Sunday, 2 October 2005

A Sign for Half the Universe (?)

When I was leaving my room in the university last Monday, a friend of mine was unease with some problem and then I asked him if the problem was a minus sign I´ve heard he talking about with another friend. He said to me that the problem was deeper, although sometimes a minus sign could be a deep problem. I answered saying: "It was for Dirac, wasn´t?".

I intended to refer to the fact that Dirac turned an undesirable minus sign in the solution of an equation in a great success. Let me tell the whole story. Paul Adrien Maurice Dirac was a British physicist that was working on a quantum relativistic wave equation for the electron and found one which has as solutions for the energy of the electron two values, one positive and one negative. Usually, the procedure would be to discard the negative energy solutions and keep going on with the positive ones. But Dirac noted that he could interpret the negative energy solutions as a new particle that had almost all the characteristics equal to the electron, but with the opposite charge. He called the particle "positron" (for positive-electron or positive particle or whatever…) and it was found experimentally some time later. He just predicted antimatter!

I had a professor called Henrique Fleming that used to say that Dirac discovered half of the universe. That was because matter and antimatter, apart from their opposite electric charge, seems to have the same characteristics and there is no reason why the universe should have more matter than antimatter. Okay, there is a deeper reason for supposing the equality. It´s because in processes that create particles with mass from ones that has no mass, matter and antimatter are created in the same proportion, such that the electric charge is conserved in the whole process. It is indeed a great mystery for physicists why in the observed universe matter dominates antimatter. There are some speculations, but just it.

Dirac discovered a lot of other things. He was one of the greatest physicists of the 20th century and probably you will heard more about him in the future posts. Antimatter is another interesting subject too and I´m planning to talk more about that later. So, as you can see, a little minus sign in an equation could lead to a big difference. I suggest you to ever remake your calculations, who knows what secret may be lurking behind a “-“.


  1. what does it mean to have negative energy? is it one of those theory that is only understood by mathematics?

  2. Nope, it has a physical interpretation. The absolute value of the energy does not matter, what really has a meaning is only differences of energy. Saying that something has negative energy means that it has less energy than the state we defined as our "zero energy", just it. If you prefer, you can change your zero such that your system will have positive energy.