Speed of Light – Why Nothing Can Go Faster

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?

Speed-of-Light

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 he transmitting medium – air and water, and there are mathematical equations that describe those properties.

wilczek_frankFields 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 its 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. 

Now let’s take another look at that proton whirling around in an accelerator, using our colored glasses to visualize the fields. We see the proton as a blob of redness “oozing” (I prefer that term to “leapfrogging”) ahead, as the amount of redness at one point affects the redness at a neighboring point. The process is very fast by our usual norms, but it is not instantaneous. The proton can’t move any faster because the field equations put a limit on how fast the redness can ooze.

The Michelson-Morley Experiment

Albert Michelson

Albert Michelson

The story of relativity did not begin in 1905.  It started in 1881 with an experiment that yielded very surprising results – results that helped lead Einstein to his theory. The experiment was inspired by a proposal made by James Maxwell to determine the earth’s motion through the ether (which was still believed in at the time) by measuring the speed of light in two directions: one parallel to the earth’s motion and the other perpendicular to that motion. By comparing these two measurements, one should be able to calculate the speed of the earth as it passes through the ether. However the measurement accuracy that would be needed (one part in 200 million) was well beyond the capability of the time, so Maxwell concluded that the experiment was impossible. It took a young American physicist to make it possible, and the result that he found caused a revolution in physics unlike any seen before.

Albert Michelson came to the United States at the age of two, the son of Jewish-German parents. After serving in the US Navy (which he rejoined at the age of 62 to serve in World War I) he pursued a career in physics. In 1881, while studying in Europe, he came across Maxwell’s “challenge” and conceived the idea of the interferometer – an instrument that can measure exceedingly small distances by observing optical interference patterns. Using this sensitive instrument, Michelson was able to perform Maxwell’s experiment.

michelson morley interferometer

The central part of the apparatus is a thinly-silvered mirror that splits a light beam into two parts, with one beam traveling through the mirror and the other reflected upward. The two beams are then reflected back to the central mirror, which sends them to a detector. The light paths are equal in length so that if the apparatus is stationary the light beams would take equal times to reach the detector. However if the apparatus is moving, the beam traveling in the direction of motion would have to cover a greater distance because the mirrors and detector move during the time of travel. The transverse beam would also be affected by motion, but not as much. (You can either take my word for this or work it out with some high school algebra.) The resulting difference in travel times would put the beams “out of phase” and would create an interference pattern when they combine at the detector.

Edward Morley

Edward Morley

When the experiment was performed, much to Michelson’s surprise there was no difference between the two directions! The two light beams took the same time to reach the detector despite the extra distance created by the earth’s motion. More accurate experiments were performed later in collaboration with Edward Morley, using more mirrors to extend the path lengths. This improvement in accuracy turned out to be critical, as Michelson had made an error in his first measurement that was pointed out by Hendrik Lorentz. The experiment, now called the Michelson-Morley (M-M) experiment, was repeated many times – at different times of day (as the earth’s surface moves in different directions because of its rotation) and at different seasons of the year (when the earth moves in different directions as it orbits the sun). The answer remained the same: The two light beams took equal times to traverse their paths, regardless of the earth’s motion.

That the speed of light should be independent of motion was most surprising… It makes no sense for a light beam – or anything, for that matter – to travel at the same speed regardless of the motion of the observer. Suppose, for example, that you are observing a very fast train from another train. The apparent speed of the fast train would clearly depend on its direction relative to yours.  If the other train is moving in the opposite direction, it would go whooshing by, but if it is moving in the same direction as you, it would pass very slowly. Yet Michelson, a passenger on a train called earth, found that another train called light always moves at the same speed no matter which way it is moving relative to the earth.

If the M-M experiment had been performed only once, there would have been no problem. We could have simply said this is the frame of reference in which the laws of physics hold, in which Maxwell’s equations apply and light travels with velocity c. But the experiment was repeated with the earth moving in different, and even opposite, directions and the result was always the same.  It is not possible for light to travel with the same velocity in all of these frames of reference unless “something funny” is going on.

The “something funny” turned out to be even more surprising than the M-M result itself.  In a nutshell, objects contract when they move! More specifically, they contract in the direction of motion. Think about it. If the path length of Michelson’s apparatus in the forward direction contracted by the same amount as the extra distance the light beam would have to travel because of motion, the two effects would cancel out. In fact, this is the only way that Michelson’s null result could be explained.

Five Unexplained Mysteries Not Explained by Quantum Field Theory

Despite the many successes of Quantum Field Theory, there are five unexplained mysteries or “gaps” that may someday be filled: 

  • Renormalization is necessary because Quantum Field Theory does not describe how an electron (or other charged quantum) is affected by its self-generated EM field.
  • Field collapse is of two types: spatial collapse, when a spread-out quantum suddenly is absorbed or becomes localized, and internal collapse, when the spin or other internal property of a quantum suddenly changes. Collapse can also occur with two or more entangled quanta. Quantum Field Theory does not describe how and when this occurs, although it can predict probabilities.
  • Whys and wherefores. Quantum Field Theory does not provide an explanation for why the masses and interaction strengths of the various fields are what they are.
  • Dark matter and dark energy are believed to exist in outer space because of astronomical evidence. They also are not explained by the known fields of Quantum Field Theory.
  • Consciousness is something that happens behind our very noses, but is not explained by Quantum Field Theory.

…How dare physicists talk about “theories of everything” when they can’t explain what goes on behind their very noses! But please understand, by consciousness I don’t mean simple information processing, such as can be done by any computer. I mean the sense of awareness, the sensations, the feelings that human and other minds experience every day – from the color red to the beauty of a Mozart sonata or the pain of a toothache. Such sensations are known as qualia. Most physicists don’t want to be bothered with the question, and it is left to philosophers like Charlie Chaplin to worry about it:

Charlie Chaplin

Billions of years it’s taken to evolve human consciousness… The miracle of all existence… More important than anything in the whole universe. What can the stars do? Nothing but sit on their axis! And the sun, shoot­ing flames 280,000 miles high. So what? Wasting all its natural resources. Can the sun think? Is it conscious? – C. Chaplin (film “Limelight”)

I see consciousness as a more urgent problem than the question of why the field constants have the values they do, and I would trade a hundred field collapses for an explanation of why we see colors. Among those physicists who are willing to consider the problem, most believe that consciousness results from the complexity of the brain – that our brains do nothing more than an extremely complex computer or robot could do. (A physicist has been defined as “the atom’s way of thinking about atoms.”) This is known as the Artificial Intelligence (AI) explanation.  However there are a few physicists who believe that the phenomenon of consciousness goes beyond our present knowledge:

steven weinberg

Of all the areas of experience that we try to link to the principles of physics by arrows of explanation, it is consciousness that presents us with the greatest difficulty. We know about our own conscious thoughts directly, without the intervention of the senses, so how can consciousness ever be brought into the ambit of physics and chemistry? The physicist Brian Pippard… has put it thus: “What is surely impossible is that a theoretical physicist, given unlimited computing power, should deduce from the laws of physics that a certain complex structure is aware of its own existence.”  I have to confess that I find this issue terribly difficult. – S. Weinberg

To me it is perfectly obvious that consciousness consists of more than electric or electro-chemical signals, as in a computer or robot. Why do I believe this? For the same reason I believe that it is impossible to make a television set out of wood. If I took the most skilled carpenters in the world, gave them an unlimited supply of wood and said, “Take this wood and make a television set, but don’t use anything except wood”, I know they couldn’t do it. Wood doesn’t have within itself the capability to do the things that a TV set does. Similarly, electrical signals and computer memories don’t have it within themselves the capability to experience the color blue or the sensation of pain. We can’t even define these sensations, much less know how to create them from computer parts.

Some scientists justify their belief in the AI explanation by asking “what else? If it’s not electro-chemical signals (which we understand), then what else is there?” My answer is, I don’t know, but that doesn’t mean there isn’t something else going on. If you the reader have learned nothing else from this book, you have learned that the entire history of physics involved the recognition that there is “something else” going on. Why is this so difficult to believe in regard to consciousness?

Will we ever find an explanation?  Ambrose Bierce didn’t think so:

ambrose-bierce

Mind, n. A mysterious form of matter secreted by the brain. Its chief activity consists in the endeavor to ascertain its own nature, the futility of the attempt being due to the fact that it has nothing but itself to know itself with. – A. Bierce (“The Devil’s Dictionary”)

The Foundations of Quantum Field Theory

occams_razoQuantum Field Theory is an axiomatic theory that rests on a few basic assumptions. Everything you have learned so far, from the force of gravity to the spectrum of hydrogen, follows almost inevitably from these three basic principles. (To my knowledge, Julian Schwinger is the only person who has presented Quatum Field Theory in this axiomatic way, at least in the amazing courses he taught at Harvard University in the 1950′s.) 

1. The field principle. The first pillar is the assumption that nature is made of fields. These fields are embedded in what physicists call flat or Euclidean three-dimensional space – the kind of space that you intuitively believe in. Each field consists of a set of physical properties at every point of space, with equations that describe how these properties or field intensities influence each other and change with time. In Quantum Field Theory there are no particles, no round balls, no sharp edges. You should remember, however, that the idea of fields that permeate space is not intuitive. It eluded Newton, who could not accept action-at-a-distance. It wasn’t until 1845 that Faraday, inspired by patterns of iron filings, first conceived of fields. The use of colors is my attempt to make the field picture more palatable. 

2. The quantum principle (discretization). The quantum principle is the second pillar, following from Planck’s 1900 proposal that EM fields are made up of discrete pieces. In Quantum field Theory, all physical properties are treated as having discrete values. Even field strengths, whose values are continuous, are regarded as the limit of increasingly finer discrete values.

The principle of discretization was discovered experimentally in 1922 by Otto Stern and Walther Gerlach. Their experiment showed that the angular momentum (or spin) of the electron in a given direction can have only two values: + ½ or – ½ Planck units. 

The principle of discretization leads to another important difference between quantum and classical fields: the principle of superposition. Because the angular momentum along a certain axis can only have discrete values, this means that atoms whose angular momentum has been determined along a different axis are in a superposition of states defined by the axis of the magnet used by Stern and Gerlach. This same superposition principle applies to quantum fields: 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). It is discretization and superposition that led to Hilbert algebra as the mathematical language of QFT.

3. The relativity principle. There is one more fundamental assumption – that the field equations must be the same for all uniformly-moving observer. This is known as the Principle of Relativity, famously enunciated by Einstein in 1905 (see Appendix A). Relativistic invariance is built into QFT as the third pillar. QFT is the only theory that combines the relativity and quantum principles.

Occam’s Razor. I’m tempted to add another principle, but it’s really more of a wish than a rule. I’m referring to Occam’s razor, which states in essence, “All things being equal, the simplest explanation is best.” Einstein put it somewhat differently: “A physical theory should be as simple as possible, but no simpler.” The last phrase is important because, as Schwinger said, “nature does not always select what we, in our ignorance, would judge to be the most symmetrical and harmonious possibility” (S1970, p. 393). If the theory were as simple as possible, there would be just one field (or perhaps none!), and the world would be very uninteresting – not to mention uninhabitable. I think it can be said that the equations of Quantum Field theory are indeed about as simple as possible, but no simpler. 

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. – F. Wilczek (W2008, p. 86)

Discovery of Electron Spin

Electron SpinWolfgang Pauli was born in Vienna in the same year that Max Planck introduced quantization. He was five when Einstein published his theory of relativity. At the age of 19, while a student at the University of Munich, he was asked to write an encyclopedia article on Einstein’s theory. The article was so brilliant that when Einstein read it he commented that perhaps Pauli knew more about relativity than he himself did. In 1925, five years before postulating the neutrino, Pauli introduced his Exclusion Principle. He showed that the various atomic spectra would make sense if the electron states in an atom are described by four quantum numbers and if each of these states is occupied by only one electron. In other words, once a given state is occupied, all other electrons are excluded from that state. Pauli realized that one of the numbers must represent energy, which is related to the distance from the nucleus (if we regard the states as orbits), while two other numbers represent angular momentum, which has to do with the shape and orientation of the orbit. However Pauli could find no physical significance for the fourth quantum number, which was needed empirically. The significance was found that same year by two Dutch physics students.

George Uhlenbeck and Samuel Goudsmit were studying certain details of spectral lines known as the anomalous Zeeman effect. This eventually led them to the realization that Pauli’s fourth quantum number must relate to electron spin.  Here is the story in Goudsmit’s delightful and self-effacing words – a story that conveys the groping and uncertainty that exist in the struggle to understand nature, as contrasted with the logic and certainty that are imposed after the battle is won.

The Pauli principle was published early in 1925… if I had been a good physi­cist, then I would have noticed already in May 1925 that this implied that the electron possessed spin. But I was not a good physicist and thus I did not realize this… Then Uhlenbeck appears on the scene… he asked all those questions I had never asked… When the day came that I had to tell Uhlenbeck about the Pauli principle – of course using my own quantum numbers – then he said to me: “But don’t you see what this implies? It means that there is a fourth degree of freedom for the electron. It means that the electron has a spin, that it rotates”… I asked him: “What is a degree of freedom?” In any case, when he made his remark, it was luck that I knew all these things about the spectra, and I said: “That fits precisely in our hydrogen scheme which we wrote about four weeks ago. If one now allows the electron to be magnetic with the appropriate magnetic moment, then one can understand all those com­plicated Zeeman-effects. – S. Goudsmit

And so was introduced the idea that the electron spins on its axis (still thinking of the electron as a particle) and that this spin has a value of ½, as contrasted with the photon’s spin of 1.

spin-quantum-number

The next step was to see if this idea is consistent with experiment. During a course at Harvard University, Prof. Wendell Furry gave the following account of how this happened (as best I recall):

After Uhlenbeck and Goudsmit had the idea that electron spin might explain the anomalous spectroscopic results, there remained the crucial task of determining if the effect is in the right direction. This involved the kind of calculation that all physics students have to suffer through in which polarity, direction of spin, direction of magnetic field, the “right-hand rule”, etc., get all confused and make the head spin (no pun intended). In other words, there are many opportunities to go wrong, and many do. Well, the story goes, each man did the calculation and when they compared notes they found they had opposite results. One of them had obviously made a mistake, so they went back to check their calculations. As it happened, each found an error, so they were still in disagreement. At this point they went to their mentor, Paul Ehrenfest, who happened to have a distinguished visitor named Albert Einstein. It was decided that the four of them would do the calculation independently (remember, we are talking about elementary physics here). When they got together the result was 2-2. They finally broke the deadlock by counting Einstein’s vote twice. – W. Furry (reconstructed)

I believe that this story was a joke, making fun of the difficulty physicists have in keeping track of the proper sign. (It is said that the difference between a good and a bad physicist is that the good one makes an even number of errors, so the final sign is correct.) It also pokes fun at the “papal” authority of Ein­stein, although Uhlenbeck did say that Einstein visited Leiden in 1925 and “gave us the essential hint” to complete the calculation.

Electroweak Unification

Since the [weak] field must have spin 1, you will not be surprised to learn that it wound up in the same family as the EM field, the only other field with spin 1. But once again, working out the details wasn’t easy, and once again it was Schwinger who made the first step, in the same paper where Julian Schwingerhe introduced the V and A equation. Using the lepton family (electron, muon and neutrino) as a model, Schwinger suggested that the two charged weak fields (which he named Z+ and Z-) be joined with the neu­tral EM field (which he renamed ZO) to make a family of three fields with spin 1. Schwinger thus was the first person to suggest what is now called electroweak unification.

From the general suggestions of a family of bosons that is the analog of the leptons, and the identification of its neutral member as the photon, we have been led to a dynamics of a charged, unit-spin Z-particle field that is interpreted as the invisible instrument of the whole class of weak inter­actions. – J. Schwinger

In postulating only two charged weak fields, Schwinger made the same mistake that Yukawa had made about the strong field. It was Schwinger’s student, Sheldon Glashow, who added a neutral weak field. Ironically, Schwinger’s Z notation survived for the neutral field that he did not introduce, while the ones he did introduce were later renamed W.

As Schwinger’s doctoral student, Sheldon Glashow was given the task of developing Schwinger’s idea that the weak field was part of a family of three fields with spin 1 (known as vector bosons).

Julian was convinced of the existence of an ‘intermediate vector boson’ and of a fundamental connection between weak interactions and electromag­netism… My task was not precisely delineated. It was to seek and perhaps find such a relation, and to explore its observable consequences… In those days of yore, our understanding of the microworld was expanding at breakneck speed. A once theoretically ‘dictated’ and experimentally ‘established’ parity-conserving model of the weak force was bit by bit giving way to the correct parity-violating V-A picture… He convinced himself (and me!) that a triplet of vector bosons … could possibly offer a plausible, elegant, and unified explanation of all EM and weak phenomena. – S. Glashow

Sheldon GlashowAfter finishing his thesis, Glashow continued his “assignment” at the Bohr Institute in Copenhagen. It was there that he finally realized that if weak interactions violate parity conservation while EM interactions do not, they cannot be as closely related as Schwinger thought. This led him to add a neutral weak field that he called Zo, following Schwinger’s Z-notation, while moving the photon to a more “cousinly” relationship. “It took me over a year to see this, since I no longer had direct access to Julian,” he said later. His article was published in 1961.

You might think that this would have ended the matter, but there still remained a problem. The mass of these fields had to be very large to explain the feebleness of the weak interactions (as indicated by the long half-lives for beta decay), and there was no explanation for such a large mass.

It was Steven Weinberg and Abdus Salam (1926-1996) who independently came up with a way to explain the large mass in 1967 and 1968. They did this by invoking what is known as the Higgs mechanism (first suggested by Schwinger in the same paper where he introduced the V and A equation). In the process Weinberg changed Schwinger’s Z notation for the charged weak fields to W (for weak – or possibly Weinberg?), but retained Z for the neutral field, resulting in the present hybrid notation. For their achievements, Glashow, Weinberg and Salam shared the 1979 Nobel Prize, while Schwinger’s contribution was, as usual, largely forgotten.

Just as with Pauli’s neutrino (“I have postulated a particle that cannot be detected”), it was clear that detecting the weak field quantum would pose a serious challenge.

The direct identification of this hypothetical particle will not be easy. Its linear couplings are neither so strong that it would be produced copiously, nor are they so weak that an appreciable life­time would be anticipated – J. Schwinger

It wasn’t until 1983 that evidence for the weak field quantum was obtained at the giant CERN accelerator in Geneva, Switzerland. In fact, all three quanta were detected: Schwinger’s charged fields and the neutral particle that Glashow introduced. The masses of the new field turned out to be over 500 times greater than that of the strong field, making it the heaviest known quantum field – and its range therefore the shortest. For this achievement, Carlos Rubbia and Simon van der Meer were awarded the 1984 Nobel Prize in physics.

Posted By: Rodney Brooks

Parity Violation

Parity conservation is the physicist’s way of saying that nature’s laws are left-right symmetric – that there is no preference for left or right. This statement is usually illustrated by the mirror test. Imagine that you are looking at some process in a mirror. If nature is left-right symmetric, then whatever you see in the mirror can also happen in real life. This law had been unquestioned for centuries, but doubts began to arise at the 1956 Rochester Conference on High-Energy Physics.

Parity Violation

I was sharing a room with a guy named Martin Block, an experimenter. And one evening he said to me, ‘Why are you guys so insistent on this parity rule?’ I thought a minute and said, ‘It would mean that nature’s laws are different for the right hand and the left hand’. The next day at the meeting, Oppenheimer said, ‘We need to hear some new, wilder ideas about this problem.’ So I got up and said, ‘I’m asking this question for Martin Block: What would be the consequences if the parity rule was wrong?’… Lee, of Lee and Yang, answered something compli­cated and as usual I didn’t understand very well. – R. Feynman

T.D. Lee at Columbia University and C.N. Yang at the Princeton Institute for Advanced Studies were the first to point out that there is no theoretical or experimental basis for the belief in left-right symmetry. They also sug­gested an experiment to test the symmetry. The experiment is not hard to under­stand; all you have to know is that nucleons, like photons, have spin.  This spin causes the nucleon to become a tiny magnet in the same way that spinning electrons create the magnetism in ordinary magnets.  It follows that if a nucleon is placed in an external magnetic field, it will tend to align itself along the field, just as a compass needle aligns itself along the earth’s magnetic field, except that the nuclear alignment force is much weaker. Yang and Lee’s idea was to study a radioactive substance that emits beta rays and see if the number of beta rays emitted in a given direction remains the same when the nuclear spins reverse their direction.

Lee and Yang

Lee and Yang’s proposed experiment was carried out at Columbia University by a team under the direction of another Chinese-American, Chien Shiung Wu, using cobalt-60 as the beta-emitter. The sample was cooled almost to absolute zero to enhance the alignment and the nuclear spins were aligned with an external magnetic field. The number of beta rays emitted upward was then counted, the mag­netic field was reversed to reverse the spin alignment and the radiation counted again. If parity is conserved, the two counts should be the same.

Get your bets in! Needless to say, interest was high in Wu’s experiment. In fact the physics community began to resemble a pari-mutuel window at a race track. Yang and Abraham Pais each bet a dollar that the result would be left-right symmetric. Wolfgang Pauli went further, saying “I am ready to bet a very large sum that the experiments will give symmetric results”, and Feynman was willing to lay 50-to-1 odds on symmetry. (Later he said he was proud that he offered only 50-to-1.) Schwinger refused even to bet, saying “I could not accept that nature could be so mischievous as to destroy one of the symmetries”.

And the winner is… To everyone’s surprise, the number of beta rays emitted upward did change, depending on the direction of spin, thereby violating the mirror test. Nature turned out to be not left-right symmetric, at least when it comes to beta decay. And so everyone lost their bet but Lee and Yang won the 1957 Nobel Prize in physics. To the disappointment of many, Dr. Wu was not included in the award.

Posted By: Rodney Brooks

The Weak Field

FermiIt didn’t take long after Pauli postulated his particle before someone came up with a theory, or at least an equation, to describe the process in which it was emitted. That someone was Enrico Fermi, the same man who gave the neutrino its name, and he did it four years later. Just as a photon is emitted when an atomic electron changes its energy state, so Fermi’s equation showed how a neutron can change its energy state to become a less massive proton while emitting an electron and a neutrino. Now there are several ways this equation could be constructed and, as it happened, Fermi chose the wrong one, but that didn’t become apparent until 20 years later. The more immediate problem was that his equation lacked a field.

The first person who tried to fill this gap was Yukawa. In the paper that contained the strong spin-0 field equations, he suggested that this same field could also explain the Fermi equation. This didn’t work because he had the wrong spin, but he was right about two things: the field responsible for beta decay must have mass (to give it a short range) and charge (so that it can convert a neutron into a proton).  It took the son of a Swedish rabbi to get the spin right.

Oskar Klein (1894-1977). Oskar Klein was an under-appreciated Swedish physicist who is not even listed among the 1500 scientists in “Asimov’s Biographical Encyclopedia of Science and Technology” (A1982). Klein was the first to realize that the field needed to explain beta decay must have spin 1, like the photon,  not 0 as Yukawa thought. (The rea­son for this is beyond our scope.) Klein presented his theory at the 1938 Warsaw Conference, but his contribution was largely over­looked or ignored until it was revived (or rediscovered) by Schwinger in 1957.

Oskar KleinColor it brown. We now need a color to help us visualize the weak field. I’ve run out of cool colors (green, blue, purple) for force fields, so I will choose brown. Brown is rather colorless and thus appropriate for a field that is so weak. Since the weak field interacts with all matter, you should picture a faint brown halo around every nucleon, electron, neutrino, etc. The halo is even smaller and tighter than the “purple” halo around nucleons because the weak field has an even shorter range, its mass being larger by a factor of 500. (Therefore there will be no illustrations of this “brown” field.)

How fields cause decay. The idea that a field can cause a particle to decay, i.e., transform itself into other particles, was a new one. The process consists of two phases.  The first phase is similar to the way an electron emits a photon while dropping to a lower energy state in an atom (i.e., moving closer to the nucleus), with the lost energy going into the photon. In the same way, the field equations for the weak force show how a neutron can change to a lower energy state (i.e., become a proton) while emitting a “brown” quantum of the weak field. However the mass of the weak field quantum is so large that there is not enough energy to create a fully independent quantum. Instead what is created is a kind of incipient quantum that doesn’t have enough energy to fly off and live an inde­pendent life of its own. We might call it a fledgling quantum – intermediate between attached and separate fields. (Particle people call it a virtual particle.)

However there is enough energy in the incipient quantum to create an electron and a neutrino. This is possible because the weak field equation contains interaction terms with both nucleon and lepton fields. Because the weak field has charge, the incipient quantum can carry away the negative charge when the neutron changes into a proton. Thus beta decay occurs when a neutron changes into a proton and in the process emits an incipient “brown” weak field quantum which transforms into an electron and a neutrino.

Posted By: Rodney Brooks

Discovery of the Neutrino

PauliIn 1932, physics was still relatively simple. There were two known force fields: gravity and EM (the strong field was yet to appear) and three known atomic particles: the electron, the proton and the neutron. (I am still calling them particles as per conventional usage, but please remember that in QFT they are field quanta.) To add another particle or field to this simple, satisfying picture of nature seemed unthinkable. On the other hand, there was this nagging mystery of beta decay.

Pauli’s postulated particle. A clue to the mystery was that the emitted beta rays have different energies, indicating that some energy must be going else­where. This led Wolfgang Pauli to suggest that if a second particle is emitted from the nucleus at the same time as the electron, it could carry away the unaccounted-for energy.  He dubbed his hypothetical particle the “neutron”, but when that name was usurped by Rutherford two years later, Enrico Fermi renamed Pauli’s particle the neutrino (Italian for “little neutral one”).

“I admit that my expedient may seem rather improbable from the first, because if neutrons [i.e., neutrinos] existed, they would have been discovered long since. Nevertheless, nothing ventured, nothing gained… We should therefore be seriously discussing every path to salvation.” – W. Pauli (quoted in F. Reines’ Nobel lecture, 1995)

Because of its very weak interaction with matter, the neutrino remained elusive. “I have done a terrible thing,” moaned Pauli, “I have postulated a particle that cannot be detected”. Hans Bethe agreed, saying, “there is no practically possible way of observing the neutrino.” (When teased about this after the discovery was made, Bethe said, “Well, you shouldn’t believe everything you read in the papers.”) Nevertheless, despite the lack of experimental evidence, the neutrino was soon accepted on theoretical grounds as an essential part of beta decay.

Confirmation. It would be 26 years before Pauli’s postulated particle (say that three times fast!) was observed in a heroic experiment by Frederick Reines and Clyde Cowan, who took on the project because “everybody said you couldn’t do it”. Because its interaction with matter is so weak, they needed a copious source of neutrinos and being at the Los Alamos Labo­ratory, their first thought was to use a nuclear bomb test. Instead, the experiment was performed at a nuclear power plant on the Savannah River in South Carolina. When Pauli was notified of their success by tele­gram, 26 years after his prediction, he wired back, “Thanks for message. Every­thing comes to him who knows how to wait.” For their achievement, Reines received half of the 1995 Nobel Prize in physics, Cowan having died in 1974. Reines, who had to wait 39 years for the award, could have given Pauli a lesson in waiting!

All in the family. Quantum fields come in families – fields that have the same spin and obey similar equations. In Chapter 4 we learned that the strong field is actually a family of three fields with charges +1, -1, and 0, and that the muon is a “fat sister” of the electron. Thus it should come as no surprise that the neutrino eventually found a place in that same family as a “baby sister” to the electron and muon. These three particles – electron, muon and neutrino – are called leptons (from Greek “leptos”, meaning small) because they are lighter than nucleons – that are called baryons (from the Greek “barys” meaning heavy). Leptons do not interact with the strong field. However it is not the neutrino that we are concerned with here.  This discovery was just one step that finally led to a theory of the force field that causes beta decay.

Posted By: Rodney Brooks  

Discovery of the Strong Force

YukawaHideki Yukawa, son of a geology professor, graduated from Kyoto University in 1929. Five years later, while a resurgent militarism was engulfing Japan that would culminate in the invasion of China in 1937 and the attack on Pearl Harbor in 1941, Yukawa came up with the answer to the nuclear force quandary that had stumped Western scientists for over 20 years. The Yukawa field, as it is sometimes called, then  joined the ranks of the gravitational and EM fields as the third fundamental force field in nature.

Starting from the analogy with Maxwell’s equations, Yukawa developed a field equation that contains a new term that changes the force from a slowly-varying one, like EM and gravity, to one that falls off rapidly – in fact, exponentially. The new term contains a constant that he called λ (lambda), and by choosing λ properly, Yukawa was able to make the theoretical range of the strong force match the experimentally-determined value. Yukawa thereby did what Maxwell had done for EM forces. He started with a force that was understood less well than EM forces, devised a mathematical expression for it, and deduced the field equations that would describe the force. But the best was yet to come.

Just as EM radiation is emitted in discrete quanta called photons, so Yukawa realized that his strong field could be emitted as unattached quanta. And just as photons are described by Maxwell’s equations, so the behavior and propagation of these quanta would be described by the field equation he had derived from the nuclear force. This is where Yukawa came up with his second surprise…

A field with mass. You will recall that mass or inertia is the tendency of an object to resist a change in its motion, or of a field to resist changes in its evolution. Yukawa realized that the λ term he added to give the strong field a short range would also affect the propagation of the quanta, causing resistance to changes in field strength. Since photons have no mass, they travel at the speed of light. Yukawa’s quanta, however, would propagate through space more slowly than the photon – in fact, like a particle with mass. Thus, because of the mass term, a quantum of the strong field behaves even more like a particle than does the photon.

When Yukawa calculated the effective mass of the field quanta from his experimentally-determined λ, he got a value about 200 times the mass of the electron. Because this is intermediate between the masses of the electron and the proton, the quantum was called the mesotron (from meso = intermediate), later shortened to meson.

A field with charge. Mass was not the only surprise that Yukawa came up with. He realized that if his new field exerts a binding force between a proton, which is positively charged, and a neutron, which has no electric charge, then it must itself carry an electric charge. In fact, he showed that there must be two charged fields – one positive and one negative. Later a third meson was found that carries no charge, completing the Yukawa family of three fields. Up to this point, fields were properties of space whose only physical manifestation is that they exert a force. Now physicists had to cope with a field that has both mass and charge – properties previously associated only with particles.

A field without spin. Even though the strong field has both mass and charge, in another respect it is simpler than the EM field.  You recall that quantum fields have a property called spin that is related to the internal complexity. You also may recall that because the EM field has both electrical and magnetic components that can point in various directions its spin is 1. Well the strong field does not have the same com­plexity; it consists of a single attractive force and its spin is zero. Now I can hear some of you screaming, “Wait a minute!  The gravitational field also consists of a single attractive force, and yet you said its internal complexity is great and its spin is 2.” This is true. For reasons that are beyond the scope of this book, Einstein’s gravitational field is more complex than any other field. I must ask you to take it on faith that the strong field is simpler than the gravitational field and that its spin is 0.

Posted By: Rodney Brooks