The Hidden Structure of Electrons?
Posted by on Friday, November 18, 2011
I was watching a lecture a few days ago on particle physics and the latest research into that field, and I was interested in a comment that there is no indication of internal structure for the leptons. Not because I disagree - in all the years of searching for structure through high energy experiments no clear evidence has appeared - but because many people seem unaware of the Koide formula which does seem to indicate some hidden properties of the leptons.
Let me start with some background information for those who are reading this without formal training in particle physics. All normal matter is formed of tiny particles called atoms. Each atom is composed of protons and neutrons forming an even tinier nuclear, and several particles called electrons which orbit the nucleus. It is these electrons that give us electricity, and that allow for chemical reactions to occur. The protons and neutrons are know to be composed of even smaller particles called quarks, and these have been studied in great detail. But the electrons appear to act as point-like particles with nothing inside of them.
Even more interesting perhaps is that they are part of a trio of particles, which all have similar properties. The other two are the muon and the tau (or sometimes tauon) which have the same electrical properties but which are hundred or thousands of times more massive. These three particles together are called leptons.
And in decades of experiments, there has been no evidence of any internal structure of these particles.
But about 30 years ago (even before the mass of the tau lepton was known accurately) a relationship between the masses was discovered. If you define a new quantity, Q, as the sum of the lepton masses, and divide it by the square of the sum of the square roots of the masses, (Unfortunately the blogging program I am using doesn't allow me to reproduce it graphically) then mathematically the result must be between 1/3 and 1.
In the most accurate experiments, the measured value of Q is exactly 2/3 and is known to 1 part in 100,000.
So the question remains, how is it that three particle which seemingly have no structure and do not seem to be three states of the same particle, should happen to have such a simple and elegant relationship between their masses? It is definitely indicative of something deeper in particle physics, but only time and hard work will uncover that connection.
Let me start with some background information for those who are reading this without formal training in particle physics. All normal matter is formed of tiny particles called atoms. Each atom is composed of protons and neutrons forming an even tinier nuclear, and several particles called electrons which orbit the nucleus. It is these electrons that give us electricity, and that allow for chemical reactions to occur. The protons and neutrons are know to be composed of even smaller particles called quarks, and these have been studied in great detail. But the electrons appear to act as point-like particles with nothing inside of them.
Even more interesting perhaps is that they are part of a trio of particles, which all have similar properties. The other two are the muon and the tau (or sometimes tauon) which have the same electrical properties but which are hundred or thousands of times more massive. These three particles together are called leptons.
And in decades of experiments, there has been no evidence of any internal structure of these particles.
But about 30 years ago (even before the mass of the tau lepton was known accurately) a relationship between the masses was discovered. If you define a new quantity, Q, as the sum of the lepton masses, and divide it by the square of the sum of the square roots of the masses, (Unfortunately the blogging program I am using doesn't allow me to reproduce it graphically) then mathematically the result must be between 1/3 and 1.
In the most accurate experiments, the measured value of Q is exactly 2/3 and is known to 1 part in 100,000.
So the question remains, how is it that three particle which seemingly have no structure and do not seem to be three states of the same particle, should happen to have such a simple and elegant relationship between their masses? It is definitely indicative of something deeper in particle physics, but only time and hard work will uncover that connection.
I am a physicist recently graduated from the University of Victoria, with a doctorate in theoretical physics. I also have training in mathematics, engineering and computer programming.