As noted in an earlier post, I am in the process of reading (and thoroughly enjoying) N. David Mermin's Boojums All the Way Through. In a couple of his essays Mermin emphasizes the incredible successes of quantum mechanics. He mentions the fact that quantum mechanics was born in 1900 (on December 14, exactly 73 years before I was born!) and that even now (he published one of these essays in 1988, but we'll update it to 2007) there are no signs that quantum mechanics is incorrect. So we've had over 100 years to overthrow the theory, or at least build some solid evidence against it, and nothing has happened. Mermin also points out that the quantum theory was developed to explain atomic processes that have a characteristic length scale of 10^-9 meters or so, but that the theory has been extended to the much smaller length scales of subatomic particles (for this we can use the length scale for weak interactions, something like 10^-17 meters). So quantum mechanics has proven successful over length scales spanning 8 orders of magnitude.
This got me thinking: Is this really all that impressive? How does it stack up to the run that classical physics had? Not very well, it turns out. Classical physics was born, to give a conservative estimate, with the publication of Newton's Principia in 1687. Classical physics was essentially unchallenged until Planck's lecture on December 14, 1900. It wasn't SERIOUSLY challenged until Einstein's "On the Electrodynamics of Moving Bodies" in 1905. That's a span of well over 300 years. As for length scales, classical mechanics was primarily devised to account for the motions of the planets in the solar system. The diameter of the solar system is on the order of 10^16 meters. Of course, Newtonian mechanics also turned out to work pretty well for small objects (let's say on the scale of 1 mm - again a conservative estimate since classical physics surely works quite well at the micrometer scale and even somewhat smaller). This conservative estimate gives us length scales spanning 19 orders of magnitude. So it looks like quantum mechanics has a long way to go before it could be considered as "successful" as classical mechanics according to these measures. But eventually we did concede that classical mechanics was not the final correct theory. Why should we then accept quantum mechanics as the final correct theory?
Now, this is not to say that I think quantum mechanics is wrong in some specific way. It really has looked pretty good so far. But the inductive argument doesn't work - just because it hasn't failed yet doesn't mean it never will. As scientists we should not consider ANY theory to be final, regardless of its level of success (as measured by time, length, or any other means). There is no doubt that quantum mechanics is impressive. The fact that it has challenged some of our basic notions of the nature of physical reality indicates, I think, that it gets at something very deep. But we also should not refuse to question quantum mechanics when the answers it provides are less than satisfying.
There is no doubt that quantum mechanics represents the best theory available right now. We should continue to use it, and to extend it in interesting ways (i.e. quantum field theory, quantum gravity if we can manage it, etc.). But the same was true of classical mechanics long ago when it was being extended in interesting ways by the likes of Lagrange, Maupertuis, and Hamilton. Let us not be guilty of the hubris of Lord Kelvin who declared at the end of the Nineteenth Century that physics was all but finished. Nature may still have some surprises in store for us, and since we cannot know if we will be surprised we must always remain open to the possibility.
Monday, October 8, 2007
Saturday, October 6, 2007
Creativity in Physics and Literature
I've been reading N. David Mermin's Boojums All the Way Through, a collection of his essays, articles, and book reviews. One of the book reviews is of a biography of Lev Landau, and one of the nuggets that Mermin extracts for the reader is Landau's logarithmic scale for rating physicists. Einstein apparently received a special rating of 0.5, while the (other) founders of quantum mechanics (Bohr, Heisenberg, Schroedinger) rate a 1. Landau apparently gave himself a 2.5 but later upgraded this to 2. Mermin, later in his book, describes himself as a 4.5. Landau apparently referred to physicists who rate a 5 (the worst score on his scale) "pathologists".
Reading about Landau's rating system has caused me to reflect on creativity in science. After all, what is it that distinguishes a 1 (or even a 0.5!) from a 5 in Landau's scale? I would argue that it is most certainly creativity. It surely is not hard work, for though the great physicists were passionate about there subject and thus undoubtedly worked quite hard I am certain that many who have worked as hard or harder still rate but a 5. It cannot be anything like mathematical ability. Einstein's self-reported troubles with math are well-known, and Bohr was apparently wretched at doing serious calculation. I suppose one might site physical intuition as the determining factor, but what exactly does that mean? Physics professors usually mean by "physical intuition" a certain level of internalizing of the known laws of physics. But the great physicists were great specifically because their thinking was NOT limited by an internalization of the known laws. They were able to see beyond what was known. I don't know what else to call this but creativity.
Creativity is an issue that has been much on my mind as I study the philosophy of science. Philosophers of science tend to ignore the creative aspect of science. I think this is for two reasons. First of all, philosophy of science is most often an attempt to rationally reconstruct the actual activities of science. How can one rationally reconstruct an act of creativity? Second, philosophers of science tend to focus on how scientific theories are tested and how the decision to modify a theory comes about. They focus much less on how new theories are constructed or how old theories are modified. The point of the philosophy of science is not so much to explain how scientists construct theories as it is to explain how we can make sure those theories are legitimate (or useful, or not blatantly wrong, or not entirely metaphysical). The creative act of science is thus outside the purview of philosophy of science. The main exception I can think of would be the early inductivists, who saw theories as generalizations from the data. But I don't think anyone would seriously argue that, even when such generalizations do occur (and I think they occur infrequently), this process is straightforward or simple.
But even if philosophers of science can't explain scientific creativity, is it possible to classify it in some way? It seems to me that scientific creativity is much like creativity in other areas. I'd like to draw some comparisons between physics and literature to illustrate this point. Let me make clear at the outset that I am no expert on English literature, and I am largely ignorant of non-English literature. But hopefully if I stick to things that I have read and that I know are widely acclaimed, I'll muddle through this without offending anyone.
Most of science is performed by people who are creative only on a small scale, in a somewhat workaday fashion. These would be Landau's 5's (I would rank myself among them, if I deemed myself worthy of any rank at all). Creating new scientific knowledge of any kind requires a certain level of creativity, in that you are doing something that has not been done before and therefore you cannot follow any sort of template. Probably most of the creativity actually comes in formulating a question to study, or at least choosing some investigation to perform (I rarely have a well-formulated question when I begin my research, but I usually do have some idea of something into which I want to poke my nose). Starting a research project involves a suite of choices that cannot usually be guided by established principles. In any field of science there are an infinite number of factors that can be analyzed, or relations that can be investigated. For most scientists the creative act comes in choosing which of these infinite possibilities will be productive or interesting. From that point on the work may involve only well-trodden pathways. I think this is something like most popular fiction. The author must come up with an idea for a novel or story, and if they are to avoid charges of plagiarism it must be an idea that is new on some level. But the typical work of popular fiction is pretty similar to something that has gone before, and both the prose and the literary conceits are likely to be standard fare. If Landau had rated novelists he would probably consider most authors on the NY Times Bestseller list to be "pathologists".
Somewhere much farther up the chain come those who extend the boundaries of the field in a significant way. This can be done by breaking new ground, or by finding hitherto unknown connections between disparate areas. In physics this might include those like Dirac or Feynman, who worked within the framework of quantum mechanics but extended that framework into new and unexpected territories (Poincare would be a similar example in the realm of classical physics). For an old school example, Johannes Kepler might fall into this category since we worked within a framework established by Copernicus but made a crucial extension (to elliptical orbits) that turned out to make all the difference. The great unifiers would also fit in this category (here I am thinking mainly of Weinberg, Glashow, and Salam for their unification of electromagnetic and weak interactions, but classical physicists like Lagrange and Hamilton might also fit this category, as might James Clerk Maxwell). In my limited knowledge of literature I would put Vladimir Nabokov in this category. Lolita was not, really, an entirely new type of novel. But it was about things that no novel had been about before. Similarly, Pale Fire turns a poem (and its exegesis) into a novel and thereby creates a connection that had not been exploited before. Note that this categorization deals only with creativity. Dirac and Feynman both possessed incredible technical prowess in addition to their creativity. Similarly, Nabokov's prose is nothing short of breathtaking. Perhaps it is impossible to separate these attributes from creativity, but I am at least not explicitly taking them into account here.
At or near the top of the creativity scale are those who change the face of their fields forever. In physics this would include Landau's 1's: Bohr, Heisenberg, Schroedinger. I'd add Boltzmann and Faraday. To go way back we could add Galileo and Copernicus in this category. These people gave us a new way of understanding the natural world. They had the vision to see far beyond the existing theories, and the courage and creativity to construct something radically new. I suppose Joyce would be in this category for literature (though I must confess that I have only read Portrait of the Artist as a Young Man, and parts of Dubliners - I'll get to Ulysses someday soon, but I may not be strong enough for Finnegan's Wake). I'd like to put Borges in this category as well (you see, I have read some non-English authors) because I think his creativity merits it, even if his prose does not (but then, I didn't read his work in Spanish so I can't really say). These authors wrote works that departed radically from the conventions of the day, and literature has not been the same since.
Now, what about that special case of Landau's: Albert Einstein, who merits a 1/2. I would argue that Isaac Newton merits the same special score. What author could merit such a special distinction? William Shakespeare? Fyodor Dostoyevsky? (OK, I admit that I'm trying to atone for my English-language leanings here.) I will let others more literate than I make that call. What is it that sets these people apart from the 1's? Again, I believe it is creativity but it is a level of creativity that inspires awe. The work of a 5 may lead one to think "I would have thought of that if I had worked on that problem." The work of, say, a 2 might lead on to think "I wish I could have thought of that, but I doubt I would have." In the case of the 1's, we might think "I can't believe they thought of that, they are geniuses." For those in this special category our thoughts are mute and we are left to gaze in awe at a mind that operates on a level entirely different from our own.
I'll close this essay by pointing out some interesting features of what I have just written. It strikes me as curious that all of the physicists I mention are theorists, not experimentalists (except Galileo and Faraday, who were both). The authors I mention are all prose authors (well, except Shakespeare). The second fact follows directly from my own personal prejudices (I prefer prose to poetry), which in turn have influenced what I have read. But the exclusion of experimentalists seems odd to me in retrospect, and it would be false to claim that I am simply unaware of highly creative experimental work. Millikan was incredibly creative, as was Michelson. James Joule certainly deserves some high marks for his creativity in studying the relation between heat and mechanical energy. In fact, I think one could argue that in recent years experimentalists have demonstrated a higher level of creativity than have theorists. But somehow this seems like a different type of creativity. For one thing, it is highly constrained creativity in that experiments must make use of apparatus that either exists or can be built with a reasonable investment of time and money. Theoretical creativity is largely free from such practical constraints. Furthermore, experimental greatness requires a set of skills that are not specifically intellectual. Perhaps one day I will write an essay comparing the great experimental physicists to the great painters. Could I, then, rate da Vinci in the same category as himself? Probably not - he was much better as a painter than as an experimental physicist, although this was probably not due to a lack of creativity. Anyway, until I write that essay I will simply apologize to the experimentalists and try to redirect the blame toward Lev Landau who got me started thinking about all of this anyway.
Reading about Landau's rating system has caused me to reflect on creativity in science. After all, what is it that distinguishes a 1 (or even a 0.5!) from a 5 in Landau's scale? I would argue that it is most certainly creativity. It surely is not hard work, for though the great physicists were passionate about there subject and thus undoubtedly worked quite hard I am certain that many who have worked as hard or harder still rate but a 5. It cannot be anything like mathematical ability. Einstein's self-reported troubles with math are well-known, and Bohr was apparently wretched at doing serious calculation. I suppose one might site physical intuition as the determining factor, but what exactly does that mean? Physics professors usually mean by "physical intuition" a certain level of internalizing of the known laws of physics. But the great physicists were great specifically because their thinking was NOT limited by an internalization of the known laws. They were able to see beyond what was known. I don't know what else to call this but creativity.
Creativity is an issue that has been much on my mind as I study the philosophy of science. Philosophers of science tend to ignore the creative aspect of science. I think this is for two reasons. First of all, philosophy of science is most often an attempt to rationally reconstruct the actual activities of science. How can one rationally reconstruct an act of creativity? Second, philosophers of science tend to focus on how scientific theories are tested and how the decision to modify a theory comes about. They focus much less on how new theories are constructed or how old theories are modified. The point of the philosophy of science is not so much to explain how scientists construct theories as it is to explain how we can make sure those theories are legitimate (or useful, or not blatantly wrong, or not entirely metaphysical). The creative act of science is thus outside the purview of philosophy of science. The main exception I can think of would be the early inductivists, who saw theories as generalizations from the data. But I don't think anyone would seriously argue that, even when such generalizations do occur (and I think they occur infrequently), this process is straightforward or simple.
But even if philosophers of science can't explain scientific creativity, is it possible to classify it in some way? It seems to me that scientific creativity is much like creativity in other areas. I'd like to draw some comparisons between physics and literature to illustrate this point. Let me make clear at the outset that I am no expert on English literature, and I am largely ignorant of non-English literature. But hopefully if I stick to things that I have read and that I know are widely acclaimed, I'll muddle through this without offending anyone.
Most of science is performed by people who are creative only on a small scale, in a somewhat workaday fashion. These would be Landau's 5's (I would rank myself among them, if I deemed myself worthy of any rank at all). Creating new scientific knowledge of any kind requires a certain level of creativity, in that you are doing something that has not been done before and therefore you cannot follow any sort of template. Probably most of the creativity actually comes in formulating a question to study, or at least choosing some investigation to perform (I rarely have a well-formulated question when I begin my research, but I usually do have some idea of something into which I want to poke my nose). Starting a research project involves a suite of choices that cannot usually be guided by established principles. In any field of science there are an infinite number of factors that can be analyzed, or relations that can be investigated. For most scientists the creative act comes in choosing which of these infinite possibilities will be productive or interesting. From that point on the work may involve only well-trodden pathways. I think this is something like most popular fiction. The author must come up with an idea for a novel or story, and if they are to avoid charges of plagiarism it must be an idea that is new on some level. But the typical work of popular fiction is pretty similar to something that has gone before, and both the prose and the literary conceits are likely to be standard fare. If Landau had rated novelists he would probably consider most authors on the NY Times Bestseller list to be "pathologists".
Somewhere much farther up the chain come those who extend the boundaries of the field in a significant way. This can be done by breaking new ground, or by finding hitherto unknown connections between disparate areas. In physics this might include those like Dirac or Feynman, who worked within the framework of quantum mechanics but extended that framework into new and unexpected territories (Poincare would be a similar example in the realm of classical physics). For an old school example, Johannes Kepler might fall into this category since we worked within a framework established by Copernicus but made a crucial extension (to elliptical orbits) that turned out to make all the difference. The great unifiers would also fit in this category (here I am thinking mainly of Weinberg, Glashow, and Salam for their unification of electromagnetic and weak interactions, but classical physicists like Lagrange and Hamilton might also fit this category, as might James Clerk Maxwell). In my limited knowledge of literature I would put Vladimir Nabokov in this category. Lolita was not, really, an entirely new type of novel. But it was about things that no novel had been about before. Similarly, Pale Fire turns a poem (and its exegesis) into a novel and thereby creates a connection that had not been exploited before. Note that this categorization deals only with creativity. Dirac and Feynman both possessed incredible technical prowess in addition to their creativity. Similarly, Nabokov's prose is nothing short of breathtaking. Perhaps it is impossible to separate these attributes from creativity, but I am at least not explicitly taking them into account here.
At or near the top of the creativity scale are those who change the face of their fields forever. In physics this would include Landau's 1's: Bohr, Heisenberg, Schroedinger. I'd add Boltzmann and Faraday. To go way back we could add Galileo and Copernicus in this category. These people gave us a new way of understanding the natural world. They had the vision to see far beyond the existing theories, and the courage and creativity to construct something radically new. I suppose Joyce would be in this category for literature (though I must confess that I have only read Portrait of the Artist as a Young Man, and parts of Dubliners - I'll get to Ulysses someday soon, but I may not be strong enough for Finnegan's Wake). I'd like to put Borges in this category as well (you see, I have read some non-English authors) because I think his creativity merits it, even if his prose does not (but then, I didn't read his work in Spanish so I can't really say). These authors wrote works that departed radically from the conventions of the day, and literature has not been the same since.
Now, what about that special case of Landau's: Albert Einstein, who merits a 1/2. I would argue that Isaac Newton merits the same special score. What author could merit such a special distinction? William Shakespeare? Fyodor Dostoyevsky? (OK, I admit that I'm trying to atone for my English-language leanings here.) I will let others more literate than I make that call. What is it that sets these people apart from the 1's? Again, I believe it is creativity but it is a level of creativity that inspires awe. The work of a 5 may lead one to think "I would have thought of that if I had worked on that problem." The work of, say, a 2 might lead on to think "I wish I could have thought of that, but I doubt I would have." In the case of the 1's, we might think "I can't believe they thought of that, they are geniuses." For those in this special category our thoughts are mute and we are left to gaze in awe at a mind that operates on a level entirely different from our own.
I'll close this essay by pointing out some interesting features of what I have just written. It strikes me as curious that all of the physicists I mention are theorists, not experimentalists (except Galileo and Faraday, who were both). The authors I mention are all prose authors (well, except Shakespeare). The second fact follows directly from my own personal prejudices (I prefer prose to poetry), which in turn have influenced what I have read. But the exclusion of experimentalists seems odd to me in retrospect, and it would be false to claim that I am simply unaware of highly creative experimental work. Millikan was incredibly creative, as was Michelson. James Joule certainly deserves some high marks for his creativity in studying the relation between heat and mechanical energy. In fact, I think one could argue that in recent years experimentalists have demonstrated a higher level of creativity than have theorists. But somehow this seems like a different type of creativity. For one thing, it is highly constrained creativity in that experiments must make use of apparatus that either exists or can be built with a reasonable investment of time and money. Theoretical creativity is largely free from such practical constraints. Furthermore, experimental greatness requires a set of skills that are not specifically intellectual. Perhaps one day I will write an essay comparing the great experimental physicists to the great painters. Could I, then, rate da Vinci in the same category as himself? Probably not - he was much better as a painter than as an experimental physicist, although this was probably not due to a lack of creativity. Anyway, until I write that essay I will simply apologize to the experimentalists and try to redirect the blame toward Lev Landau who got me started thinking about all of this anyway.
Monday, October 1, 2007
Interpretating Quantum Mechanics
I just got my copy of the October American Journal of Physics (the best, though not the most prestigious, physics journal in the world). The Letters to the Editor section contains a letter by Art Hobson, written in response to a book review by N. David Mermin. The book that Mermin reviewed was Quantum Enigma by Rosenblum and Kuttner. I've not read the book myself, but I did read Mermin's review. One of his chief complaints (though not his only complaint, nor was his review wholly critical) was that in discussing various interpretations of quantum mechanics Rosenblum and Kuttner ignore the view that quantum states represent not physical states of a particle but rather states of our knowledge. Hobson rejects this view (as well as the view, evidently emphasized by Rosenblum and Kuttner, that perception of a measurement result by a conscious entity brings about a collapse of the wavefunction).
Now I have a great deal of admiration for both of the participants here. I am in the process of reading Mermin's Boojums All the Way Through. Mermin is without question the best prose stylist in physics (and apparently a major contributor in condensed matter physics, though that's not my field so I can hardly judge). Hobson, on the other hand, has been a champion for the social relevance of physics and for the teaching of physics to non-science students. I use his Physics: Concepts and Conncetions textbook for my liberal-arts physics course. While I would have read any letters on interpreting quantum mechanics with interest, the name recognition definitely made these letters stand out to me.
Hobson claims the view that quantum states are states of knowledge rather than states of some objective physical reality is an unnecessary extravagance. He argues that the analysis should really be done from the perspective of quantum field theory, and that most physicists certainly believe that quantum fields are objectively real (offering a quote from Weinberg that I have seen him use before). He then goes on to explain how decoherence explains how a quantum superposition can be transformed, through interaction between the quantum system and its environment, into an incoherent state that can be described with a diagonal density operator. Hobson then declares that these incoherent states are no more mysterious than the proposition that there is a 0.5 probability that a coin flip will come up heads.
I find this last comment by Hobson particularly interesting in light of the position he is attacking. He wants to avoid the claim that quantum states are states of knowledge, but yet he is reduced to saying that quantum probabilities are just like the probabilities involved in flipping a coin. But classical probabilities, like those for a coin toss, are invoked exactly because we lack knowledge. The equal probability of getting heads or tails when a coin is flipped does not represent anything objectively real about the state of the coin on a given flip. What it represents is the state of our knowledge about the coin. If we knew a great deal more about the coins initial state, and about all the forces that act upon the coin, we could determine with near certainty which side of the coin would land up. It is only because we are ignorant of all this information that we must resort to probabilities. So Hobson's invocation of decoherence seems to support Mermin's view, rather than refute it. Indeed, decoherence can only be deemed to have fully solved the measurement problem if quantum states are only states of knowledge (because it reduces the quantum superposition to a classical mixture). If we believe that quantum states represent an objective reality then we are left wondering why decoherence fails to produce a single outcome (rather than a classical mixture of various outcomes). Certainly when we do measurements in the lab we get a single outcome each time (though not the same outcome every time we repeat the measurement).
I also find Hobson's reliance on quantum field theory to be a little problematic. Not so much for technical reasons as for pedagogical reasons. In fact, I have avoided moving to the new edition of his text in part because of this. It is not clear to me that all of the mysteries of quantum mechanics can be swept under the rug of quantum field theory. Quantum field theory has been very successful in describing a rather limited range of phenomena. But it's not clear to me that quantum field theory, as a model of physical interactions, completely contains and therefore exceeds non-relativistic quantum mechanics. In the same way, I have yet to be fully convinced that quantum mechanics completely contains classical mechanics. The idea that our "most fundamental" theory might not contain all the other "less fundamental" theories is anathema to most physicists, but it doesn't bother me since I don't believe in the idea of a final theory anyway. In any case, from the perspective of a non-science student I think blaming the whole mess on quantum fields is a bit like saying the Wazzleblatchet did it (which might be great for a Dr. Seuss tale, but not in my physics class).
Now this isn't to say that I side fully with Mermin on this debate. I have some issues with the idea that quantum states are "nothing more" than states of knowledge. As I said above, we use classical probabilities to represent states of knowledge. But clearly there is something different going on in quantum mechanics. So if quantum states are states of knowledge then our knowledge about quantum particles is constrained in some rather odd ways. In this sense, saying that quantum states are states of knowledge does little to dispel the mysteries of quantum mechanics. I'm not sure that is really Mermin's goal. His goal in the review was to combat the idea that consciousness brings about physical changes in some objectively real quantum state. If quantum states are states of knowledge then it is no surprise that the quantum state changes when a conscious entity becomes aware of a measurement result. But even this point of view does not wholly discount the idea that there IS an objective physical reality. I personally view any science (not just quantum mechanics) as the result of an interplay between our minds and an objective physical reality. Neither piece is wholly absent from classical physics, nor from quantum physics.
Now I have a great deal of admiration for both of the participants here. I am in the process of reading Mermin's Boojums All the Way Through. Mermin is without question the best prose stylist in physics (and apparently a major contributor in condensed matter physics, though that's not my field so I can hardly judge). Hobson, on the other hand, has been a champion for the social relevance of physics and for the teaching of physics to non-science students. I use his Physics: Concepts and Conncetions textbook for my liberal-arts physics course. While I would have read any letters on interpreting quantum mechanics with interest, the name recognition definitely made these letters stand out to me.
Hobson claims the view that quantum states are states of knowledge rather than states of some objective physical reality is an unnecessary extravagance. He argues that the analysis should really be done from the perspective of quantum field theory, and that most physicists certainly believe that quantum fields are objectively real (offering a quote from Weinberg that I have seen him use before). He then goes on to explain how decoherence explains how a quantum superposition can be transformed, through interaction between the quantum system and its environment, into an incoherent state that can be described with a diagonal density operator. Hobson then declares that these incoherent states are no more mysterious than the proposition that there is a 0.5 probability that a coin flip will come up heads.
I find this last comment by Hobson particularly interesting in light of the position he is attacking. He wants to avoid the claim that quantum states are states of knowledge, but yet he is reduced to saying that quantum probabilities are just like the probabilities involved in flipping a coin. But classical probabilities, like those for a coin toss, are invoked exactly because we lack knowledge. The equal probability of getting heads or tails when a coin is flipped does not represent anything objectively real about the state of the coin on a given flip. What it represents is the state of our knowledge about the coin. If we knew a great deal more about the coins initial state, and about all the forces that act upon the coin, we could determine with near certainty which side of the coin would land up. It is only because we are ignorant of all this information that we must resort to probabilities. So Hobson's invocation of decoherence seems to support Mermin's view, rather than refute it. Indeed, decoherence can only be deemed to have fully solved the measurement problem if quantum states are only states of knowledge (because it reduces the quantum superposition to a classical mixture). If we believe that quantum states represent an objective reality then we are left wondering why decoherence fails to produce a single outcome (rather than a classical mixture of various outcomes). Certainly when we do measurements in the lab we get a single outcome each time (though not the same outcome every time we repeat the measurement).
I also find Hobson's reliance on quantum field theory to be a little problematic. Not so much for technical reasons as for pedagogical reasons. In fact, I have avoided moving to the new edition of his text in part because of this. It is not clear to me that all of the mysteries of quantum mechanics can be swept under the rug of quantum field theory. Quantum field theory has been very successful in describing a rather limited range of phenomena. But it's not clear to me that quantum field theory, as a model of physical interactions, completely contains and therefore exceeds non-relativistic quantum mechanics. In the same way, I have yet to be fully convinced that quantum mechanics completely contains classical mechanics. The idea that our "most fundamental" theory might not contain all the other "less fundamental" theories is anathema to most physicists, but it doesn't bother me since I don't believe in the idea of a final theory anyway. In any case, from the perspective of a non-science student I think blaming the whole mess on quantum fields is a bit like saying the Wazzleblatchet did it (which might be great for a Dr. Seuss tale, but not in my physics class).
Now this isn't to say that I side fully with Mermin on this debate. I have some issues with the idea that quantum states are "nothing more" than states of knowledge. As I said above, we use classical probabilities to represent states of knowledge. But clearly there is something different going on in quantum mechanics. So if quantum states are states of knowledge then our knowledge about quantum particles is constrained in some rather odd ways. In this sense, saying that quantum states are states of knowledge does little to dispel the mysteries of quantum mechanics. I'm not sure that is really Mermin's goal. His goal in the review was to combat the idea that consciousness brings about physical changes in some objectively real quantum state. If quantum states are states of knowledge then it is no surprise that the quantum state changes when a conscious entity becomes aware of a measurement result. But even this point of view does not wholly discount the idea that there IS an objective physical reality. I personally view any science (not just quantum mechanics) as the result of an interplay between our minds and an objective physical reality. Neither piece is wholly absent from classical physics, nor from quantum physics.
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