Of Particular Significance

Quantum Field Theory, String Theory and Predictions (Part 4)

This post is a continuation of three previous posts: #1, #2 and #3.

When the Strong Nuclear Force is Truly Strong

Although I’ve already told you a lot about how we make predictions using the Standard Model of particle physics, there’s more to the story. The tricky quantum field theory that we run into in real-world particle physics is the one that describes the strong nuclear force, and the gluons and quarks (and anti-quarks) that participate in that force. In particular, for processes that involve

distances comparable to or larger than the proton‘s size, 100,000 times smaller than an atom, and/or
low-energy processes, with energies at or below the mass-energy (i.e. E=mc² energy) of a proton, about 1 GeV,

the force between quarks, gluons and anti-quarks becomes so “strong” (in a technical sense: strong enough that it makes these particles rush around at nearly the speed of light) that the methods I described previously do not work at all.

That’s bad, because how can one be sure our equations for the quarks and gluons — the quantum field theory equations of the strong nuclear force — are the correct ones, if we can’t check that these equations correctly predict the existence and the masses of the proton and neutron and other hadrons ( a general term referring to any particles made from quarks, anti-quarks and gluons)?

Fortunately, there is a way to check our equations, by brute force. We simulate the behavior of the quark and gluon fields on a computer. Sounds simple enough, but you should not get the idea that this is easy. Even figuring out how to do this requires a lot of cleverness, and making the calculations fast and practical requires even more cleverness. Only expert theoretical physicists can carry out these calculations, and make predictions that are relevant directly for the real world. Don’t try this at home.

The first step is to simplify the problem, and consider an imaginary world, an idealized world that is simpler than the real world. Since the strong nuclear force is extremely strong inside a proton, the electromagnetic and weak nuclear forces are small effects by comparison. So it makes sense to do the calculation in an imaginary world where the strong nuclear force is present but all other forces are turned off. If you put those unimportant forces in, you’d have a much more complicated computer problem and yet the answers would barely change. So including the other forces would be a big waste of time and effort.

Here we use an imaginary world as an idealization — a bit like treating the earth as a perfect sphere. Obviously the earth is not a sphere — it has mountains and valleys and tides and a slight bulge at the equator — but if you’re computing some simple properties of the earth’s effect on the moon, including these details will waste a lot of your time without affecting your calculation very much. The art of being a scientist requires knowing what you need to include in your calculations, and knowing what not to include because it makes no difference. In fact we do this all the time in particle physics; gravity’s effect on measurements at the Large Hadron Collider [LHC] is tiny, so we do our calculations in an imaginary world without gravity, a harmless simplification.

Here’s another idealization: although there are six types (often called “flavors”) of quarks — up, down, strange, charm, bottom and top — the last three are heavier than a proton and consequently don’t play much of a role in the proton, or in the other low-mass hadrons that I’ll focus on here. So the imaginary, idealized, simplified world in which the calculations are carried out has (see Figure 1)

Three “flavors” of quark fields: up, down and strange, each with its own mass, and each with a charge (analogous to electric charge in the case of the electric force) which is whimsically called “color”. Color can take three values, whimsically called “red”, “green” or “blue”. These fields give rise to both the quark particles and their antiparticles, called anti-quarks, which carry anti-color (anti-red, anti-blue, anti-green);
Eight gluon fields (each carrying a “color” and an “anti-color”.) [You might have guessed there’d be nine; but when color and anti-color are the same there are some little subtleties which aren’t relevant today, so I ask you to just accept this for now.]

So now we have a quantum field theory of three flavors of quarks with three possible colors, along with corresponding anti-quarks, and eight gluons which generate the strong nuclear force among the quarks, antiquarks and gluons. This isn’t the real world, but it is close enough to give us very accurate answers about the real world. And this is the one the experts actually put on a computer, to see if our equations do indeed predict that quarks, antiquarks and gluons form protons and other hadrons.

Fig. 1: The fields of the stripped-down world in which calculations of proton and other hadron masses are done. Up, down and strange quark fields (responsible for both quarks and anti-quarks) interact with gluon fields (responsible for gluon particles.) Each of the eight quark fields has a ``charge'' (named, whimsically, red, green or blue) and each gluon field has a color and an anti-color. — Fig. 1: The fields of the stripped-down world in which calculations of the proton mass and other hadron masses are done. Up, down and strange quark fields (responsible for both quarks and anti-quarks) interact with gluon fields (responsible for gluon particles.) Each of the eight quark fields has a “charge” (named, whimsically, red, green or blue) and each gluon field has a color and an anti-color.

Does it work? Yes! In Figure 2 is a plot showing the experimentally measured and computer-calculated values of the masses of various hadrons found in nature. Each hadron’s measured mass is the vertical location of a horizontal black line; the hadron’s symbol appears below that line at the bottom of the plot. I’ve written the names of a few of the most famous hadrons on the plot:

the spin-zero pions,
the spin-1 rho mesons and omega meson,
the spin-1/2 “nucleons”, meaning the proton and the neutron, and
the spin-3/2 Delta particles.

The colored dots represent different computer calculations of the masses of these hadrons; the vertical colored bars show how uncertain each calculation is. You can see that, within the uncertainties of the calculations, the measurements and calculations agree. And thus we learn that indeed the quantum field theory of this idealized world

predicts that hadrons such as protons do exist
predicts the ones we observe, without a lot of extra ones or missing ones
predicts correctly the masses of these hadrons

from which we conclude that

the quantum field theory with the fields shown in Figure 1 has something to do with the real world
we were wise to choose the imaginary world of Figure 1 for our study, because clearly the idealizations we made didn’t affect our final results to an extent that they caused disagreements with the real world
Fig. 2: The masses of various hadrons, whose names appear at bottom and whose measured masses appear as grey horizontal lines, as calculated by computer: each colored dot is a particular calculation, whose uncertainty is shown by a vertical bar. I have written the names of some famous hadrons.

All looks great! And it is. However, I’ve lied to you. I haven’t actually told you how hard it is to obtain these answers. So let me give you a little more insight into what you have to do to obtain these calculations. You have to go off into even more imaginary worlds.

How the Calculation is Really Done: Off In Imaginary Worlds

The imaginary world I’ve described so far is still not simple enough for the calculation to be possible. The actual calculations require that we make predictions in worlds very different from our own. Two simplifications have to do with something you’d think would be essential: space itself. In order to do the calculation, we have to imagine

that the world, rather than being enormous, is made of just a tiny little box — a box only large enough to hold a single proton or other hadron;
that space itself, rather than being continuous, forms a discrete grid, or lattice, in which the distances between points on the grid are somewhat but not enormously smaller than the distance across a proton.

This is schematically illustrated in Figure 3, though the grids used today are denser and the boxes a bit larger. The size of a proton, relative to the finite grid of points, is indicated by the round circle.

Fig. 3: The calculations are done in a world whose space is a small grid. This picture of a 4 x 4 x 4 grid is a cartoon to make the idea clear; today, grids of 32 x 32 x 32 are not unusual. — Fig. 3: The calculations are done in a world whose space is a small grid. Note, however, that this picture of a 4 x 4 x 4 grid is a cartoon to make the idea clear; with modern computers, grids of 32 x 32 x 32 are not unusual.

Advances in computer technology are certainly helping avoid this problem… the better and faster are your computers, the denser you can take your grid and the larger you can take your box. But simulating a large chunk of the world, with space that is essentially continuous, is way out of reach right now. So this is something we have to accept, and deal with. Unlike the idealizations that led us to study the quantum field theory in Figure 1, choosing to study the world on a finite grid does change the calculations substantially, and experts have to correct their answers after they’ve calculated them.

And there’s one more simplification necessary. The smaller are the up and down and strange quark masses, the harder the calculation becomes. If these masses were zero, the calculation just would be impossible. Even with the real world’s quark masses (the up quark mass is about 1/300 of a proton’s mass, the down quark 1/150, and the strange quark about 1/12) calculations still aren’t really possible — and they weren’t even close to possible until rather recently. So calculations have to be done in an imaginary world with much larger quark masses, especially for the up and down quark, than are present in the real world.

Fig. 4: Two types of imaginary worlds arise here. First, the real world is stripped down, with all irrelevant particles and forces dropped, giving the red imaginary world. Then this world's space is made into the grid of Figure 3, and the up, down and strange quark masses are raised. In this purple imaginary world, calculations are easier, but give very wrong answers; only by extrapolating (Figure 5) are the predictions extracted. — Fig. 4: Two types of imaginary worlds arise here. First, the real world is stripped down, with all irrelevant particles and forces dropped, giving the red imaginary world. Then this world’s space is made into the grid of Figure 3, and the up, down and strange quark masses are raised. In this purple imaginary world, calculations become practical, but they give incorrect answers; only by extrapolating (Figure 5) are useful predictions extracted.

So since we can’t calculate in the real world, but have to calculate in a world with a small spatial grid and heavier quarks, how can we hope to get reasonable answers for the hadron masses? Well, this is another place where the experts earn our respect. The trick is to learn how to extrapolate. For example:

Do the calculation for fields in a small box.
Then do the calculation again in a medium-sized box (which takes a lot longer.)
Then do the calculation in a larger box (still small, but big enough that it uses about as much computer time as you can spare.)

Now, if you know how going from a small to medium to larger box should change your answer, then you can infer, from the answers you obtain, what the answer would be in a huge box where the walls are so far away they don’t matter.

The experts do this, and they do the same thing for the space grid, computing with denser grids and extrapolating to a world where space is continuous. And they do the same thing for the quark masses: they start with moderately large quark masses, and they shrink them in several steps. And knowing from theoretical arguments what should happen to the hadron masses as the quark masses change, they can extrapolate from the ones they calculate to the ones that would be predicted if the quark masses were the real-world ones. You can see this in Figure 4. As the up and down quark masses are reduced, the pion mass gets smaller, and the “nucleon” (i.e. proton and neutron) masses becomes smaller too. (Also shown is the Omega hadron; this has three unpaired strange quarks, and you can see its mass doesn’t depend much on the up and down quark masses.) The experts take the actual calculations (colored dots), and draw a properly-shaped curve through all the dots. Then they go to the point on the horizontal axis where the quark masses equal their real-world values and the pion mass comes out agreeing with experiment, and they draw a vertical black line upward. The intersection of the black vertical and blue curved line (the black X mark) is then the prediction for what the proton and neutron mass should be in the real world. Well, you can see that the black X is pretty close, within about 0.030 GeV/c², to what we find in experiments: 0.938 and 0.939 GeV/c² for the proton and neutron mass. And this is how all of the results shown in Figure 2 are obtained: extrapolating to the real world by calculating in a few imaginary ones.

Fig. 5: Calculations (colored dots) are done with larger quark masses than in the real world, and one must extrapolate to the smaller quark masses of the "real" world (black dotted vertical line) to make predictions (black X's). "N" stands for "nucleon", meaning both protons and neutrons. — Fig. 5: Calculations (colored dots) are done with larger quark masses than in the real world, and the results are as much as 50% too large. One must extrapolate to the smaller quark masses of the “real” or “physical” world (black dotted vertical line) to make predictions (black X’s). “N” stands for “nucleon”, meaning both protons and neutrons.

The Importance of Such Calculations

This is a tremendous success story. The equations of the strong nuclear force were first written down correctly in 1973. Calculations like this were just becoming possible in the mid-1980s. Only in the 1990s did the agreement start to become impressive. And now, with modern computer power, it’s become almost routine to see results like this.

More than that, these methods have become essential tools. There are many important predictions made for experiments which are partly made with the methods I described in my previous post and partly using these computer calculations. For example, they are extremely important for precise predictions of the decays of hadrons with one heavy quark, such as B and D mesons, which I have written about here and here. If we didn’t have such precise predictions, we couldn’t use measurements of these decays to check for unknown phenomena that are absent from the Standard Model.

But There’s So Still Much That We Can’t Compute

Despite all this success, the limitations of the method are profound. Although computers are fine for learning the masses of hadrons, and some of their other properties, and quite a few other interesting things, they are terrible for understanding everything that can happen when two protons (or other hadrons) bump into each other. Basically, computer techniques can’t handle things that change rapidly over time.

For example, the data in Figure 6 show two of the simplest things you’d like to know:

how does the probability that two protons will collide change, if you increase the energy of the collision?
what is the probability, if they collide, that they will remain intact, rather than breaking apart into a spray of other hadrons?

We can measure the answer (the black points are data, the black curve is an attempt to fit a smooth curve to the data.) But no one can predict this curve by starting with the quantum field theory of the strong nuclear force — not using successive approximation, fancy math, brute force computer simulation, string theory, or any other method currently available. [Experts: there are plenty of attempts to model these curves (look up “pomeron”.) But the models involve independent equations that can’t actually be derived from or clearly related to the quantum field theory equations for quarks and gluons.]

Fig. 6: The probability for two protons to collide (upper data points) and to collide without breaking (lower data points) as a function of the collision energy. — Fig. 6: The probability for two protons to collide (upper data points, “total”) and to collide without breaking (lower data points, “elastic”), as a function of the energy of one proton as viewed by the other proton. Data are taken from many experiments, including the LHC at the far right. The curve shows an attempt to fit the data, but this data cannot currently be predicted starting from the equations for quarks and gluons.

At the LHC, when a quark from one proton hits a quark from another proton, we can predict, using the successive approximation (“perturbative”) methods described in my previous post, what happens to the quarks. But what happens to the other parts of the two protons when the two quarks strike each other? We can’t even begin to predict that, either with successive approximation or with computers.

My point? The quantum field theory of the strong nuclear force allows us to make many predictions. But still, many very basic natural phenomena for which the strong nuclear force is responsible cannot currently be predicted using any known method.

Stay Tuned. It’s going to get worse.

Continued here…

POSTED BY Matt Strassler

ON October 7, 2013

Some Pre-Nobel Prizes

This year’s Nobel Prize, presumably to be given for the prediction of the particle known today as the “Higgs boson”, will be awarded next week. But in the meantime, the American Physical Society has made a large number of awards. A few of them are to people whose work I know about, so I thought I’d tell you just a little about them.

The J. J. Sakurai prize went to Professors Zvi Bern, Lance Dixon and David Kosower, for the work that I have already described on this website here and here. Dixon, a wide-ranging expert in particle physics, quantum field theory and string theory, was a young professor at the Stanford Linear Accelerator Center when I was a Stanford graduate student. He taught an excellent course on string theory, and provided a lot of scientific advice and insight outside the classroom. Bern and Kosower were young scientists using string theory to learn about how to do computations in quantum field theory, and their surprising results formed the starting point for my Ph. D. thesis (which has their names in its title.) The range of their work is hard to describe in a paragraph, but let’s just say that no one is surprised that they were awarded a prize of this magnitude.

The Dannie Heineman Prize for Mathematical Physics was awarded to my former colleague Greg Moore, a professor at Rutgers University. “For eminent contributions to mathematical physics with a wide influence in many fields, ranging from string theory to supersymmetric gauge theory, conformal field theory, condensed matter physics and four-manifold theory.” Allow me to translate:

string theory: you’ve heard about it, probably
supersymmetric gauge theory: quantum field theories with supersymmetry, which I’ll be writing about soon
conformal field theory: basically, quantum field theories that are scale invariant
condensed matter physics: the study of solids and liquids and their mechanical and electrical properties, and lots of other things too, in which quantum field theory is sometimes a useful tool
four-manifold theory: the mathematics of spaces which have four-spatial dimensions, or three-spatial dimensions and one-time dimension. These spaces are very interesting to mathematicians, and also, they’re interesting because we live in one.

This is not the complete range of Moore’s work by any means. Unfortunately this website doesn’t yet have pages that can put his work in proper context, but perhaps I’ll return to it later. But again, no surprise here to see Moore’s name on this award.

The Tom W. Bonner Prize in Nuclear Physics was awarded to experimental physicist William A. Zajc, currently chairman of the Columbia University physics department. Zajc has been heavily involved in one of the most surprising discoveries of the past fifteen years: that a hot dense fireball of quarks, anti-quarks and gluons (produced in the collision of two relatively large atomic nuclei) behaves in a very unexpected way, more like a very low viscosity liquid rather like than a gas. I’ve known him partly because of his interest in the attempts to apply string theory to certain quantum field theories that are perhaps relevant in the modeling of this novel physical system… something I’ll also probably be writing about in the relatively near future.

And the W.K.H. Panofsky Prize in Experimental Particle Physics went to Kam-Biu Luk (Berkeley) and Yifang Wang (Director of China’s Institute of High Energy Physics): For their leadership of the Daya Bay experiment, which produced the first definitive measurement of the theta-13 angle of the neutrino mixing matrix. For the same experiment, the Henry Primakoff Award for Early-Career Particle Physics went to Daniel A. Dwyer of Lawrence Berkeley Laboratory. I wrote about the Daya Bay measurement here; their result is one of the major measurements in particle physics in the past few years.

I wish I knew more about the other recipients outside my areas of expertise, but other bloggers will have to cover those stories.

Anyway, no surprises, but some very deserving scientists. Let’s see if next Tuesday brings the same result.

POSTED BY Matt Strassler

ON October 3, 2013

Quantum Field Theory, String Theory and Predictions (Part 3)

[This is the third post in a series; here’s #1 and #2.]

The quantum field theory that we use to describe the known particles and forces is called the “Standard Model”, whose structure is shown schematically in Figure 1. It involves an interweaving of three quantum field theories — one for the electromagnetic force, one for the weak nuclear force, and one for the strong nuclear force — into a single more complex quantum field theory.

SM_Interactions — Fig. 1: The three non-gravitational forces, in the colored boxes, affect different combinations of the known apparently-elementary particles. For more details see http://profmattstrassler.com/articles-and-posts/particle-physics-basics/the-known-apparently-elementary-particles/

We particle physicists are extremely fortunate that this particular quantum field theory is just one step more complicated than the very simplest quantum field theories. If this hadn’t been the case, we might still be trying to figure out how it works, and we wouldn’t be able to make detailed and precise predictions for how the known elementary particles will behave in our experiments, such as those at the Large Hadron Collider [LHC].

In order to make predictions for processes that we can measure at the LHC, using the equations of the Standard Model, we employ a method of successive approximation (with the jargon name “method of perturbations”, or “perturbation `theory’ ”). It’s a very common method in math and science, in which

we make an initial rough estimate,
and then correct the estimate,
and then correct the correction,
etc.,

until we have a prediction that is precise enough for our needs.

What are those needs? Well, the precision of any measurement, in any context, is always limited by having

a finite amount of data (so small statistical flukes are common)
imperfect equipment (so small mistakes are inevitable).

What we need, for each measurement, is a prediction a little more precise than the measurement will be, but not much more so. In the difficult environment of the LHC, where measurements are really hard, we often need only the first correction to the original estimate; sometimes we need the second (see Figure 2).

Fig. 2: LONLONNLO — Fig. 2: Top quark/anti-quark pair production rate as a function of the energy of the LHC collisions, as measured by the LHC experiments ATLAS and CMS, and compared with the prediction within the Standard Model. The measurements are the colored points, with bars indicating their uncertainties. The prediction is given by the colored bands — purple for the initial estimate, red after the first correction, grey after the second correction — whose widths indicate how uncertain the prediction is at each stage. The grey band is precise enough to be useful, because its uncertainties are comparable to those of the data. And the data and Standard Model prediction agree!

Until recently the calculations were done by starting with Feynman’s famous diagrams, but the diagrams are not as efficient as one would like, and new techniques have made them mostly obsolete for really hard calculations.

The method of successive approximation works as long as all the forces involved are rather “weak”, in a technical sense. Now this notion of “weak” is complicated enough (and important enough) that I wrote a whole article on it, so those who really want to understand this should read that article. The brief summary suitable for today is this: suppose you took two particles that are attracted to each other by a force, and allowed them to glom together, like an electron and a proton, to form an atom-like object. Then if the relative velocity of the two particles is small compared to the speed of light, the force is weak. The stronger the force, the faster the particles will move around inside their “atom”. (For more details see this article. )

For a weak force, the method of successive approximation is very useful, because the correction to the initial estimate is small, and the correction to the correction is smaller, and the correction to the correction to the correction is even smaller. So for a weak force, the first or second correction is usually enough; one doesn’t have to calculate forever in order to get a sufficiently precise prediction. The “stronger” the force, in this technical sense, the harder you have to work to get a precise prediction, because the corrections to your estimate are larger.

If a force is truly strong, though, everything breaks down. In that case, the correction to the estimate is as big as the estimate, and the next correction is again just as big, so no method of successive approximation will get you close to the answer. In short, for truly strong forces, you need a completely different approach if you are to make predictions.

In the Standard Model, the electromagnetic force and the weak nuclear force are “weak” in all contexts. However, the strong nuclear force is (technically) “strong” for any processes that involve distances comparable to or larger than a proton‘s size (about 100,000 times smaller than an atom) or energies comparable to or smaller than a proton’s mass-energy (about 1 GeV). For such processes, successive approximation does not work at all; it can’t be used to calculate a proton’s size or mass or internal structure. In fact the first step in that method would estimate that quarks and anti-quarks and gluons are free to roam independently and the proton should not exist at all… which is so obviously completely wrong that no method of correcting it will ever give the right answer. I’ll get back to how we show protons are predicted by these equations, using big computers, in a later post.

But there’s a remarkable fact about the strong nuclear force. As I said, at distances the size of a proton or larger, the strong nuclear force is so strong that successive approximation doesn’t work. Yet, at distances shorter than this, the force actually becomes “weak”, in the technical sense, and successive approximation does work there.

Let me make sure this is absolutely clear, because the difference between what we think of colloquially as “weak” is different from “weak” in the sense I’m using it here. Suppose you put two quarks very close together, at a distance r closer together than the radius R of a proton. In Figure 3 I’ve plotted how big the strong nuclear force (purple) and the electromagnetic force (blue) would be between two quarks, as a function of the distance between them. Notice both forces are very strong (colloquially) at short distances (r << R), but (I assert) both forces are weak (technically) there. The electromagnetic force is much the weaker of the two, which is why its curve is lower in the plot.

Now if you move the two quarks apart a bit (increasing r, but still with r << R), both forces become smaller; in fact both decrease almost like 1/r², which would be your first, naive estimate, same as in your high school science class. If this naive estimate were correct, both forces would maintain the same strength (technically) at all distances r.

But this isn’t quite right. Since the 1950s, it was well-known that the correction to this estimate (using successive approximation methods) is to make the electromagnetic force decrease just a little faster than that; it becomes a tiny bit weaker (technically) at longer distances. In the 60s, that’s what most people thought any force described by quantum field theory would do. But they were wrong. In 1973, David Politzer, and David Gross and Frank Wilczek, showed that for the quantum field theory of quarks and gluons, the correction to the naive estimate goes the other direction; it makes the force decrease just a little more slowly than 1/r². [Gerard ‘t Hooft had also calculated this, but apparently without fully recognizing its importance…?] It is the small, accumulating excess above the naive estimate — the gradual deviation of the purple curve from its naive 1/r² form — that leads us to say that this force becomes technically “stronger” and “stronger” at larger distances. Once the distance r becomes comparable to a proton’s size R, the force becomes so “strong” that successive approximation methods fail. As shown in the figure, we have some evidence that the force becomes constant for r >> R, independent of distance. It is this effect that, as we’ll see next time, is responsible for the existence of protons and neutrons, and therefore of all ordinary matter.

Fig. 3: How the electromagnetic force (blue) and the strong nuclear force (purple) vary as a function of the distance r between two particles that feel the corresponding force. The horizontal axis shows r in units of the confinement scale R; the vertical axis shows the force in units of the minimum strength of the strong nuclear force, which it exerts for r > R. — Fig. 3: How the electromagnetic force (blue) and the strong nuclear force (purple) vary as a function of the distance r between two quarks. The horizontal axis shows r in units of the proton’s radius R; the vertical axis shows the force in units of the constant value that the strong nuclear force takes for r >> R. Both forces are “weak” at short distances, but the strong nuclear force becomes “strong” once r is comparable to, or larger than, R.

So: at very short distances and high energies, the strong nuclear force is a somewhat “weak” force, stronger still than the electromagnetic and weak nuclear forces, but similar to them. And therefore, successive approximation can tell you what happens when a quark inside one speeding proton hits a quark in a proton speeding the other direction, as long as the quarks collide with energy far more than 1 GeV. If this weren’t true, we could make scarcely any predictions at the LHC, and at similar proton-proton and proton-antiproton colliders! (We do also need to know about the proton’s structure, but we don’t calculate that: we simply measure it in other experiments.) In particular, we would never have been able to calculate how often we should be making top quarks, as in Figure 2. And we would not have been able to calculate what the Standard Model, or any other quantum field theory, predicts for the rate at which Higgs particles are produced, so we’d never have been sure that the LHC would either find or exclude the Standard Model Higgs particle. Fortunately, it is true, and that is why precise predictions can be made, for so many processes, at the LHC. And the success of those and other predictions underlies our confidence that the Standard Model correctly describes most of what we know about particle physics.

But still, the equations of the strong nuclear force have only quarks and anti-quarks and gluons in them — no protons, neutrons, or other hadrons. Our understanding of the real world would certainly be incomplete if we didn’t know why there are protons. Well, it turns out that if we want to know whether protons and neutrons and other hadrons are actually predicted by the strong nuclear force’s equations, we have to test this notion using big computers. And that’s tricky, even trickier than you might guess.

Continued here

POSTED BY Matt Strassler

ON October 1, 2013

Freeman Dyson, 90, Still Disturbing the Universe

I spent the last two days at an extraordinary conference, “Dreams of Earth and Sky”, celebrating the life and career of an extraordinary man, one of the many fascinating scientists whom I have had the good fortune to meet. I am referring to Freeman Dyson, professor at the Institute for Advanced Study (IAS), whose career has spanned so many subfields of science and beyond that the two-day conference simply wasn’t able to represent them all.

The event, held on the campus of the IAS, marked Dyson’s 90th year on the planet and his 60th year as a professor. (In fact his first stay at the IAS was a few years even earlier than that.) The IAS was then still a young institution; Albert Einstein, John Von Neumann, Kurt Gödel and J. Robert Oppenheimer were among the faculty. Dyson’s most famous work in my own field was on the foundations of the quantum field theory of the electromagnetic force, “quantum electrodynamics”, or “QED”. His work helped explain its mathematical underpinnings and clarify how it worked, and so impressed Oppenheimer that he got Dyson a faculty position at the IAS. This work was done at a very young age. By the time I arrived to work at the IAS in 1996, Dyson had officially retired, but was often in his office and involved in lunchtime conversations, mostly with the astronomers and astrophysicists, which is where a lot of his late career work has been centered.

Retirement certainly hasn’t stopped Dyson’s activity. His mind seems to be ageless; he is spry, attentive, sharp, and still doing science and writing about it and other topics. When I went up to congratulate him, I was surprised that he not only remembered who I was, he remembered what I had been working on in 1992, when, as an unknown graduate student on the other coast, I had sent him a paper I had written.

By the way, it’s somewhat bizarre that Dyson never won a Nobel Prize. Arguably it is part of the nature of the awarding process, which typically rewards a specific, deep line of research, and not a polymath whose contributions are spread widely. Just goes to show that you have to look at the content of a person’s life and work, not the prizes that someone thought fit to award to him or her. Still, he has his share: Dannie Heineman Prize for Mathematical Physics 1965; German Physical Society, Max Planck Medal 1969; Harvey Prize 1977; Wolf Foundation Prize in Physics 1981; American Association of Physics Teachers, Oersted Medal 1991; Enrico Fermi Award 1995; Templeton Prize for Progress in Religion 2000; Henri Poincaré Prize 2012.

The thirteen talks and several brief comments given at the conference, all of which in one way or another related to Dyson’s work, were organized into sessions on mathematics, on physics and chemistry, on astronomy and astrobiology, and on public affairs. All of the speakers were eminent in their fields, and I encourage you to explore their websites and writings, some of which were controversial, all of which were interesting. For non-scientists, I especially recommend Stanford Professor Emeritus Sid Drell’s extremely interesting talk about nuclear disarmament (which he’s been working towards for decades), and a thought-provoking if disconcertingly slick presentation by Dr. Amory Lovins of the Rocky Mountain Institute on what he sees as a completely realistic effort, already underway, to wean the United States of its addiction to oil — with no net cost. Those with a small to moderate amount of scientific background may especially enjoy MIT Professor Sara Seager’s work on efforts to discover and study planets beyond our own solar system, Texas Professor Bill Press’s proposal for how to rethink the process of drug trials and approvals in the age of electronic patient records, Sir Martin Rees’s views on the state of our understanding of the universe, and Caltech’s Joseph Kirschvink’s contention that scientific evidence tends to favor the notion that life on this planet most likely started on Mars.

But really, if you haven’t heard about all the different things Freeman Dyson has done, or read any of his writings, you should not miss the opportunity. Start here and here, and enjoy!

Many happy returns, Professor Dyson; you have been an inspiration and a role model for several generations of young scientists, and may you have many more happy and healthy years to come!

POSTED BY Matt Strassler

ON September 29, 2013

Quantum Field Theory, String Theory, and Predictions (Part 2)

[This post is a continuation of this one from Monday]

Coming to Terms

Before we continue, a little terminology — trivial, yet crucial and slightly subtle.

Think about the distinction between the words “humanity” and “a human” and “humans”; or “higher education”, “university” and “universities”; or “royalty”, “king” and “kings”. In each case, the three words refer to the general case, the specific case, and a group of specific cases. Sometimes you even have to use context to figure out whether you’re dealing with the general case or a group, because “humans” or “kings” is sometimes used in place of “humanity” or “royalty”.

In a similar way:

The words “quantum field theory” (with no word in front) refers to the general case: the general type of equations that we use for particle physics and many other fields of study.
The words “a quantum field theory” refers to a particular case; an example of a set of equations drawn from the general case called “quantum field theory”.
The words “quantum field theories” refers to a group of particular cases: a set of examples, perhaps ones that share something in common. We might talk about “some quantum field theories”, or “all quantum field theories”, or “a few quantum field theories”.

Before I go on, I should probably point out that string theory/M theory is different, for a weird (and perhaps temporary) reason — it appears (currently) that there’s only one such theory that has fully consistent mathematics and contains a quantum version of Einstein’s theory of gravity. That was figured out in the 1990s.

However, in that theory you need another, similar distinction. Let me postpone a proper definition until later, but roughly, a “string vacuum” is a particular way that string/M theory could manifest itself in a universe; if you changed the string vacuum that we’re in (says string theory), we’d end up with different particles and forces and somewhat different laws governing those particles and forces. Many such vacua would have particles and forces described by a quantum field theory, along with Einstein’s gravity; many (perhaps most) other vacua might not have this property. And so, as before, we need to distinguish “string vacua in general”, “a string vacuum”, and “string vacua”, plural.

Now it’s time to talk about quantum field theory — the general case — in more detail.

Quantum Field Theory and Its Predictions

Does quantum field theory as a whole predict anything? In short, if you knew a universe had physics described by a quantum field theory, but you didn’t know which particular quantum field theory, what could you predict?

The answer is: almost nothing.

If you’ve been following this blog with care, or have read some books or articles about particle physics, you might well think: quantum field theories have fields; and fields have particles; so here’s a prediction: there should be some particles of some type.

Nope. You’ve learned your lesson well — everything I’ve told you on this website suggests that it is true — but the conclusion is false. I’ve been white-lying to you this whole time, and I have to apologize for that. Quantum fields do often have particles. But many quantum field theories are scale-invariant. A scale-invariant thing looks and behaves more or less the same in a microscope no matter how strong a lens you use. The wikipedia article on scale invariance actually has a nice animation of a scale-invariant process. Another example of something scale-invariant is a fractal. And in a scale-invariant quantum field theory (except for one in which there are no forces at all), there are no particles. I’ve told you that particles are well-behaved ripples in fields… well, it’s true, but in a scale-invariant quantum field theory with at least one force, any such ripples die away and turn into several ripples, which die away and turn into several ripples, which die away and turn into several ripples, which die away and turn into several ripples, which…

Click here to see an animation of a scale-invariant process, called the Wiener process. Animation from Wikimedia Commons (author Cyp). For more information, see http://en.wikipedia.org/wiki/File:Wiener_process_animated.gif

In short, no particles. This has been known for many decades (I’m actually not sure how far it goes back in the form I just described.) We observe this behavior in experiments — not in particle physics, where it isn’t relevant (at least currently), but in many solids, liquids, electrical conductors, magnets etc. that are undergoing “phase transitions”, such as melting, or spontaneous magnetization. In some cases we can also calculate this behavior, exactly or approximately. In some cases we can see this behavior emerge in computer simulations of real or imaginary materials. So we know there are many quantum field theories that don’t have particles.

[This might make you wonder if there are string/M theory vacua that don’t have strings. Good thinking… though actually there are other, unrelated ways to end up without strings… more on this later in the month.]

But If There Are Particles… A Prediction!

But here’s something important that we can predict. If we are studying a quantum field theory that does have particles (now we are talking not about all quantum field theories, but an interesting subset of them) then

the particles will come in types (in our world, electrons are examples of a type of particle, Higgs particles are an example of another, etc.); and
two particles of the same type will be identical in all their intrinsic properties. They will have the same electric charge, spin, mass [i.e. rest mass] etc.; if somebody swaps one for another, you won’t be able to tell the difference. (In our world, all electrons are identical.)
Furthermore, in a world with three (or more) spatial dimensions in which Einstein’s special relativity is true, then particles of each type will be either fermions or bosons. (The Pauli Exclusion Principle, which determines all of atomic physics and chemistry, is a consequence of the facts that all electrons are identical and that electrons are fermions.)

Again, these are general prediction, not of quantum field theory as a whole, but of the subset of quantum field theories that have particles in the first place. The Standard Model, the quantum field theory that seems to describe much of our world very well so far, is an example of one that has particles.

That these are the most important predictions of quantum field theory with particles was pointed out to me, when I was just out of graduate school 20 years ago, by none other than Freeman Dyson, who helped develop quantum field theory back in its infancy.

Moving Toward Particular Quantum Field Theories

Now, what about specific quantum field theories. What can we predict about them?

The answer, hardly surprising, is: it depends.

In some quantum field theories, we can predict an enormous amount, by doing some straightforward type of calculation.
In others, brute-force computer simulation of the quantum fields makes it possible to study the particles and forces described by that quantum field theory, and allows us to make some predictions.
In some quantum field theories, we can predict a smattering of things very well, using fancy math methods (for example, using fancy geometry, or supersymmetry, or string theory).
In still others… unfortunately, many of the most interesting… we have absolutely no idea what’s going on. Sometimes we have the equations we’re supposed to use, but none of our methods for calculation work for those equations. Occasionally we can make a good guess, but we can’t always check it.
In yet others, we don’t even know what the equations are that we should use to start studying them. In fact, the existence of some of these theories was, until relatively recently, unknown. We didn’t even suspect they existed. Maybe there are even more that we still don’t know about.

I’ll start describing these categories of quantum field theories in my ensuing posts. Fortunately for particle physicists, the Standard Model is mostly in the first category, with a little leakage into the second.

The Standard Model: A Quantum Field Theory Of Particular Significance

Continued HERE.

POSTED BY Matt Strassler

ON September 24, 2013

Quantum Field Theory, String Theory, and Predictions

One of the important lessons of last Tuesday’s debate about string theory is that if I’m going to talk about theories that do or don’t predict things, I’d better be very clear about

what’s a theory?
what’s a scientific theory expected to do?
what’s a prediction?

On Thursday I asked my readers if they felt misled by Tuesday’s article. Most didn’t feel that way (I’m gratified), but if you’re a good scientist you focus attention on the negative feedback you receive, because that’s where you are most likely to learn something. And you also look for negative signs in the positive feedback. So thank you, especially those who were critical yet reasonable. I will respond in due course, by putting out a better, clearer article on what string theory can and cannot do, on what we know and do not know about it, a bit about its history, etc. Then I can avoid creating or contributing to confusions, such as the ones Dr. Woit expressed concerns about.

But today I want to explain why I found my conversation with Dr. Woit troubling scientifically (as opposed to pedagogically or politically). It wasn’t because I’m a string theorist — in fact, I’m not a string theorist, by anyone’s reasonable definition (except possibly Dr. Woit’s [and probably not even by his.])

I’m a quantum field theorist. Quantum field theory is the mathematical language of particle physics; quantum field theory equations are used to describe and predict the behavior of the known elementary particles and forces of nature. Throughout my 25 year career I have mainly studied quantum field theory and some of its applications. Its applications are many. I have focused on the applications to particle physics, with some also to string theory, astronomy and cosmology, and even quantum gravity. (Other applications that I haven’t worked on include the physics of “condensed matter” — solids and liquids; magnets; electrical conductors, insulators, and superconductors; and a lot of weirder things — and phase transitions, such as the melting of a solid to a liquid, or the change of a material from magnet to a non-magnet.)

And meanwhile, while doing quantum field theory, I use every tool I can. I use fancy math. I use what I can learn from other people’s experiments, or from their big numerical simulations. Sometimes I use string theory. Sometimes I use computers. If loop quantum gravity were useful as a tool for quantum field theory, I’d use it. Heck, I’d use formaldehyde, bulldozers, musical instruments and/or crowds of hypnotized rats if it would help me understand quantum field theory. I’ve got a job to do, and I’m not going to stray from it just because somebody with a different job (or an axe to grind) loves or hates my tools.

The Scientific Issue

So here’s what bothers me about Dr. Woit’s argument. First he said: “to deal with the scientific issue here and make an accurate statement, one needs to first address the following:

What is a prediction?
What is string theory?
What are the vacuum states of string theory?“

Hard to argue with that! [He elaborated on each of these three points, but I leave it to you to go back and read the elaboration if you like.] And then he concludes:

“What is the difference between this situation and Quantum Field Theory? That’s pretty simple: no problems 2 and 3. And those problems are not problems of calculations being hard.”

Woit’s implication is that we do know what field theory is and we do understand the vacua of field theory… and that while prediction in field theory is merely hard in practice, we know what we are doing… and that we understand so little about string theory that prediction in string theory is impossible in principle. This, as a quantum field theorist, I strongly disagree with.

If you are concerned, as you should always be in these situations, that Woit’s being misquoted or quoted out of context, you can go back and reread the comment exchange to Tuesday’s post.

What bothers me about this is that this kind of sweeping statement does a disservice to both subjects: it understates what we know about string theory and overstates what we know about quantum field theory. If only quantum field theory always made it straightforward (albeit difficult) to make predictions! My job would be a lot easier, and it might even be much easier to solve some of the deepest puzzles in nature.

Also, this blanket statement leaves it completely unclear and mysterious why string theory could be such a helpful tool for a quantum field theorist like me — which is a real loss, because the usefulness of string theory for field theory is one of the most interesting aspects of both subjects.

Our understanding of quantum field theory, while perhaps no longer in its infancy, is still clearly in adolescence, at best — and it seems likely to me that we know even less than we think. And I think that many of my readers would like to hear more about this.

What I intend to do over the coming weeks, as time and news permits, is

describe to you what we do and don’t know about quantum field theory
describe to you what we do and don’t know about string theory
explain how, over the past 20 or so years, we have used some of the things we do know about string theory to learn some things we didn’t know (and often didn’t know we didn’t know) about quantum field theory.
describe how one can use quantum field theory to learn something more about string theory

I’ll do items numbers 1 and 3 carefully. Specifically, in number 3, I will focus on predictions made for quantum field theory using string theory [and we’ll talk very carefully, at that time, about what “prediction” means.]) Both 2 and 4 are more nebulous, and I don’t work on them directly, but I think I can do a decent job on them. I’m sure my colleagues will correct me if I get any facts wrong.

What Does “Theory” Mean to a Physicist?

First, an important, fundamental question. When I say: “quantum field theory”, or “string theory”, or “theory of relativity” — well, what is a theory?

It’s not what it means in Webster’s dictionary of the English Language. It’s not the same as a guess or a hypothesis. It’s not the opposite of a “fact”. It’s something much more powerful than either one. And it’s certainly not what it means in various academic departments like Literature or Art or even Sociology.

I could write a whole article on this (and someday I might) but here’s the best definition I have at the moment. Probably there are better definitions out there. But here’s my best shot for now: in my line of research, a theory is a set of mathematical equations, along with a set of accompanying concepts, that can be used to make predictions for how physical objects will behave, on their own and in combination — and these predictions may be relevant either in the real world or in imaginary (but reasonable, imaginable) worlds.

Wait! Why are imaginary worlds important? Why focus on anything other than the real world? How could studying imaginary worlds be “scientific”?

Because:

By studying imaginary particles and forces, we gain insight into the real world: which properties of our universe are true of all possible universes? which properties are common but not ubiquitous? which ones are special and unique to our own?
Sometimes the math that describes a specially chosen combination of particles and forces turns out to be much simpler than the mathematics that describes the particles and forces in our own universe. In an imaginary world described by these equations, it may be possible to solve problems that are too hard to solve in the real world. And even though the lessons learned don’t apply directly to our world, they may still yield fundamental insights into how the real world works.
The future may surprise us. Things that are imaginary today might actually turn up, in future, in the real world. For instance: the top quark that we find in nature was imaginary for over 20 years; the Higgs particle was imaginary for almost 50; supersymmetry is still imaginary, and no one knows if it will remain so.]
Note Added: commenter Kent reminded me of another excellent reason, and an example of it: “Sometimes it is not possible to understand the real world until we have first understood an idealization of it. There are many examples … [including] the discovery of the laws of motion by Galileo and Newton. For hundreds of years, people followed Aristotle in believing that a moving object would return to its “natural state” of being at rest unless a force acted on it. Galileo and Newton’s breakthrough was their ability to imagine a world without friction or air resistance. Only after they understood this imaginary world could they properly understand the real one and learn that the natural state of an object is to continue moving in the same way UNLESS a force acts on it.“

Notice that this strategy is not unique to physics! Biologists who want to understand humans also study flies, mice, yeast, rabbits, monkeys, etc.. From this type of research — often much easier, cheaper and safer than direct research on humans — they can perhaps learn what is common to the biology of all primates, or of all mammals, or of all animals, and/or of all life on Earth, and perhaps also ascertain what it is that makes humans unique. Many experts on Earth’s geology and climate are fascinated by Mars, Venus, and the rocky moons of Saturn and Jupiter, whose similarities to and differences from Earth give us a perspective on what makes the Earth special, and what makes it typical. Kierkegaard, the philosopher, famously uses the technique of “what-if” stories — a story retold with slight differences and a quite different outcome — to try to tease apart the meaning of religious faith within the Abraham-and-Isaac story, in his famous work “Fear and Trembling”.

The Lesson: If you want to understand a particular case, study the general case, and other similar-but-yet-different particular cases, in order to gain the insights that the particular case, on its own, cannot easily give you. Meanwhile, what you learn along the way may have wider implications that you did not anticipate. In short, putting one’s imagination to work, in order to learn about the real, is a powerful, tried and true approach to theoretical physics.

Continued here…

POSTED BY Matt Strassler

ON September 23, 2013

Quantum Field Theory, String Theory and Predictions (Part 4)

POSTED BY Matt Strassler

Some Pre-Nobel Prizes

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Quantum Field Theory, String Theory and Predictions (Part 3)

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Freeman Dyson, 90, Still Disturbing the Universe

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Quantum Field Theory, String Theory, and Predictions (Part 2)

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Quantum Field Theory, String Theory, and Predictions

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Quantum Field Theory, String Theory and Predictions (Part 4)

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Some Pre-Nobel Prizes

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Quantum Field Theory, String Theory and Predictions (Part 3)

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Freeman Dyson, 90, Still Disturbing the Universe

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Quantum Field Theory, String Theory, and Predictions (Part 2)

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Quantum Field Theory, String Theory, and Predictions

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