Sucked into the Black Hole of Imagination

I was listening to a lecture given at Cornell University by renowned theoretical physicist Nima Arkani-Hamed a decade ago. It stretches my imagination to travel to the edge of science and join a vibrant conversation of great minds. The challenge of taking on such thought-play and massaging it into lay language is great mental gymnastics. Here is what I took away from the lecture.

The theory of Space-Time is restricted and elusive. Since the days of Einstein and Planck we really have never been able to put together the Theory of General Relativity (which is the theory of the very big) with Quantum Mechanics (which is the theory of the very small). To get some sense of the limits of scientific understanding, let's examine a particular thought experiment.

If we took a pair of electrons and brought them closer and closer together, let's take a look at what would happen to the gravitational force between them. When the electrons are a great distance apart, there is certainly a gravitational attraction between them and an electric repulsion between them, both readily measurable. The gravitational force is relatively very weak in relation to the other fundamental forces. For instance, the electric repulsion is 10^-42 times stronger than the gravitational attraction.

By most measures we find that no matter how far apart they are, this difference between the fundamental forces is conserved. It remains this way until we get to a proximal distance of around 10^-11 cm apart. What happens as you start pushing the electrons closer and closer together is that you have to supply more and more energy in that region of space in order to hold them together because of the Uncertainty Principle. Because gravity is always directly proportional to the mass, as you bring them closer and closer together and force so much mass into such a small region, the gravitational force starts going up, increasing until they are about 10^-33 cm apart at which point the gravitational force between them would reach, then exceed the level of the electromagnetic force. By 10^-33 cm apart, we would find that the gravitational force between the electrons is massively strong. The Planck Length (10^-33 cm) is considered the point at which gravity catches up in strength to all the other fundamental forces. (Of course, this is a thought experiment - because the smallest distance we have ever observed is 10^-17 cm - so everything is essentially a mathematical extrapolation.)

Time and space make no sense when they reach the Planck Length apart. At some point in the experiment, you have put so much energy into pushing the electrons closer and closer into a smaller and smaller region of space with a particle accelerator, increasing the force of gravity to such a great extent, that you collapse it into a black hole and then can no longer get any information out, defeating your own purpose. Everything stops working; nothing is measurable, including space and time.

If you put even more energy into the electrons with an even bigger (imaginary) accelerator, all you are going to do is create an even bigger black hole. There is no way of probing physics questions at distances smaller than this. That's why physics can not offer any understanding about what happened before the Big Bang. Before that, time and space essentially had no meaning. The whole notion of “before” ceases to make any sense. We might think that time and space continue to exist “before”, but since there is and may never be a way to measure what happens before – by definition – we must conclude that time and space did not exist before the Big Bang.

No one really understands what is going on in a black hole. Space no longer makes any sense. A black hole is not some point in space that sucks everything into it. If anything, a black hole is a singularity in time. We can only imagine that all matter is getting crunched down to unimaginable densities until it hits the Planck scale. Whenever something disappears beyond the horizon of a black hole, it hits the singularity and no one knows what happens after that. Our theories just break down and we're only left with speculation. That's the kind of question physicists love to ask – the fascinating, but frustrating kind that just gets sucked into a black hole of the imagination.