The Road to Reality
I have been slowly reading the book The Road to Reality by Roger Penrose. I am only about 10% of the way through the book, about to start chapter 7 on Complex-number calculus. This is a layman’s book about physics that includes the math!
In the first six chapter, Penrose has been presenting mathematical concepts starting with counting numbers, integers, real numbers and irrational numbers, moving through basic geometry, complex numbers and calculus. He has a neat way of presenting this material that makes it exciting and an adventure. You will still need a traditional math text book if you want to learn the math. Roger Penrose presents the beauty of the mathematics, the mystery and the fun. Reading these chapters has brought back a lot of math memory of stuff that I have learned back in my school days and I love the spin that he puts on it. It makes me wonder what type of math teacher he would be if he taught high school math.
What originally drew my attention to this book was an article in Discover Magazine, the June 2005 cover story If an Electron Can Be in Two Places at Once, Why Can’t You?. This article talks about a theory that Penrose has come up with on why we do not see quantum effects in the macroscopic world.
In a nutshell, his theory is based on gravity and why microscopic objects can exist in multiple states until observation forces the states to collapse into a single state and macroscopic objects exist in a single state. Take the classic double slit experiment where photons are produced on once side of a wall with two slits and detected on the other side. If photons behaved classically, they would only be able to pass through one slit and have a smooth guassian distribution on the other side. The quantum behavior is that the photon could pass through either slit and therefore does pass through both slits resulting in an interference pattern distribution. Experiements show the interference pattern which means that the photon exists in two states, one for each slit, and the states collapse into a single photon when it reaches the detector.
According to Penrose’s theory, each path the photon takes has a gravitational field associated with it and each gravitational field represents energy. In the case of the photon, the energy in the gravitational fields is extremely small. If we were to repeat the same experiment with cannon balls instead of photon, we would get the smooth guassian distribution (assuming that the slits are big enough to allow the cannon balls to pass and the wall is strong enough so that they do not punch holes in it 
). In the case of the cannon balls, even though there were two possible states, one for each slit, the cannon balls only travel along one of them. The difference here is the amount of energy represented by the gravitational fields of both states; the energy is great enough so that both states cannot exist simultaneously for a long period of time. I believe the amount of time that both states can simultaneously is based on the Heisenberg Uncertainty Principle.
There interesting thing about this theory is that it can be used to predict how long multiple simultaneous states can exist before being forced to collapse into a single state based on the mass of the particles involved. This prediction can be tested and verified or disproven. According to the Discover Magazine article, work is already underway to create this experiment and the physicists working on it hope to have results in about four years after working out the details of getting fine enough measurements.
