* The development of integrated theories of quantum field physics has led to a desire to fully integrate all the four forces. This effort has led to various models of unified field theories, such as "string theories" and "loop quantum gravity", which have so far not established themselves, and some wonder if it's even worth the bother.
* One of the great achievements of 19th century physics was James Clerk Maxwell's theory of electromagnetism, which described electricity and magnetism as simply different manifestations of the same basic force, electromagnetism.
The 20th century identified a total of four forces: electromagnetism, the strong force, the weak force, and the gravitational force. In that century, quantum physicists managed to come up with acceptable theories for electromagnetism (QED), the strong force (QCD), and the weak force (the electroweak model, which also incorporates QED). This set of theories is known as the "Standard Model".
The Standard Model is a significant achievement, but it leaves more than a little to be desired. It is clearly complicated, and it also features 18 "adjustable parameters" -- essentially, constants that have to be plugged in to get the model to agree with reality. Even Steven Weinberg once called it "repulsive". Dick Feynman called the Standard Model "three theories", saying the theories were "linked because they seem to have similar characteristics" and asked: "Where does it all go together?"
Nobody thinks the standard model is the last word, or even all that close to the last word. The challenges, though not the solutions, are obvious. Electroweak theory has managed to consolidate electromagnetism and the weak force. The next step is to properly integrate the strong force as well. Schemes that propose to do so are known as "grand unified theories (GUT)".
There is a general belief that at the high energies filling the Universe before the separation of the electromagnetic and weak forces, the electromagnetic, weak, and strong forces all acted identically, with the symmetry breaking apart as energies decreased, but nobody has yet figured out the details. One of the hopes for a workable GUT is that it will give some clue as to why the particles are arranged as they are, in three generations of leptons and quarks.
Group theory, having proven so handy for particle physics so far, was an obvious avenue of investigation for physicists working on GUTs. At first, work focused on a group named SU(5) that encompassed the SU(3) x SU(2) x U(1) architecture of the standard model, but the results didn't match observed measurements. Work moved on to a still larger group, SO(10). SO(10) was found to have all sorts of nice properties, for example accounting for why protons and electrons have precisely equal but opposite electric charges, but it had a feature that physicists originally found distressing: it predicted the proton would decay, if over a very long period of time, disintegrating into an electron and pion+. Sakharov had made the same suggestion in the 1960s; proton decay would prove to be a common feature of GUTs, suggesting there might be something to Sakharov's idea.
* The next step beyond GUTs is the consolidation of all four forces, including gravity, or what physicists call a "theory of everything (TOE)" -- of course, making a GUT a "theory of almost everything". Physicists have also been working on TOEs for a long time -- in fact, much of Einstein's later life was devoted to this end, without much useful result -- and it hasn't been easy, either.
The real problem is the lack of a satisfactory quantum theory of gravity. It is taken very much as a given that gravity is mediated by a force carrier named the "graviton", which is a massless spin-2 boson. However, since the graviton only responds to the gravitational force, which is so very weak, gravitons have never been even implicitly observed in experiments. Worse, quantum gravity theories are not consistent with Einstein's theory of General Relativity, which is currently regarded more or less as "law" as far as gravity is concerned. Quantum mechanics as it stands is flatly incompatible with General Relativity.
One approach that has received much attention is an extension of the systems of symmetries that underlie the standard model, of course known as "supersymmetry (SUSY)". The symmetries that exist in the standard model show that, for example, for every particle there is an associated antiparticle. SUSY takes this notion one big step farther, proposing that for every particle there is a "supersymmetric" partner. Particles that are fermions, such as the electron, will have a supersymmetric partner that is a boson, in this case called a "selecton"; quarks will similarly be paired with "squarks".
Of course, particles that are bosons, such as the photon, will have a supersymmetric partner that is a fermion, in this case called a "photino"; gluons will be similarly paired with "gluinos". At least two Higgs fields are required, with a total of five flavors of Higgs bosons. However, nobody has found any supersymmetric particles yet. Advocates of SUSY believe such particles are too massive to be created in contemporary particle accelerators -- if they even exist. Some SUSY advocates have got tired of waiting, and moved on.
BACK_TO_TOP* There is a more ambitious approach to understanding the elementary particle zoo known as "string theory". The field traced its origins, somewhat indirectly, back to 1919, when a mathematician named Theodor Kaluza (1885:1954) at the University of Konigsberg began to tinker with Einstein's theory of general relativity. General relativity is based on the concept that the three dimensions of space are intimately related to time, forming a four-dimensional "spacetime". Kaluza was curious as to how Einstein's equations might look if a fifth dimension were thrown in.
Somewhat surprisingly, Kaluza's modified equations could be seen to encompass both Einstein's equations of general relativity and James Clerk Maxwell's classic equations for electromagnetism. The fifth dimension could "ripple" and this ripple turned out to model the electromagnetic field. This was more in the nature of an interesting curiosity than a grand revelation, in particular because Kaluza had no idea of what his fifth dimension really signified.
In 1926, the Swedish mathematician Oskar Klein (1894:1977) suggested that Kaluza's fifth dimension was actually another spatial dimension, one that couldn't be perceived because it was on a subatomic scale. Klein pointed out that a tube seen from a distance might seem to be a two-dimensional line; the fact that any point on the line really amounted to a cross-section of the tube, a simple circle, couldn't be noticed from a distance. The whole matter was somewhat academic, and this was the time of the distracting emergence of the new quantum physics, so the "Kaluza-Klein" theory was shelved as a footnote in the physics literature and more or less forgotten for decades.
In the late 1960s, an Italian physicist named Gabriele Veneziano (born 1942) was looking for a new approach to the description of the strong force, and came across a set of equations created by the 19th-century Swiss mathematician Leonard Euler that seemed to be remarkably convenient for describing particle interactions. The only problem was that rationalizing the equations for such an application meant invoking 26 spatial dimensions, which seemed excessive. Veneziano's work might have ended up in the same pile of footnotes as the Kaluza-Klein theory, but the Japanese-American physicist Nambu Yoichiro (1921:2015), then at the University of Chicago, noticed that the equations described by Veneziano seemed to match the mathematics of vibrating strings. Nambu suggested that the various types of hadrons could be explained as being different resonant modes of a stringlike entity about the size of a proton.
The physics community found Nambu's "string theory" exciting and there followed a rash of papers on string theory. There was one serious limitation of Nambu's theory in that it only covered bosons -- in effect, it was a "mesons only" theory -- but in 1971 Pierre Ramond of Yale (born 1943) modified it to cover fermions as well. John H. Schwartz (born 1941) of Princeton and Andre Neveu (born 1946) in France were covering similar ground, with the end result being the "Ramond-Neveu-Schwartz" theory, which dealt with all the hadrons, and also reduced the embarrassing 26 dimensions to a more manageable if still cumbersome ten dimensions -- nine in space, one in time.
* However, that was about as far as it went for the moment. Particle physics was in its own era of great discoveries, such as the electroweak force and the quark model, and so string theory, like the Kaluza-Klein theory before it, was sidelined. String theory was a sideshow at best, hobbled by its postulate of ten dimensions. Worse, the various string theories gave inconsistent results. The flow of papers all but ceased.
John Schwartz, who moved to Caltech in 1972, worked with French physicist Joel Scherk (1946:1979) to try to keep the string flame burning -- though it seemed to them at the time they were just tidying up what they had done, so it could be put on the shelf if anyone wanted to investigate the matter again in a later generation. However, in the course of their efforts, the two physicists came to an interesting revelation: string theory could encompass the graviton, the mysterious undiscovered messenger particle of gravity, and so string theory stood a chance of uniting gravity with the other three forces, the grand unification that physicists had been after for years.
There was a catch, as it would turn out a big one: adding the graviton required adjusting the scale of the strings downward by 20 orders of magnitude, from about 10^-13 centimeter, the scale of the proton, to 10^-33 centimeter. This minuscule measure is called the "Planck length", which in a sense defined by the uncertainty principle is effectively the minimum possible meaningful length that anything could have. Incidentally, the concept of the Planck length also leads to the related concept of the "Planck mass", which corresponds to a particle with a wavelength given by the Planck length, which by the de Broglie relation gives a value of 10^-5 grams. This sounds like a large value by particle standards, and it is, corresponding to an incredible density in the small space defined by the Planck length. By the Einstein mass-energy relationship, the Planck mass corresponds to about 10^19 GeV -- an energy whose scale can be appreciated when it is remembered that the most powerful particle accelerators on Earth achieve energies of not much more than 10^4 GeV.
In any case, Schwartz and Scherk published papers on their ideas in the mid-1970s that attracted little attention. In 1979, however, Schwartz was on a visit to CERN and ran into a British physicist, Michael B. Green (born 1946) of the University of London, who was a fellow string-theory diehard. They chatted a bit and parted company with a general idea that they might get together later. When they met again in 1980 at a physics meeting at Aspen Center for Physics in Colorado -- a summer retreat for the physics community -- they began to work together, coming up with a series of "superstring" theories that merged string theory with SUSY. Schwartz and Green published a series of papers; they were not surprised when the papers were generally ignored.
However, on meeting again in Aspen in 1984, the two physicists found that the problems with their earlier work seemed to dissipate. They published a refined paper, thinking it would be ignored, but it was picked up by the highly regarded Edward Witten of Princeton (born 1951), who found the paper exciting as well and enthusiastically promoted their ideas. Suddenly, the physics community got excited about strings. A group of four other Princeton string enthusiasts -- David Gross (born 1941, who would share the Nobel Prize for his work on asymptotic freedom), Jeffrey Harvey (born 1955), Emil Martinec (born 1958), and Ryan Rohm (born 1957), who called themselves the "Princeton String Quartet" -- published a refined model of the Schwartz-Green theory that visualized the strings as closed loops. Their model incorporated elements of Nambu's earlier work and so the quartet called it the "heterotic" theory, the term coming from genetics and more or less meaning "crossbred".
In early 1985, Witten and a few of his colleagues extended the notion of closed strings by suggesting, as in the old Kaluza-Klein theory, that the six additional spatial dimensions required were curled up on such a small scale that they were not noticeable. Two mathematicians, Eugenio Calabi (born 1923) of the University of Pennsylvania and Yau Shing-Tung (born 1949) of the University of California at San Diego, had already considered the possible configurations that such closed strings might take. Witten contacted Yau to see which of these "Calabi-Yau manifolds" might prove useful for heterotic string theory, and Yau came back with literally thousands of possibilities.
* In modern string theory, the configurations of these manifolds determine the modes of vibration of the strings, creating leptons or quarks as observed. The number of possible string configurations may well be infinite, meaning that the number of possible particles is infinite as well. Only a finite number of particles is observed because the rest imply higher and higher energies that are not observed in our cosmic era, much less attainable with our technologies.
The attractions of this theory were obvious to many physicists. One was that it gave a consistent model for all elementary particles; the other was that it reconciled Einstein's theory of General Relativity with quantum physics, a reconciliation that has long evaded physicists.
General relativity claims that gravity is caused by a curvature of spacetime due to the presence of a mass. However, at the Planck length the uncertainty principle claims that spacetime becomes chaotic and unpredictable, becoming a "quantum foam" that makes calculations go mad, introducing infinities that cause results to explode. String theory got around the mad behavior of spacetime below the Planck length because the strings were long relative to the scale of the quantum foam, allowing the foam to be ignored. String theory imposed a minimum level of detail to the Universe that was greater than the scale of the quantum foam.
String theory had become a "big thing" in physics, and not surprisingly it attracted critics. The loudest was Sheldon Glashow, who saw the concept as too theoretical, particularly with its postulate of ten dimensions, and not very closely tied to observations. Glashow was particularly troubled by the fact that the string structures were so incredibly small. If an atom were the size of a galaxy, a string structure would be about the size of a beachball. There was no prospect that any experiment could detect them directly and prove or disprove the theory. Glashow put it: "The theory is safe, permanently safe. Is that a theory of physics, or a philosophy?"
Indeed, string theory quickly began to bog down, with five variations emerging. It wasn't until 1995 that Witten delivered a talk in which he reconciled the competing string theories, showing they were all aspects of a single unifying theory, which he called "M-theory". Witten never insisted on the definition of the "M" in the name, saying that it could be interpreted according to taste as "membrane", "master", "matrix", "mother", or "mystery". Witten also honestly added that some interpreted it as "murky". M-theory did resolve the tangle of five string theories, but to no surprise at the price of increased complexity -- most significantly in adding another spatial dimension, giving a total of eleven dimensions in the scheme.
The additional spatial dimension allowed the strings to be aspects of sheets or "branes" that could span Universes. The strings then became projections of a brane; one string theorist compared the concept to that of a grove of aspen trees, in which the trees share a common root network but appear to be independent above the ground. The branes provided a very direct link between quantum mechanics, which concerns itself with the world of the very tiny, and cosmology, which concerns itself with the Universe as a whole.
String theory seemed to be converging on a solution again, but then in the late 1990s, astronomers measuring the expansion of the Universe determined to everyone's surprise that the rate of expansion was accelerating. It implied that a significant portion of the Universe was bound up in what for lack of a better term was called "dark energy", which provided a repulsive force to drive the galaxies apart. The only way string theorists could figure out how to account for dark energy was to modify their theories to accommodate a boundless range of alternative universes, each with its own form of dark energy, with our particular Universe just happening to fit the description of ours. There was considerable skepticism over this idea, with even some string theorists suggesting it was on the wrong track. In any case, string theories began to diverge from a solution once again, and even enthusiasts can't claim they've honestly proven their case to the skeptics.
* There are a number of different TOEs currently in play. As the string theorists had discovered, one way to get around the conflict between quantum physics and general relativity was to quantize spacetime, ensuring that nasty infinities didn't arise. The string theorists dealt with this problem by creating manifolds in additional spatial dimensions, but another faction simply bit the bullet and simply said that the unified spacetime described by Einstein was quantized.
Not too surprisingly, the level of quantization is very small, on the order of the "Planck volume", which is the Planck length cubed: 10E-33 * 10E-33 * 10E-33 = 10E-99. Notice that this a spacetime quanta, implying not only that space is divided into irreducible small elements, but time then must be as well. The scheme was somewhat confusingly called "loop quantum gravity (LQG)", though the "loops" had little to do with strings, instead simply referring to a calculational approach.
LQG immediately brings up a vision of spacetime being chopped into a matrix of tiny, really tiny Lego blocks, but to no surprise it's not quite that simple. Instead of representing spacetime as made up of a mass of cubes of fundamental spacetime quanta, the LQC model visualizes spacetime as made up of "nodes" connected by "links", a "connect-the-dots" scheme called simply a "graph". The graphs defined by LQG are specifically known as "spin networks" because their properties are related to quantum-mechanical spin. Different types of particles are represented as nodes in the network, with their mediating force particles making up the lines in the network, something like a monstrous Feynman diagram. A succession or "movie" of a spin network going through changes is called a "spin foam".
Analysis of a spin foam shows that it can be used to calculate all four force interactions. LQC does seem to have one of the big problems of string theory in that the Planck volume LQC is based on is so very small, too small to be directly detected. However, LQC advocates say that indirect effects can be calculated and measured. One of the most important is that high-energy gamma-ray photons will have a slightly smaller speed than low-energy light photons. The difference is so slight that it could only be measured from the emissions of objects in the far distant Universe, billions of light-years away, but such a measurement still seems practical. This discrepancy does cause some trouble for Einstein's theory of special relativity, which states that the speed of light is an invariant constant, but work has been done that shows special relativity still works fine if a few tweaks are added.
BACK_TO_TOP* Layfolk find discussion of TOEs hard to get a handle on, for two reasons:
This is not to judge TOEs in one way or another, only to say that TOEs are an argument among physicists, who will discuss the matter among themselves, and come to conclusions among themselves. Layfolk are merely spectators.
This is more or less true for quantum physics in general. It is often said that layfolk cannot understand quantum physics, but not true -- they can understand it perfectly well, at a layfolk's level of useful comprehension. Quantum physics is no more or less than a model to explain observations, and a simplified model is adequate for those who don't do anything that looks like quantum physics for a living. The fact that strange things at the limits of observation is interesting, but not significant to layfolk.
In discussing quantum physics, physicists have a tendency to slip into "greedy reductionism" -- grasping at dubious connections, driven by a tendency to believe their knowledge is more generally applicable than it really is. Physicists have an inclination to "invoke quantum mechanics" in a wide range of fields where it has no very useful insights, most notably in studies of consciousness. Those who study cognition for a living are not, in general, very enthusiastic about the idea that consciousness can only be explained by quantum physics, suggesting it's saying:
In reality, most cognitive researchers would say they do understand consciousness, if not in all details; while again, physicists do understand quantum physics, as a model that conforms to observations and allows predictions of results -- much the same as in other theories of physics. Yes, weird things happen at the quantum level, but we can't see them directly, and nobody but physicists see any reason to worry about them.
Some physicists will even say that quantum indeterminacy solves the "free will problem". As best it can be figured out -- it's not a very clear idea -- if we lived in a predictably deterministic Universe, then everything we did would be predetermined, and we would have no free will.
Okay, that's silly on the face of it. We do live in a deterministic Universe, meaning one that follows regular rules that we call "laws of nature". However, we do not have absolute determinism -- the unlimited ability to predict events -- even in principle. Absolute determinism implies the ability to observe all the particles in the Universe and all their interactions. That would require a measurement apparatus much bigger than the Universe itself, and whose operation would drastically interfere with the normal operations of the Universe long before it was big enough to do the job. The uncertainty principle also applies, to a degree, to the macroscale Universe. Yes, quantum uncertainty does impose an absolute limit to observability, but the "law of large numbers" of elements of the Universe means we don't, in general, even get close to that limit.
In addition, the "free will problem" suffers from a failure to usefully define the term "free will". The courts don't have a problem with the concept of free will, normally referring to it when establishing legal culpability. Bob is culpable if he committed a criminal act of his own free will; he is not culpable if he was coerced into doing it, or was out of his mind for reasons not under his control. Those who object to this definition seem to be implying that people who are out of their minds have free will, but sane people do not.
Finally, the "free will problem" is not really a problem, because nobody loses any sleep over it. They do over personal liberty; people will die for it, they will kill for it. Nobody ever said: "Give me free will, or give me death!" Again, this is not to imply that there is anything wrong with quantum physics -- it may be messy, but it works well enough -- only to say that it is no more or less a matter of concern in the daily lives of the populace than say, once again, football. Indeed, people in general pay a lot more attention to football.
* This document started out in 2006 covering a wider range of topics, including atomic physics, particle physics, and solid-state physics. In 2017, I decided it made more sense in all respects to break the document down into several different documents, retaining core material on quantum physics under the original title, and tracing back to 2006 in the revision history.
* Sources include:
Some materials were obtained from the Microsoft Encarta encyclopedia and the Wikipedia online encyclopedia -- the Wikipedia was particularly handy for figuring out birth and death dates of even relatively obscure scientists -- and various elementary chemistry texts were consulted for the chapter on the electronic structure of atoms.
* Revision history:
v1.0.0 / 01 dec 06 v1.0.1 / 01 sep 07 / General polishing. v1.0.2 / 01 aug 09 / Cleanup of various small matters. v1.1.0 / 01 oct 11 / Cut from 20 chapters to 18. v1.2.0 / 01 sep 13 / Cut out section on deep-underground detectors. v1.2.1 / 01 sep 15 / Added comments on Hume. v2.0.0 / 01 aug 17 / Broke into four documents, cut to 6 chapters. v2.0.0 / 01 aug 17 / Broke into four documents, cut to 6 chapters. v2.0.1 / 01 aug 19 / Review & polish. v3.0.0 / 01 jul 21 / Further reshufflings of documents, 8 chapters. v3.0.1 / 01 jul 21 / Further reshufflings of documents, 8 chapters.BACK_TO_TOP
