Solution to puzzle 9: do electrons exist?
Do electrons exist as material objects? Are electrons nothing more than theoretical constructs helping to interpret the results of experiments?
Aristotle believed that the objects can be described in two ways: one can specify their essence or one can provide the full list of their attributes. The ever changing physical picture of the electron prevents us from taking the first road. We do not know what the electrons are. Can we do it in the second way? This was the common theme in the recent discussion in sowa’s journal. The electrons have well-defined charge, spin, and the rest mass that are unique to these elementary particles. One can postulate that every time the observed behavior is consistent with such attributes one deals with the electrons - and the problem goes away.
I do not think much of this argument. Consider electron’s mass. What is mass? It never had fixed meaning. First, the mass was the measure of weight. Newton redefined it as the gravitational charge and the measure of body’s inertia. Einstein showed that the mass is relative. The standard model of particle physics interprets mass as the strength of electron’s interaction with the universal scalar field. The electron has no mass; it acquires it exclusively through the interaction with this hypothetical field. The problem with the latter concept is that nobody yet observed the quantum of this field, aka Higgs boson, despite 30+ years of experimentation. The actual mechanism for electroweak symmetry breaking is yet unknown, whereas all of the previous field theories postulating such a scalar field turned out to be incorrect. One can argue whether the electrons are real in the philosophical sense, but at least these particles are detectable, in the physical sense. Whether the Higgs exist in this sense has not been settled. There is no experimental proof for Higgs occurrence and I, for one, doubt that it will ever be furnished. This part of the standard model has always been a mystery, and many a theorist believe that Higgs’ mechanism is no more than an approximation to a more complex mechanism of which we know nothing about. In other words, we do measure a property we call mass, but we have no clear idea what do we actually measure. Furthermore, metrological schemes for measuring the electron mass heavily rest on the assumed physical picture of the electron, because direct measurement of this mass is impossible. The electron mass is determined from the combined measurement of the Rydberg constant, the fine structure constant, and the Planck constant. Once high precision is required, one has to rely on the validity of QED to extract the fine structure constant from the measurement of anomalous magnetic moment, etc. Josephson effect, integer quantum Hall effect all go into this measurement, but the accuracy of the current models for these effects is not known with the necessary precision. In any case, relying on such effects presumes the validity of quantum mechanics, condensed matter physics, etc. - all of which postulate certain physical picture of the electron. This picture comes first, the mass comes very far down the line. See more on http://www.aip.org/pt/vol-54/iss-3/p29.html
The same pertains to other electron properties; the “trivial” property of countability is one of them. Are the electrons countable? The answer depends what electrons we are talking about. In quantum mechanics the electrons are countable. In quantum field theories electrons are fields that are not countable. One can think of vacuum as repository of uncountable electron-positron pairs that are polarized by the presence of the probe charge. Once more, the electron is what you want it to be for the convenience of theory rather than what it actually is, and this goes for any of its properties, however mundane. What we call the “electron” is a grab bag for manifold physical theories that interpret its properties and its nature in a variety of different ways.
There is more to it. Suppose we take the position that electrons do “exist” materially in some fuzzily defined way. Do quasiparticles - collective excitations - also exist, or are these merely mental props for description of complex collective phenomena -- all of these phonons, magnons, polarons, plasmons? These are excitations of many-particle systems that can be treated, with some degree of accuracy, simply as particles. Our refusal to consider these quasiparticles on the same footing with the electron is that these are not fundamental particles; the excitations “exist” in a medium made of the fundamental particles, like electrons. That may be correct, but where is the guarantee that the electrons are different in this sense? For all we know the electrons may also be “quasiparticles” like phonons, arising from the excitations of a more fundamental entity. The situation can be messier: it may not be possible to tell the difference between these two situations in principle, because the theory can be formulated in two equivalent ways in which the states and vacua of one theory are mapped onto entirely different states and vacua of another theory (S-duality and Olive-Montonen duality are common examples of such a situation). It is entirely up to us whether we consider electrically charged particles (conserved quantities) or magnetic monopoles (topological charges) as elementary. One can argue that “monopoles have not been found,” but there is no other way to explain charge quantization. Higgs bosons have never been found too, but we do not say that mass is unreal. The dualities imply that there may be no real distinction between the collective and elementary excitations at the most fundamental level. Then the distinction between the elementary vs. quasi- particles boils down to convenience and tradition rather than anything else.
I am afraid that mathematician Owas is correct: the mental picture of the electron as a material object (as opposed to the view that the electron is a set of concepts that help us to systematize experimental observations) seem to lead nowhere. However one looks at it, this particular admission is not helpful in thinking about its nature or its properties. Even from the standpoint of physics, its status is unsettled and it may never be settled because it cannot be settled in a unique way. The economy of treatment, history, and easy-to-visualize imagery of the material point floating in space naturally lead us to this particular mental picture. It is appealing, but indefensible.
But then, what objects are “material”? Are not tables made of the electrons? What makes tables material is not that such objects are macroscopic. It is that we can systematize such objects intuitively, without the need for conscious conceptualization. I believe that this is the only difference between the electrons and the tables. In the course of the discussion, an argument has been reiterated many times that electrons are different because we cannot perceive them with our senses directly, unlike the tables. So aids are needed and the theories of their operation are required, etc. That is not true. A single high energy electron can be seen by a naked eye, about 100 electrons in helium can be heard, and a few thousands electrons in water (on the authority of Ed Hart who did such experiments in the late 1960s) can be tasted.
http://lsda.jsc.nasa.gov/books/skylab/Ch14.htm
http://www.sciencedaily.com/releases/2007/06/070606113357.htm
http://www.aip.org/pt/feb00/maris.htm
What differs seeing the electron from seeing the table is one’s ability to recognize the act of direct excitation of retinal isomerization by inelastic scattering of MeV electron (or emission of the Cerenkov light in the eyeball) as “seeing the electron.” Would we be endowed intuition that allowed us to make such a distinction, the electrons would be as real to us as tables. However, we do not have this inborn recognition ability, and all our theorizing and reasoning does not replace it. For that reason alone the electrons may never be as real to us as tables, but the problem is with our heads rather than our eyes.
Do electrons exist? One can answer this question in a Platonic sense: that any idea, such as the idea of the electron, exists as long as it partakes of the Ideal. Still, one would like to know why this particular idea seem to work so well; why can we start with this seemingly incoherent and even contradictory set of ideas and predict many properties of tables. It seems that not all ideas have the same currency. This is what puzzle 10 is about. In Leibniz’s parlance, there is something in the idea of the electron that makes it especially potent and hence gives it the property of existence. I remind what the perfection to Leibniz is: suppose A already exists. If B is compatible with A and only A, but C is compatible with A and D, C is more perfect than B. If C is the most perfect, then it exists. To Leibnitz, existence is the property of maximum mutual compatibility and perfection of the ideas. I suggest considering the existence of the electrons along these lines. Translating it back to physics, do electrons exist because this allows maximal variety of choices for structure? Do electrons exist in order to make tables possible?
Aristotle believed that the objects can be described in two ways: one can specify their essence or one can provide the full list of their attributes. The ever changing physical picture of the electron prevents us from taking the first road. We do not know what the electrons are. Can we do it in the second way? This was the common theme in the recent discussion in sowa’s journal. The electrons have well-defined charge, spin, and the rest mass that are unique to these elementary particles. One can postulate that every time the observed behavior is consistent with such attributes one deals with the electrons - and the problem goes away.
I do not think much of this argument. Consider electron’s mass. What is mass? It never had fixed meaning. First, the mass was the measure of weight. Newton redefined it as the gravitational charge and the measure of body’s inertia. Einstein showed that the mass is relative. The standard model of particle physics interprets mass as the strength of electron’s interaction with the universal scalar field. The electron has no mass; it acquires it exclusively through the interaction with this hypothetical field. The problem with the latter concept is that nobody yet observed the quantum of this field, aka Higgs boson, despite 30+ years of experimentation. The actual mechanism for electroweak symmetry breaking is yet unknown, whereas all of the previous field theories postulating such a scalar field turned out to be incorrect. One can argue whether the electrons are real in the philosophical sense, but at least these particles are detectable, in the physical sense. Whether the Higgs exist in this sense has not been settled. There is no experimental proof for Higgs occurrence and I, for one, doubt that it will ever be furnished. This part of the standard model has always been a mystery, and many a theorist believe that Higgs’ mechanism is no more than an approximation to a more complex mechanism of which we know nothing about. In other words, we do measure a property we call mass, but we have no clear idea what do we actually measure. Furthermore, metrological schemes for measuring the electron mass heavily rest on the assumed physical picture of the electron, because direct measurement of this mass is impossible. The electron mass is determined from the combined measurement of the Rydberg constant, the fine structure constant, and the Planck constant. Once high precision is required, one has to rely on the validity of QED to extract the fine structure constant from the measurement of anomalous magnetic moment, etc. Josephson effect, integer quantum Hall effect all go into this measurement, but the accuracy of the current models for these effects is not known with the necessary precision. In any case, relying on such effects presumes the validity of quantum mechanics, condensed matter physics, etc. - all of which postulate certain physical picture of the electron. This picture comes first, the mass comes very far down the line. See more on http://www.aip.org/pt/vol-54/iss-3/p29.html
The same pertains to other electron properties; the “trivial” property of countability is one of them. Are the electrons countable? The answer depends what electrons we are talking about. In quantum mechanics the electrons are countable. In quantum field theories electrons are fields that are not countable. One can think of vacuum as repository of uncountable electron-positron pairs that are polarized by the presence of the probe charge. Once more, the electron is what you want it to be for the convenience of theory rather than what it actually is, and this goes for any of its properties, however mundane. What we call the “electron” is a grab bag for manifold physical theories that interpret its properties and its nature in a variety of different ways.
There is more to it. Suppose we take the position that electrons do “exist” materially in some fuzzily defined way. Do quasiparticles - collective excitations - also exist, or are these merely mental props for description of complex collective phenomena -- all of these phonons, magnons, polarons, plasmons? These are excitations of many-particle systems that can be treated, with some degree of accuracy, simply as particles. Our refusal to consider these quasiparticles on the same footing with the electron is that these are not fundamental particles; the excitations “exist” in a medium made of the fundamental particles, like electrons. That may be correct, but where is the guarantee that the electrons are different in this sense? For all we know the electrons may also be “quasiparticles” like phonons, arising from the excitations of a more fundamental entity. The situation can be messier: it may not be possible to tell the difference between these two situations in principle, because the theory can be formulated in two equivalent ways in which the states and vacua of one theory are mapped onto entirely different states and vacua of another theory (S-duality and Olive-Montonen duality are common examples of such a situation). It is entirely up to us whether we consider electrically charged particles (conserved quantities) or magnetic monopoles (topological charges) as elementary. One can argue that “monopoles have not been found,” but there is no other way to explain charge quantization. Higgs bosons have never been found too, but we do not say that mass is unreal. The dualities imply that there may be no real distinction between the collective and elementary excitations at the most fundamental level. Then the distinction between the elementary vs. quasi- particles boils down to convenience and tradition rather than anything else.
I am afraid that mathematician Owas is correct: the mental picture of the electron as a material object (as opposed to the view that the electron is a set of concepts that help us to systematize experimental observations) seem to lead nowhere. However one looks at it, this particular admission is not helpful in thinking about its nature or its properties. Even from the standpoint of physics, its status is unsettled and it may never be settled because it cannot be settled in a unique way. The economy of treatment, history, and easy-to-visualize imagery of the material point floating in space naturally lead us to this particular mental picture. It is appealing, but indefensible.
But then, what objects are “material”? Are not tables made of the electrons? What makes tables material is not that such objects are macroscopic. It is that we can systematize such objects intuitively, without the need for conscious conceptualization. I believe that this is the only difference between the electrons and the tables. In the course of the discussion, an argument has been reiterated many times that electrons are different because we cannot perceive them with our senses directly, unlike the tables. So aids are needed and the theories of their operation are required, etc. That is not true. A single high energy electron can be seen by a naked eye, about 100 electrons in helium can be heard, and a few thousands electrons in water (on the authority of Ed Hart who did such experiments in the late 1960s) can be tasted.
http://lsda.jsc.nasa.gov/books/skylab/Ch14.htm
http://www.sciencedaily.com/releases/2007/06/070606113357.htm
http://www.aip.org/pt/feb00/maris.htm
What differs seeing the electron from seeing the table is one’s ability to recognize the act of direct excitation of retinal isomerization by inelastic scattering of MeV electron (or emission of the Cerenkov light in the eyeball) as “seeing the electron.” Would we be endowed intuition that allowed us to make such a distinction, the electrons would be as real to us as tables. However, we do not have this inborn recognition ability, and all our theorizing and reasoning does not replace it. For that reason alone the electrons may never be as real to us as tables, but the problem is with our heads rather than our eyes.
Do electrons exist? One can answer this question in a Platonic sense: that any idea, such as the idea of the electron, exists as long as it partakes of the Ideal. Still, one would like to know why this particular idea seem to work so well; why can we start with this seemingly incoherent and even contradictory set of ideas and predict many properties of tables. It seems that not all ideas have the same currency. This is what puzzle 10 is about. In Leibniz’s parlance, there is something in the idea of the electron that makes it especially potent and hence gives it the property of existence. I remind what the perfection to Leibniz is: suppose A already exists. If B is compatible with A and only A, but C is compatible with A and D, C is more perfect than B. If C is the most perfect, then it exists. To Leibnitz, existence is the property of maximum mutual compatibility and perfection of the ideas. I suggest considering the existence of the electrons along these lines. Translating it back to physics, do electrons exist because this allows maximal variety of choices for structure? Do electrons exist in order to make tables possible?