Published 8 July 2010 by Alexander Bastidas Fry

A Conversation with Gross on the Edge of Knowledge

Before I can get to the conversation with David Gross and the work he did to receive the Nobel Prize for I have to talk about quarks. Three or two quarks in concert together make up a class of particles known as hadrons which include protons and neutrons. Hence the Large Hadron Collider (LHC) is a collider of protons and neutrons.  The logical conclusion may be that smashing hadrons together in the LHC would produce jets of quarks, but quarks are elusive. Quarks are confined inside hadrons, due to the strong force. The strong force does not let quarks move away from each other but is arbitrarily weak when the quarks are packed closely together due to the property known as asymptotic freedom. The entire model for how quarks interact comes from the elegant theory of quantum chromodynamics.
Asymptotic freedom and quantum chromodynamics (QCD) is an observationally supported theory for which David Gross, David Politzer and Frank Wilczek received the 2004 Nobel Prize. At the Lindau meeting I had the chance to sit down with Gross and talk with him as well as hear his lecture on the frontiers of physics. In this post I want to give  brief background of asymptotic freedom and QCD before summarizing Gross’s talk and then I will present the first half of my conversation with Gross on technical topics. In a follow up post I will present the second half of my conversation with Gross where we discuss the generalities of being a scientist.
Asymptotic freedom and QCD allows for the precise prediction of various results in quantum physics such as the calculation of the mass of a proton.  These theoretical results underlay all of the work that will be done at the LHC to probe the current frontier of physics. The LHC accelerates and smashes protons (and sometimes lead nuclei, which are just larger collections of hadrons) together because the proton is a charged particle which can be guided with a magnetic field and accelerated with an electric field. Understanding the proton is key to understanding the current state of particle physics. 
A proton is made up of two up quarks which each effectively carry 2/3 of the charge of positron and one down quark which effectively carries 1/3 of the charge on an electron.  Thus the proton has exactly the inverse charge of an electron. Quarks are confined inside protons due to the uniquely acting strong force. Unlike any sensible force in nature the force between quarks does not decrease with increasing distance (consider this in contrast to the electrostatic or gravitational forces which are inverse square laws); quarks cannot escape from a hadron because as they move further apart the attractive force between the constituent quarks never decreases. In fact nature abhors the separation of quarks to the extent that upon separating quarks to a sufficient distance it seems it seems under certain conditions that nature would rather pair produce more quarks from the vacuum than see a lonely quark carry on. On other other hand as quarks get closer and closer together the force doesn’t increase but asymptotically converges to zero at some infinitely small separation; this is the so called asymptotic freedom. The strong force is also responsible for the nuclear force which binds neutrons and protons together. The nuclear force can be thought of as the residual strong force, however, the nuclear force does diminish in strength with distance.
Gross began his lecture on the frontiers of physics by proclaiming that, ‘physics works from the Planck length to the edge of the universe over sixty order of magnitude and we physicists are quite proud of the precision we bring to bear on the natural world.’  Gross cites three problems on the edge of knowledge: the unification of the forces, the mass scale of the standard model, and dark matter. The first problem is that the fundamental forces in nature, the electroweak force, the strong force, and gravity, are wildly discrepant with each other. Theories predict that the forces unify at ~1019 Gev, but given 30 years of experiments with null results physicists musk ask whether something missing from the model or whether the forces simply don’t unify. The second problem is that the although some may say that if the LHC discovers the Higgs we will learn the secret of making mass the reality is that the so called Higgs coupling is more subtle than this. Finally, dark matter is an incontrovertible part of our universe, but we do not know its exact origin.  Gross is not content to be at the edge of knowledge. He pushes beyond the standard model by talking about a speculation which is supersymmetry. He explains that the secret of nature is symmetry and continuous symmetries in nature lead to conservation laws. Ultimately supersymmetry would mean that we live in a Universe with anti-commuting quantum dimensions. For example if you observed a particle collision in the detectors at the LHC where a jet of particles is produced but has no energy balancing counterpart then you may conclude the counterpart does exist in the form of hidden supersymmetric particles. Further, supersymmetric extensions to the standard model naturally produce stable massive particles in the mass range of 100 Gev to 1 Tev which are known as Weakly Interacting Massive Particles (WIMPs) that are the best candidate we have for dark matter believes Gross. You can catch the entire lecture online on the Frontiers of Physics.
The following is excerpt of some of my conversation with Gross touching on infinities, dark energy, and coincidence.
Alexander: You received the 2004 Nobel prize for work on asymptotic freedom in quantum chromodynamics. Can you explain what that is?
Gross: Yes, I can.
Alexander: There are a lot of infinities that come up in physics and in field theory, particularity in your problem on the strong force, how did you solve these?
Gross: No, actually there are no infinities. 
Alexander: Where did the infinities go?
Gross: If you do things in the wrong way you get infinities. So you know the infinities that occur in quantum field theory, the so called divergences, are a reflection of comparing quantities which are infinitely different. So for example one of the infinities which is related to asymptotic freedom is the measure of the forces between charged particles like electrons and  positrons or charged particles like quarks which have more than one kind of charge, 3 kinds of charge we call colors, that force varies with distance and so if you measure the force it is characterized by the certain strength of force and it varies with distance because these particles are immersed in the vacuum.
Alexander: The charge varies with distance so if I take three quarks in combination, like the up, up, and down in a proton and move them apart what happens?
Gross: The nature of the force changes because the strength changes. It gets stronger or weaker. What we discovered is that in particular kinds generalizations of electromagnetism where there are three colors, three charges, the force gets weaker when you move the charges closer together and in fact vanishes if you could asymptotically approach zero separation. Now if you then try to compare the force at a finite distance and a force at zero distance you are comparing zero distance with something finite. Something divided by zero gives you infinity and that’s where you get infinities. If you divide something by zero you get infinity, no big deal. But nothing actually blows up or is singular. The force actually goes to zero. At any finite distance no matter how small it is nonzero and then it grows as you pull the quarks apart and becomes bigger and bigger and the ratio of those two you can calculate in terms of the ratio of those two distances. So if you do things carefully in theory like QCD there are never any infinities and the proof1 of that is you can solve QCD by putting the theory on a lattice by dividing space and time up into points in a finite volume where there are only a finite number of points. The theory gets complicated in lattice QCD, but there you can calculate say the mass of the proton and let the separation of points gets smaller smaller recovering the true theory when you get to zero. Of course you never get  to zero, but as you approach zero you can see the proton mass approaches a value and you can control the errors to say you have calculate the proton mass to 1% and if I try harder after some time I could reduce it to a tenth of a percent. Since your never getting to zero, in fact you can’t since that would require an infinite number of points and no computer can deal with an infinite, you never get that infinities.
Alexander: Are there any singularities in physics?
Gross: Physicists tend to believe not because it would be sort of ridiculous and in cases where the formalism gives rise to singularities we suspect something is wrong with the theory. So the fact that in QCD there are no singularities at all is very nice and  one the reasons by itself the theory seems to be very complete and shows no indications of breaking down. But in other theories that we have come up with over the centuries singularities have occurred. They don’t occur in measurements. An experimentalist isn’t going to go out and measure something and say my answer was infinity. It is hard to measure infinity. And they occurred in electrodynamics early on. The self energy of a point like electron is infinite. An electron creates a field which divergences at the origin, at the point. The force goes as one over r squared and for r equals zero that is singular. If you calculate the energy in the electromagnetic field produced by that electron it is infinite. It is an infinite self energy of the electron and in classical electrodynamics that was a problem. Another example was what happens in an atom. In the atom the electron could fall into the proton and that would have infinite energy and that would be the ground state energy. This was Bohr’s problem that quantum mechanics solved, but you still didn’t solve the self energy of the electron and for a theory like QED those self energies are problematic for QCD they are not. But then there are other singularities which we encounter in general relativity where we still don’t know the explanation. 
Alexander: QCD has extended the realm validity of physics to smaller scales, but is inadequate at the Planck scale, what is next?
Gross: We don’t know. We have been exploring for many years string theory which seems now days to be more an extension of field theory than a revolution replacement and it seems some kinds of singularities are removed. Things are much smoother because the very notion of arbitrarily short distances gets supplanted, but we are still in the process of exploring what that means and how that helps avoid all the possible singularities of space and time. In general relativity it is a lot more complicated because the dynamics is of space and time itself and the singularities are much more severe. They are singularities of the space time manifold. In many cases with the ordinary way of looking at it using classical or semi classical Einsteinen gravity you encounter singularities which string theories avoid and maybe in all cases this approach will avoid singularities. But we don’t know. One of the hardest singularities to understand are the so called cosmological singularities. If you take everything we know about the structure of the Universe and extrapolate back in time we know the Universe was getting smaller and smaller. It was contracting as we go back and getting denser and hotter and particles get arbitrarily high energies at some point so we encounter singularities which we think just means we need better treatments. So far sting theory hasn’t been able to resolve those issues.
Alexander: You’ve been working on string theory a long time. What testable theories is string theory going to make?
Gross: I was around at the beginning which was 42 years ago. Well, it is not yet a theory it is more a frame work. I think somethings missing. One thing we know for sure is that it isn’t different from QFT. In this frame work strings play a special role as do particles because in terms of them we can create formulate consistent perturbative expansions on quantum states.
Alexander: What is an assumption in your field that turned out to be completely wrong?
Gross: The cosmological constant had to be zero. For years, I, and most of my friends believed very strongly the cosmological constant had to be zero. Because anytime you estimated it, before string theory, you got infinity and anything that is infinite can’t be really be infinite therefore it has to be zero. You do an estimate and proportional to there is a number of order one, well zero is of order one and you multiply anything by zero so any naive estimate of the cos constant coming from fluctuations of the vacuum.
Alexander: But you can calculate the vacuum energy using a simple QED estimation.
Gross: You can? In QED it is actually infinite
Alexander: Well I pick a cut off and I avoid the ultraviolet catastrophe2.
Gross: Ah, but how do you avoid it?
Alexander: I pick the Planck energy scale.
Gross: Then it is only off by and order of 10120. So indeed very bad. But is only proportional to 10120 times what is now measured so that could mean there could be a secret reason it has to be multiplied by zero… So for years before there wasn’t any evidence for accelerated cosmological expansion theorists believed pretty uniformly there had to be some reason, some symmetry, something to make it zero. And that was a very strong prejudice and that is why people where very surprised and suspicious in the beginning by the evidence for a non vanishing cosmological constant.
Alexander: Our current measurements that constrain the cosmological model are either at very high redshift like the cosmic microwave background or very recent like the type Ia supernovae data. Dark energy should only have become dominant in our universe in the last few billion years according to conventional wisdom, but isn’t it possible we live in a so called Hubble bubble or that expansion has had an unusual history?
Gross: It could be, but there is no reason to think so. It could be time dependent. There could be all sorts of bubbles. A de Sitter3 like universe which is what we would eventually evolve into raises various conceptual problems which are tricky, because any two particles separate and become casually disconnected eventually. But conceivably it could  be something, and some people are trying to argue that, a decay of de Sitter space  occurs naturally into something that is asymptotically flat. That would be good. That still wouldn’t explain the current magnitude. The real puzzle with the cosmological constant is its absurdly small magnitude at the moment and that there is no good explanation for.
Alexander: We should reason as if we are a standard observer. Is it a coincidence or something special that the cosmological parameters add up to exactly unity. Is it exactly one?
Gross: Well they have to add up to one. Inflation predicts it is one to extraordinary precision. But why matter and the cosmological constant are of comparable magnitude is a puzzle. Coincidence perhaps.  perhaps obviously a consequence of what the cosmological constant it, but since we don’t know what sets that it is hard to say whether that is a coincidence or something deeper, but there are coincidences. The apparent size of the moon and the sun is the same which is kind of important. Presumably it is totally coincidental it is changing as you know so wont be true in a billion years. 
1. The proofs shown from lattice QCD are not necessarily satisfactory to mathematicians. Generally no non-analytical proof is. The Clay Mathematics Institute has a Millennium Prize Problem concerning this.
2. See my blog post on the cosmological constant and the dark sector to get a flavor of the math.
3. A de Sitter universe has effectively no matter and is dominated be a positive cosmological constant. The scale factor is such a universe is exponentially growing in proportion to the time and the Hubble constant.

Alexander Bastidas Fry