Archive for August, 2008

The prophetic promise of category theory

Monday, August 11th, 2008

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When it comes to  creating the final theory of everything, physicists have an ever broadening (and bewildering) choice of mathematical tricks with which to tackle the mysteries of the universe.

A couple of years ago, random matrix theory cropped up as a potential framework for a new kind of science. And a fascinating idea it is too.

Talking of a new kind of science, what  cellular automatons can’t do, isn’t worth knowing, or so we’re told.

Then there is the non-compact real form of the E8 Lie algebra, a surfer’s dream of a final theory.

Today there’s a new kid on the block called category theory, a kind of stripped down, souped up group theory that has been taking mathematics by storm since it was invented in the 1940s.

It’s chief claim is that it has become a hugely powerful tool for unifying concepts in mathematics and so is obviously going to do the same for physics. (That kind of reasoning may not be as madcap as it sounds).

Chief among the category theory evangelists is Bob Croeke at the University of Oxford who today publishes a kind of idiot’s physicists guide to category theory, to give any interested parties a taste for the field.

“Category theory should become a part of the daily practice of the physicist,” argues Croeke. “The reason for this is not that category theory is a better way of doing mathematics, but that monoidal categories constitute the actual algebra of practicing physics.”

For an old dog, this will surely be a trick too far. But for any whipper snappers out there, it looks intriguing, no?

Ref: arxiv.org/abs/0808.1032: Introducing Categories to the Practicing Physicist

Spook ‘n’ spock (part 2)

Sunday, August 10th, 2008

More highlights from the physics arXiv this week:

Quantum Algorithms

Dark Stars: Dark Matter in the First Stars leads to a New Phase of Stellar Evolution

Sensing Shallow Seafloor and Sediment Properties, Recent History

A 3D Discrete Model of the Diaphragm and Human Trunk

Terahertz Metamaterials on Free-Standing Highly-Flexible Polyimide Substrates

Nonlinear Energy Harvesting

Feasibility of Acoustic Neutrino Detection in Ice: Design and Performance of the South Pole Acoustic Test Setup (SPATS)

Spook ‘n’ spock (part 1)

Saturday, August 9th, 2008

The best of the rest from the arXiv this week:

Placing Direct Limits on the Mass of Earth-Bound Dark Matter

Self-Organized Periodicity of Protein Clusters in Growing Bacteria

Neutrino Astrophysics

Using the Energy Spectrum at DAMA/LIBRA to Probe Light Dark Matter

Spin-Independent Elastic WIMP Scattering and the DAMA Annual Modulation Signal

Introductory Lectures on String Theory

Reconstruction of Quantum Mechanics with Information Operators

Spooky action at a distance gets spookier

Friday, August 8th, 2008

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Take a pair of entangled photons and perform a measurement on one of them. According to the strange laws of quantum mechanics, this measurement immediately influences the state of the second photon, no matter how far apart they are. Einstein bridled at the possibility that an instantaneous influence could take place. He called it spooky action at a distance and the term stuck.

Today spooky action at a distance just got spookier. Stephen Harris at Stanford University posts details of an experiment in which he zaps one photon in an entangled pair in a way that ensures that this photon is modulated.

But his extraordinary result is that after zapping the first photon, he can then zap the second photon in way that negates (or enhances) the modulation  of the first.

That’s not just spooky, it’s double spooky.  It opens up the possibility of a few neat new tricks such as pulse shaping photons at a distance. And it raises some interesting questions about the nature of entanglement and how it may come to be exploited in future.

Ref: arxiv.org/abs/0808.0903: Nonlocal Modulation of Entangled Photons

Schroedinger-like PageRank wave equation could revolutionise web rankings

Thursday, August 7th, 2008

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The PageRank algorithm that first set Google on a path to glory measures the importance of a page in the world wide web.  It’s fair to say that an entire field of study has grown up around the analysis of its behaviour.

That field looks set for a shake up following the publication today of an entirely new formulation of the problem of ranking web pages. Nicola Perra at the University of Cagliari in Italy and colleagues have discovered that when they re-arrange the terms in the PageRank equation the result is a Schroedinger-like wave equation.

So what, I hear you say, that’s just a gimmick. Perhaps, but the significance is that it immediately allows the entire mathematical machinery of quantum mechanics to be brought to bear on the problem–that’s 80 years of toil and sweat.

Perra and pals point out some of the obvious advantages and disadvantages of the new formulation.

First, every webpage has a quantum-like potential. The topology of this potential gives the spatial distribution of PageRank throughout the web. What’s more, this distribution can be calculated in a straightforward way which does not require iteration as the conventional PageRank algorithm does.

So the PageRank can be calculated much more quickly for relatively small webs and the team has done a simple analysis of the PageRanking of the .eu domain in this way. However, Perra admits that the iterative method would probably be quicker when working with the tens of billions of pages that make up the entire web.

But the great promise of this Schroedinger-like approach is something else entirely. What the wave equation allows is a study of the dynamic behaviour of PageRanking, how the rankings change and under what conditions.

One of the key tools for this is called perturbation theory. It’s no understatement to say that perturbation theory revolutionised our understanding of the universe when it was applied to quantum theory in the 1920s and 1930s.

The promise is that it could do the same to our understanding of the web and if so, this field is in for an interesting few years ahead.

Ref: arxiv.org/abs/0807.4325: Schroedinger-like PageRank equation and localization in the WWW

Creating random numbers the quantum way

Wednesday, August 6th, 2008

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The stream of high quality papers continues from the lab of Andrew Shields at Toshiba Research in Cambridge, UK. Today, his team unveils a new type of quantum random number generator and a fine looking machine it appears to be.

Here’s the idea. Create a stream of single photons are emitted at random intervals that depend entirely on quantum processes–an attenuated continuous wave laser should do the trick. Fire them at a gated photon detector which accurately records their (entirely random) arrival time. The arrival time within a gated time period is then a random number ready for use in quantum cryptography or whatever app you happen to need it for.

The team uses the souped up photodiode that we saw a couple of weeks back to make the photon detections at rates of 4MB/s. And Shields says 100MB/s is possible–that’s two orders of magnitude faster than existing quantum random number generators.

What’s more, the new device is much simpler than other quantum random generators. One popular approach is to send a photon through a beam splitter and see which way it goes. In principle, the outcome is perfectly random but in practice it ain’t because it’s almost impossible to make a beam splitter with perfect 50% probability split.

In practice, the data from these devices needs a certain amount of massaging which can be costly and time-consuming.

So Shields looks to be on a roll.  Exciting times in his lab.

Ref: arxiv.org/abs/0807.4111: A High Speed, Post-Processing Free, Quantum Random Number Generator

Quantum communication: when 0 + 0 is not equal to 0

Tuesday, August 5th, 2008

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One of the lesser known cornerstones of modern physics is Claude Shannon’s mathematical theory of communication which he published in 1948 while juggling and unicycling his way around Bell Labs.

Shannon’s theory concerns how a message created at one point in space can be reproduced at another point in space. He calls the conduit for such a process a channel and the limits imposed by the universe on this process the channel capacity.

The capacity of a communications channel is hugely important idea. It tells you, among other things, the rate at which you can send information from one location to another, without loss. If you’ve ever made a phone call, watched television or surfed the internet you’ll have benefited from the work associated with this idea.

In recent years, our ideas about communication have been transformed by the possibility of using quantum particles to carry information. When that happens the strange rules of quantum mechanics govern what can and cannot be sent from one region of space to another. This kind of thinking has has spawned the entirely new fields of quantum communication and quantum computing.

But ask a physicist what the capacity is of a quantum information channel and she’ll stare at the floor and shuffle her feet. Despite years of trying, nobody has been able to update Shannon’s theory of communication with a quantum version.

Which is why a paper today on the arXiv is so exciting. Graeme Smith at the IBM Watson Research Center in Yorktown Heights NY (a lab that has carried the torch for this problem) and Jon Yard from Los Alamos National Labs have made what looks to be an important breakthrough by calculating that two zero-capacity quantum channels can have a nonzero capacity when used together.

That’s interesting because it indicates that physicists may have been barking up the wrong tree with this problem: perhaps the quantum capacity of a channel does not uniquely specify its ability for transmitting quantum information. And if not, what else is relevant?

That’s going to be a stepping stone to some interesting new thinking in the coming months and years. Betcha!

Ref: arxiv.org/abs/0807.4935: Quantum Communication With Zero-Capacity Channels

Deconstructing DiMaggio’s 56-game hitting streak

Monday, August 4th, 2008

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“The incredible record of Joe DiMaggio in the summer of 1941 is unparalleled. No one has come close—before or since—to equaling his streak of hitting safely in 56 games in a row.”

So begin Steve Strogatz and Sam Arbesman from Cornell University in their paper discussing the likelihood of DiMaggio’s record.

“People have…stated that it is the only record in baseball (or perhaps even in all of sports) that never should have happened, statistically speaking: while other records can be explained by expected outliers over the long and varied history of professional baseball (nearly 150 years), DiMaggio’s record stands alone”

But as with so many statistical assumptions, a proper analysis can reveal counterintuitive results, say Strogatz and Arbesman. The pair have modelled the phenomenon of hitting streaks using a number of simple models and guess what…DiMaggio’s record is not as unexpected as it looks.

The models suggest that while a DiMaggio-like record is unlikely in any given year, it is not unlikely to have occurred about once within the history of baseball.

But having plugged the statistical performance of a number of players into the model, DiMaggio is not the most likely to have picked up such a record. That honour goes to one of Ross Barnes, Willie Keeler or Hugh Duffy (there is no single most likely player). DiMaggio, it turns out, is 47th most likely player to have reached the record in one of the models used.

More curious is why Strogatz, widely considered to be the father of the small world network theory, has taken up the baton in examining baseball statistics. He joins a small but select group of physicists and mathematicians with a passion for the game including Gene Stanley and Percy Diaconis.

So what’s next? Surely the task now is to find a record that defies statistics in the sense that it is truly unlikely. Let me be the first to suggest Don Bradman’s 99.94 batting average in test cricket.

Ref: arxiv.org/abs/0807.5082: A Monte Carlo Approach to Joe DiMaggio and Streaks in Baseball

In case ya missed ’em…

Sunday, August 3rd, 2008

The iced buns from the physics arxiv blog this week:

The Casimir conundrum

The painful search for gravitational waves

The day the solar wind disappeared

Why small black holes cannot grow

Push ‘n’ shove

Saturday, August 2nd, 2008

The best of the rest from the physics arxiv:

The NASA EPOXI Mission of Opportunity to Gather Ultraprecise Photometry of Known Transiting Exoplanets

EconoThermodynamics, or the World Economy “Thermal Death” Paradox

How the Surrounding Water Changes the Electronic and Magnetic Properties of DNA

Traffic by Small Teams of Molecular Motors

IceCube: A Cubic Kilometer Radiation Detector

The Cosmology of the Divine Comedy