Updates
10/3/2015. I recently realized that QFT offers an answer to the question: When do fields collapse? After the section “The Necessity” in Chapter 8, I will insert a modification of the following:
A major question in physics today is about collapse of the “wave-function”: When does it occur? There have been many speculations (see, e.g., Ghirardi–Rimini–Weber theory, Penrose Interpretation, Physics forum) and experiments (e.g., “Towards quantum superposition of a mirror”) about this. The most extreme view is the belief that Schrödinger’s cat is both alive and dead, even though Schrödinger proposed this thought-experiment (like Einstein’s less-well-known bomb experiment) to show how ridiculous such an idea is.
The problem arises because Quantum Mechanics can only calculate probabilities until an observation takes place. However Quantum Field Theory, which deals in real field intensities – not probabilities, provides a simple unequivocal answer. Unfortunately, QFT in its true sense of “there are no particles, there are only fields” (Art Hobson, Am. J. Phys. 81, 2013) is ignored or misunderstood by most physicists. In QFT the “state” of a system is described by the field intensities (technically, their expectation value) at every point. These fields are real properties of space that behave deterministically according to the field equations – with one exception.
The exception is field collapse, but in QFT this is a very different thing from “collapse of the wave function” in QM. It is a physical event, not a change in probabilities. It occurs when a quantum of field, no matter how spread-out it may be, suddenly deposits its energy into a single atom and disappears. (There are also other types of collapse, such as scattering, coupled collapse, internal change, etc.) Field collapse is not described by the field equations – it is a separate event, but just because we don’t have a theory for it doesn’t mean it can’t happen. The fact that it is non-local bothers some physicists, but this non-locality has been proven in many experiments, and it does not lead to any inconsistencies or paradoxes.
So when field collapse occurs, the final “decision” – the point of no return – is reached. This is QFT’s answer to when does collapse occur: when a quantum of field colapses. In the case of Schrödinger’s cat, this is when the radiated quantum (perhaps an electron) is captured by an atom in the Geiger counter.
Before a field quantum finally collapses, it may have interacted or entangled with many other atoms along the way. These interactions are described (deterministically) by the field equations. However the quantum cannot have collapsed into any of those atoms, because collapse can happen only once, so whatever you call it – interaction, entanglement, perturbation, or just “diddling” – these preliminary interactions are reversible and do not lead to macroscopic changes. Then, when the final collapse occurs, those atoms become “undiddled” and return to their unperturbed state.
To sum up, in QFT the “decision” is made when a quantum of field deposits all its energy into an absorbing atom. Besides answering this question, QFT also explains why time dilates in Special Relativity and resolves the wave-particle duality question of Quantum Mechanics. One can only wonder why this theory hasn’t been embraced and made the basis for our understanding of nature.after
10/3/2015. In Chapter 8, “Your choice”, after the sentence “…consistent with all the data known to date”, insert the following:
In particular, QFT answers Oerter’s concern in a very simple way. In QFT, each quantum has a life and death of its own, spread-out as it may be. A field quantum cannot divide and appear somewhere as “half a quantum”; it either collapses into an absorbing atom, or it doesn’t. There is nothing mysterious about this.
9/28/2015. In Chapter 3, the section “Goodbye ether” should begin:
Maxwell, however, never liked the ether. He gave it lip service, but called it “a most conjectural scientific hypothesis”. To him it was enough to have “waves propagated through the electromagnetic field” (S1986, p. 26)….
Also, in the bibliography the two references S1989 and S1986 should be interchanged.
9/20/15: In Chapter 3, at the end of the “Field Collapse” paragraph add:
As Sean Carroll said, in a different context:
… the puzzle of “action at a distance”… disturbed Newton as well as his critics. At some point, however, when your theory does an amazing good job at explaining a multitude of phenomena, you shrug your shoulders and admit that nature apparently just works that way. – S. Carroll (C2012, p.
Also, in “Where’s the field? section in Chapter 2, I omitted LaPlace’s work. The last paragraph must be modified to include the following quote (cf. quote by Einstein on p. 31):
Laplace’s theory… fits in much better with our intuition that all physics, like politics [joke], is local. It’s not that earth just reaches out and attracts the moon; earth affects the gravitational potential nearby, and that affects the potential right next door, and onward in a smooth sequence all the way to the moon (and beyond). The force of gravity isn’t a mysterious effect that leaps over infinite distances; it arises from the smooth variation of an invisible field that permeates all of space. – S. Carroll (C2012, p. 120)
Also, add to the bibliography: C2012. The particle at the end of the universe by Sean Carroll, Plume, Penguin group, NY.
9/19/15: I just ran across an “Einstein quote” that I want to add. It’s actually a fictional quote, appearing in a novel “The Einstein Prophecy”, but it’s so apropos that I can’t resist it. In the section on “Randomness” in Chap. 8, after the sentence “But still Einstein held out the smile of a hope that causality might someday be restored,” add the following footnote:
The same smile of a hope is to be found in a fictional context in the novel The Einstein Prophecy by Robert Masello. After being told that he once said “God does not play dice with the universe; the cosmos cannot simply be a game, designed at random and made without reason”, the fictional Einstein replies, “But perhaps He is playing some other game, a game we don’t know yet, with rules we don’t understand.”
9/17/15: Several reviews on Amazon.com (where my rating is now 4.4/5.0 stars) criticized the appendices as being inadequate. I think Appendix B (General Relativity) is the main culprit. I don’t think I spent enough time discussing the “curvature of space-time” interpretation. Here is some material, written in response to the “Einstein” issue of Scientific American (September 2015), that should be incorporated into this appendix.
Throughout the September “Einstein” section readers are told that gravity is caused by curvature of space-time. On the first page we read “gravity… is the by-product of a curving universe”, on p. 43 “the Einstein tensor G describes how the geometry of space-time is warped and curved by massive objects”, and on p. 56 “Albert Einstein’s explanation of how gravity emerges from the bending of space and time”.
The problem is, that’s NOT what Einstein said. Einstein believed that gravity is a force field and not “curvature of space-time. In the very paper that you cite (“The foundation of the general theory of relativity”, 1916) he wrote, “[there is] a field of force, namely the gravitational field, which possesses the remarkable property of imparting the same acceleration to all bodies”. The G tensor, said Einstein “describes the gravitational field.” The term “gravitational field” or just “field” occurs 58 times in this article, while the word “curvature” doesn’t appear (except in regard to “curvature of a ray of light”).
According to Einstein, the gravitational field causes physical changes in the length of measuring rods (just as temperature can cause such changes) and it is these changes that create a non-Euclidean metric of space. In fact, as he pointed out, these changes can occur even “In a space which is free of gravitational fields [i.e., a rotating system].” (Incidentally Einstein made a mistake in this section: he got the direction of the change wrong.)
So where does “curvature” come in? In this same paper Einstein showed how this non-Euclidean geometry is mathematically equivalent to the geometry on a curved surface, developed by Gauss, and extended (mathematically) to any number of dimensions by Riemann.
One may well ask, “if the gravitational field is equivalent to curvature of space-time, what difference does it make if we attribute gravity to such curvature?” It makes a lot of difference.
First, most people (including me) can’t picture four-dimensional curvature (except by mathematical analogy). The conventional approach says that if they can’t do that then they can’t understand general relativity. The fact is that the field concept that was introduced by Faraday in 1845 can be grasped by anyone.
Second, by eliminating or suppressing the role of the gravitational field, the great unity that the field concept
4/3/15: Correction on p.iii. “The nature of the physical universe” should be “The nature of the physical world”.
3/23/15: The description of Schwinger’s work around 1950 doesn’t go far enough. The second paragraph should read:
Schwinger’s final version of the theory was published between 1951 and 1954 in a series of five papers entitled “The Theory of Quantized Fields”. In these papers he not only incorporated matter and force fields QFT (including gravity) on an equal basis, he also provided a firm axiomatic basis for QFT, as will be described in the next chapter, and he formulated elegant mathematics to do the calculations, including Green’s functions and his Action Principle. In fact, Schwinger believed that this later work was far more important that renormalization calculation for which he received the Nobel Prize, saying “I wouldn’t have thought that the electrodynamic work would be it. It’s splashy and all that, but it was an obvious development of ideas that were in the air. Frankly I much prefer the [later] work centering on the action principle…”* (p. 355)
Unlike his Nobel Prize achievement, this later – and more important – work is largely unknown or forgotten. The main reason these masterpieces have been ignored is that many physicists found them too hard to understand. (I know one who couldn’t get past the first page.) As Sylvan Schweber said* (p. 371-2), “And so a tragedy ensued. His need to do things his own way made him develop his own language, his own approaches and techniques… As he became more isolated, fewer people understood and spoke the newer languages he created… contributing to his further isolation… It was a mutual loss, for both Schwinger and the community were the losers.” And so it was that particles won round three, and are still winning. And that’s why I wrote this book.
*QED and the Men Who Made It” by Silvan Schweber, (Princeton University Press, NJ, 1994)
11/3/14. The “intuitive explanation” of time dilation in App. A isn’t very clear. It should read:
Consider two atoms in a rocketship (or in its contents). Suppose that the rearward atom creates a field disturbance and when that disturbance reaches a more forward atom, something happens. (It is the interaction among atoms, after all, that causes everything to happen.) By the time the disturbance reaches the second atom will have moved farther ahead, so the disturbance must travel a greater distance to get there than if the rocketship were stationary, even after taking the F-L contraction into account. Therefore, since fields travel at a fixed rate, it will take longer (as observed from earth) for the disturbance to reach the second atom. Of course disturbances that propagate in the backward direction have a shorter distance to travel, but this effect turns out to be not as great. (I’m afraid that demonstrating this is beyond our scope.) In short, things happen more slowly when you’re moving because the fields have to travel a greater distance.
Further, in footnote 6 it should be made clear that the distance d includes the effect of the F-L contraction: “Let d be the distance between the two men (taking into account the F-L contraction)…”
4/20/14. A typo in Chap. 6, “The Matter Field”, “The atom revisited”: The reference to Fig. 4-2 should be to Fig. 4-1.
4/12/14. I recently ran across “The Evolution of Physics” by Albert Einstein and Leopold Infeld published in 1938. It is consistent with what I wrote about Einstein’s “rejection” of Quantum Field Theory in Chap. 1. As I said, “QFT was neither complete nor successful at the time.” But the preface to the 1960 edition by Infeld is unforgivable, so please add the following footnote after the first sentence in “Einstein rejects QFT”:
Of course Einstein was not the only physicist to reject QFT at the time, or for that matter, even today. (That’s why I wrote this book.) However what his colleague Leopold Infeld wrote in a 1960 preface to “The Evolution of Physics” by Einstein and Infeld is inexcusable. Ten years after the great renormalization success of QFT (see “Another Final Fix” in Chap. 6), and 6 years after Schwinger’s monumental series on “Quantized Fields”, Infeld claimed that “the principal ideas of physics… have remained essentially the same”, and “with these few changes, the book becomes up to date.” Sorry, Leopold, but you missed a revolution in physics as great as the one created by your pal Einstein.
3/15/14. In Chapter 2 under “Newton’s Gravity”, remove the paragraph heading “The moon is falling”. The moon is NOT falling in the sense of descending closer to the earth, as is made quite clear in the following text. The heading only serves to distract and confuse.
3/1/14: The following updates have been added to the 2nd edition, 2nd printing:
1. Chap. 7. After Fig. 7-1 add:
Discretization leads to an important difference between quantum and classical fields. In classical physics the field intensity at a given point has only one value. In QFT, just as the angular momentum of an atom can be a superposition of values (Fig. 7-1), so the field intensity at a point can be a superposition of values. And just as interaction of the atom with a magnet “selects” one of the values with corresponding probabilities, so “measurement” of field intensity at a point will select one of the possible values with corresponding probability (see “Field Collapse” in Chapter 8). This is why the “expectation value” is used to describe field intensity of a quantum field, rather than a definite number.
2. Chap. 7. After the e = mc2 section, add:
The Higgs boson. On July 4, 2012 it was announced that a new particle was discovered and believed to be the Higgs boson, also known as the “God particle”. Ironically, this discovery of a “particle” is a further validation and triumph of quantum field theory. You see, the Higgs mechanism, as described in “Electroweark unification” (Chapter 5), was suggested as a way to explain the large mass of weak field quanta, and the way this is accomplished – the only way – is via a Higgs field.
There is a Higgs field filling space that interacts with the particles moving through it and giving some of them mass… the Higgs boson is the particle we observe when we interact with a vibration in that field. Both of these ideas are part of quantum field theory, which we generally don’t try to explain in physics popularizations. – Sean Carroll, “How to explain the Higgs mechanism”, 2012 (www.preposterousuniverse.com)
Thus the discovery of the Higgs boson, which is really a quantum of the Higgs field (or “vibration” as Carroll calls it), validates the theory of the Higgs mechanism and produces another triumph for QFT.
3. Chap. 3. Delete last sentence of footnote 12. It turns out that Planck did not use the word photon – it was inserted by the translator. Nevertheless, I do not believe that the word wasn’t used until Gilbert Lewis – a chemist, no less – “coined” it in 1927, even though I don’t have any evidence.
4. Bibliography. Add “W1992. Dreams of a Final Theory by Steven Weinberg”
5. p. 152, In place of the section “Breaking News”, substitute:
Today more and more physicists are beginning to recognize that the QM particle picture doesn’t make sense. Some examples are “There are no particles, there are only fields” by Art Hobson (Am. J. Phys. 81, 2013), “Beyond the Higgs Boson” by Sean Carroll (Jan. 18, 2013, youtube), “On the reality of the quantum state” by N. Pusey et al. (Nature Physics 8, 2012), and of course “The Lightness of Being” by F. Wilczek (W2008). Perhaps the day will come when the physics community will finally abandon the QM ship made of particles floating on a sea of paradox for smoother sailing on the seas of quantum fields.
6. There is insufficient attention to the vacuum field throughout the book. In “Attached vs. Separate Fields” in Chap. 3 I added the footnote “In fact there is a third field that exists in space even if there are no quanta or attached fields. It is known as the vacuum field.”. And in “Separate vs. attached (review)” in Chap. 6, I changed the first sentence to: “We also saw that there are two types of field, attached and separate, not counting the “vacuum” field which exists even if no quanta or attached fields are present.”