The Universe in a Black Hole

Dr. David Lowe of Brown University recently won a research grant from FQXi to research something very peculiar: whether or not our entire universe exists in something like a black hole. The title and the proposal sound enigmatic and groundbreaking, but it is doubtful that our entire universe exists inside a literal black hole. Instead, what Lowe is proposing is the expansion of an idea first proposed by physicist Gerard 't Hooft when studying information loss and entropy with respect to black holes, namely, the Holographic Principle.

What 't Hooft and other physicists like Stephen Hawking were curious about was what happened to objects and the information they represent when they crossed the event horizon of a black hole, that mysterious point of no return on approach to a black hole where the force of its gravitational attraction is so strong that even an escape velocity equal to the speed of light (186,000 miles per second) would not be enough to free you from its pull.

The Second Law of Thermodynamics basically states that the entropy of the universe always increases with time. It's a fundamental concept that most physicists think gives direction to the arrow of time and why we perceive things moving in a certain direction and why we can remember the past and not the future. The Second Law has gone through a number of formulations as the field of physics has evolved, but has stayed true nonetheless. In the mechanical age of Industrialization it was used by thermodynamically oriented engineers and physicists to simply state that heat never flows from a colder body to a hotter one. Makes sense right? If you put a cube of ice in a room temperature glass of water, the ice cube doesn't give off heat making the water warmer and the cube colder. On the contrary, the opposite happens and the water heats the ice cube until it goes through a phase transition and becomes water as well. With the advent of atomistic theories toward the end of the 19th century and Boltzmann's creation of a statistical way of examining and explaining this behavior the Second Law was recast yet again. This time, the definition included a new word: entropy (a statistical measure of the amount of disorder in a system). Boltzmann mainly studied gases, hypothetical boxes of gases and the interplay between the particles of gas and how they occupied and their arrangements evolved over time. He found that another way of saying the Second Law is this: ordered things tend, over time, to evolve into disordered things. If we take a box and place a divider in the middle and fill one side with oxygen, we have an ordered system. Exactly half the box contains all the oxygen particles, the other is a vacuum. Remove the divider and let the oxygen move freely. If you came back in an hour, chances are you'd find a more disordered box. Particles of oxygen would be all over the place and would no longer be neatly arranged on one side or in one corner. The gas would fill the space to create a sort of equilibrium. Imagine the same thing happening with two gases in the box instead of one - oxygen on the right, nitrogen on the left. Remove the divider, and the gases would mix and it would be incredibly difficult to separate them again. Why does this happen? Simple statistics. It's far more likely to find something mixed, heterogeneous and disordered than it is to find something neatly arranged. Therefore, the system will tend toward the most likely scenario. It's not that the box can't spontaneously separate, it can, but it's exceedingly unlikely to find the atoms in their original configuration neatly arranged with nitrogen on one side and oxygen on another.  Atoms are constantly moving, never standing still, and as a result, ordered systems break down. With the dawn of the information age, Claude Shannon put another twist on the Second Law. All of the particles in a box of gas represent bits and pieces of information. In order to describe the state of the box at any given time we have to be able to describe the position and momentum of given particles. The more particles, the more information required to describe the box accurately. In its initial state, the box is easy to describe. "There are 30 atoms of oxygen on one side and 30 atoms of nitrogen on the other." Not a lot of information is necessary to describe this. Once the gases mingle freely, it becomes increasingly more difficult to describe the state of the box. You need to convey more information about each individual particle to get an accurate picture. "Oxygen atom #1 is in the upper left corner of the box at this particular moment, but moving away from that corner at a speed of..." For each of the 60 atoms. Entropy (disorder) can also refer to the amount of information in a system as well. So if entropy always increases, so does the amount of information needed to describe a system.

http://cde.nwc.edu/SCI2108/course_documents/stars/smallest/black_holes.htm

Black holes presented a bit of a problem. Once an object, a particle for instance, is sucked into a black hole, it is forever beyond our cosmic horizon, we can never see it or gain any information about it ever again. In fact, the "no hair theorem" states that all black holes are essentially the same, and information about what they potentially swallowed or how they were created is forever lost. This is a direct contradiction of the Second Law. Information cannot be lost in these black holes. If it was, the entropy of the universe as a whole would decrease as more and more stuff was swallowed up.

Back to the Holographic Principle. What t'Hooft and others like Hawking discovered was that information isn't really lost. You can't tell what exact particles were swallowed by a black hole, but you can tell how much it has in it. When a particle like a photon is consumed by a black hole, the size of the black hole's event horizon increases in three dimensional space. A better way of putting it is that it's surface area increases. The area is what's important to us because we can't know what's beyond that surface. Think of an opaque balloon being blown up. The more air inside the balloon, the larger the balloon gets - it's surface area stretches to compensate for the new material inside. From the outside, we can't tell what filled up the balloon because we can't see into it through the rubber, it could be oxygen, nitrogen, helium, hydrogen, whatever, but we know that there's more stuff in it if it gets bigger (yes I know we can kind of guess based on how the ballon interacts with the atmosphere, whether it's lighter than air or not...) Similarly, black holes get bigger when they're fed and we can calculate the entropy (the amount of information in a black hole) as a function of that surface area. Specifically, the entropy is equal to (1/4*Area)/(hG) where h is Planck's constant and G is the gravitational constant. In reality, information is not lost because it is encoded on the surface area of black holes. If the universe as a system includes those black holes, then the total entropy of the universe never decreases because the loss of visible information about the universe is captured and recorded on the surface areas of all of the black holes in the universe.

What's interesting is that the universe seems to preserve three dimensions worth of information (particles have length, width, and depth) on a two dimensional surface. Like a hologram. A hologram is printed in two dimensions, but when reflected in the light, forms a three dimensional image. What physicists like Lowe are beginning to speculate is whether or not the entire universe behaves the same way. If we went to the outer boundaries of the universe, would we find that the universe, like a balloon that is inflating, preserves all the information about everything that's inside it on its surface area? More radically, is the universe fundamentally two dimensional with the third dimension a mere projection? We experience three dimensions because we're inside the hologram, but that third dimension could be an illusion. This line of reasoning could have profound implications for the laws of physics. Newton's laws and relativity are postulated on the assumption that the universe has three spatial dimensions and these laws successful predict mechanical motion, but the more we delve into the realm of the very small, the more we see a disjoint between the way tiny things behave and the way larger objects behave. Newton and Einstein break down in the realm of the very small. Could it be because those laws only explain what life is like in the simulated third dimension and don't apply to a "reality" that's only two dimensions? Maybe.

There's quite a bit of research going on in this field and results are coming out all the time confirming it or signaling its death. I'll give a couple examples tomorrow.