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arbitrarily long range, which does not seem to follow from the description of twistor theory and which would seem to grossly disagree with observation. We seem to see non-locality as an effect of entanglement, the part of the wave function that does not contribute to the correspondence principle, on particular particles and variables that we have isolated. But if there were a fundamental non-local R process, it would affect many variables, not just the few we are able to predict from detailed QM, so its effects would not be so limited. The problems with a theory that predicts a fundamental R process is that it must reduce both to QM and to classical physics independently. Otherwise, the theory only needs to reduce to non-relativistic QM and the usual sort of case-specific rules for making approximations, added to the correspondence principle, take care of classical physics and ordinary language.
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experiments do not always work, implying that the R process cannot be fundamental. One expects the validity of an approximation like classical mechanics or geometric optics to be sensitive to the details of the problem and to how it is applied, but a fundamental low is supposed to always act the same way. For example, it is usually said that large-scale optical systems are well approximated by geometric optics, but the diffraction limit of a telescope is an exception because a telescope is specialized for measuring small angles. The diffraction must be calculated separately and folded in. Similarly, in an EPR experiment, the constraint that the spins add up correctly when the notebooks are compared needs to be imposed in
90:
494:(Taking what I have learned, mostly from field theorists and fellow nuclear experimentalists as correct) if one manages to formulate a theory in which there is a non-local non-deterministic R-like process, it will remain to show that it reduces to the standard local and deterministic U process (in a sort of anti-correspondence principle). As for my own experience, all of the interactions present in common experiments are also present within a nucleus, except for a very flat and classical gravity; so any deviation from the U process should have been seen by us.
464:
physics would instabilities and finite temperature not lead to macroscopic irregularities. The graininess of matter seems forgotten. This is clearly at least as large as any imaginable "R process" (wave function collapse). I used to think that "quantum fluctuations" were something I did not understand, but the book makes them sound more like something the people who talk about them do not understand. Or do they just mean the atomic nature of matter?
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to be true, whatever our classical descriptions and intuition tell us. "Interpretations of quantum mechanics" such as
Copenhagen, entanglement, de-coherence, etc. are useful rules of thumb, but only the U process is fundamental. Penrose hase let these messy experimental details of how to make valid approximations and of mixed classical and quantum descriptions intrude on the deeper issues of quantum gravity.
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Hilbert spaces and it all became perfectly clear to him. I get a similar feeling reading this book. What I have only heard glossed over before is really mathematics. But I think the flip side is that the book lacks some basic physics that might be there if a less mathematical author, trained as a physicist and perhaps with experimental experience, had helped to write it.
530:, the fact that the electrons are bound to atoms and molecules, etc. Classically, with exact coordinates, the detailed structure of molecules and nuclei is described by the small differences in coordinates, but when the position of a molecule is described by a wave function, all lower level structure must appear in these extra many-body variables.
441:
a higher entropy state than black holes, in the very late stages of an open universe. So, the expansion does increase a temporary entropy ceiling. Up until this point, I had the impression that the small size and low entropy of the early universe were distinct, inviting different explanations, but at this point they appear to be closely linked.
504:... but the apparatus that we use to measure these variables—and we ourselves—are described by a wave function that evolves deterministically. So there is a missing element in quantum mechanics: a demonstration that the deterministic evolution of the wave function of the apparatus and observer leads to the usual probabilistic rules.
463:
30.14, raises the question of where the asymmetry came from, and then mentions that the temperature is 10 K. If the state had perfect symmetry, would not the temperature be 0 K? Clearly, classically or in QM, a finite temperature implies density fluctuations on the atomic level. Only in pre-atomic
451:
Note 28.1 still does not do justice to iron. I believe that the main reason that soft iron does not hold much net magnetization is that the magnetic field energy is smaller if the domain directions lead around in little loops. This is demonstrated by the Scotty dog magnet toys. (Sufficiently small
440:
The book says that statement that the entropy ceiling increases as the universe expands is incorrect because its size is just one of its dynamical variables. Later, it says that, if the universe expands indefinitely, black holes will decay, over many ages of the universe. This implies that there is
431:
I enjoyed and learned much from this book. I have some comments, most of which are apparent inconsistencies or problems. I feel that this is quite a different book than would be written by a mathematical physicist who had been originally trained in physics. The mathematics is more mathematical and
302:
He attempts to explain the mathematics needed to describe contemporary physics, as a physicist with little knowledge of cosmology and field theory, I find this works quite well. A non-mathematical reader would at best have to exert great effort to understand the more mathematical parts of the book.
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may be fundamental. I am continually amazed that many physicists still think so classically. I rarely heard of such a way of thinking when I was doing research or in School. The book (very nicely) describes
Einstein, Podolsky and Rosen experiments that appear to me to show that the same rules for
594:
Is the section on errata really necessary? i.e. "...provides a comprehensive list of mistakes and errors (and their respective corrections) which have been found in the text, so that readers are able to update their version of the book without buying a new copy." Providing lists of errors is common
490:
with any classical description. As emphasized, there are sufficient variables left over after satisfying the correspondence principle to account for entanglement. Since the world evolves according to a quantum
Hamiltonian, anything that can actually be calculated about it quantum mechanically has
472:
In the Schrödinger's lump experiment, the system is poorly defined, the lump being entangled with thermal motion in the floor, etc. In addition, I do not see the point of it. The following 30.11 seems to raise objections to the compatibility of quantum mechanics with general relativity that are no
512:
In 34.7, the role of the observer here is the same as in classical statistical mechanics. It is hard to see how twistor theory (or anything else) could explain EPR and a fundamental R process without the extra variables of multi-body QM. That would require non-locality with undiminished effect at
275:
The article suggests that this book, while not avoiding all mathematics, is of the popular kind. Since the two concepts might be considered somewhat mutually exclusive, the article would benefit from a more precise description of what category this book falls into. Is it, for example, not suitable
579:
I, with another physicist, once had the rare chance to briefly explain quantum mechanics to a mathematician. We tried the usual discussions of particles, waves, uncertainty and experiments, and he just looked blankly at us. Then we began to remember something about how to express it in terms of
521:
I do not agree that the extra variables of an n body wave function, not in n one-body wave functions, are mysteriously invisible. They are seen to do many other things besides macroscopic entanglement. They account for the fact that charged particles repel each other, the symmetry of the wave
415:
Roger
Penrose has always been a controversial author. He was interested in highly speculative subjects such as possible quantum processes in the brain, or telepathy. Nonetheless, he has made a lot of major discoveries, he's always had a very intuitive mind, and he has participated in some very
313:
Have you read Roger
Penrose's "The Emperor's New Mind"? This is not the first time that Penrose proposes difficult sujects to "general" readers. While it proposes a challenge to the untrained mind, anyone with a college degree and some background knowledge in mathematics (as well as a pinch of
291:
The book comes with a 'National
Bestseller' inscription, implying at least some form of popularity. It could be, though, that literacy has fallen off so much that a couple hundred book sales to mathematicians and physicists are enough to make any book a bestseller.
609:
I am a great fan of Sir Roger
Penrose's works, and if I may be so bold as to add a quote from my own perception of the Ultimate Reality that I once sent to him, "The Universe works backwards to get us to the future we are supposed to have."
508:
Because the microstate of a macroscopic system is never completely known, it is easier for a deterministic theory to have probabilistic consequences than visa versa. The apparatus adheres to the U evolution, but we describe it classically.
404:
Of course a professor emeritus needs not respond to comments about his earlier publications, but I see so many relevances to
Knowledge articles that I might post my comments here, even if I am not able to contact the author..
551:
I agree that it is possible that the brain is other than a classical computer. The alternative is that it might have elements of quantum computer in it. It seems to me that a good candidate for testing that might be the
416:
interesting scientific debates (some of which he had initiated). He's always fascinating, even when proven wrong (for instance, his theories about microtubules creating quantum effects in the brain).
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I think it might be useful to have a 'further discussion' section where people could pose queries about sections they get stuck on, and others could attempt answers.
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22.5, 34.8 Yes, observables are not always real numbers. I worked on a radio direction finding system that used receivers whose output was complex numbers.
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of a fly. If the fly's vision turns out to be better than the diffraction limit of the individual eyelets, then the compound eye must be functioning as a
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I have some problems with the consistency of some parts of this book's physics, but have decided to send them to the author before listing them here.
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The solutions will be on www.roadsolutions.ox.ac.uk in
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560:. That would indicate that neurons can remain phase coherent and would suggest that nerves may be capable of quantum computing.
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curiosity, an open mind and some general culture) will appreciate, and eventually grasp, the concepts exposed in his books.
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the physics is less physical. This is refreshing but sometimes frustrating.
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To me, it seems old fashioned to speculate that the R process of
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