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I believe that common sense is choosing, wherever possible, the simplest, most intuitively-satisfying explanation that is consistent with observations.
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Rodney A. Brooks |
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Quanta of force fields can even overlap each other and yet maintain their separate identities. Each field quantum lives and dies a life and death of its own. For example, a quantum of the EM field can be emitted from an atom in the sun, travel through millions of miles of space, spreading out as it goes, and then interact as a single unit with an atom in your eye.
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Rodney A. Brooks |
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NOTHING CAN GO FASTER THAN LIGHT Of course the idea that there is an ultimate speed of light is very high by earthly standards, the magnitude is not the point; any kind of speed limit in nature doesn't make sense. Suppose, for example, that a spaceship is traveling at almost the speed of light. Why can't you fire the engine again and make it go faster-or if necessary, build another ship with a more powerful engine? Or if a proton is whirlin..
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Rodney A. Brooks |
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NOTHING CAN GO FASTER THAN LIGHT Of course the idea that there is an ultimate speed limit seems absurd. While the speed of light is very high by earthly standards, the magnitude is not the point; any kind of speed limit in nature doesn't make sense. Suppose, for example, that a spaceship is traveling at almost the speed of light. Why can't you fire the engine again and make it go faster-or if necessary, build another ship with a more powerf..
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Rodney A. Brooks |
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So if you want, you can believe that gravitational effects are due to a curvature of space-time (even if you can't picture it). Or, like Weinberg, Wilczek (and me), you can view gravity as a force field that, like the other force fields in QFT, exists in three-dimensional space and evolves in time according to the field equations.
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Rodney A. Brooks |
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edea571
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In QFT, the various fields, even the matter field, appear separately, each with its own equation and its own behavior. They are not combined into a single field as Einstein hoped, but they are related - members of the same family, so to speak. This theory, so little known or appreciated by the public, is the true fulfillment of Einstein's desire for a world made of fields and only fields.
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Rodney A. Brooks |
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The way that fields propagate and the speed at which they propagate are determined by the field equations.
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Rodney A. Brooks |
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The Higgs mechanism was actually suggested earlier by Schwinger, in the same paper where he introduced the V and A equation. Like the V-A discovery, this contribution by Schwinger is also largely forgotten.
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Rodney A. Brooks |
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Fields of color. A special feature of this book is the use of color to depict fields that in themselves are unpicturable. Just as the color blue permeates the sky, so you will be asked to picture space as permeated with colors, with different colors representing different fields. Color is an appropriate tool for this job because color is something that does not exist in itself; it exists only as a property of something else. By using colors..
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Rodney A. Brooks |
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The fact is, either approach is correct and one does not preclude the other. Yes, the Principle of Relativity is elegant and the top-down approach is easier to use; physicists love it for that reason. But the field equations are also elegant and they not only contain the Principle of Relativity within them, they also provide a physical explanation for effects that otherwise are paradoxical. We can never know if God started with the Principl..
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Rodney A. Brooks |
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The move from a particle description to a field description will be especially fruitful if the fields obey simple equations, so that we can calculate the future values of fields from the values they have now...Maxwell's theory of electromagnetism, general relativity, and QCD [quantum chromodynamics] all have this property. Evidently, Nature has taken the opportunity to keep things relatively simple by using fields.
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Rodney A. Brooks |
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SUMMARY The theory of Special Relativity as formulated by Einstein in 1905 was based on the postulate that the laws of physics are the same regardless of the state of motion of the observer, so long as it is uniform. This is known as the Principle of Relativity, from which there follow many strange effects. While these behaviors seem paradoxical, they make perfectly good sense when seen as a result of the way fields behave: Objects contract..
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Rodney A. Brooks |
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Feynman converts! According to Frank Wilczek, Feynman eventually lost confidence in his particles-only view of nature: Feynman told me that when he realized that his theory of photons and electrons is mathematically equivalent to the usual theory, it crushed his deepest hopes...He gave up when, as he worked out the mathematics of his version of quantum electrodynamics, he found the fields, introduced for convenience, taking on a life of the..
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Rodney A. Brooks |
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Schrodinger, despite some misgivings, believed that the electron is "a real wave spread throughout all of space"
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Rodney A. Brooks |
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We assert that the atom in reality is merely the...phenomena of an electron wave captured, as it were, by the nucleus of the atom...From the point of view of wave mechanics, the [particle picture] would be merely fictitious. I have, however, already mentioned that we have yet really observed such particle paths [see, for example, Fig. 6-6]...We find it confoundedly difficult to interpret the traces we see as nothing more than narrow bundles..
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Rodney A. Brooks |
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Field Collapse. The answer to Schrodinger's dilemma is what we now call field collapse. In QFT, when a field quantum interacts, it must interact as a unit. Half of the quantum cannot do one thing while the other half does another. If a quantum is absorbed by a molecule, the entire quantum must be absorbed, no matter how spread out it may be. If a quantum is scattered by a molecule in a cloud chamber, it can interact only with that molecule,..
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Rodney A. Brooks |
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Note about youth. Before ending this chapter, I'd like to say something about youth. It was a popular edict in the 1960's to never trust anyone over 30. Whether or not this is true in general, it has great validity in theoretical physics. When Einstein discovered his theory of relativity he was 25. Bohr was 28 when he developed his atomic theory. De Broglie was 28 when he had his ephiphany. Pauli was 25 when he announced his exclusion princ..
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Rodney A. Brooks |
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Mass is Inertia......In physics, mass means the tendency of an object to resist changes in course or speed. It is what physicists call inertia. Inertia is a kind of "I don't like to be pushed" feeling. It represents the difficulty in getting something going and the difficulty in stopping it once it is moving, or even the difficulty in deflecting it from its path."
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Rodney A. Brooks |
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Mass is not weight.....Weight is the pull of gravity -the downward force exerted by the earth. If there is no gravity there is no weight, but there is still inertia. In ordinary speech the two concepts are often blurred, as in "a heavy object is harder to push". Nevertheless, weight is the pull of gravity and mass is inertia, and they are different concepts."
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Rodney A. Brooks |
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That the physics community has so ignored the only understandable, paradox-free picture of nature that we have boggles my mind. Maybe physicists like being seen as "high priests" who are entrusted with mysteries that mere mortals cannot hope to comprehend."
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Rodney A. Brooks |
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MASS INCREASES The final paradox of relativity is the increase in mass due to motion. Mass increase has been observed experimentally in particle accelerators, with increases as great as 3000% for particles traveling at over 99.9% the speed of light. How can the mass of an object get bigger just because it's moving? Intuitive explanation. As we saw in Chapter 2, mass means inertia - i.e., resistance to acceleration. If you push something and..
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Rodney A. Brooks |
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A delicate balance. In summary, nuclei are held together by a delicate balance among (a) the attractive strong force between nucleons, (b) the electrical repulsion between protons, (c) the dilution of this repulsive force by neutrons, and (d) the instability created by the Exclusion Principle if there are too many neutrons. Thus, for a given number of protons there is a narrow range of allowable neutron numbers: not enough and the protons w..
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Rodney A. Brooks |
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Enigmas answered. Not only is QFT the answer to Einstein's search, it also answers or resolves his Enigmas, and in a way that can be understood by the man (or woman) on the street. In Appendix A you will see how the paradoxes of special relativity become natural and understandable consequences of the way fields behave. In Appendix B you will see that the problematic curvature of space-time in general relativity is gone; in QFT gravity is ju..
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Rodney A. Brooks |
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What is a field? To put it briefly, a field is a property or a conditions of space.
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Rodney A. Brooks |
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Instead of the ordinary numbers used in conventional mathematics, the quantum nature of the fields requires the use of Hilbert algebra, in which the physical properties are described by "vectors" in an abstract Hilbert space and by "operators" that act on those vectors."
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Rodney A. Brooks |
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Apparently it did not occur to Feynman that these discrete clicks could also be produced by field quanta that live and die as a unit.
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Rodney A. Brooks |
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There is another reason why imaginary color is an appropriate tool for visualizing fields. You may be surprised to hear this, but the colors that we perceive in nature are also imaginary; they exist only in our minds. In nature there are no colors - only light waves of various frequencies. Even the vivid colors of a rainbow are not really there; the rainbow is created by water droplets that reflect light of different frequencies through dif..
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Rodney A. Brooks |
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Limitation of color. There is, of course, a limit to how far the use of color can take us. A single color can help us visualize a field that is otherwise invisible, but it cannot inform us about the complexity of the field - and the fields we will encounter are complex. The EM field, for example, contains both electric and magnetic components, each of which has a direction associated with it, yet we will picture it simply as a green field. ..
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Rodney A. Brooks |
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I understand," says Schwinger, "and I admit that QFT has not solved the causality problem. But at least it has localized the probability aspect to a single event called field collapse-an event that is not covered by the equations of QFT. That is to say (Schwinger's favorite expression), QFT itself is causal, but it only takes us so far. At some point a discontinuous event takes place that is not covered by the theory. It is possible that at..
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Rodney A. Brooks |
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The number of matter quanta in a given region or state is limited by the Exclusion Principle.
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Rodney A. Brooks |
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Neutron limit. As stated in Chapter 4, the Exclusion Principle places a limit on the number of electrons in an atomic nucleus. Just as electrons added to an atom must go into higher energy states if the lower ones are occupied, so neutrons added to a nucleus must go into higher energy states if the lower ones are occupied. Then, because of their higher energy, these neutrons may be able to escape the strong binding force and leave. This is ..
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Rodney A. Brooks |
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I once read that for every equation, you lose a thousand readers.
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Rodney A. Brooks |
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The uncertainty principle. The uncertainty principle, introduced by Heisenberg in 1927, states that the position of a particle cannot be determined, but provides a mathematical formula relating its uncertainty to the uncertainty of the particle's momentum. Now in QFT what we call particles are really fields, and since fields spread out, there is no precise "position". However there is a property of fields in general, known as Fourier's theo..
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Rodney A. Brooks |
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Energy. In classical physics, energy means the ability to do work, which is defined as exerting a force over a distance. This definition, however, doesn't provide much of a picture, so in classical physics, energy is a rather abstract concept. In QFT, on the other hand, the energy of a quantum is represented by oscillations in its field. In fact, Planck's famous relationship between energy and frequency of oscillation (see Chap. 3) is a dir..
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Rodney A. Brooks |
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It may seem strange that the same term that slows the spatial evolution of a field also causes it to oscillate, but it is actually straightforward mathematics to show that the frequency of oscillation is given by f=mc^2/h, where h is Planck's constant.
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Rodney A. Brooks |
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those events proceed, not in
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Rodney A. Brooks |
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Because quanta are fields, they do not have sharp edges and can spread over large distances, but no matter how spread out they are, each quantum maintains its own identity. If it is absorbed or changes its spin state, it does so as a unit. Because of this all-or-nothing behavior, quanta in many ways mimic the behavior of particles.
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Rodney A. Brooks |
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The vacuum field. Separate and attached fields are not the only fields that exist in QFT. Even in a region where they are absent, or essentially zero, there still is a background field known as the vacuum field.
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Rodney A. Brooks |
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Force. Before fields were recognized, forces were thought (except by Newton) to happen through "action at a distance". That is, a body or particle in one place causes a body in another place to move, without any medium in between. When Faraday introduced the concept of fields, this picture was changed: The first body creates a field in the surrounding space and this field then exerts a force on the second body. In QFT, everything is fields,..
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Rodney A. Brooks |
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The helium nucleus, for example, contains two protons and two neutrons. If the neutrons were not there, the electrical repulsion between the protons would overcome the strong binding force. However if two neutrons are also present, the binding force is increased (because there are now four nucleons), while the electrical repulsion between the protons is weakened because they are not as close together. The result is a stable helium nucleus-a..
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Rodney A. Brooks |
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My mission soon turned into a labor of love, with emphasis on labor. I had not anticipated the breadth and depth of the subject, or the drama as our greatest minds waged what I think is our greatest battle: to understand the world we find ourselves in (a far more worthy battle than the wars we are so good at waging against each other). By drama I mean not only the philosophic struggle to wrest nature's secrets from their most hidden recesse..
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Rodney A. Brooks |
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I hope that, like Schwinger, Weinberg, Wilczek, Hobson (and me), you will choose a reality made of quantum fields - properties of space that are described by the equations of QFT. This is a picture that resolves all three of Einstein's enigmas (see Appendices), a picture that solves the action-at-a-distance problem that even Newton found unacceptable, a picture based on simple and elegant equations (take my word for that), a picture that ex..
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Rodney A. Brooks |
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Non-locality. One of the most troubling aspects of field collapse is that it is instantaneous and occurs at the same time at widely separated points. Physicists call this non-locality. This is especially bothersome when the sudden change involves two entangled field quanta. Einstein argued vehemently against the idea of non-locality, claiming that it violated a result of his Principle of Relativity - that nothing can be transmitted faster t..
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Rodney A. Brooks |
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The job of science is to look beyond our intuition, to find out by any means possible what's really going on, and to give up old ways of thinking when the evidence requires it.
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Rodney A. Brooks |