About Physics
Let me explain a few things about what I do. This essay is nontechnical and may not be too interesting to working physicists, but if you are intent on reading it, I hope you will find some interesting perspectives. Mostly I wrote this for theraputic reasons.

Science is about the study of systems, what they are and how they change over time. A system is the thing we want to study with science.

Physics is a subfield of science. While there are many ways one might describe what physics is, I think a useful definition is simply that physics is the subfield of science where mathematics proves useful for characterizing the system, both its current state and its evolution over time.

Even within physics, there are important subfields. One division is between experimental and theoretical physics. Experimental physics is about using systems we do understand to probe systems we don't, hopefully gaining some useful information about the later. Theoretical physics is about interpreting and codifying information (gathered by the experimentalists) into a working body of knowledge. This working body of knowledge is often called a "theory," hence the term "theoretical physics." What constitites a successful theory is a slippery issue. In my opinion, a successful theory is one which gives a conceptually satisfying account of all of the relevant information about the system. Note that I use the words "conceptually satisfying." Not just any old account of the system will do. If the theory is unnecessarily complicated, counterintuitive, or involves superfluous structure it is generally not a good thing. Unfortunately these criteria are fairly subjective, and it is never clear if even the most successful theories we have constitute the clearest, simplest account of the system possible. To a large degree, therefore, a lot of what we talk about as "knowledge" in physics is really just useful convention. Still, any theory, ellegant or inellegant, should yeild information about the system which can be measured in real life and therefore can be thought of as objectively true. It is important not to lose sight of this.

There is sometimes a bitter divide between experimental an theoretical physics. Theorists are sometimes arrogant, regarding the fruits of their labor as the pinacle of science. Experimentalists may regard theorists as intentionally abstruse and out of touch, unaware of the practical workings of the physical world and our ability to observe it. Of course, without experiment theorists would not have a job, and without theory experiment would be pointless. We need them both.

Anyway, I was talking about subfields of physics. Besides the experimental/theoretical division, there are divisions according to subject matter, i.e. the type of systems being studied. They include biophysics, molecular and atomic physics; astrophysics, cosmology, gravitation; geophysics and condensed matter physics; nuclear and particle physics; quantum gravity and unified field theory. Many (though not all) of these fields have useful applications in technology. Biophysics and molecular physics contribute to developing medicines and industrial chemicals. Condensed matter physics helps us devolop novel electronic devices. Nuclear physics provides us with alternative energy sources, and (famously) with weapons of mass destruction. The remaining fields, however, seem somewhat far from technological application. Gravitation and astrophysics would seem relevant to space travel, but since we are not yet really a spacefaring civilization these applications would seem limited. I know of no technology that directly utilizes particle physics or quantum gravity, even in as far as anything about the later is known.

So physics seems to be covered by a collage of subfields, all of them seemingly distinct yet overlaping. This brings a natural question: is there a single theory which incorperates all of these fields seemlessly into a whole, so that they can all be understood from a single perspective? In practice, the answer seems to be "no." This may seem surprising since there is only one real world and we presumably need only one framework to understand it. The problem here seems to be with the limits of human intelligence. Though it is presumably possible to unify all we know into a single framework with a simple set of axioms, in practice so much detailed physics is known and so difficult to derive from a common starting point that no single human could ever construct or understand such a theory in its entirety. Of course we try to understand what our fellow physicists are doing and its relation to our work, but individually our understanding is never remotely close to comprehensive. So we divide and conquer, separating physics into convenient subfields which, at least in some approximation, can be understood independently by someone with finite intelligence.

Still, there is a sense in which some branches of physics are more "fundamental" than others, in that in principle it is possible to derive all of the knowlege in one field from more basic postulates in another. Sometimes, the in principle translates fairly easily into an in practice--- for example the laws of nonrelativistic mechanics follow easily from those of relativistic mechanics---but in such cases usually the less fundamental field is no longer considered an independent branch of inquiry. Most often, the in principle does not easily translate to in practice, and the fields are distinct. For example, there is no sense in which the physics of living organisms follows easily from the many body quantum mechanics of electrons and nuclei.

In the search for more "fundamental" physics, there is a useful rule of thumb: The physics of the large follows from the physics of the small. This rule is easy to understand. If we know how to describe very small things, how they evolve and interact, we can pile a lot of small things on top of each other to get large things. Since the whole is nothing but the sum of its parts, we have reduced large physics to small physics. One might wonder why we can't turn this around---take large physics and subdivide it into small physics. In many theories we can do precisely this, but usually it gives the wrong answer. This is not surprising, since usually we describe large aggregates in more general terms than small, individual constituents.

Thus, the most fundamental branches of physics are those which study physics at the smallest distances. By the Heisenberg uncertainty principle, \delta x \delta p > \hbar, probing small distances \delta x inevitably involves large momenta \delta p, and therefore high energies. High energy physics, as it is called, is the branch of physics I work on. The limit of what is truly known about high energy physics is encapsulated by the Standard Model of elementary particles, with its theoretical underpinnings in quantum field theory. The Standard Model seems to be a complete description of the physics we know up to energies of about 100 GeV (about a hundred times the mass of a proton), and down to distances of about 10^-18 meters (about a thousanth the width of a proton).

The Standard Model describes the world at these distances as composed of various types of pointlike quantum particles (or, if you'd rather, local quantum fields). There are two broad types of particles, matter-like particles (fermions, obeying the Pauli exclusion principle) and force-mediating particles (bosons, obeying Bose-Einstein statistics). As my terminology suggests, fermions are the constituents of ordinary matter---tables, marbles, and pens for example ---while bosons transmit interactions between matter, making it stick together and capable of applying pressure. The matter content of the Standard Model includes quarks (the fundamental constituents of protons and neutrons), electrons (the things circling the nucleus of an atom), neutrinos and their lepton cousins. Many matter-like particles in the Standard Model are unstable and decay radioactively, much like uranium, and so we do not notice their effect in everyday circumstances. These include, for example the strange quark, with a lifetime of about 10^-8 seconds, and the tau lepton, with a lifetime of about 10^-12 seconds. Neutrinos, on the other hand, seem to be stable, but we rarely notice their effects in everyday circumstances since their interactions are incredibly weak.

Bosons, the force mediating particles, come in two types: Gauge fields and the Higgs. The gauge particles are the quantum excitations of an SU(3)*SU(2)*U(1) nonabelian gauge theory. A nonabelian gauge theory is a simple generalization of electrodynamics where the electric and magnetic fields are taken to be non-commuting matrices, rather than just ordinary numbers. The "SU(3)*SU(2)*U(1)" is a terminology for describing what type of matrices the electric and magnetic fields are. After symmetry breaking (see Higgs) the gauge particles of SU(3)*SU(2)*U(1) have three fundamental manifestations: Gluons, mediating the "strong force," which binds quarks together into protons and holds protons and neutrons together into the nucleus; photons, mediating the electromagnetic force, responsible for the many effects of electromagnetism; W and Z bosons, mediating the "weak force," which is responsible for various types of radioactivity. For example, the weak force is responsible for the fact that one of the elements of the periodic table, Technitium, never occurs naturally in our world. The most stable isotope of Technitium has a half life of about four million years, and it decays via the weak force into an electron, an electron antineutrino and Ruthenium. More importantly, the weak force is responsible for the fact that many of the matter-like particles in the standard model are unstable. If it weren't for this, we would have many more types of matter in our world---we could have very heavy hydrogen-like atoms, whose nucleus is made of two top quarks and a bottom quark, or atoms where a some of the negatively charged particles surrounding the nucleus are muons rather than electrons. Our world would look very different without the weak force.

Finally, there is the Higgs. The precise nature of the Higgs is shrouded in mystery. The Higgs is not a gauge field like the photon, gluon, and the W and Z. In the simplest models, the Higgs appears to be the quantum of a scalar field---not a vector field as in gauge theory. At the time of writing, the Higgs particle has not been directly observed, and its mass must be larger than 100 GeV. The existence and nature of the Higgs has been inferred indirectly, through the effect it has on the other particles. Most notably, it is though interaction with the Higgs that all of the particles in the Standard Model recieve their mass, and the weak and electromagnetic interactions take the particular form that they do.

The Standard Model represents pretty much all we know about physics at the smallest observable distances. The basic form of the Standard Model has been in place since the mid seventies, and since then all of our measurements have confirmed its basic structure. The notable exception is the recent discovery of a very small neutrino mass, on the order of an eV, a thousand times smaller than the mass of the electron. This has been a breakthough since neutrinos are notoriously difficult to observe, but it requires only a minor modification of the Standard Model. Other than this, true progress in high energy physics has been rather slow for the past 30 years.

Yet it is clear that the Standard Model is not the end of the story in high energy physics. At the most basic level, this is because we have not observed any small distance physics that has anything to do with the 4th fundamental force, gravity. By particle physics standards, gravity is an incredibly weak force. The effects of gravity at short distance only become important on length scales on the order of 10^-35 meters---a length again as small relative to the proton as the proton is smaller than a meter---and energies of the order of 10^19 GeV. To probe such a regime using current technology, we would need to build a particle accelerator the size of the galaxy!

The only reason why we know about gravity at all is that its effect is cumulative; given large enough amounts of matter/energy, the effects of gravity eventually become measureable. These effects have only been tested at fairly large distances---on the order of meters---and appear to be well described by Einstein's classical theory of General Relativity. Einstein's theory describes gravity as "curvature" in the fabric of spacetime due to the presence of matter/energy.

Of course, we know from experience that just because a theory works at lengths of meters does not mean that it works at arbitrarily small distances. At the very least, we must have a theory which allows gravity to consistently couple to quantum mechanical matter. A general rule of thumb says that only a quantum system can couple to another quantum system. Therefore, beyond the Standard Model, we at the very least need a quantum theory of gravity. We know of no measureable consequences of such a theory, but nevertheless it is easy to construct a hypothetical theory of quantum gravity by more or less standard procedures that have worked for the Standard Model. However, in this precedure we run into a problem. Because of the particular nature of the interactions of the graviton---the quantum of the gravitational field---the quantum theory of gravity requires us to introduce an infinite number of undetermined parameters into the theory. Since we do not know what these parameters are, nor do we have a principle for determining them, this makes the theory unpredictive.

Even putting quantum gravity to the side, there are hints from the Standard Model that something deeper is lurking under the surface. One of the more baffling questions goes by the name of the "heirarchy problem." In short, the question is why the energy scale of the Standard Model is so much lower than that of quantum gravity, or conversely, why gravity is so weak. The energy scale of the Standard Model is set by the mass of the Higgs, which most people estimate cannot be larger than, say, 1000 GeV. However, by standard arguments from quantum field theory, saving a miraculous fine tuning we expect the mass of a scalar particle (like the Higgs) to be as large as the fundamental energy scale of the theory---which can be nothing else than that of quantum gravity, ~10^19 GeV. Of course, even the most conservative estimates of the Higgs mass come nowhere close to this. The only plausable explanation for this is that there is new physics beyond the Standard Model which stablizes the Higgs mass to such a small number. One of the more popular proposals along these lines is supersymmetry. Supersymmetry is an exotic symmetry generalizing rotation and translation invariance which relates bosons and fermions. This symmetry produces some remarkable cancellations which can stablize the Higgs mass. The Standard Model does not possess supersymetry, but many think that this is because we do not live in a supersymmetrically invariant state---that is supersymmetry is "spontaneously broken." Perhaps, then, the Standard Model is a limit of a yet more fundamental theory which incorperates supersymmetry. Whether or not this is true has yet to be determined, but many think that the next generation of particle accelerators will answer this question one way or the other.

Another even more troubling puzzle goes by the name of the "cosmological constant problem." Quantum field theory predicts that, even when the quantum field is in its ground state, empty space itself carries a nonzero energy density, the so-called "cosmological constant." In ordinary particle physics experiments, the existence of this vacuum energy has no observable effect, since it does not couple to any of the fields in the Standard Model. However, the cosmological constant couples directly to gravity, since it is merely a form of matter/energy. Recent observations indicate that the cosmological constant has a very small positive value, ~(10^-3 eV)^4. The trouble is that quantum field theory arguments---analogous to those which gave us the heirarchy problem---tell us that the cosmological constant should be of the order of the fundamental energy scale, ~(10^19 GeV)^4. Except for a miraculous fine-tuning, nobody has a plausalbe explanation for the 120 orders of magnitude discrepancy between observation and the generic quantum field theory prediction. The cosmological constant problem is certainly the biggest outstanding conundrum in high energy physics.

All of these troubles, it seems, have something to do with the question of quantum gravity. Therefore, most theoretical work in high energy physics for the last 20 or so years has been devoted to constructing a workable model for quantum gravity. Though there has been much progress, it must be emphasized that no concrete predictions have emerged from these efforts and no experiments have been proposed which could definitively test them. This is hardly a surprise, since the relevant energies of quantum gravity are so far beyond those currently available that it would take extremely exquisite theoretical control to reconstruct the complexity of phenomena at observed energies from a more basic theory at 10^19 GeV. Imagine the amount of work we would have to do to reconstruct all of the complex chemistry of the periodic table from the Standard Model. And here, we at least know what the more fundamental theory is, and we have experiments to guide our understanding.

The most popular proposal for a theory of quantum gravity goes by the name of string theory. In the narrowest sense, string theory is a proposal for calculating well-defined and predictive scattering amplitudes which include gravitons as assymptotic states. Perhaps this needs a little explanation. Given an initial state, in the infinite past, corresponing to freely moving (i.e. noninteracting) quantum mechanical particles (for example photons or electrons), a scattering amplitude allows you to calculate the probability that this initial state will become, in the infinite future, some other configuration of freely moving quantum mechanical particles. These initial and final states, describing freely moving particles, are called assymptotic states. As hinted at before, a naive attempt to include gravitons into assymptotic states requires the introduction of an infinite number of undetermined parameters into the theory, rendering it unpredictive. String theory seems to fix all of these parameters in a unique way, thus giving a simple picture of graviton scattering.

The way string theory achieves this is quite interesting. In quantum field theory, various particles are realized as the excitations of various types of local quantum fields. In string theory, particles are realized as the vibrational modes of a quantum mechanical, one-dimensional extended object---the "string." Since all of the particles in the world are realized as different quantum states of a single object---the string---people often say that string theory represents a unification of all fundamental forces and matter, a "theory of everything." The different vibrational modes of the string actually accomodate an infinite variety of particle types, most of which are very massive and have not been observed. Thankfully, string theory also describes the types of particles that have been observed: gauge fields, fermions, and (most importantly) the graviton. Rougly speaking, gauge fields are associated with "open strings"---open like shoelaces---and the graviton is associated with "closed strings"--- closed like rubber bands. Strings also seem to require supersymmetry at fundamental scales, making a connection with the promising solution to the heirarchy problem.

If the string is quantized in the simplest possible situation---on a flat spacetime with no extra background fields or D-branes (surfaces on which open strings can end)---the resulting theory describes a world quite unlike our own. The theory only seems consistent in a 10 dimensions (our world only has 4), has too much supersymmetry, and the gauge groups that emmerge do not resemble the SU(3)*SU(2)*U(1) of the Standard Model. Luckly, it is possible to quantize strings in more complicated situations which have a better chance of approximating the real world. These models usually involve "curling up" 6 of the 10 dimensions into tiny unobservable balls, so that the universe appears 4-dimensional at low energies, and possibly including D-branes or background fields into the picture. Though noone has yet succeeded in reproducing the Standard Model precisely from the low energy limit of a string theory, many semi-realistic models exist, and there seems to be no reason to believe that the Standard Model could not in principle emmerge from string theory.

In a sense, there are many, many types of string theory. In particular, there are a huge number of different "backgrounds"---including curled up dimensions, background fields, and D-branes---on which it is possible to quantize the string and calculate scattering amplitudes. However, it is widely belived that all of these different scenarious actually correspond to different physical situations arising from the same underlying theory. I have not called this underlying theory "string theory" since, honestly, we do not know what the theory is. We do not know its physical principles, obervables, degrees of freedom, or precisely how it gives rise to the various backgrounds where we know how to calculate scattering amplitudes. Some people like to call this hypothetical theory "M-theory," but, again, this theory does not yet exist. Still, we do understand some special physical situations arising from "M-theory" which do not seem to correspond to string theory as I narrowly defined it. These include a theory of quantum 2-dimensional "membranes" living in a flat 11 dimensional spacetime, and a quantum mechanical description of a certain curved spacetime, AdS, in terms of a special nonablelian gauge theory living on the boundary of AdS.

Why do people believe that all of the different string scattering amplitudes are manifestations of the same fundamental theory? The answer to this question is quite remarkable. In choosing a string background, you must make many choices: specifying the shape of spacetime, turning on relavant background fields, adding D-branes. If you make these choices consistently, it is possible to quantize the string and interpret its vibrational modes as various particle states. The amazing coincidence is that these particle states always correspond small quantum fluctuations of the choices you made when specifying the background! This is clearest in the case of the graviton, which represents a small quantum fluctuation in your choice of the shape of spacetime. In a sense, then, the background is "made up" out of strings, and what at first seemed to be an arbitrary choice must in fact be constrained by the same fundamental laws that govern the strings themselves. Still, noone has formulated a completely satisfactory framework where we can see this picture arise clearly from a set of more basic principles. There is one notable approach that goes by the name of string field theory, which is what I'm working on right now. String field theory turns out to be extremely complicated, however, and only small amounts of what we know to be true about string theory and its underlying M-theory have emmerged tractably from this framework. Most people hope that something simpler and more powerful must be the underlying basis of string theory.

Though string theory is a very nontrivial and interesting theory, I would say that we are still quite far from having a satisfactory theory of quantum gravity. Without a working definition of M-theory, much less tractable methods to compute with it, establishing a connection to the Standard Model seems out of reach. String theory seems consistent with everything we know about the universe, but at the same time has not yielded any prediction which could in principle be falsified; it is hard to be sure that string theory is not, at a fundamental level, incorrect. Personally, if string theory or any theory of quantum gravity never yielded testable predictions, but gave a simple, plausable, and revolutionary picture of physics at the highest energies, I would consider it a success. Some theory must describe physics at 10^19 GeV, but even if we knew what the theory was, it seems questionable that we could reliably extrapolate across 17 orders of magnitude to obtain sharp predictions at observable energies. Yet even by this reduced standard I think string theory has only been partially successful. The deepest issues we would like to understand about quantum gravity---for example, the nature of the Big Bang, vacuum selection, resolution of black hole singularities---simply cannot be addressed with a simple scattering amplitude calculation; the thing we understand best about string theory seems to be the least able to answer the most interesting questions. We have a lot of work to do.

This brings me to the conclusion of my survey of physics! I may add more later...
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