Fields of Color Quotes

“In the field picture there is no such thing as empty space. Fields pervade space; they are a condition or property of space; you can't have space without fields. Fields obey laws that specify how a change at one point affects the field at adjacent points, and thus how that change is propagated through space.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“Relativistic twins? When one looks at the paths that Newton and Einstein followed while pursuing their theories of gravity, one is struck by the many similarities: the unexplained data on orbits, the sudden insight about falling objects, the need for a new mathematics, the calculational difficulties, the retroactive agreements, the controversy, the problem-plagued expeditions, and the final triumph and acclaim.. Both men had worked in the same eccentric and lonely way, divorced from other scientists, armed with a great feeling of self-reliance while struggling with new concepts and difficult mathematics, and both produced earth-shaking results. One can't help but wonder if these two greatest of scientists, born 237 years apart, were "relativistically related", conceived as twins in some ethereal plane in a far-off galaxy and sent to earth to solve a matter of some gravity.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“Propagation speed. An important feature of fields is that changes in their intensity do not propagate through space instantaneously but proceed, point by point, with a speed that is limited by a number in the equations. This number is about 300,000 km/sec (186,000 miles/sec) and, since light itself is a field, it's no coincidence that this number is the speed of light. If we imagine that an object suddenly appears in space, the gravitational field generated by that object will first appear near the object and then rapidly extend outward until all of space has acquired, to some extent, the attractive property created by that field. Similarly, if the object were suddenly to disappear, the field would continue to exist for some time afterward. If the earth were suddenly to disappear, the moon would continue in its orbit for another second and a half before the gravitational field in its vicinity vanished. If the sun were suddenly to disappear, earth would continue in its orbit for eight and a half minutes before heading off into space.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“Force fields are directional. The gravitational field is a force field and forces are directional. In the case of gravity, the direction of the force is toward the object that created the field. What, you may then ask, happens when there are several gravitational fields set up by several objects? For example, the gravitational field at the surface of the earth also contains component fields arising from the moon and the sun. The answer is that the various fields combine to give a net gravitational field, but they don't add numerically; each field has its own direction, and the directions must be taken into account. Thus there is a point between the earth and the moon where the two gravitational fields, being in opposite directions, cancel each other out. When a moon rocket is fired, it must have enough power to reach that point or else it will fall back to the earth. Beyond that point it will be pulled toward the moon. This compounding of forces also causes the tides as the water in oceans and seas is pulled toward the sun and moon. Even though those tugs are imperceptible to us, they create a variety of tides, such as neap and ebb tides, depending on the positions of the sun and moon.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“Whether it is a falling man or an orbiting satellite, the effect of inertia is to create an apparent upward force that depends on the mass of the object. It is the same force we feel when riding in a car that goes around a tight curve. This inertial effect is equal and opposite to gravity and therefore cancels the pull of gravity. In physicist language, the "gravitational mass" and "inertial mass" are equal. This is not a tautology, as Ambrose Bierce thought, but a recognition that the pull of gravity is proportional to the inertia of the object being pulled. Einstein called this the "Principle of Equivalence", and it became the basis for his new theory of gravity that he called the general theory of relativity.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“I believe that common sense is choosing, wherever possible, the simplest, most intuitively-satisfying explanation that is consistent with observations.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“I once read that for every equation, you lose a thousand readers.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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 just another force field and space and time are the same space and time we intuitively believe in. Finally, in Appendix C you will see how the infamous wave-particle duality of QM is eliminated because there are no particles - only fields - and hence there is no duality. However abandoning the familiar picture of solid particles and replacing it with intangible fields is not easy. It will require a leap of imagination greater than did the atomic picture that Eddington struggled with.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“those events proceed, not in”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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 when moving because motion affects the interaction of fields that hold the object together. Space itself contracts because space is made of fields.

Things happen more slowly in a moving system because the interacting fields must travel a greater distance (despite the contraction).

Nothing can go faster than light because everything is made of fields that propagate at a finite rate determined by the field equations.

Mass increases with speed because mass means resistance to acceleration and acceleration beyond the speed of light is impossible.

I call this the bottom-up approach. Although most physicists prefer to start with the Principle of Relativity (top-down approach), the bottom-up method provides insight into why these strange things happen. Even the Principle of Relativity follows from the bottom-up approach.

Either way, one must cope with a Rashomon reality in which observers in differently-moving systems see the same reality in different ways.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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 Principle of Relativity and derived the field equations or started with the field equations from which follows the Principle.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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 it doesn't respond much, then by definition it has a large mass or inertia. Now we just saw that pushing on something that is traveling at close to the speed of light has little effect on its speed because the underlying fields are already moving almost as fast as they can. Thus its resistance to acceleration has become greater and this means its mass has increased. Mass increase is just another way of saying that fields can't propagate faster than c.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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 powerful engine? Or if a proton is whirling around in a cyclotron at close to the speed of light, why can't you give it additional energy boosts and make it go faster?

Intuitive explanation. When we think of the spaceship and the proton as made of fields, not as solid objects, the idea is no longer ridiculous. Fields can't move infinitely fast. Changes in a field propagate in a "laborious" manner, with a change in intensity at one point causing a change at nearby points, in accordance with the field equations. Consider the wave created when you drop a stone in water: The stone generates a disturbance that moves outward as the water level at one point affects the level at another point, and there is nothing we can do to speed it up. Or consider a sound wave traveling through air: The disturbance in air pressure propagates as the pressure at one point affects the pressure at an adjacent point, and we can't do anything to speed it up. In both cases the speed of travel is determined by properties of the transmitting medium- air and water, and there are mathematical equations that describe those properties.

Fields are also described by mathematical equations, based on the properties of space. It is the constant c in those equations that determines the maximum speed of propagation. If the field has mass, there is also a mass term that slows down the propagation speed further. Since everything is made of fields - including protons and rocketships - it is clear that nothing can go faster than light. As Frank Wilczek wrote,

One of the most basic results of special relativity, that the speed of light is a limiting velocity for the propagation of any physical influence, makes the field concept almost inevitable. - F. Wilczek ("The persistence of Ether", p. 11, Physics Today, Jan. 1999)

David Bodanis tried to make this point in the following way:

Light will always be a quick leapfrogging of electricity out from magnetism, and then of magnetism leaping out from electricity, all swiftly shooting away from anything trying to catch up to it. That's why it's speed can be an upper limit - D. Bodanis

However, Bodanis only told part of the story. It is only when we recognize that everything, not just light, is made of fields that we can conclude that there is a universal speed limit.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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 whirling around in a cyclotron at close to the speed of light, why can't you give it additional energy boosts and make it go faster?

Intuitive explanation. When we think of the spaceship and the proton as made of fields, not as solid objects, the idea is no longer ridiculous. Fields can't move infinitely fast. Changes in a field propagate in a "laborious" manner, with a change in intensity at one point causing a change at nearby points, in accordance with the field equations. Consider the wave created when you drop a stone in water: The stone generates a disturbance that moves outward as the water level at one point affects the level at another point, and there is nothing we can do to speed it up. Or consider a sound wave traveling through air: The disturbance in air pressure propagates as the pressure at one point affects the pressure at an adjacent point, and we can't do anything to speed it up. In both cases the speed of travel is determined by properties of the transmitting medium- air and water, and there are mathematical equations that describe those properties.

Fields are also described by mathematical equations, based on the properties of space. It is the constant c in those equations that determines the maximum speed of propagation. If the field has mass, there is also a mass term that slows down the propagation speed further. Since everything is made of fields - including protons and rocketships - it is clear that nothing can go faster than light. As Frank Wilczek wrote,

One of the most basic results of special relativity, that the speed of light is a limiting velocity for the propagation of any physical influence, makes the field concept almost inevitable. - F. Wilczek ("The persistence of Ether", p. 11, Physics Today, Jan. 1999)

David Bodanis tried to make this point in the following way:

Light will always be a quick leapfrogging of electricity out from magnetism, and then of magnetism leaping out from electricity, all swiftly shooting away from anything trying to catch up to it. That's why it's speed can be an upper limit - D. Bodanis

However, Bodanis only told part of the story. It is only when we recognize that everything, not just light, is made of fields that we can conclude that there is a universal speed limit.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“Another analogy. The idea of length contraction and time dilation may be easier to accept when you consider that objects contract and processes slow down when cooled. The only difference between the effect of temperature and the effect of motion is the mechanism: In a cooler chest it is the slowing down of atomic motion that affects rates and interatomic distances, while in moving objects it is the extra distance through which fields must propogate. Would we think it paradoxical if a twin was placed in a cold chamber for 50 years and then emerged to find that her brother was old and she was young? No, we would not; in fact there are firms that offer to preserve people by freezing them. Why then should we not accept that motion can have a similar effect on chemical and physical processes? As Lorentz himself said,

We may, I think, even go so far as to say that...the conclusion is no less legitimate than the inferences concerning the dilation by heat. - H. Lorentz”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“Misconception #3. Some physicists claim that length contraction and time dilation are not real and that the physical explanations of Fitzgerald, Larmor and Lorentz are not to be taken seriously. This is not true. As N. David Mermin points out in his popular book on relativity "It's About Time":

Moving clocks really do run slowly and moving sticks really do shrink, if the concept of a clock or the length of a stick has any meaning at all...It is necessary for clocks and sticks really so to behave if the while subject is to fit coherently together, and not collapse into a mass of self-contradiction. - N.D. Mermin

NASA routinely observes time dilation in orbiting satellites and corrections are applied to keep atomic clocks on the GPS satellites in sync with clocks on earth. Time dilation has also been seen in particle accelerators. At the CERN accelerator radioactive particles traveling at 99.9% the speed of light are observed to decay 30 times more slowly than they do at rest.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“Intuitive explanation. The explanation is again based on the field nature of matter, described by the field equations. Consider two atoms in a rocketship (or in its contents). Suppose that one atom creates a field disturbance and when that disturbance reaches the second atom something happens. (It is the interaction among atoms, after all, that causes everything to happen.) Now if the rocketship is moving, the second atom will have moved farther ahead, so the disturbance must travel a greater distance to get there, even after taking the F-L contraction into account. Since fields travel at a fixed rate, ti will therefore take longer for the disturbance to reach the second atom. (Disturbances that propagate in the backward direction have a shorter distance to travel, but this effect turns out to be not as great.) In short, things happen more slowly when you're moving because the fields have to travel a greater distance.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“Furthermore, it is not just objects that contract. Space also contracts because space, as we have seen, is not empty. It is filled with fields, and these fields are always interacting with each other, even if there are no atoms or molecules present. So not only do objects contract, space itself contracts. Anything made of fields contracts when in motion.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“But will she not see that her meter sticks are contracted when laid out in the [direction of motion] - and even decontract when turned in the [other] direction? No, because the retina of her eye will also be contracted, so that just the same cells receive the image of the meter stick as if both stick and observer were at rest.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“Intuitive explanation. While I hope you can accept, as did FitzGerald and Lorentz, that length contraction happens because the field equations require it, it would be nice to have some intuitive insight into the phenomenon. We must recognize that even if the molecular configuration of an object appears to be static, the component fields are always interacting with each other. The EM field interacts with the matter fields and vice versa, the strong field interacts with the nucleon fields, etc. These interactions are what holds the object together. Now if the object is moving very fast, this communication among fields will become more difficult because the fields, on the average, will have to interact through greater distances. Thus the object in motion must somehow adjust itself so that the same interaction among fields can occur. How can it do this? The only way is by reducing the distance the component fields must travel. Since the spacing between atoms and molecules, and hence the dimensions of an object, are determined by nature and configuration of the force fields that bind them together, the dimensions of an object must therefore be affected by motion.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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 explains or is consistent with all the data known to date. And on top of that, QFT provides the most philosophically acceptable picture of nature that I can imagine.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“QFT deals with the structure and operation of the cosmos in the here-and-now, and not the whys and wherefores.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“It is clear the field collapse and renormalization have something in common: they both arise because something happens at the single quantum level that is not described by QFT. Renormalization is necessary because QFT is not able to explain the way in which a field quantum interacts with its self-field. Field collapse is a mystery because QFT doesn't predict when or how a quantum will change its state or be absorbed. If one of these gaps should ever be filled, I believe that the other one may be also.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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 than the speed of light. Now Einstein's postulate (which we must remember was only a guess) is indeed valid in relation to the evolution and propagation of fields as described by the field equations. However field collapse is not described by the field equations, so there is no reason to expect or to insist that it falls in the domain of Einstein's postulate. Non-locality is a fact; it has been experimentally documented. Nor does it lead to any paradoxes or inconsistencies. Even those who believe in particles as the ultimate reality acknowledge that something happens non-locally. Just as we said, "So the earth is round, not flat; that's surprising but I can live with it", so we can say, "Fields suddenly collapse. It's not what I expected but I can live with it." There are no logical contradictions involved.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“e=mc^2. I know. I promised there would be no equations and, except for a few footnotes, I've kept my promise. But I think you will forgive me for making an exception for the world's most famous equation-the only equation to have its biography written. And the thing is this: e = mc^2 pops right out of QFT. Einstein had to work hard to find it (it was published in a separate paper that followed his breakthrough paper on relativity theory in 1905), but in QFT it appears as an almost trivial consequence of the two previous results. Since both mass and energy are associated with oscillations in the field, it doesn't take an Einstein to see that there must be a relationship between the two. Any schoolboy can combine the two equations and find (big drum roll, please) e = mc^2. Not only does the equation tumble right out of QFT, its meaning is seen in the oscillations or "shimmer" of the fields. Frank Wilczek calls these oscillations "a marvelous bit of poetry" that create a "Music of the Grid" (Wilczek's term for space seen as a lattice of points):

Rather than plucking a string, blowing through a reed, banging on a drumhead, or clanging a gong, we play the instrument that is empty space by plunking down different combinations of quarks, gluons, electrons, photons,...and let them settle until they reach equilibrium with the spontaneous activity of Grid...These vibrations represent particles of different mass m...The masses of particles sound the Music of the Grid. ----- Frank Wilczek”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein

“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 direct consequence of the equations of QFT. In our color analogy, we might say that the oscillations cause the color to "shimmer", and the faster the shimmer, the greater the energy of the field.”
― Rodney A. Brooks, Fields of Color: The theory that escaped Einstein