## Friday, September 19, 2008

### SCIENCE- Paul Dirac and the Big Number Theory

So what did Dirac do that was so all fired great? Some mundane stuff like predicting the first antimatter particle. (Though he didn’t think of it as a particle, he called it a “hole in the Dirac Sea”. Didn’t like poetry my ass.) But the thing I’ve always thought was the coolest thing Dirac ever came up with is called the BIG NUMBER HYPOTHESIS.

Dirac was a born mathematician. In fact he once said that “getting beauty in one's equations” was the path to progress. Often he found himself playing with numbers and equations for the simple joy of it; the way a gifted pianist might sit and noodle at the keys. And just like that pianist might stumble onto a classic melody, Dirac stumbled onto one of the great mysteries of the universe. A mystery that is sometimes pointed to as evidence that the universe is a constructed thing.

In other words- evidence of God.

He realized that the ratio of the electromagnetic force and gravitational force between a proton and an electron was on the order of 10 to the 40th power. That’s a 10 with 40 zeros after it. A big number. Human beings have a hard time comprehending large numbers so we look for things to compare them to in order to get a sense of scale. What do you compare such a number to in a person’s experience? It’s a big number, so how about all the grains of sand on the beach? Problem is that it wouldn’t even be close. All the grains of sand on all the beaches in the world? That’s about 7.5 x (10)18th grains of sand.

http://www.hawaii.edu/suremath/jsand.html

which is still only (10)-21st of Dirac’s number.

So all the sand on all the beaches on the entire earth is such a pitifully small number in comparison that it can’t help us. What else might he compare it to?

How about the ratio of an electron to the radius of the Universe? That’s got to be a pretty big number. The calculated radius of an electron is (10)-15th and the radius of the universe is about 10)23rd resulting in a final ratio of (10)40th.

Wait. That’s a really good comparison. In fact it’s within the same order of magnitude. It’s unusual to find anything that matches up that closely when dealing with numbers of this size.

So, The relationship between the interactions of protons and electrons is about the same as the relationship between the size single electron and the size of the universe. Interesting.

What else might be a number that big? We’ve compared two of the four basic forces of the universe and we’ve compared a unit of distance. So, what about time? The universe has given us a fancy stopwatch in the form of the speed of light so let’s compare the length of time it takes a photon to travel the length of the radius of that electron we measured earlier and the length of time that the universe has existed since the big bang.

And guess what. That turns out to be about 10)40 as well!

Things were starting to get really weird.

What about a comparison of the mass of a proton to the mass of the universe? Well that doesn’t wind up being on order of magnitude of 10)40 instead it winds up being roughly the square of 10)40. That’s a little odd too. How about the number of elementary charged particles in the universe. That also winds up being about 10)80, the square of the number that kept cropping up.

By now Dirac was getting pretty excited. As he started comparing the fundamental constants of the universe the number 10)40 just kept cropping up. I’m sure he was beginning to feel a little like Jim Carry in the movie THE NUMBER 23. He figured that anything with this close a correlation must be important. But the connections were so odd. Why would the age of the universe and the size of a proton be related? Dirac continued to fool around and eventually figured out that all this could be the result if the Universal Gravitational Constant varied with the age of the universe. So he immediately set out to do what physicists do when they hit upon a new idea. He built a universe around it.

In 1937 Dirac published his paper on the Large Number Hypothesis and the possible Cosmology it implied. The problem was that his cosmology didn’t seem to support the big bang and for the next 20 years big bang was to become all the rage in cosmology. So most physicists said yes, that’s interesting, but it’s just a coincidence. Scientific numerology, it was called.

But the story didn’t end there.