Category Archives: Quantum Gravity

Quantum Field Theory, String Theory and Predictions (Part 8)

Last year, in a series of posts, I gave you a tour of quantum field theory, telling you some of what we understand and some of what we don’t. I still haven’t told you the role that string theory plays in quantum field theory today, but I am going to give you a brief tour of string theory before I do.

What IS String Theory? Well, what’s Particle Theory?

What is particle theory? It’s nothing other than a theory that describes how particles behave.  And in physics language, a theory is a set of equations, along with a set of rules for how the things in those equations are related to physical objects.  So a particle theory is a set of equations which can be used to make predictions for how particles will behave when they interact with one another.

Now there’s always space for confusion here, so let’s be precise about terminology.

  • “Particle theory” is the general category of the equations that can describe particles, of any type and in any combination.
  • A particle theory” is a specific example of such equations, describing a specific set of particles of specific types and interacting with each other in specific ways.

For example, there is a particle theory for electrons in atoms. But we’d need a different one for atoms with both electrons and muons, or for a bottom quark moving around a bottom anti-quark, even though the equations would be of a quite similar type.

Most particle theories that one can write down aren’t relevant (or at least don’t appear to be relevant) to the real world; they don’t describe the types of particles (electrons, quarks, etc.) that we find (so far) in our own universe.   Only certain particle theories are needed to describe aspects of our world.  The others describe imaginary particles in imaginary universes, which can be fun, or even informative, to think about.

Modern particle theory was invented in the early part of the 20th century in response to — guess what? — the discovery of particles in experiments. First the electron was discovered, in 1897; then atomic nuclei, then the proton, then the photon, then the neutrino and the neutron, and so on… Originally, the mathematics used in particle theory was called “quantum mechanics”, a set of equations that is still widely useful today. But it wasn’t complete enough to describe everything physicists knew about, even at the time. Specifically, it couldn’t describe particles that move at or near the speed of light… and so it wasn’t consistent with Einstein’s theory (i.e. his equations) of relativity.

What is Quantum Field Theory?

To fix this problem, physicists first tried to make a new version of particle theory that was consistent with relativity, but it didn’t entirely work.  However, it served as an essential building block in their gradual invention of what is called quantum field theory, described in much more detail in previous posts, starting here. (Again: the distinction between “quantum field theory” and “a quantum field theory” is that of the general versus the specific case; see this post for a more detailed discussion of the terminology.)

In quantum field theory, fields are the basic ingredients, not particles. Each field takes a value everywhere in space and time, in much the same way that the temperature of the air is something you can specify at all times and at all places in the atmosphere. And in quantum field theory, particles are ripples in these quantum fields.

More precisely, a particle is a ripple of smallest possible intensity (or “amplitude”, if you know what that means.)  For example, a photon is the dimmest possible flash of light, and we refer to it as a “particle” or “quantum” of light.

We call such a “smallest ripple” a “particle” because in some ways it behaves like a particle; it travels as a unit, and can’t be divided into pieces.  But really it is wave-like in many ways, and the word “quantum” is in some ways better, because it emphasizes that photons and electrons aren’t like particles of dust.

To sum up:

  • particles were discovered in experiments;
  • physicists invented the equations of particle theory to describe their behavior;
  • but to make those equations consistent with Einstein’s special relativity (needed to describe objects moving near or at the speed of light) they invented the equations of quantum field theory, in which particles are ripples in fields.
  • in this context the fields are more fundamental than the particles; and indeed it was eventually realized that one could (in principle) have fields without particles, while the reverse is not true in a world with Einstein’s relativity.
  • thus, quantum field theory is a more general and complete theory than particle theory; it has other features not seen in particle theory.

Now what about String Theory?

In some sense, strings also emerged from experiments — experiments on hadrons, back before we knew hadrons were made from quarks and gluons.  The details are a story I’ll tell soon and in another context. For now, suffice it to say that in the process of trying to explain some puzzling experiments, physicists were led to invent some new equations, which, after some study, were recognized to be equations describing the quantum mechanical behavior of strings, just as the equations of particle theory describe the quantum mechanical behavior of particles.  (One advantage of the string equations, however, is that they were, from the start, consistent with Einstein’s relativity.) Naturally, at that point, this class of equations was named “string theory”. Continue reading

A Solar System Test of String Theory?!

Baloney.  Hogwash.  Garbage.

That’s what’s to be found in the phys.org news article claiming that “Scientists at Towson University in Towson, Maryland, have identified a practical, yet overlooked, test of string theory based on the motions of planets, moons and asteroids, reminiscent of Galileo’s famed test of gravity by dropping balls from the Tower of Pisa.”

Sounds too good to be true, right?  And it is.

What the scientists have done (or at least claim to have done, and I’ll be happy to take their claims at face value, since I can’t easily check them) is carry out  a technique to test the equivalence principle, a foundation stone of Einstein’s theory of gravity, which implies that all objects, no matter what material they are made of and no matter how heavy they are, will be pulled by gravity in the same way… with the same acceleration.  This principle, in Einstein’s theory, lies behind why all objects on earth fall with the same acceleration (when air resistance can be neglected), and behind why astronauts float in their space stations.

By looking at the precisely measured orbits of different objects in the solar system, which are made from different materials, the authors (James Overduin, Jack Mitcham and Zoey Warecki of little-known Towson University) claim in their July 2013 paper to have provided new tests that the equivalence principle applies to different materials.  That’s very nice work.  The principle works to the precision reached by their tests — which aren’t as precise as some other types of tests, but do explore some domains that haven’t previously been explored.

But what’s that got to do with string theory?  If you read their paper, you will notice that the word “String Theory” appears in only one obscure sentence in the introduction, referring to a very specific form of string theory [with an extremely light spin-zero field, called the dilaton], implying that their work might be relevant for string theory if we lived in a stringy universe that had such a field.  Not even the conclusion, much less the bulk of the paper, mentions strings or string theory.  That’s because the paper has nothing to do with testing string theory; it is merely testing Einstein’s theory of gravity. 

The reason it can’t test string theory is

  1. String theory doesn’t make a precise prediction for how the equivalence principle will be modified, and among the many possible universes string theory can lead to, many have no measurable modification of the equivalence principle;
  2. Even if a violation of the equivalence principle had been detected, or is detected in the future, it isn’t necessarily due to string theory.  It might be due to some other modification of Einstein’s gravity — in fact, the authors consider one such modification in their paper!

So here we have a nice little paper that tests Einstein’s theory of gravity and puts constraints on various alternatives to it — though none of those alternatives is unique to string theory nor is uniquely predicted by string theory.  How did this get billed as a practical test of string theory?

You’ll have to ask the author of the phys.org article, which appears to be a Towson University press release.  [“Provided by Towson University”, says the last line of the phys.org article.] Or you’ll have to ask the scientists involved (unless one of them is the author) — who ought to be pretty darned embarrassed that their work was billed in this way.  I hope they didn’t do this on purpose.  It’s certainly great free advertising for Towson University; who cares if the article’s right if people are willing to read it?  But a willingness to distort the facts to impress and mislead the public is not a worthy attribute.

Visiting the University of Maryland

Along with two senior postdocs (Andrey Katz of Harvard and Nathaniel Craig of Rutgers) I’ve been visiting the University of Maryland all week, taking advantage of end-of-academic-term slowdowns to spend a few days just thinking hard, with some very bright and creative colleagues, about the implications of what we have discovered (a Higgs particle of mass 125-126 GeV/c²) and have not discovered (any other new particles or unexpected high-energy phenomena) so far at the Large Hadron Collider [LHC].

The basic questions that face us most squarely are:

Is the naturalness puzzle

  1. resolved by a clever mechanism that adds new particles and forces to the ones we know?
  2. resolved by properly interpreting the history of the universe?
  3. nonexistent due to our somehow misreading the lessons of quantum field theory?
  4. altered dramatically by modifying the rules of quantum field theory and gravity altogether?

If (1) is true, it’s possible that a clever new “mechanism” is required.  (Old mechanisms that remove or ameliorate the naturalness puzzle include supersymmetry, little Higgs, warped extra dimensions, etc.; all of these are still possible, but if one of them is right, it’s mildly surprising we’ve seen no sign of it yet.)  Since the Maryland faculty I’m talking to (Raman Sundrum, Zakaria Chacko and Kaustubh Agashe) have all been involved in inventing clever new mechanisms in the past (with names like Randall-Sundrum [i.e. warped extra dimensions], Twin Higgs, Folded Supersymmetry, and various forms of Composite Higgs), it’s a good place to be thinking about this possibility.  There’s good reason to focus on mechanisms that, unlike most of the known ones, do not lead to new particles that are affected by the strong nuclear force. (The Twin Higgs idea that Chacko invented with Hock-Seng Goh and Roni Harnik is an example.)  The particles predicted by such scenarios could easily have escaped notice so far, and be hiding in LHC data.

Sundrum (some days anyway) thinks the most likely situation is that, just by chance, the universe has turned out to be a little bit unnatural — not a lot, but enough that the solution to the naturalness puzzle may lie at higher energies outside LHC reach.  That would be unfortunate for particle physicists who are impatient to know the answer… unless we’re lucky and a remnant from that higher-energy phenomenon accidentally has ended up at low-energy, low enough that the LHC can reach it.

But perhaps we just haven’t been creative enough yet to guess the right mechanism, or alter the ones we know of to fit the bill… and perhaps the clues are already in the LHC’s data, waiting for us to ask the right question.

I view option (2) as deeply problematic.  On the one hand, there’s a good argument that the universe might be immense, far larger than the part we can see, with different regions having very different laws of particle physics — and that the part we live in might appear very “unnatural” just because that very same unnatural appearance is required for stars, planets, and life to exist.  To be over-simplistic: if, in the parts of the universe that have no Higgs particle with mass below 700 GeV/c², the physical consequences prevent complex molecules from forming, then it’s not surprising we live in a place with a Higgs particle below that mass.   [It’s not so different from saying that the earth is a very unusual place from some points of view — rocks near stars make up a very small fraction of the universe — but that doesn’t mean it’s surprising that we find ourselves in such an unusual location, because a planet is one of the few places that life could evolve.]

Such an argument is compelling for the cosmological constant problem.  But it’s really hard to come up with an argument that a Higgs particle with a very low mass (and corresponding low non-zero masses for the other known particles) is required for life to exist.  Specifically, the mechanism of “technicolor” (in which the Higgs field is generated as a composite object through a new, strong force) seems to allow for a habitable universe, but with no naturalness puzzle — so why don’t we find ourselves in a part of the universe where it’s technicolor, not a Standard Model-like Higgs, that shows up at the LHC?  Sundrum, formerly a technicolor expert, has thought about this point (with David E. Kaplan), and he agrees this is a significant problem with option (2).

By the way, option (2) is sometimes called the “anthropic principle”.  But it’s neither a principle nor “anthro-” (human-) related… it’s simply a bias (not in the negative sense of the word, but simply in the sense of something that affects your view of a situation) from the fact that, heck, life can only evolve in places where life can evolve.

(3) is really hard for me to believe.  The naturalness argument boils down to this:

  • Quantum fields fluctuate;
  • Fluctuations carry energy, called “zero-point energy”, which can be calculated and is very large;
  • The energy of the fluctuations of a field depends on the corresponding particle’s mass;
  • The particle’s mass, for the known particles, depends on the Higgs field;
  • Therefore the energy of empty space depends strongly on the Higgs field

Unless one of these five statements is wrong (good luck finding a mistake — every one of them involves completely basic issues in quantum theory and in the Higgs mechanism for giving masses) then there’s a naturalness puzzle.  The solution may be simple from a certain point of view, but it won’t come from just waving the problem away.

(4) I’d love for this to be the real answer, and maybe it is.  If our understanding of quantum field theory and Einstein’s gravity leads us to a naturalness problem whose solution should presumably reveal itself at the LHC, and yet nature refuses to show us a solution, then maybe it’s a naive use of field theory and gravity that’s at fault. But it may take a very big leap of faith, and insight, to see how to jump off this cliff and yet land on one’s feet.  Sundrum is well-known as one of the most creative and fearless individuals in our field, especially when it comes to this kind of thing. I’ve been discussing some radical notions with him, but mostly I’ve been enjoying hearing his many past insights and ideas… and about the equations that go with them.   Anyone can speculate, but it’s the equations (and the predictions, testable at least in principle if not in practice, that you can derive from them) that transform pure speculations into something that deserves the name “theoretical physics”.

Wednesday: Sean Carroll & I Interviewed Again by Alan Boyle

Today, Wednesday December 4th, at 8 pm Eastern/5 pm Pacific time, Sean Carroll and I will be interviewed again by Alan Boyle on “Virtually Speaking Science”.   The link where you can listen in (in real time or at your leisure) is

http://www.blogtalkradio.com/virtually-speaking-science/2013/12/05/alan-boyle-matt-strassler-sean-carroll

What is “Virtually Speaking Science“?  It is an online radio program that presents, according to its website:

  • Informal conversations hosted by science writers Alan Boyle, Tom Levenson and Jennifer Ouellette, who explore the explore the often-volatile landscape of science, politics and policy, the history and economics of science, science deniers and its relationship to democracy, and the role of women in the sciences.

Sean Carroll is a Caltech physicist, astrophysicist, writer and speaker, blogger at Preposterous Universe, who recently completed an excellent and now prize-winning popular book (which I highly recommend) on the Higgs particle, entitled “The Particle at the End of the Universe“.  Our interviewer Alan Boyle is a noted science writer, author of the book “The Case for Pluto“, winner of many awards, and currently NBC News Digital’s science editor [at the blog  “Cosmic Log“].

Sean and I were interviewed in February by Alan on this program; here’s the link.  I was interviewed on Virtually Speaking Science once before, by Tom Levenson, about the Large Hadron Collider (here’s the link).  Also, my public talk “The Quest for the Higgs Particle” is posted in their website (here’s the link to the audio and to the slides).

A Quantum Gravity and Cosmology Conference

I attended a conference this past week celebrating two great physicists (Steve Shenker and Renata Kallosh) whom I got to know pretty well during the early part of my career. Unlike most of the conferences I’ve attended in recent years, there were no talks at all about the Large Hadron Collider; the community of speakers was largely drawn from experts on quantum field theory, quantum gravity, string theory and cosmology.

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Any one of the talks would require an extensive article, especially since the required background material isn’t currently explained on this website. So rather than get bogged down in details, I thought I’d try to give you more of the general flavor — reflective, perhaps, of the tenor of the field at the moment. I’ll cover a couple of the talks later, if time permits (though I’m a bit under the gun at the moment…)

If you like to put labels on people, you’d probably call most of the speakers “string theorists.” This is a useful label if you’re in a hurry and not very interested, or if you want to abuse people, but not so useful if you want to actually understand their research. Indeed, out of about 21 talks, there were 3 on string theory.  That said, many of the speakers have in the past done some research in string theory, and many of the talks owe a debt to lessons that have been learned from string theory.

So what were the talks about?  What are these people actually doing? Continue reading

Why You Can’t Easily Dismiss the Cosmological Constant Problem

I’m still early on in my attempts to explain the “naturalness problem of the Standard Model” and its implications.  A couple of days ago I explained what particle physicists mean by the term “natural” — it means “typical” or “generic”.  And I described how, at least from one naive point of view, the Standard Model (the equations we use to describe the known elementary particles and forces) is unnatural.  Indeed any theory is unnatural that has a

  • a spin-zero particle (in the Standard Model, the newly discovered Higgs particle), which
  • is very lightweight in the following sense: it has a very very low mass-energy compared to the energy at which gravity becomes a strong force, and which
  • isn’t accompanied (in the Standard Model specifically) by other related particles that also have small masses.

But I didn’t actually explain any of this yet; I just described it.

Specifically, I didn’t start yet to explain what causes the Standard Model to be unnatural.  This is important to do, because, as many attentive readers naturally complained, my statements about the unnatural aspect of the Standard Model was based on a rather arbitrary-sounding statistical argument, and story-telling, which is hardly enough for scientific discussion.  Patience; I’ll get there, not today but probably the next installment after today’s.

To see why the argument I gave is actually legitimate (which doesn’t mean it is right, but if it’s wrong it’s not for a simple reason you’ll think of in five minutes), it is necessary to look in a little bit more detail at one of the most fundamental aspects of quantum field theory: quantum fluctuations, and the energy they carry.  So for today I have written an article about this, reasonably complete.

Be prepared — the article runs headlong into the only naturalness problem in particle physics that is worse than the naturalness problem of the Standard Model (the one I wrote about on Tuesday)!  I am referring to the “cosmological constant problem”.  In a nutshell:

  • we can calculate that, in any typical quantum field theory with gravity, the amount of energy in empty space (often called `dark energy’) should be huge, and we know of no way to avoid having it in a typical somewhat-realistic theory of the universe,
  • yet measurements of the cosmos — in fact, the very existence of a large and old universe — assure that, if Einstein’s theory of gravity is basically right, then instead of a huge amount of `dark energy’, there’s just a very small amount — not much more than the total amount of mass-energy [E=mc² energy] found in all the matter that’s scattered thinly throughout the universe.

After you’ve read about quantum fluctuations and the cosmological constant problem, and have a bit of a sense as to why it is so hard to make it go away, we can go back to the Standard Model, and try to understand the naturalness problem that is associated with the Higgs particle and field.  It all has to do with another aspect of quantum fluctuations — the fact that their energy depends on, and therefore helps determine, the average value of the Higgs field.

A First Stab at Explaining “Naturalness”

Arguably the two greatest problems facing particle physicists, cosmologists, string theorists, and the like are both associated with an apparent failure of a notion called “naturalness”.  Until now, I’ve mostly avoided this term on this site, because to utter the word demands an extended explanation.  After all, how could nature be unnatural, by definition?

Well, the answer is that the word “natural” has multiple meanings.  The one that scientists are using in this context isn’t “having to do with nature” but rather “typical” or “as expected” or “generic”, as in, “naturally the baby started screaming when she bumped her head”, or “naturally it costs more to live near the city center”, or “I hadn’t worn those glasses in months, so naturally they were dusty.”  And unnatural is when the baby doesn’t scream, when the city center is cheap, and when the glasses are pristine. Usually, when something unnatural happens, there’s a good reason.

I’ve started writing an article about naturalness and unnaturalness, and how there are two great mysteries about how unnatural our universe is, one of which lies at the heart of the Large Hadron Collider‘s [LHC’s] research program.  What I’ve written so far explains what naturalness means and (in part) how it applies to the Standard Model (the equations we use to describe the known elementary particles and forces).  I’ll be extending the article to explain this in more detail, and to explain the scientific argument as to why it is so unnatural to have a Higgs particle that is “lonely” — with no other associated particles (beyond the ones we already know) of roughly similar mass.  This in turn is why so many particle physicists have long expected the LHC to discover more than just a single Higgs particle and nothing else… more than just the Standard Model’s one and only missing piece… and why it will be a profound discovery with far-reaching implications if, during the next five years or so, the LHC experts sweep the floor clean and find nothing more in the LHC’s data than the Higgs particle that was found in 2012.

Courses, Forces, and (w)Einstein

This week and next, I’m very busy preparing and delivering a new class (four lectures, 1.5 hours each), for a non-technical audience, on the importance of and the discovery of the Higgs particle.  I’ll be giving it in Western Massachusetts (my old stomping grounds).  If it goes well I may try to give these lectures elsewhere (and please let me know if you know of an institution that might be interested to host them.)   Teaching a new class for a non-technical audience requires a lot of concentration, so I probably won’t get too much writing in over that period.

Still, as many of you requested, I do hope soon to follow up last week’s article (on how particle physicists talk about the strength of the different forces) with an article explaining how both particles and forces arise from fields — a topic I already addressed to some extent in this article, which you may find useful.

Now — a few words on the flap over the suggestion that math Ph.D. and finance expert Eric Weinstein, in his mid-40s, may be the new Albert Einstein.  I’ve kept my mouth shut about this because, simply, how can I comment usefully on something I know absolutely nothing about?  (Admittedly, the modern media, blogosphere and Twitter seem to encourage people to make such comments. Not On This Blog.) There’s no scientific paper for me to read.  There’s no technical scientific talk for me to listen to.  I know nothing about this person’s research.  All I know so far is hearsay.  That’s all almost anyone knows, except for a few of my colleagues at Oxford — trustworthy and experienced physicists, who sound quite skeptical, and certainly asked questions that Weinstein couldn’t answer... which doesn’t mean Weinstein is necessarily wrong, only that his theory clearly isn’t finished yet.  (However, I must admit my expert eye is worried that he didn’t have ready answers to such basic questions.)

What I do know is that the probability that Weinstein is the new Einstein is very low.  Why?  Because I do know a lot about how very smart people with very good ideas fail to be Einstein.  It’s not because they’re dumb or foolish. Continue reading