# Astrophysics and Gravitation:

### Fundamental constants: Big G revisited

Davis, R. (2010). Fundamental constants: Big G revisited Nature, 468 (7321), 181-183 DOI: 10.1038/468181b

Davis, R. (2010). Fundamental constants: Big G revisited Nature, 468 (7321), 181-183 DOI: 10.1038/468181b

Category: This Week In The Universe
Tagged AdS/CFT correspondence, antihydrogen, antimatter, black holes, fundamental constants, gauge symmetries, gauge/gravity duality, supergeometry, supernovae
Comments Off on This “Week” in the Universe: November 9th – November 22nd

The father of modern observational cosmology, Allan Sandage, passed away on November 13th at the age of 84. He is remembered for arriving at the first credible value of the Hubble constant, the age of the universe, and his Hilbert-esque list of important outstanding problems in cosmology.

In 1995, at a conference in the Canary Islands, Sandage formulated “23 astronomical problems for the next three decades“.

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Negrello, M., & et al. (2010). The Detection of a Population of Submillimeter-Bright, Strongly Lensed Galaxies Science, 330 (6005), 800-804 DOI: 10.1126/science.1193420

Category: This Week In The Universe
Tagged ALICE, astrophysics, asymptotic freedom, ATLAS, CERN, CMS, CP-violation, fine-structure constant, galaxy formation, gamma rays, gravitational lens, Higgs, ions, lead, lensing, leptons, LHC, MiniBooNE, protons, sterile neutrino, symmetry
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From NASA, ESA, and J. Anderson and R. van der Marel (STScI):

The multicolor snapshot, at top, taken with Wide Field Camera 3 aboard NASA’s Hubble Space Telescope, captures the central region of the giant globular cluster Omega Centauri. All the stars in the image are moving in random directions, like a swarm of bees. Astronomers used Hubble’s exquisite resolving power to measure positions for stars in 2002 and 2006.

From these measurements, they can predict the stars’ future movement. The bottom illustration charts the future positions of the stars highlighted by the white box in the top image. Each streak represents the motion of the star over the next 600 years. The motion between dots corresponds to 30 years.

By precisely observing the stars in Omega Centauri, a 10 million star globular cluster within our galaxy, the NASA/ESA team has been able to predict the stars’ movements over the next 10,000 years. Considering how many variables are in this system, this is an awfully impressive achievement.

For more, see Hubble Data Used to Look 10,000 Years into the Future.

Two weeks of news in one!

Dan Hooper, & Lisa Goodenough (2010). Dark Matter Annihilation in The Galactic Center As Seen by the Fermi Gamma Ray Space Telescope arXiv arXiv: 1010.2752v1

Analyzing old data from the Fermi Gamma Ray Space Telescope, the authors have noticed gamma ray emissions consistent with predictions for a certain type of dark matter. Unfortunately, these things are never nice, clear problems where they’ve definitely seen dark matter or have definitely not seen it, but it’s an exciting collection of data points for astrophysicists who are on the dark matter hunt. It could turn out to be the evidence that people have been looking for, but it’s too early to say anything definitively.

For more, see Signs of Destroyed Dark Matter Found in Milky Way’s Core, Fermilab theorist sees dark matter evidence in public data.

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Category: This Week In The Universe
Tagged AdS/CFT correspondence, astrophysics, cosmic distance ladder, cosmology, dark matter, experimental quantum gravity, funding, gamma rays, general relativity, Horava-Lifshitz gravity, Inflation, loop, loop quantum gravity, neutrinos, observatory, pulsars, quantum gravity, standard candle, string theory, supernovae, symmetry breaking
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Last week, I received a copy of MASSIVE: The Missing Particle that Sparked the Greatest Hunt in Science (November 2010) written by Ian Sample from the good PR people at Perseus Books. It was clear from the beautifully assembled prose in the prologue, that this book was going to live up to my expectations.

Instead of being yet another book on the LHC or the history of the Standard Model, *MASSIVE* is an utterly human account of how the times leading up to the exposition of the Higgs field shaped the science of the day and continue to shape our current searches in modern physics.

The human element of this story was so bizarrely engaging, from Peter Higgs stopping to buy stamps on the late Einstein’s birthday to Prentiki’s crushing referee report on Higgs’s second paper; the way that the history was braided with physics and personal accounts makes *MASSIVE *a really exceptional read.

On October 21st, 1914, the great American mathematics writer and popularizer, Martin Gardner was born. While not a mathematician himself, Gardner’s popular works inspired a generation of young people to pursue mathematics with his great efforts to bring recreational mathematics into the American home. From 1956 to 1981, he wrote the *Mathematical Games * column in Scientific American and over the course of his long career, authored more than 70 books (not just limited to recreational mathematics; he was also a great friend to sceptics).

Since Martin Gardner was notoriously shy and often would choose not to attend awards ceremonies honouring him, in 1993, a puzzle collector by the name of Tom Rodgers convinced him to attend an event devoted to mathematical puzzle solving. The event was held again in 1996, and again attended by Gardner (for the second and final time), and has since become a semi-annual-tradition, being held near Atlanta. The program for this event, called Gathering for Gardner, consists of any topic which Gardner wrote on during his career.

In May of this year, Gardner passed away at the age of 95. While he wanted no memorials* in his honour, he did want the Gatherings for Gardner to continue. This year, the first gathering since his death, the *Martin Gardner Global Celebration of Mind Gatherings* will take place in dozens of different locations around the world, on October 21st, 2010 (on what would have been Gardner’s 96th Birthday).

To celebrate Gardner’s work and life, and to share in his love for mathematics, science, magic and puzzles, the *G4G Foundation* is encouraging everyone to perform a magic trick, share a puzzle or recreational mathematics problem with friends.

In a week where New York Magazine publishes an anti-math article on “ridiculous sounding” popular mathematics classes, I think the world needs a little dose of recreational mathematics, and to remember how fun and exciting Gardner made mathematics for the general public.

Many of these originally appeared in Gardner’s Scientific American column, if you want solutions, I can post those next week (although Google should be able to find the answers to any people can’t get).

1. You are in a room with no metal objects except for two iron rods. Only one of them is a magnet. How can you identify which one is a magnet?

2. Write out the alphabet starting with J* (like: JKLMNOPQRSTUVWXYZABCDEFGHI)*. Erase all letters that have left-right symmetry (such as A) and count the letters in each of the five groups that remain.

3. Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys? Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?

4. A logician vacationing in the South Seas finds himself on an island inhabited by the two proverbial tribes of liars and truth‐tellers. Members of one tribe always tell the truth; members of the other always lie. He comes to a fork in a road and has to ask a native bystander which branch he should take to reach a village. He has no way of telling whether the native is a truthteller or liar. The logician thinks a moment and then asks one question only. From the reply, he knows which road to take. What single yes/no question does he ask?

5. Make a single cut (it needn’t be straight) to divide the brownie below into two identical pieces.

6. A woman either always answers truthfully, always answers falsely, or alternates true and false answers. How, in two questions, each answered by yes or no, can you determine whether she is a *truther*, a *liar*, or an *alternater*?

7. Two missiles speed directly toward each other, one at 9,000 miles per hour and the other at 21,000 miles per hour. They start 1,317 miles apart. Without using pencil and paper, calculate how far apart they are one minute before they collide.

8. Can you change the giraffe into a different giraffe by moving just one toothpick?

9. Family planning. A Family of four (father, mother, son, and daughter) went on a hike. They walked all day long and, when evening was already drawing on, came to an old bridge over a deep gully. It was very dark and they had only one lantern with them. The bridge was so narrow and shaky that it could hold no more than two persons at a time. Suppose it takes the son 1 minute to cross the bridge, the daughter 3 minutes, the father 8 minutes, and the mother 10 minutes. Can the entire family cross the bridge in 20 minutes? If so how? (When any two persons cross the bridge, their speed is equal to that of the slower one. Also the lantern must be used while crossing the bridge.)

10.

For more math puzzles try Cliff Pickover or the G4G Hosting site.

*Scientific American did do an excellent tribute piece for Gardner after his death.

Category: Local News
Tagged Martin Gardner, mathematics, puzzles, recreational mathematics
9 Comments

This is the firstguestpost on The Language of Bad Physics by Cosmic Variance‘s Sean Carroll. This post is cross-posted on Cosmic Variance.

A few weeks ago there was a bit of media excitement about a somewhat surprising experimental result. Observations of quasar spectra indicated that the fine structure constant, the parameter in physics that describes the strength of electromagnetism, seems to be slightly different on one side of the universe than on the other. The preprint is here.

Remarkable, if true. The fine structure constant, usually denoted α, is one of the most basic parameters in all of physics, and it’s a big deal if it’s not really constant. But how likely is it to be true? This is the right place to trot out the old “extraordinary claims require extraordinary evidence” chestnut. It’s certainly an extraordinary claim, but the evidence doesn’t really live up to that standard. Maybe further observations will reveal truly extraordinary evidence, but there’s no reason to get excited quite yet.

Chad Orzel does a great job of explaining why an experimentalist should be skeptical of this result. It comes down to the figure below: a map of the observed quasars on the sky, where red indicates that the inferred value of α is slightly lower than expected, and blue indicates that it’s slightly higher. As Chad points out, the big red points are mostly circles, while the big blue points are mostly squares. That’s rather significant, because the two shapes represent different telescopes: circles are Keck data, while squares are from the VLT (“Very Large Telescope”). Slightly suspicious that most of the difference comes from data collected by different instruments.

But from a completely separate angle, there is also good reason for theorists to be skeptical, which is what I wanted to talk about. Theoretical considerations will always be trumped by rock-solid data, but when the data are less firm, it makes sense to take account of what we already think we know about how physics works.

The crucial idea here is the notion of a scalar field. That’s just fancy physics-speak for a quantity which takes on a unique numerical value at every point in spacetime. In quantum field theory, scalar fields lead to spinless particles; the Higgs field is a standard example. (Other particles, such as electrons and photons, arise from more complicated geometric objects — spinors and vectors, respectively.)

The fine structure constant is a scalar field. We don’t usually think of it that way, since we usually reserve the term “field” for something that actually varies from place to place rather than remaining constant, but strictly speaking it’s absolutely true. So, while it would be an amazing and Nobel-worthy result to show that the fine structure constant were varying, it wouldn’t be hard to fit it into the known structure of quantum field theory; you just take a scalar field that is traditionally thought of as constant and allow it to vary from place to place and time to time.

That’s not the whole story, of course, When a field varies from point to point, those variations carry energy. Think of pulling a spring, or twisting a piece of metal. For a scalar field, there are three important contributions to the energy: kinetic energy from the field varying in time, gradient energy from the field varying in space, and potential energy associated with the value of the field at every point, unrelated to how it is changing.

For the fine structure constant, the observations imply that it changes by only a very tiny bit from one end of the universe to the other. So we really wouldn’t expect the gradient energy to be very large, and there’s correspondingly no reason to expect the kinetic energy to matter much.

The potential energy is a different matter. The potential is similar to the familiar example of a ball rolling in a hill; how steep the potential is near its minimum is related to the *mass* of the field. For most scalar fields, like the Higgs field, the potential is extremely steep; this means that if you displace the field from the minimum of its potential by just a bit, it will tend to immediately roll back down.

*A priori*, we don’t know ahead of time what the potential should look like; specifying it is part of defining the theory. But quantum field theory gives us clues. At heart, the world is quantum, not classical; the “value” of the scalar field is actually the expectation value of a quantum operator. And such an operator gets contributions from the intrinsic vibrations of all the other fields that it couples to — in this case, every kind of charged particle in the universe. What we actually observe is not the “bare” form of the potential, but the renormalized value, which takes into account the accumulated effects of various forms of virtual particles popping in and out of the quantum vacuum.

The basic effect of renormalization on a scalar field potential is easy to summarize: it makes the mass large. So, if you didn’t know any better, you would expect the potential to be as steep as it could possibly be — probably up near the Planck scale. The Higgs boson probably has a mass of order a hundred times the mass of a proton, which sounds large — but it’s actually a big mystery why it isn’t enormously larger. That’s the hierarchy problem of particle physics.

So what about our friend the fine structure constant? Well, if these observations are correct, the field would have to have an extremely tiny mass — otherwise it wouldn’t vary smoothly over the universe, it would just slosh harmlessly around the bottom of its potential. Plugging in numbers, we find that the mass has to be something like 10^{-42} GeV or less, where 1 GeV is the mass of the proton. In other words: extremely, mind-bogglingly small.

But there’s no known reason for the mass of the scalar field underlying the fine structure constant to be anywhere near that small. This was established in some detail by Banks, Dine, and Douglas. They affirmed our intuition, that a tiny change in the fine structure constant should be associated with a huge change in potential energy.

Now, there are loopholes — there are always loopholes. In this case, you could possibly prevent those quantum fluctuations from renormalizing your scalar-field potential simply by shielding the field from interactions with other fields. That is, you can impose a symmetry that forbids the field from coupling to other forms of matter, or only lets it couple in certain very precise ways; then you could at least imagine keeping the mass small. That’s essentially the strategy behind the supersymmetric solution to the hierarchy problem.

Problem is, that route is a complete failure when we turn to the fine structure constant, for a very basic reason: we can’t prevent it from coupling to other fields, it’s the parameter that governs the strength of electromagnetism! So like it or not, it will couple to the electromagnetic field and all charged particles in nature. I talked about this in one of my own papers from a few years ago. I was thinking about time-dependent scalars, not spatially-varying ones, but the principles are precisely the same.

That’s why theorists are skeptical of this claimed result. Not that it’s impossible; if the data stand up, it will present a serious challenge to our theoretical prejudices, but that will doubtless goad theorists into being more clever than usual in trying to explain it. Rather, the point is that we have good reasons to suspect that the fine structure constant really is constant; it’s not just a fifty-fifty kind of choice. And given those good reasons, we need really good data to change our minds. That’s not what we have yet — but what we have is certainly more than enough motivation to keep searching.

J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum, R. F. Carswell, & M. B. Bainbridge (2010). Evidence for spatial variation of the fine structure constant arXiv arXiv: 1008.3907v1

Category: Language and Physics
Tagged astrophysics, fundamental constants, guest blogging
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Brilliant mathematician and the father of fractals, Benoît Mandelbrot, died on Thursday, October 14th at the age of 85.

If you take the beginning and the end, I have had a conventional career… But it was not a straight line between the beginning and the end. It was a very crooked line.

Watch his TED talk from February of 2010: Benoit Mandelbrot: Fractals and the art of roughness, the NOVA special on fractals (with Mandelbrot interview), and read his tribute in The New York Times.

You know that friend you have, the one who likes cars, watchin’ action flicks and talking about physics, except the last time they actually “studied” any science was in junior high? Yeah, *that* friend… Well, I read *the *book for them today.

*E=MC*²*: Simple Physics: Why Balloons Rise, Apples Fall, and Golf Balls Go Awry* by Jeff Stewart, published by Readers Digest.

A kind publicist sent a copy of the latest in the Reader’s Digest Blackboard Books™ series last week and I have to say, it was a pretty cute read.

The book basically covers all of the content that you’d find in a high school curriculum, but without any math, making it ideal for an adult learner looking for a qualitative picture of physics. It also ends with a little bit of general relativity, quantum mechanics, and cosmology, because, frankly, that’s where popular interest lies (and should, because it’s the good stuff, after all).

What makes this book a little different from the sea of popular physics books out there is that it is written in very simple language (*okay, so I wasn’t wild about that… or the fragment sentences*) and is dense in everyday examples (*if driving and action movies are everyday examples for you… okay, so they’re aren’t so much for me*). I did, however, throughly enjoy all the puns and pop-culture references contained within the witty section titles like, “Float like a feather, fall like a hammer”, “The good, the bad, and the impossible”, and “Why are so many physicists growing a GUT?”.

Often, one of my complaints with popular books written for such a general audience is that they are written from a perspective totally removed from how science is done and who scientists really are. Authors often make physicists sound like these lofty pillars of men who are untouched by anything but the pursuit of ultimate universal truth, and blah, blah, blah. I knew I was going to have respect for Stewart by the time I made it to the 20th page and came across this:

It’s also worth remembering that physics -like football, fashion, fishing, and even things we do that don’t start with “f” – is a human activity. Physicists are people. They argue about their ideas, they make mistakes, and they do what needs to be done to make sure they have money to continue their work next year.

*Yes!* So, after he starts with a nice introduction on what physics is, why people do physics, and who physicists are, Stewart starts into classical mechanics and begins defining the building blocks of our modern physical theories (with concepts like force, energy, work, power, etc.) without any offensive over simplifications.

I admit, 100 pages later, I was a little nervous when I started the relativity section, but again, all was (mostly) well. I *do* have to give the author credit though for making general relativity (arguably the sexiest theory of all time, of any field) sound as *unsexy *as possible.

One way to picture the curvature of time and space and the movement that it causes is to think of space[time] as a cheap old mattress on a cheap old bed, the kind that sags a lot when you lie on it. Whoever gets into bed with you will enter your gravitational field (which is the bit of space and time -that is, mattress- that you’ve curved). Once that person is on that curved part, they’ll slide into your pit and there’ll be two of you down there, and with their mass added that gravitational pit will be even deeper and more difficult to struggle out of than it was. If a couple of children, the dog, and Grandma then also climb on the bed and roll into the pit you’ve made, then together you’ve pretty much created your own black hole: an area of space and time so curved by a huge and compact mass that it is impossible for anything – even light – to escape its gravity.

*Ugh*. I wish light really *couldn’t* escape that scene so I never, *ever,* have to picture it again.

Thankfully, quantum mechanics made it out without needing the proverbial bag over its head for its walk of shame home:

I’m sure you remember our day on the beach: the sun, the surfers, the double slit experiment, which seemed to prove that light is made up of waves, not particles, because the light waves interfere and cause a diffraction pattern. You even made diffraction fringes in the gap between your fingers.

Alright, so a popular physics book with a good sense of humour is always fine by me. Perhaps my favourite part was the brief section on inflation:

Maybe our universe was created by some bug-eyed monster who’d discovered the same laws as Alan Guth, a slimy bug-eyed monster who just happened to have some false vacuum handy.

*Yeah*, maybe that *is* what happened, Alan Guth, maybe it is…

In summary, this was actually a cute read. I wouldn’t recommend it to someone with a science background, but I would definitely recommend it to an interested outsider whose regular meat-and-potatoes world wanted some added depth. It’s the popular physics version of a Disney movie that is short and kind of shallow, but it has a few good jokes thrown in for mom and dad*.

I’ll end with another quote from Stewart:

Read on, and see for yourself. Just remember, at all times, to keep your clothes on and your wits about you.**