An obvious play on the title of the book and the film “The Unbearable Lightness of Being,” this book attempts to explain the concepts of modern physics to “the common man.” Ironically the film has always struck The Slicer as unbearably heavy (and potentially depressing) to watch, whereas this book wasn't too heavy to read. The author’s credentials are beyond dispute, in terms of academic physics, since he was awarded the Nobel Prize in 2004 for his work on Quantum Chromodynamics (QCD). However, that’s no guarantee that he will be talented at explaining esoteric and counter-intuitive concepts in physics to those of us who are not versed in the discipline beyond our school days... and make it interesting to boot. Slicer concludes that Wilczek is largely successful in both of these aims. Early on, Wilczek quotes a tip from one of his mentors: “Very few people get offended when you make them feel clever.” This is a book that makes you feel clever, but not without a bit of effort. Short chapters and simple stories make it much more readable than you might imagine.
The subtitle of the book could have been “Things aren’t always just what they seem” and its sound track could be “Upside down” by Jack Johnson, which contains the same line, along with the themes of exploring nature, rotating things “to find the things they say just can’t be found,” and singing along to nature’s tune.
As Wilczek explains, we are limited by our senses, which were not designed to help us function at a quantum level. We have traditionally separated things by how we perceive them using our senses, eg whether via our eyes (eg light), or by touch (mass). We have concluded (incorrectly) that light and mass are very different, in part because of assumptions arising from how we sense them. This conclusion serves us well in everyday life (despite the fact that it’s wrong), as we interact with the world around us, but it leads to errors in perception of how things really are. He states that our senses operate in the “more peaceful, well-settled districts of reality,” and that much of reality underpinning what we can see and touch is unsettled and unpredictable. We perceive that matter is substantial, weighty and permanent; and that mass is its essence, when this is not actually the case.
In tackling a book like this, and drawing comparisons with other things, Slicer is aware of his limitations, being neither a mathematician nor a physicist. If there are any errors in what follows, they are unintentional, and Slicer would be happy to have them pointed out by experts. He has followed one of Wilczek's own maxims - that it is better to take risks (asking forgiveness later for getting it wrong) than to wait and ask permission for sin. At school Slicer remembers being taught Newton’s 3 laws. What he doesn’t remember being taught was that they were all based on an assumption that was not made explicit – the conservation of mass. Most people today still think of matter as being made of elementary particles – if you get to the fundamental building blocks they can neither be created nor destroyed. When the atom was split, it just showed that the fundamental building blocks are smaller than we had previously imagined. The total mass of matter was still thought to be the sum of (the masses of) the parts. There was a theological assumption that God created fundamental building blocks (once), which we can’t create or modify, although we can move them around a bit and join them together. Finding out that the building blocks are neither “concrete” nor fundamental doesn’t affect how you live your life from day to day, as you move around the “more peaceful districts of reality.”
Amongst other reasons why we now know that the conservation of mass is incorrect are the experiments made possible by high energy particle accelerators, including the forerunners of the Large Hadron Collider at CERN. These devices accelerate subatomic particles to very close to the speed of light and smash them together. Wilczek describes how, after a typical experiment, the mass of particles at the end is 30,000 times(!) the mass of the particles that were put in at the start, because of the relationship/interchangeability of energy and mass predicted by Einstein. There goes the notion that we can’t create mass...
The converse idea of mass being a source of energy is perhaps better known, whether in the nuclear fission of an atomic bomb, or in the fusion which energises the sun and stars. However, it is the energy states of the quarks within protons (within the atoms), rather than the mass of the quarks themselves which contributes the lion’s share of the protons’ mass. The fact that energy and mass are interchangeable seems to Slicer to give added validity to the imagery in Bruce Cockburn’s Lord of the Starfields: “Oh Love that powers the sun keep me burning” (if we think of energy as a relatively intangible, but activating, force whose results can be felt and even measured).
Another error of Newtonian thinking was that gravity, being proportional to mass, was exerted only by bodies with mass, and only on bodies with mass. However, we now know that light (composed of massless photons) is affected by gravity. Hence Einstein’s theory of gravity (general relativity) is more accurate than Newton’s, and explains how black holes entrap light.
Back to the building blocks: The nuclei of atoms consist of one or more protons, often combined with one or more neutrons. However, when we use special tools to “take snapshots” of the interior of a proton, it looks different each time due to quantum mechanical uncertainty eg once it will have 3 quarks; another time under identical conditions, 3 quarks in different positions and a gluon. Also, if we go for finer resolution snapshots, what appeared to be a quark turns out to be a quark and a gluon; what appeared to be a gluon resolves into a quark and an anti-quark. Hence there is an “abundance of co-existing possibilities.” Yet all protons behave the same, as they cycle unpredictably through their internal possibilities. Infinity is a hard “number” to work with in mathematics, hence the value of the term Googol (since adopted and modified to form the name for an internet search engine, presumably to highlight the potential of that tool). A Googol is 10100. That's a difficult number to visualize but represents more atoms than are present in the visible universe... Modern quantum theory suggests googols of googols of possibilities. Fortunately short-term unpredictability at quantum level is perfectly compatible with long-term predictability in terms of atoms and molecules. So chemistry and biology and other large scale science can actually occur in a repeatable and predictable fashion: drugs have reliable effects (and side effects), aeroplanes don’t drop out of the sky (if all the bits are working).
So far so good with the description of “normal” matter – what we’re made of and what we’re used to studying. A real shock was to discover that this matter is only 4% of the total matter in the universe. “Normal” matter (atoms, quarks, electrons) could be seen as an “impurity” in most of what the universe is constructed from! The remaining 96% of mass in the universe seems to arise from a combination of so-called Dark Matter (22%) and Dark Energy (74%), which are, strictly speaking, transparent rather than dark.
The central theme of the book is a description of the journey to find the Holy Grail of modern physics – the unification of forces. In the late 19th Century, the Scotsman James Clerk Maxwell found that electricity and magnetism were not two distinct entities, and that light particles are a vibration of electromagnetic fields. This discovery was made mathematically first, and confirmed subsequently by experiment. Modern physicists understand the physical world to be a product of multiple layered fields. Whilst the strong nuclear force (which holds quarks and gluons at their prescribed distance within protons), the weak interaction (which transforms subatomic particles eg changes one type (flavour) of quark into another), and electromagnetic force all seem distinct in the way that electricity and magnetism once did, physicists believe they are at heart different manifestations of the same fundamental force, and that gravity may also be a manifestation of that fundamental force.
Space is not empty, as it appears to us, but rather is filled with multiple spontaneously fluctuating quantum fields (somewhat analogous to the ethers of old). Particles of matter are understood to be “condensates” of these fields, much like dew condenses apparently out of thin air. Hence space is the primary reality, with matter as a secondary product by condensation. The best understood condensate is quark-anti-quark pairs, which exist as a space-filling mist known as Chiral Symmetry-Breaking condensate (QQ`). QQ` forms because empty space is unstable. “Empty space” is an explosive environment, ready to burst forth with real quark-antiquark “molecules.” If our eyes could see events lasting 10-24 seconds, over a distance of 10-14 cm, “empty” space would look like a lava lamp.
What seems to be a repeated experience, over at least the last century, is that mathematics is a tool that has served physicists (and the rest of us) extremely well. Mathematical equations have been formulated to describe the world, and their findings and predictions have often then been confirmed by experiment. Symmetry is perhaps the central mathematical principle which has been rather successfully used in the pursuit of better human understanding of how the physical world works/is sustained/is. The best equations are symmetrical ie they describe processes to be the same from multiple viewpoints: “distinction without a difference.” Slicer understands this to mean that, if you find the right viewpoint, you may perceive things to be the same which appear to be different from other view points. Hence Slicer thinks that the search for symmetry is the mathematical equivalent of finding the right point of view from which to see things as the same (but would welcome correction from experts if this is a misunderstanding).
Special relativity was a search for symmetry: that the laws of physics should look the same after you boost everything appearing in them by the same constant velocity. In order to achieve this, Einstein had to change Newtonian Theory to allow it to fit with Maxwellian Electromagnetic Theory. Newtonian models envisioned the universe in terms of particles exerting forces on one another across empty space. The inverse square law of Newtonian gravitational theory doesn't fit what is observed across vast distances in space, where the influence of one body on another is instantaneous.
General relativity was Einstein’s subsequent work of extending special relativity to include gravity. It's a field-based theory of gravity, using the concept of curved space-time. Newton’s 2nd law of motion stated that objects move in a straight line unless a force acts upon them; general relativity modifies this to state that they move through the straightest possible paths. When space-time is curved, the straightest possible paths are bent. This bending is a more accurate description of the effect formerly known as gravitational force. (A mathematically-equivalent description is known as metric field, which is further touched on below). Cosmic density affects the curvature of space. Wilczek mentions that it’s only if the overall density lies within narrow range that you would get a “nice slowly evolving universe that is sufficiently user-friendly to be observed.” Slicer understands this to be part of what is commonly known as the Anthropic Principle – that the universe seems finely tuned for intelligent life to emerge. Wilczek concedes that the commonly stated explanation of this is speculative - that we find the universe the way it is (tuned for intelligent life) because if it were any other way we wouldn’t be around to observe it. However, this explanation is known to trouble some physicists, and is the subject of one of Slicer’s favourite books, “The Goldilocks Enigma,” by Paul Davies.
Wilczek quotes St Augustine’s answers to a question that bothered him:
Q. “What was God doing before He created the world?
Answer 1. Preparing Hell for people who ask foolish questions (har har!)
Answer 2. Until the world is created, no past or future exists – there is only the present.”
In modern physics terms, the flow of time commences after the big bang, with the condensation of the metric field. The metric field gives rigidity to space-time and causes gravity. As electromagnetic fields bend trajectories of electrically-charged bodies, in general relativity the metric field bends the trajectories of bodies which have energy and momentum. In QCD, the trajectories of bodies with colour charge are bent by colour gluon fields. Wilczek points out “In all cases the deep structure of the equations is very similar.”
Quantum Chromodynamics (QCD) is the best current understanding of the strong nuclear force. It deals with the characteristic that quarks (which come in "flavours"), and other subatomic particles, have colour charge. (The term colour is used to differentiate the charge from electrical charge rather than to imply anything literal in terms of selective absorption/reflection of given frequencies of light). QCD invokes virtual (ephemeral) particles. Wilczek’s theory of “Asymptotic Freedom” explains how the colour charge of the fundamental particle is amplified by a cloud of virtual particles that it attracts, which themselves arise from spontaneous polarisation of the “ether”. (This is the opposite of screening of electrical charge, where virtual particles dampen, or slow down, the building up of an electrical charge). The cloud is responsible for the strong nuclear force, which takes a little distance to develop but is then kept short-range. Gluons are the equivalent in QCD of photons in Quantum Electrodynamics. Gluons respond to, or both respond to and transform, the colour charge of quarks.
In this book Slicer did, at times, find it difficult to distinguish between what is actual, and what is a metaphor for a mathematical concept. Examples of this include charge (especially weak and strong colour charge, as well as fractional electrical charge and hypercharge), spin/chirality (handedness), grid disturbance, condensate, transformation between fields, and extra dimensions. However, it may be that this isn’t so much a limitation of the author as one of the capacity of language and metaphor to convey what often start out as mathematical concepts, even if they are subsequently confirmed experimentally (or by other means) to be correct. Quarks, their flavours, colour gluons, W & Z bosons, and all 3 types of neutrinos were seen mathematically before being demonstrated physically.
So where do mass and little boys come from? Mass (95% of it anyway) is a consequence of “resolution” of two competing effects:
(a) Disturbance of gluon fields (putting them into a higher energy state) by quark colour charge. The latter is produced by a growing cloud of virtual particles, requiring energy to grow (in order to provide the strong nuclear force), but whose growth is limited in order to limit the energy expenditure.
(b) Complete cancellation of the higher energy state requires very precise superposition of a quark and one of a cancelling colour charge. Heisenberg’s Uncertainty Principle requires that, in order to achieve precise position, the possibility of large momentum has to be permitted. Large momentum requires high energy. Non-cancellation requires high energy, and complete cancellation requires high energy. A variety of stable compromises result where the total energy is not zero. Each of these compromises will have a different amount of non-zero energy, and (by Einstein’s 2nd Law, E=mc2) its own mass. Wilczek highlights that these masses do not arise from the mass of the quarks/gluons – “We get mass without mass.” We can match stable, localized concentrations of energy to protons, neutrons etc; if localized concentrations are present for a while but then dissipate, we’ve found unstable particles e.g. hadrons such as the rho meson & Delta baryon.
However, Slicer wants to know why are the stable energy compromises at these specific levels? In other words, why is the mass of the proton the value that it is?
Wilczek states that protons and neutrons are the mass they are because of the size of the seed charge, which influences how fast the quark colour charge builds, which in turn defines the size of the energy needed to nullify it, or almost nullify it. To Slicer, this seems just to push the question back a step rather than answer it. There is a postulated link between the seed colour charge and the strength of gravity and Wilczek describes that, in order to “prove” this relationship, a step of faith is required that the laws of physics we know extrapolate well beyond where they have been observed experimentally. Wilczek states that science has to step out in faith, and be prepared to be wrong, because we can learn from our mistakes. He quotes a Jesuit credo - although he claims no personal religious faith - that it is better to take risks (asking forgiveness later for getting it wrong) than to wait and ask permission for sin. He goes so far as to say that an unscientific theory “has no sense of sin,” which Slicer takes to mean is blind to its own weaknesses.
Back to the unification of forces: The established explanation of fundamental particles and forces is known as the Standard Model. However it’s a considerable distance from unification in that the three symmetry groupings (strong, weak and electromagnetic forces) are distinct and not transformable into one another. Efforts have been made to find a master symmetry of which these 3 are different facets. SO(10) is a key example of such a master symmetry, and consists of rotations in a ten-dimensional space. This is purely mathematical “space.” The ten dimensions arise from each of 5 colour charges being represented by a different 2-dimensional plane. What is impressive is that quarks and leptons (eg electrons) are included in the unification, and are capable of being transformed into one another. However, gravity remains a real obstacle to unification because (and this may come as a surprise) it’s so weak compared to other forces; and unification requires some way of (or viewpoint for) reaching equivalence of strength between forces. Between elementary particles, gravitational forces are ridiculously small compared to electric or strong forces - the difference in strength between electrical and gravitational force is 1040! The electron is held captive to the atomic nucleus by electrical attraction. If we were able to switch off the electrical attraction and just depend on gravity, how tightly would the electron be held? How big would the radius of the atom be? Answer - 100 times that of the visible universe! Gluons are held by the strong force in the proton in an analogous manner (by deviation of path). Wilczek puts it this way: “Faith in the possibility of unification drives us into a state of denial. We can’t accept that gravity really is feeble, even though it appears that way.”
This particular problem requires a new type of symmetry, known as Supersymmetry, or SUSY to those who know her well. SUSY involves adding motion into new dimensions. However, these are quantum dimensions. When a body moves into a quantum dimension, there is no distance involved: the amount of its spin changes. Because the equations stay the same, despite the “superboost,” SUSY allows us to view seemingly different particles as the same particle moving through the quantum dimensions of superspace. The quantum dimensions can be thought of as new layers to the “ether.” However, these different layers predict the existence of yet more fields (a partner field for every one we know about already) and these fields have associated new predicted particles. Virtual particles associated with these quantum dimensions distort how things appear but, once correction for them is applied, we find convergence of known forces at one point (at high energy and short distance, ~16 log10 mu/GeV). What is more gravity converges at this region as well. However, this does not provide us with a complete theory of gravity (which is what superstring theory aims to do, but has yet to deliver on).
The lightest partner particle that SUSY predicts may account for dark matter. (Another possible candidate for dark matter is the axion - named after a washing powder! – which is a theoretical particle predicted by one way of tidying up a loose end in QCD.)
“Okay,” you might say, “but so what? What difference does this knowledge make to me in terms of how I live my life?” In terms of how you relate to your spouse and kids, or to your work colleagues, probably not a lot right now (unless any of them happen to be physicists!). However, history would suggest that might be just because you’re not very imaginative. In centuries past, thinking that the earth was flat, or the sun revolved around it, didn’t get in the way of everyday living – but don’t we benefit from, and wonder at, the beauty of the solar system now that we are better informed? At the very least, knowing that the earth is (nearly) a sphere gives you confidence when going on a foreign holiday that you’re not going to fall off the edge. Package holidays and air travel were unachievable concepts to “flat-earthers” at the time. Prior to Maxwell unifying the understanding of electricity and magnetism as electromagnetic radiation, who would have foreseen the benefits from understanding X-rays, microwaves, ultraviolet, and radio waves? Around 1930 Dirac’s improved equations for electrons predicted the existence of an oppositely charged particle, the positron, discovered shortly thereafter by Anderson – now used in PET scanning of the brain. Who knows what future benefits and blessings might be delivered on the back of better understanding of the true nature of matter?
Hence Slicer would beg to differ with the fictional physicist in the “Dead Irish Writers” episode of the West Wing (Series 3). The same guy, when asked what practical benefit would accrue for society if he got his wish for funding to build a large particle accelerator, replied “none whatsoever.” Maybe that explains why the LHC was built in Geneva rather than the US (although there are rumours suggesting a different reason)...
Pertinent to high energy particle accelerators, Wilczek says “So it’s quite possible that by investigating the basic laws of physics at ultra-short distances, we’ll solve a major cosmological riddle, and begin to shed some of [our] irksome humility.” Slicer hopes not. Sure, he hopes that we solve a major cosmological riddle, but he feels that should make us more humble. Humble in the context of the vastness of the universe, and the beauty of its construction in terms of mathematics. Would we be tempted to be less humble because we believe that the acquisition of such knowledge would make us like God? – haven't we heard of that temptation somewhere before? Let’s hope that the Large Hadron Collider realizes its potential, but does not become for us a tower of Babel (albeit one below ground), a symbol of arrogance in the face of Googol.
Mention has already been made of the central role of mathematical equations in investigating and explaining the laws of nature. Wilczek quotes Pythagoras’ philosophy that “all things are number.” This related to the mathematical relationship he observed between notes which the human ear perceives as harmonious (eg ratios of lengths of strings, other things being equal). Slicer is fascinated by why mathematics works at all, in describing the laws of nature, never mind seems to work so well and so consistently, in helping us discover new ones. It’s like finding out that the language we have a basic vocabulary in naturally just happens to be the one (of all possible languages and none) that the laws are “written” in, even if we have to learn some fancy grammar as we pursue the language. And as we learn the fancy grammar, our understanding of the universe grows. What’s more, mathematicians and physicists perceive good equations to be beautiful in themselves. Perhaps it’s because, as Keats observed in Ode on a Grecian Urn,
“‘Beauty is truth, truth beauty,’ - that is all
Ye know on earth, and all ye need to know.”
Bertrand Russell stated “Mathematics, rightly viewed, possesses not only truth, but supreme beauty, a beauty cold and austere.”
Ian Stewart, a distinguished mathematician at the University of Warwick in England, concludes his book "Why Beauty is Truth: a history of symmetry" with two principles:
1. "In physics, beauty does not automatically ensure truth, but it helps."
2. "In mathematics beauty must be true - because anything false is ugly."
Hertz put it this way: “One cannot escape the feeling that these mathematical formulae have an independent existence and intelligence of their own, that they are wiser than we are, wiser even than their discoverers.”
According to the physicist Eugene Wigner, the statement that the laws of nature are written in the language of mathematics was properly made three hundred years ago (attributed to Galileo). Wigner wrote in 1960 of “the unreasonable effectiveness of mathematics” in describing the physical world.
Slicer thinks the question is still worth asking: “Why does the universe have a language/logic we can understand at all?”