Sunday, October 3, 2010

The Holographic Principle and Information

So I read a couple interesting developments in the end all physics category recently. One big one was the demonstration of something like Hawking Radiation. This radiation was predicted by Stephen Hawking (hence the name) based on quantum particles materializing on each side of an event horizon of a black hole. A virtual event horizon was created using some interesting physical properties in a contrived way. The reason this is such a big deal is that the notion of a black hole "destroying" information (i.e. swallowing EVERYTHING at the event horizon) violates basic accepted principles of conservation. This good article from Scientific American covers the subject in greater depth.

I emailed my friend, Dr Aaron Smith, a physicist at the University of Arizona a post I wrote about the state of technology, and innovation as I see it a few months ago. Ironically my note got lost and he found it a bit later, and was telling me about the holographic principle, which I think is best demonstrated at the boundary of a black hole, and even the boundary of the universe. I asked him to write on the subject for me, and his expose, is below.
Holography and information are two key notions that are beginning to invade the world of physics.  Beware, mind-melting may occur if you read further!

In short, the holographic principle in physics says that a given theory in D-dimensions is equivalent to a different theory that describes the D-1 dimensional boundary of that D-dimensional space.  So, the physical principles that describe our universe must be equivalent to a different set of physical principles that describe the behavior of the boundary of our universe.  Confused yet?  A convenient way to think about this is that everything in the universe can be represented as information, or encoded somehow, and everything on the boundary of the universe is just another representation of this same information, encoded differently.  A radical interpretation is emerging:  the universe may be made up entirely of information...
What realm of physics did this bizarre realization emerge from?  Black hole thermodynamics.  But before diving in, we need a quick review of entropy.

Entropy is a macroscopic property of a system originating from the microscopic details.  Given a collection of particles with macroscopic properties(temperature, pressure, volume) there is a specific number of ways of reconfiguring the particles while still maintaining the same macro-properties.  For example, take a gas in a tank at high temperature: if one particle moves slightly faster and another moves slightly slower than the micro-configuration is different but the macro-properties are unchanged.  

Entropy is simply the number of ways that a system can be reconfigured and still have the same macro-properties (actually, entropy = logarithm of the number of ways, but that is irrelevant for now).  

Entropy is intimately related to information: high entropy means it takes more information to specify the micro-details of a system.  Entropy and information may in fact be one and the same.

It turns out that the entropy of an isolated system can never decrease, which basically means that information can never be erased.  If you disagree because you erase information on your computer every day, then consider the fact that there is far more information in your computer than the bits you know of; there are all the details about every electron flowing throughout, the tiny amounts of radiation released, and so on.  So when you erase something on your computer, the information isn't truly gone, it has just been re-encoded in the microscopic properties of particles and fields in and around your computer.  But don't worry about your security, extracting that re-encoded information is next-to-impossible.  

And now, onto black holes.  A black hole has mass, charge, and angular momentum(they can spin) and has only one unique configuration once you specify those three parameters--at least that's what general relativity tells us(the "no hair theorem").  This suggests that a black hole has very low entropy since very little information is needed to fully describe it.  This leads to a disturbing paradox.  When a system with high entropy falls into a black hole, the entropy of that system must disappear and the information describing it would thus be erased.  This cannot be, as it violates sacred laws of physics.  The resolution is that the entropy of a black hole is actually quite large, ask Stephen Hawking if you don't believe me, and so it must have microscopic parts that can be reconfigured in many different ways and leave the bulk properties unchanged.  General relativity is thus missing some very important details.

This is all pretty abstract but what does it mean?  One more detour, first.  

The boundary of a black hole, the event horizon, is a region in which space-time is so warped that the interior and exterior are not causally connected; anything inside can never affect anything outside.  Hmmm, weird.  When a system falls into a black hole, an outside observer never actually sees it get passed the boundary!  This is because of that warping of space-time.  An outside observer sees the infalling system get closer to the surface, eventually becoming a distortion of the surface.  The infalling system goes right through the boundary, no problem, and sees itself in the interior but can no longer see anything outside.  This means that the information describing the infalling system is now contained within the black hole and is also written onto the boundary somehow.  

Here is the crux, folks: a description of the boundary of a black hole is informationally equivalent to a description of the interior.  At last, holography!

This holographic understanding of black holes has led to many new ideas in physics and has the potential to revolutionize the discipline.  Lets explore some more of the realm of holography.  

A direct consequence of black hole entropy is that a given region of space-time has a upper bound on its total entropy.  In other words, you can't cram an infinite amount of information in a finite region of space.  This 'information capacity' is highly suggestive.  Space-time itself must be indivisible on some length scale; the universe must be truly digital!  Current estimates suggest that a spherical region of space, one meter in radius, can hold a maximum of about 10^70 bits of information(1 with 70 zeros after it)!  But remember, the universe is holographic, so it is really the area of the region of space we must consider, not the volume; two volumes of space will have a different information capacity if their boundaries have a different area.  In fact,the information capacity of a volume of space is simply proportional to the area.

Another consequence.  Modern particle physics(AKA quantum field theory) must be extremely redundant.  The standard model of particle physics says there are many different particles each with a large number of internal degrees of freedom.  A simple calculation shows that the amount of information that can be encoded in a region of space, using fundamental particles such as electrons and quarks, is far greater than what holographic reasoning suggests.  Therefore, particle physics is not a fundamental theory, but an effective theory in which the true information content of the universe is encoded redundantly.  What is the fundamental theory then?  The best known candidate is string theory, in which all things in existence can be broken down into very tiny little vibrating strings; an electron is fundamentally a vibrating string and a quark is too, just vibrating differently.

Gravity, dark energy, dark matter, cosmic inflation, the big bang, the nature of time, and many other ideas in physics have seen the holographic principle lend an interesting perspective.  It is all very cutting edge stuff and a lot of speculation is going on right now.

So what was the definition of the holographic principle?  Well, it is too poorly understood to give a rigorous definition at this point in time.  But, as holographic ideas help us understand to better understand physics, we in turn better understand the mysterious holographic principle.  The race is on to figure it out, and will likely happen by the current generation of physicists.  Keep your eyes and ears open folks!

For more, read the Scientific American article written by highly regarded physicist Jacob Bekenstein.  He is the one who originally proposed in the 70s that black holes have large entropy, proportional to the area of the event horizon.

The Wikipedia page also has some good insight and citations for further reading.

In the end that's a pretty cool reductionist viewpoint as I see it. The universe is nothing but our observed reality, of information. Light, and fundamental particles (gravity loops, quarks, strings whatever) are all quantized, because they are just information as we see them. Of course there's lots of details, but after a century of basic physics becoming increasingly convoluted, we are ready for some understanding and simplification. Let's see what happens.

1 comment:

aaron said...

I wanted to add in something about Hawking Radiation, but felt I already wrote too much. Since Tom opened with it I want to make a short comment about Hawking Radiation.

Stephen Hawking had a very public bet going with noted physicist John Preskill that information was destroyed upon being swallowed by a black hole. More hot shot physicists got interested, including nobel laureate Gerardus t'Hooft, and finally settled the debate. In particular, Leonard Susskind used the Holographic Principle with String Theory to show that all of the information about what a black hole swallowed is eventually spewed out in the form of Hawking Radiation. Pretty cool. Hawking conceded defeat and gave Preskill his prize: a baseball encyclopedia!