidability of a question within an experimental set-up (Bohr). The former is about the absolute truth of an answer to a yes or no question, and follows binary logic (true or false), the latter about what an experimental set-up can decide and tell about the truth of that answer, and follows ternary logic (true, false or undecidable). Binary and ternary logic are incompatible. The viewpoints of Bohr and Einstein are thus operating on different levels and it is only by confusing these two levels that these two viewpoints seem to be irreconcilable. We show that the expression $\psi_{1} + \psi_{2}$ for the wave function of the double-slit experiment is numerically correct, but logically flawed. It has to be replaced in the interference region by the logically correct expression $\psi'_{1} + \psi'_{2}$, which has the same numerical value as $\psi_{1} + \psi_{2}$, such that $\psi'_{1} + \psi'_{2} = \psi_{1} + \psi_{2}$, but with $\psi'_{1} = {\psi_{1} +\psi_{2}\over{\sqrt{2}}} \,e^{\imath {\pi\over{4}} } \neq \psi_{1}$ and $\psi'_{2} = {\psi_{1} +\psi_{2}\over{\sqrt{2}}}\,e^{-\imath {\pi\over{4}}}\neq \psi_{2}$. Here $\psi'_{1}$ and $\psi'_{2}$ are the correct contributions from the slits to the total wave function $\psi'_{1} + \psi'_{2}$. We have then $p = |\psi'_{1} + \psi'_{2}|^{2} = |\psi'_{1}|^{2} + |\psi'_{2}|^{2} = p_{1}+p_{2} $ such that the paradox that quantum mechanics (QM) would not follow the traditional rules of probability calculus disappears. The paradox is rooted in the wrong intuition that $\psi_{1}$ and $\psi_{2}$ would be the true physical contributions to $\psi'_{1} + \psi'_{2} =\psi_{1} + \psi_{2}$ like in the case of waves in a water tank. The solution proposed here is not {\em ad hoc} but based on an extensive analysis of the geometrical meaning of spinors within group representation theory and its application to QM. Working further on the argument one can even show that an interference pattern is the only way to satisfy simultaneously two conditions: The condition obeying binary logic (in the spirit of Einstein) that the electron has only two mutually exclusive options to get to the detector (viz. going through slit S$_{1}$ or going through slit S$_{2}$) and the condition obeying ternary logic (in the spirit of Bohr) that the question which one of these two options the electron has taken is experimentally undecidable. A very important element in the analysis is the problem of the non-existence of {\em common} probability distributions for different experimental set-ups. And this is a recurrent theme in other situations that are felt as paradoxical. The CHSH inequality used in the experiments of Aspect {\em et al.} clashes with quantum mechanics because it is based on the assumption that there would exist a {\em common} probability distribution for the hidden variables in the different experiments that have to be made to determine the various quantities that intervene in the inequality. That common probability distribution for measured quantities does not exist is well known from quantum mechanics itself (because the operators that come into play do not commute and therefore do not have common eigenstates, i.e. common probability amplitudes). But this non-existence of common probability distributions applies also to certain variables in the set-ups of the different experiments and the latter fact can also be explained by purely classical reasoning.

•Oct 26, 2016•2 citations

A Quantum Theory of Optical Dispersion

C. G. DARWIN

When a theory is framed trying to explain a discrepant system of facts, it is a necessary process of thought to take some branch of the theory as more completely true than the rest, and to adjust the remaining parts in such a way that they will fit in with this base, though they may still conflict with one another. This has certainly been true of the quantum theory; the speculations connected with it have as their base the law of the conservation of energy. Now a critical examination of fundamentals does not by any means justify this faith. It is of course a fact of observation that in the gross energy is conserved, but this only means an averaged energy; and as pure dynamics has failed to explain many atomic phenomena there seems no reason to maintain the exact conservation of energy, which is only one of the consequences of the dynamical equations. Indeed it is hardly too much to say that had the photoelectric effect been discovered a century ago, it is probable that no one would ever have suggested that the status of the first law of thermodynamics was in any way different from that of the second. On the other hand, Bohr's theory, and especially Sommerfeld's extension of it, have given great encouragement to the belief that in dynamics lay the way to the complete truth, so that in consequence of the triumphs of that theory there has been little thought in other directions. Another impediment is that our whole ideas are saturated with the principles of energy, so that denying it leaves hardly any foundation from which to start.

Proceedings of the National Academy of Sciences•Jan 1, 1923•11 citations
The following views regarding the mode of transmission of light are of so unorthodox a character that I set them down with some reluctance; but it seems to be generally admitted that the paradox of quantum theory cannot be resolved without doing violence to one or more of our cherished common notions.Some of the consequences of the theory that I am going to advance are repugnant to common sense, yet, searching in vain for an alternative and finding no physical fact of optics or of thermodynamics in opposition to the theory, I have come to regard it as a natural and indeed inevitable extension of Einstein's principle of relativity.Let me start with two statemefits which seem now to be well supported by experiment, although perhaps not entirely demonstrated.They are, however, the postulates upon which the following theory is built.
More them any other topic in the foundations of physics, the problem of the arrow (or arrows!) of time seems to be characterized by a unique ‘slipperiness’: it is not only difficult to find answers to the questions once posed, but difficult to find meaningful questions to ask in the first place. Perhaps this is because an asymmetry with respect to the sense of time is built into us at an even deeper level than other ‘synthetic a priori’ conceptions about the world such as the continued existence of unknown objects. However that may be, in this situation, rather than trying to pose general questions which may turn out in the end to be ill-defined, there may be something to be said for trying to formulate much less speculative, indeed perhaps in retrospect trivial questions to which at least we have a hope of finding a definite answer. This is what I shall do in this essay: to be specific, I shall ask whether a test which is currently being designed concerning the validity of a certain ‘common-sense’ view of the macroscopic world (‘macrorealism’) would be affected if we were to relax our common-sense assumptions about the direction of causality in time. Let me start with a very brief review of established ideas concerning the formal (a)symmetry of the quantum theory with respect to the direction of time. The classic works on this subject are the paper of Aharonov et al. (‘ABL’) and the book by Belinfante. In these discussions the notion of ‘measurement’ is taken as primitive and undefined.
In a recent article in these Proceedings (1) Professor G. N. Lewis has suggested that the conflict between the quantum theory of light and the known facts of interference might be resolved by assuming that an atom never emits a quantum of light except to another atom, the possibility of transmission of the quantum being determined by the nature of the paths connecting the two atoms in such a manner that the transmission will not occur if forbidden by the known laws of interference. The idea is made more plausible by describing such transmissions with the help of Minkowski's four-dimensional geometry of relativity.
I greatly enjoyed reading Reinhold Bertlmann’s article “Magic moments with John Bell.” Sprinkled with levity, it discussed Bell’s life, work, and outstanding insights and achievements in the foundations of quantum mechanics (QM). In my view, the reading should also make one acutely aware that scientists, despite our expectations of them, are sometimes still prone to the same failings that beset the rest of humanity.Bertlmann outlines very nicely Bell’s theorem and inequalities and the consequences of their violation; that work led to the subsequent startling experimental results on “entangled” quantum mechanical states, which, Bertlmann writes, showed “that nature contains a nonlocality in its structure.” Nonlocality, in Bell’s conception of it, is clearly a violation of special relativity (SR), so we have a problem. The startling thing for me is that Bell actually does appear to solve the problem, at least in principle, but at the same time he seems afraid to say so and, in fact, distances himself from the proposed solution.The essence of his ambivalence is conveyed in the following paragraph, quoted by Bertlmann:It may be that we have to admit that causal influences do go faster than light. The role of Lorentz invariance in the completed theory would then be very problematic. An “ether” would be the cheapest solution. But the unobservability of this ether would be disturbing. So would be the impossibility of “messages” faster than light.Clearly, faster-than-light propagation is not possible in SR. But it is permissible in the approximately 100-year-old ether-based Lorentzian theory of relativity (LR), developed by Joseph Larmor, Hendrik Lorentz, Henri Poincaré, and others. Bell was explicitly cognizant of LR and discussed it in his book Speakable and Unspeakable in Quantum Mechanics (2nd edition, Cambridge University Press, 2004). It is well known that LR and SR are totally congruent in their kinematics and dynamics, for speeds equal to or less than c. All predictions are identical. However—though one cannot find this in any standard textbooks—the LR ether theory differs from SR by allowing, without contradiction, speeds greater than c.Historically, Einstein’s SR gained ascendancy, and LR was relegated to the scrap heap of history for many reasons, but I think predominantly for the following. SR was viewed as being far more elegant and simple to develop—from the perspective of theory formation—because it followed deductively from Einstein’s two simple axioms. On the other hand, LR theory was developed from a realism perspective, where waves were thought to need a medium to wave in (the luminiferous ether).Considering that Bell was clearly aware of LR and was entertaining the idea, albeit reluctantly, of “causal influences [going] faster than light”—that is, being consonant with LR—I find it difficult to understand his expressions in the quote above about cheap solutions and disturbing features. It seems to be part of human psychology that once a set of ideas or a theory is accepted as valid for a long enough time by a community of people, as has been the case for SR, it gets transformed into belief, psychologically not unlike religious belief. Once that happens, those who would question the established dogma are treated as if the questioning was ill-intentioned, if not downright sacrilegious.© 2015 American Institute of Physics.
We argue that the double-slit experiment can be understood much better by considering it as an experiment whereby one uses electrons to study the set-up rather than an experiment whereby we use a set-up to study the behaviour of electrons. We also show that the concept of undecidability (like e.g. occurs in G\odel's theorem) can be used in an intuitive way to make sense of the double-slit experiment and the quantum rules for calculating coherent and incoherent probabilities. We meet here a situation where the electrons always behave in a fully deterministic way, while the detailed design of the set-up may render the question about the way they move through the set-up experimentally undecidable. It is very important to make a distinction in quantum mechanics between the determinism of nature (Einstein) and the decidability of a question within an experimental set-up (Bohr). The former is about the absolute truth of an answer to a yes or no question, and follows binary logic (true or false), the latter about what an experimental set-up can decide and tell about the truth of that answer, and follows ternary logic (true, false or undecidable). Binary and ternary logic are incompatible. The viewpoints of Bohr and Einstein are thus operating on different levels and it is only by confusing these two levels that these two viewpoints seem to be irreconcilable. We show that the expression ψ1+ψ2\psi_{1} + \psi_{2}ψ1​+ψ2​ for the wave function of the double-slit experiment is numerically correct, but logically flawed. It has to be replaced in the interference region by the logically correct expression ψ1′+ψ2′\psi'_{1} + \psi'_{2}ψ1′​+ψ2′​, which has the same numerical value as ψ1+ψ2\psi_{1} + \psi_{2}ψ1​+ψ2​, such that ψ1′+ψ2′=ψ1+ψ2\psi'_{1} + \psi'_{2} = \psi_{1} + \psi_{2}ψ1′​+ψ2′​=ψ1​+ψ2​, but with ψ1′=ψ1+ψ22 eıπ4≠ψ1\psi'_{1} = {\psi_{1} +\psi_{2}\over{\sqrt{2}}} \,e^{\imath {\pi\over{4}} } \neq \psi_{1}ψ1′​=2​ψ1​+ψ2​​e4π​=ψ1​ and ψ2′=ψ1+ψ22 e−ıπ4≠ψ2\psi'_{2} = {\psi_{1} +\psi_{2}\over{\sqrt{2}}}\,e^{-\imath {\pi\over{4}}}\neq \psi_{2}ψ2′​=2​ψ1​+ψ2​​e−4π​=ψ2​. Here ψ1′\psi'_{1}ψ1′​ and ψ2′\psi'_{2}ψ2′​ are the correct contributions from the slits to the total wave function ψ1′+ψ2′\psi'_{1} + \psi'_{2}ψ1′​+ψ2′​. We have then $p = |\psi'_{1} + \psi'_{2}|^{2} = |\psi'_{1}|^{2} + |\psi'_{2}|^{2} = p_{1}+p_{2} $ such that the paradox that quantum mechanics (QM) would not follow the traditional rules of probability calculus disappears. The paradox is rooted in the wrong intuition that ψ1\psi_{1}ψ1​ and ψ2\psi_{2}ψ2​ would be the true physical contributions to ψ1′+ψ2′=ψ1+ψ2\psi'_{1} + \psi'_{2} =\psi_{1} + \psi_{2}ψ1′​+ψ2′​=ψ1​+ψ2​ like in the case of waves in a water tank. The solution proposed here is not {\em ad hoc} but based on an extensive analysis of the geometrical meaning of spinors within group representation theory and its application to QM. Working further on the argument one can even show that an interference pattern is the only way to satisfy simultaneously two conditions: The condition obeying binary logic (in the spirit of Einstein) that the electron has only two mutually exclusive options to get to the detector (viz. going through slit S1_{1}1​ or going through slit S2_{2}2​) and the condition obeying ternary logic (in the spirit of Bohr) that the question which one of these two options the electron has taken is experimentally undecidable. A very important element in the analysis is the problem of the non-existence of {\em common} probability distributions for different experimental set-ups. And this is a recurrent theme in other situations that are felt as paradoxical. The CHSH inequality used in the experiments of Aspect {\em et al.} clashes with quantum mechanics because it is based on the assumption that there would exist a {\em common} probability distribution for the hidden variables in the different experiments that have to be made to determine the various quantities that intervene in the inequality. That common probability distribution for measured quantities does not exist is well known from quantum mechanics itself (because the operators that come into play do not commute and therefore do not have common eigenstates, i.e. common probability amplitudes). But this non-existence of common probability distributions applies also to certain variables in the set-ups of the different experiments and the latter fact can also be explained by purely classical reasoning.
When a theory is framed trying to explain a discrepant system of facts, it is a necessary process of thought to take some branch of the theory as more completely true than the rest, and to adjust the remaining parts in such a way that they will fit in with this base, though they may still conflict with one another. This has certainly been true of the quantum theory; the speculations connected with it have as their base the law of the conservation of energy. Now a critical examination of fundamentals does not by any means justify this faith. It is of course a fact of observation that in the gross energy is conserved, but this only means an averaged energy; and as pure dynamics has failed to explain many atomic phenomena there seems no reason to maintain the exact conservation of energy, which is only one of the consequences of the dynamical equations. Indeed it is hardly too much to say that had the photoelectric effect been discovered a century ago, it is probable that no one would ever have suggested that the status of the first law of thermodynamics was in any way different from that of the second. On the other hand, Bohr's theory, and especially Sommerfeld's extension of it, have given great encouragement to the belief that in dynamics lay the way to the complete truth, so that in consequence of the triumphs of that theory there has been little thought in other directions. Another impediment is that our whole ideas are saturated with the principles of energy, so that denying it leaves hardly any foundation from which to start.