Friday, April 6, 2012

Holographic Universe

The idea that we, Earth, the stars, everything, live in a hologram seems stranger than any cooked up sci-fi fantasy, and yet that is exactly what a contemporary theory of the universe tells us.

Where Did this Weird Theory Come From?

The inspiration for this theory came from Stephen Hawking's work on black hole entropy. Entropy is the energy in a system that is available to do work. According to the second law of thermodynamics, the entropy of any closed system always increases or stays the same, and in many ways entropy can be described as the state of disorder in a system. Another law in physics states that all physical laws should work the same everywhere in the universe. Black holes, like the one shown below, present a big problem because they decrease entropy, and thus violate the second law of thermodynamics.

(Wikipedia copyright user: Alain r)

They reduce the entropy of the universe because the information encoded in objects that are sucked in is irretrievably lost.

What's just as strange about black hole entropy is the maximum possible entropy in any region of a black hole scales with its radius squared not cubed, as if a black hole were a flat two-dimensional object. This means that all the information about all the objects that have ever fallen into a black hole somehow seems to be confined to the spherical surface of the event horizon. The event horizon is like the outer shell of a black hole. It is the point of no return, where even light itself cannot escape, and no one knows what lies within this shell. Current theory tells us that all the mass of the original collapsed star and all the objects that have been swallowed since are reduced to a radius of zero at a central point inside the horizon, called a singularity.

The Holographic Principle solves two closely related important problems with black hole entropy. The first problem is that black holes decrease entropy, as described above. Second, they violate the law of conservation of information. This law, a more specific interpretation of the second law of thermodynamics, is most often described in a quantum sense. When an atom, for example, falls into a black hole, all of its information is lost. For an atom, that means its wave function, according to quantum mechanics, is gone from the universe. This loss violates an important principle in science - that information is conserved in the quantum sense.

Hawking showed us that black holes slowly radiate their energy away, they slowly evaporate in other words. According to the no-hair theorem in physics, this too is a problem. Hawking radiation should be completely independent of the material going into a black hole. It should be a mixed (think of it as generic) quantum state. Any particular initial quantum state of the material going into a black hole is therefore lost, and according to the law of information conservation, it can't be.

The problem of information loss can also be described by something called the entangled pure state situation. This is how it works: Let's say a photon has just spontaneously annihilated in space (they do this all time according to quantum theory). When it does so, an electron and a positron are spontaneously created. These two particles should quickly annihilate each other and release a new photon. But what if one particle is sucked into a black hole while the other one escapes? Half the information of the photon (called a partial trace) is lost from a closed physical system (the universe). This also violates the second law of thermodynamics on a quantum level.

From Black Hole Riddles to Holograms

The information problem led to a huge battle between physicists, with Hawking and Kip Thorn on one side insisting that quantum information must be lost, and Leonard Susskind and Gerard t' Hooft on the other side, insisting that that is impossible. Eventually, T' Hooft proposed a holographic theory as a solution to the problem and Susskind provided a string theory interpretation of that solution.

Hawking, recognizing the problem of information loss, suggested that quantum fluctuations on the event horizon could theoretically allow all information to escape from a black hole. As long as information comes back out, the information paradox is solved. From this solution they arrived at the idea of information being contained on the event horizon of a black hole, contained in a two-dimensional space in order words, and that is the kernel at the center of the Holographic Principle, introduced here in this 3-minute video:

(from MICHAEL COULSON on Vimeo)

What is the Holographic Principle?

A hologram is a three-dimensional image confined in two dimensions. Below is a mouse hologram for example. Two photos are taken from different views.

What's really interesting about thinking of the universe as a holographic projection is that it offers a possible description of quantum gravity, something that physicists have been seeking for decades. String theory allows us a lower dimensional description of the universe, in which gravity emerges from it in a holographic way. This could account for why physicists haven't been able to find a force-carrier particle for gravity. The other three fundamental forces each have a gauge boson, a virtual particle that mediates a fundamental force. It also offers an explanation for why gravitational force is so much weaker than the other three forces as well. It is so weak, in fact, that it can be completely omitted from quantum equations.

Quantum mechanics describes the tiny subatomic world very well, and relativity describes the behaviours of massive objects in the vastness of space. The Holographic Principle could be the bridge between quantum mechanics and relativity that physicists have been searching for in their quest to find a single unified theory that can describe both the very small and the very big. String theory attempts to describe gravity as an emergent property of tiny fundamental vibrating strings. It doesn't attempt to describe gravity in terms of a force-mediating particle. Instead, gravity is an illusion. String (or strings as there is a whole set of these theories right now) theory is based on an elegant set of mathematical formulae but there are many physical phenomena it cannot describe and there is no way to test it, so far. Gravity, as an emergent holographic illusion, could bridge two competing (and as of now mutually exclusive) theories of how the universe works:

(QFT stands for quantum field theory)

Black holes present a riddle to physicists because they require both a relativistic and a quantum description in order to understand them, and the Holographic Principle offers a potential way to describe them in which both quantum mechanics and relativity can be satisfied.

Physicist Juan Maldacena came up with a mathematical description of spacetime, called anti de Sitter space, which describes the holographic universe. To us, the universe seems infinite yet we can deduce that it has some kind of boundary that has been expanding ever since the Big Bang. His mathematical metric solves this apparent anomaly. He used a three-dimensional analogue of what is called the hyperbolic plane, the boundary or surface of our universe. This plane is two-dimensional but it is wildly twisted (and impossible to visualize). We, living within this bounded surface, don't notice the twisting. It is sort of like the distortion you see when looking at a global map, a 2-D representation of a 3-D world. His 3-D analogue of this plane coupled with a fourth dimension, time, gives us a model holographic universe. String theory, describing the interior of the universe, has a sort of 2-D shadow on the inner boundary of it. Every fundamental particle has a 2-D counterpart on that boundary. Using this theory, you can describe any object in a gravitational field, whether it's a subatomic particle or a massive neutron star. You could describe a black hole. Try this 83-minute video from the 2010 World Science Festival called "Black Holes and Holographic Worlds," where the world's best physicists describe this topic for nonscientists:

As you can see, it has been very tempting to expand the holographic idea to the universe as a whole. In this sense, the universe is a two-dimensional information structure "painted on" the cosmological horizon, the edge of space analogous to the event horizon of a black hole. It even provides a new conceptualization of entropy - as the surface of the universe expands, more information can be stored on its 2-D surface and the entropy of the universe increases as a result.

According to this theory, our familiar three dimensions of space only work at the macroscopic scale and at low energies. When we look at very high-energy events or at the subatomic scale, or both simultaneously in the case of black holes, the underlying reality of a 2-dimensional space seems to become apparent. The event horizon of a black hole is, therefore, a peek at this inner reality of the universe. Leonard Susskind describes the Holographic Principle in his own words in this 13-minute interview:

In order for this theory to work, there must be a limit on information density. Entropy can be described as degrees of freedom in a system of matter and/or energy. There is an upper limit to the density of information that can be packed into a given volume that can be translated to two spatial dimensions. As you subdivide matter into its atoms and then into its sub-particles and finally down into various fundamental particles, you increase the degrees of freedom. The Holographic Principle implies that at some point there is a limit to the subdivisions you can make, and at that point you reach some kind of fundamental particle containing a single bit of information (like the zeros and 1's of a computer's binary language - or like a 1-dimensional string in string theory). And here is where the universe, according to the Holographic Principle, should ultimately break down into fundamental pixels of reality, like the pixels in a photographic image, in this case grains of spacetime calculated to be Planck length.

Searching for the Universe's Pixels First Try: Gravitational Wave Noise

Some scientists, such as Craig Hogan of Fermilab, believe that this graininess, equivalent to quantum fuzziness, can be scaled up across the holographic universe and detected as very minute gravitational waves. The GEO 600 in Germany is the latest and most sensitive gravitational wave detector built. Recall general relativity for a moment. Gravity bends spacetime. As a result it can shorten distances. Disturbances in spacetime caused by heavy-weight binary star systems made up of white dwarfs, neutron stars or black holes can ripple right across the universe as waves. The Hulse-Taylor binary, two neutron stars orbiting a common center of mass, has an orbital decay that is in exact agreement with the loss of energy through gravitational waves predicted by general relativity. These ripples, however, are expected to be very minute and none so far have been directly detected (by any instrument). The GEO 600 can detect relative changes in distance on the scale of 10-21 m, that's about the size of a single atom compared to the distance between the Sun and Earth! Along with detecting minute gravitational waves, noise in the GEO 600 may be holographic noise. Hogan's interpretation of the noise from GEO 600 caused quite a stir in late 2010. He suggested that the noise is scaled up Planck-length graininess, massively scaled up graininess. Planck-length is on the scale of 10-35 m, a difference of 1014 between Planck length and the detector's sensitivity! Hogan claims that the noise should grow grainier across great distances, much like a low-res movie played on a screen that is too big. So, larger scale (10-21 or more) changes in distance could be traced back to Planck-scale graininess at the edge of the universe, and it could be detected by the GEO 600.

Unfortunately, it is very common for gravitational wave detectors to detect a noise background - they are extremely sensitive instruments. And physicists are still in the process of identifying and removing sources of noise. And, as mentioned, gravitational waves have yet to be directly detected.

Searching for the Universe's Pixels Second Try: Gamma Ray Polarization

Some physicists calculate holographic noise, if it exists, to be on a much smaller scale than any current instrument can measure, much smaller than Hogan's estimate. And so they have devised another ingenious way to look for evidence of holographic graininess in spacetime. The European Space Agency used its Integral Gamma-ray Observatory in 2002 to look at gamma ray bursts. These are bursts of extremely high-energy gamma photons from supernovae. When the photons travel through spacetime, their polarization (you can think of it as a twist) is slightly affected. A polarized gamma ray preferentially scatters in a direction perpendicular to the direction of polarization. If spacetime is smooth, as Einstein predicted, the polarization should remain random. That means there shouldn't be any difference between higher and lower energy photons no matter how far they travel. But if spacetime is grainy as the Holographic Principle predicts, the degree of polarization of the gamma rays should depend on distance and energy. The detector should detect random polarizations if Einstein was right or it should detect a bias toward a particular polarization if the Holographic theory is right. I'm going to leave you in suspense for a moment about what they found, in order to introduce you to another very interesting problem that the Holographic Principle might solve, called locality.

A Fascinating New Look at Reality

Hogan's hypothesis violates a tenet of special relativity called locality. This means that an object is directly influenced only by its immediate surroundings. At first thought, this might seem to be a deathblow against the Holographic Principle. But, locality is already violated by a widely accepted (and experimentally verified) phenomenon called quantum entanglement. Let me give you an example to illustrate how this works: During nuclear decay processes, the events that take place must obey various conservation laws in physics. This means in the quantum world that various new particles that are generated as a particle decays must have specific quantum states. If a pair of particles is generated having a two-state spin, for example, one particle must be spin up and the other must be spin down. These particles are called an entangled pair. Lets say they fly away in opposite directions. Now here is the rub: when two objects (they can be subatomic particles, molecules or even diamonds have been observed to obey this!) interact physically and then become separated, each member of that pair is described as having the same quantum description. That means their state is indefinite until it is measured, according the the Copenhagen interpretation of quantum mechanics. They are each in an equivalent state of quantum superposition. Much later, when they are across the universe from each other, one person measures the spin of one of these particles. There is a 50% chance it will be spin-up and 50% chance it will be spin-down, depending on which one of the pair he measures. When one particle is measured, the quantum states of both particles collapses. If a second person then measures the second particle, its spin is 100% predictable - it will be the opposite spin of the first one measured. Let's say particle A collapsed into a spin up quantum state. How did Particle B instantly get wind of that news from across the universe and collapse into a spin down state?

Nonlocality implies some kind of across-the-universe instantaneous communication between two particles. That's a violation of special relativity, which states that nothing, star ships, light or communication, can exceed light speed. Experimental results have shown that effects due to entanglement travel at least thousands of times faster than the speed of light.

What does this mean? It suggests that either nonlocality operates in quantum physics or there are hidden variables we don't know about yet. Perhaps the measured spin of the particles is just one element of a larger yet unknown physical reality OR the assumption that we can measure a particle and collapse its spin into one definite state is not quite accurate. There is no transmission of information possible - no force transmission fast enough to account for projecting information across space between two separate physical systems. The fact that it happens is deeply unsettling. It is not easy to live in a classical world looking out into a quantum mechanical world, to use the words of physicist John Stewart Bell, who proposed the entanglement experiment described above and formulated Bell's theorem based on it. These results led to the Bohm Interpretation of quantum mechanics. This interpretation gives non-locality a place in quantum mechanics, where all particles in the universe are able to instantaneously exchange information with all other particles. Basil Hiley, Professor of Physics, describes the challenge of thinking about particles and locality, and extends it to the conundrum of Heisenberg's uncertainty principle, in this fascinating 10-minute video:

The Bohm Interpretation, as I understand it, does not provide us with an easy 1-step answer to the problem of locality. Instead, it asks us to rethink the problem of wave-particle duality and challenge our assumptions about particle reality.

Does the Holographic Principle provide a viable answer to the nonlocality problem? Well, yes, in the sense that this principle implies a reality outside of spacetime, so that problems involving separation by space or time are transcended. Nonlocality means that no particle in this universe is separate from any other particle. An electron in Young's two-slit experiment, for example, seems to know beforehand where other electrons are going to be. According to this principle, we can view a particle such as an electron not as a material object moving through space but as something that unfolds out of a deeper level of reality that is outside of spacetime. In this reality, particles like electrons and photons can sniff out space before them. There is lots of evidence that they do just that. It's just that we can't observe their process because our perception of them is stuck in space and time.

The Holographic Principle, therefore, seems to solve two very tricky problems in physics - black hole entropy and nonlocality.

Experimental Proof of the Holographic Theory?

I left you in suspense over the gamma ray polarization experiment, so let's get back to it now. A gamma ray burst, such as the NASA artist's illustration below, is a random event and in order to detect and measure its photons, our detector (and Earth in general) must be in line with one of its bipolar jets (shown as yellow).

Luckily, such a burst happened in 2004 (well, for us anyway), called GRB 041219A. It was extremely bright and far away (300 million light years), making its data a perfect candidate to test the Holographic Principle.

No polarization difference was detected.

The Integral Gamma-ray Observatory detector is so precise it would be able to detect graininess down to a scale of 10-48 m, which is 1013 times smaller than Planck length. Some researchers, attempting to restore the Holographic Principle, have suggested that gamma rays perhaps don't behave as expected in this grainy universe.

To conclude, no one has yet experimentally verified the Holographic Principle. So far, two experiments appear to refute its existence. Specifically, they refute a measurable graininess or pixilation of spacetime. It might be possible that the assumption of underlying pixilation is itself incorrect but the idea of a three-dimensional projection of spacetime of a two-dimensional universe may still hold some validity. I suspect physicists right now are busy thinking of new ways to verify the principle.

The Next Step: Peering Past a Quantum-Uncertain Universe

When the Holographic Principle was introduced in 2010, it captured the imagination of people worldwide. We can play with the bizarre possibility that we, and everything around us, are merely projections cast from some distant 2-dimensional screen, that we are ignorant of our true flatness as we live out our lives inside an enormous sphere at least 13.7 billions of light years across as projections from its inner surface. Certainly this idea has huge philosophical implications. Can you imagine God observing us as characters in a moving film projected over the surface of the universe? What does this mean for time? How about free will? This notion is at once absurd and alluring.

This is why most physicists refer to the Holographic Principle as a principle. It is a reasoned argument, a starting point for a true scientific theory, which is a set of principles that can explain and predict phenomena.

This principle, perhaps a work in progress, has enormous implications for how we understand spacetime and it suggests possible solutions to some very vexing problems in physics. Rather than being abandoned by the scientific community because it has not been successfully verified through experiment, it seems destined to be a jumping-off point in physics where our very understanding of the rules themselves will be challenged to its core.

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