Making Waves

Gravitational waves are already the science story of the week but if the rumours hold up they will one of the science stories of the century. We’ll know soon enough, as there will be a press conference in Washington DC at 10:30am (local time) on Thursday. And this revolution will be broadcast; you can catch a livestream on Youtube.

The rumour doing the rounds is that the LIGO team will announce the detection of gravitational waves emitted during the merger of two black holes. Here’s a quick explainer as we head into the (we hope!) big day…


What Are Gravitational Waves? Gravitational waves are waves that travel through the fabric of space, just as ripples move across the surface of a pond.

Waves In Space?  Yep. By detecting gravitational waves we are watching space bend and stretch.

Gravitational fields are encoded in the curvature of space CC BY-SA 3.0

Gravitational fields are encoded in the curvature of space CC BY-SA 3.0

Really? Waves in Space? Yep, Really. Once upon a time, physicists thought space was rigid and unchanging. However, in 1915 Einstein’s General Theory of Relativity told us that gravitational forces are communicated via the curvature of space. This is often described via the “rubber sheet model”; curved space is analogous to a rubber sheet warped by massive objects that sit upon it. But what really matters for gravitational waves is not just that space (or, more properly, spacetime) can curve, but that its curvature can change. As stars and planets move the curvature of space must adapt itself to their new positions. If the curvature didn’t change the universe would be a very strange place as a moving object would leave its gravitational field behind, a little like Peter Pan losing his shadow. Mathematically, the ability of space to bend and stretch means that waves can move through it, and this led Einstein to predict that gravitational waves could exist.

Why Is This So Exciting?  Science waited 100 years for this; who wouldn’t be excited? For physicists, LIGO is testing a key prediction of General Relativity, which is one of the most fundamental theories we have. On top of that, if LIGO sees gravitational waves emitted by a pair of black holes as they collide and merge we will have ringside seats to some of the most remarkable events in the universe. And a detection by LIGO will mark the culmination of decades of work by a cast of thousands who have built what is probably the world’s most sensitive scientific instrument.

How Does LIGO Work? LIGO has two giant L-shaped detectors; one in Washington State and the other in Louisiana, on the other side of the United States. Each detector is 4 kilometres on a side. Gravitational waves always stretch space in one direction while squeezing it in another, so a passing gravitational wave expands one side of the “L” while shrinking the other. Powerful lasers then pick up the resulting change in the lengths of the arms. The stretching and squeezing is tiny – each arm may grow and shrink by only a quadrillionth of a millimetre, far less than the diameter of a single atom. By having two detectors LIGO rules out spurious signals from local vibrations, traffic or tiny earthquakes; LIGO also pools its data with two smaller European experiments, GEO and VIRGO.

Spacetime near two orbiting black holesImage: Swinburne University

Spacetime near two orbiting black holesImage: Swinburne University

How Are Gravitational Waves Made? Two black holes (or any pair of orbiting objects) stir up space as they circle one another, creating gravitational waves. If the black holes are far apart the gravitational waves are unimaginably small. But gravitational waves carry away energy, and that energy has to come from somewhere – so the orbit slowly shrinks. But a smaller orbit is a faster orbit, increasing the output of gravitational radiation and the orbit shrinks faster and faster. This is the inspiral, and can take hundreds of millions or even billions of years. But eventually the two black holes are orbiting one other at a decent fraction of the speed of light, churning space like an out-of-control cosmic egg-beater. This phase lasts seconds but produces a huge burst of gravitational waves: this is the signal that LIGO detects. The black holes then plunge towards a merger, followed by the ringdown as the new black hole settles into a stable shape.

Didn’t Everyone Get All Excited About Gravitational Waves A Couple of Years Ago? We did, and it was a false alarm. Several things are different this time, though. That claim was made by BICEP2, a telescope that looks at the microwave background, fossil light from the Big Bang. BICEP2 did not observe gravitational waves directly, as LIGO does. The signal BICEP2 saw turned out to be associated with dust in our own galaxy; this was quickly realized as astrophysicists checked and re-checked the results. (I blogged about the latest news from BICEP2; it is producing lovely data and starting to test a number of different theories about the Big Bang.) Moreover, the LIGO team has built a reputation for caution – going so far as to do “signal injections”, where the analysis teams are unknowingly fed synthetic data to test their ability to extract real gravitational waves from the experimental noise. Finally, the rumour is that their results have been through peer review, and will have stood up to scrutiny from independent scientists.

What Next? Physicists will use LIGO to make stringent tests General Relativity: do its predictions match the behavior of spacetime seen during black holes mergers? And for astronomers it will like growing a new set of eyes: LIGO is an entirely new kind of telescope that lets us explore the universe with gravitational waves. Watch this space.

Destiny’s Child

Until recently, I hadn’t played “computer games” with any regularity since the mid-90s, when Doom and Nethack were procrastination tools for young cosmologists. (Both games are available for the iPhone, by the way – the more things change, the more they stay the same.) However, for better or worse, my household finds itself with a Playstation 4 and the attendant opportunities for 21st century parent-child bonding. 

So I have been playing Destiny with my kids. Created by Bungie in 2014, Destiny did $500 million worth of business on the day it was released. But if you somehow avoided this cultural tsunami, Destiny is a “first person shooter” and players fight their way through the shattered remnants of human settlements on nearby planets in the solar system.

And it is fun, if somewhat repetitive. From the parental perspective it is more palatable than many similar titles, thanks to cartoonish enemies and a distinct lack of actual gore. I will admit that I haven’t figured out the bewildering variety of aliens but it doesn’t matter much: you shoot them all, and my offspring are on top of the finer details if it ever matters. 

Every so often theoretical physics, gaming, and parenting overlap. Not that often, but it happens. For instance, in the final moments of The World’s Grave level of Destiny, your Ghost (an annoying sidekick that follows you around, offering advice and resurrecting you after your frequent deaths) hacks into an alien library, announcing that it holds so much information that its curators must have found a way past the Bekenstein limit. 

So what is the Bekenstein limit, asked the kids. Turns out, Dad’s got this one: its a real thing in physics – the ultimate limit on the amount of information that can be stored in a finite volume.

Jacob Bekenstein, who died last month, deduced this limit by asking what happens to the entropy of stuff (e.g. a giant dying star) that collapses into a black hole. Possibly not the most obvious of things to ask, but it unlocks a hidden door to a vast storeroom of fundamental questions.

Jacob Bekenstein, with the tools of his trade... [Wikimedia]

Jacob Bekenstein, with the tools of his trade… [Wikimedia]

Entropy is a measure of disorder in a system, and is often synonymous with degradation and decay. Even if you are not sure what entropy is, you very possibly know it increases with the passage of time or, at best, stays constant, thanks to the Second Law of Thermodynamics. (This is why your house gets messier, not tidier, if you leave it to its own devices). But wherever there’s entropy, there’s information. Information is entropy’s B-side, its secret identity: a disordered system is more complex than an orderly one, so more information is needed to describe it. 

But does stuff – and its associated entropy – disappearing into a black hole provide a loophole to the Second Law? Starting from thought experiments like this in the early 1970s, Bekenstein realised that black holes themselves have entropy, and entropy does not vanish when a black hole is formed. Not only that, it seems that no object can have more entropy than a black hole of the same mass. If it did, turning that object into a black hole would engineer a violation of the Second Law. It is this ceiling on entropy that yields the Bekenstein limit on information density which, according to the makers of Destiny, was bypassed by the Hive. 

Why the Hive would bother violating the Bekenstein limit is a different question. A sphere 1 meter in diameter holds 1070 bits of data at the Bekenstein limit, and that is a lot of data. Also unexplained is how your Ghost, an object roughly the size of your fist (at least when it is encased in an armoured gauntlet) carries this information away – presumably the Bekenstein limit doesn’t bother it, either. (If you took every atom that makes up the planet Earth and attached all the data transferred on the internet in 2015 to each and every one of those atoms – about a zettabyte apparently – you would have to pack all that information into the abovementioned 1 metre sphere for it to hit the Bekenstein limit.)

The Bekenstein limit may seem almost simple (at least for something involving black holes and thermodynamics), but its consequences are still being understood. Entropy is not some sort of sauce that can be poured over a physical system; the entropy of a system is defined by how its internal components are organised. But a black hole has no internal components, and even if it did, anything inside the black hole is supposed to be hidden from observers on the outside. So if a black hole has entropy, where does it live?

Much like a game, this question leads to a new and tougher level for physics: quantum gravity. If black holes have microstates that encode the information that corresponds to their entropy, the microstates are presumably quantum mechanical, like all the other fundamental building blocks of the universe. On the other hand, a black hole is ruled by gravity, and quantum gravity is a boss fight on the path to a “theory of everything”. One toolkit for tackling quantum gravity is string theory; and in the mid-90s, “stringy” calculations starting from a microscopic description of nature produced black hole entropy results like the ones Bekenstein and others found in the 1970s. This doesn’t prove that the universe is made out of strings, but it is one why reason why physicists are excited by string theory. 

Physicists have been playing with the connections between black holes, thermodynamics, gravity and quantum mechanics for over 40 years, and no-one knows where the adventure will end. Simply announcing that he was on the trail of a solution to the “information paradox” – the question of exactly what happens to information stored inside a black hole – during a lecture in Stockholm last month got Stephen Hawking worldwide news coverage, although the solution is at best a work in progress. (See Sabine Hossenfelder’s Backreaction blog for commentary.) 

One thing we do know is that while the phrase “Bekenstein limit” is a throwaway line in Destiny there is a huge amount of information hidden in those two words, with far more left to discover than we have already learnt. If you are trying to ask the questions that will lead to the “next big breakthrough” in fundamental physics, black holes and thermodynamics are a great place to look.

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They’ve broken the Bekenstein limit…


Coda: The full formula for the entropy of a black hole is due to both Bekenstein and Hawking. And while a black hole represents the upper limit on the entropy and information that can be stored in a given volume it seems that the microstates of a black hole all live on its surface. This leads to a proposal known as holography, suggesting that our apparently three-dimensional universe may, at some fundamental level, need only two dimensions. But that is a story for another day. 

Einstein’s Magic Bag

In 1915, Berlin was at the centre of an empire locked into a global war. But at least one resident of that city had his mind elsewhere: Albert Einstein was working to reconcile gravity with the theory of relativity he had invented a decade earlier. Einstein solved the problem by year’s end, and in doing so he changed our understanding of space and time forever. 

For Newton, space and time are the stage upon which the play-of-the-world takes place. The actors – planets, stars, people, atoms, and even light itself – move in space, but space itself is fixed and unchanging. In Newton’s universe, space tells us where things happen and time tells us when things happen but nothing happens to space or time; gravity reaches across space, but does not change space itself. 

In Einstein’s universe, space is shaped by matter and that shape changes when matter changes its position. Einstein brings the wooden stage of Newtonian physics to life; space now responds as the actors move about. For a physicist, Einstein’s understanding is as shocking and wonderful as a play in which the theatre springs to life and takes a speaking role in the drama.

Einstein welded space and time together into spacetime and showed that mass curves spacetime, and that gravity is encoded in this curvature. In Newton’s universe, gravity drags the earth around the sun. In Einstein’s universe the sun bends spacetime and the earth circles the sun by following the simplest path it can find though spacetime. 

This year marks the centenary of Einstein’s breakthrough, his General Theory of Relativity. The mathematical expression of the theory, the Einstein field equations,  would fit on a postcard:

 The Einstein Field Equations: the left hand side depends on the shape of spacetime while the right-hand side tracks the distribution of energy and momentum. Or, as John Wheeler put it, space (the left hand side) tells matter how to move, while…

 

The Einstein Field Equations: the left hand side depends on the shape of spacetime while the right-hand side tracks the distribution of energy and momentum. Or, as John Wheeler put it, space (the left hand side) tells matter how to move, while matter (the right hand side) tells space how to curve.  

But the Einstein equations are a magic bag: far bigger on the inside than they appear on the outside. One hundred years later physicists and mathematicians are still working to unpack this expression and to fit it to the rest of our knowledge about the universe. Einstein’s new theory immediately solved a 100 year old riddle, explaining why Mercury’s orbit around the sun did not quite match Newton’s predictions. Within 10 years, the underpinnings of the Big Bang and the expanding universe tumbled out of the magic bag of General Relativity: the universe is not expanding because distant galaxies move through space; the galaxies move because space itself is expanding. “Expanding space” is an idea you can have only after General Relativity tells you that spacetime is dynamical, rather than fixed and static.

Beyond clearing up the niggling behaviour of Mercury, Einstein made two predictions, each of which is a test that General Relativity must pass. First, gravity bends the passage of light itself; second, clocks run more slowly in strong gravitational fields. The bending of starlight was detected in 1919, via the changing positions of stars near the sun during a total solar eclipse; the slowing of time was inferred from observations in the 1920s and spectacularly confirmed in 1959. (And understanding this phenomenon is key to getting the GPS system to work, believe it or not.)

And there is much, much more. In 1915, also Einstein showed that as large objects accelerate they generate waves in spacetime. One hundred years later these “gravitational waves” have never been directly observed, but Advanced LIGOthe first observatory that should be sensitive enough to find them, is being commissioned just in time for the theory’s 100th birthday. 

 The LIGO gravitational wave detector - the strongest gravitational waves that we hope to observe will the move mirrors at each end of the "arms" by a distance that is a billion times smaller than the diameter of a typical atom.  

 

The LIGO gravitational wave detector – the strongest gravitational waves that we hope to observe will the move mirrors at each end of the “arms” by a distance that is a billion times smaller than the diameter of a typical atom.  

Likewise, a fully unified theory, a self-consistent quantum mechanical description of gravity alongside the other forces in nature is as elusive today as it was for Einstein, who searched in vain for such a model during the last two decades of his life.

So 100 years on, physicists are still unpacking the magic bag Einstein that discovered in 1915… 


Coda: Watch the World Science Festival programme Reality Since Einstein recorded in May this year…

The Sand Reckoner

Driving home one night last week, Auckland’s Spaghetti Junction was more than normally congested and my thoughts turned to physics. Sluggish traffic provided my initial topic – the differences between sand and water. – as well as letting me follow my train of thought (an actual train would be a welcome option, but that’s another story) without endangering my fellow road-users. Admittedly, many of the differences between sand and water are obvious to anyone who visits a beach, but I was thinking about how sand sometimes flows like a liquid.

Anyone who has seen an old-fashioned egg timer knows sand can flow, but flowing sand is not the same as flowing water. If a hose is leaking from a pinprick, increasing the pressure makes the water flow faster. On the other hand, pressing down on sand flowing through a narrow funnel can cause the grains to lock together, stopping the flow entirely. The technical term for this is “jamming”, which is how I got to be thinking about sand while sitting in traffic.

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Simulation showing spontaneous jamming in a granular material.

Physicists often explain the properties of “granular materials” like sand by looking at interactions between adjacent grains. The same reasoning can be used with other systems – the complex movements of flocking birds are reproduced by boids, “birdoid-objects” that obey a few simple rules; avoid collisions but stay close to the flock…

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Simulated starlings…