Neutrino, the particle that travels faster than light [Part 1]

Today, 23 September, during the Cern Neutrino to Gran Sasso experiment the Oscillation Project with Emulsion-tRacking Apparatus (OPERA) obtained a remarkable result. Neutrinos were found to be faster than light, a 60 nanoseconds gap in their 2.43 milliseconds trip from CERN to Gran Sasso, which is almost 732 kilometers. According to Antonio Ereditato, University of Berna, the uncertainty in the measurement is only 10 nanoseconds. Anyway Ereditato itself says it's too early to declare relativity wrong: OPERA researchers are only presenting a result that they cannot explain and asking the community to confirm it.

This experiment, if confirmed will mark the biggest discovery of physics in the last 50 years, because it contradicts Einstein's relativity.  In fact it would lead to a reformulation of the special relativity, because speeds greater than light's one are not covered by this theory.


Special relativity is based on a limit speed, that until now was c. It was formulated to rectify Newton's laws of motion, which are correct only at low speeds, if compared to light's one. Those laws in fact had to be corrected using the Lorentz factor.

Here we can see that if we put into the equation a speed greater than c, we get the square root of a negative number, also known as imaginary number, that until now had no physical meaning in this branch of physics.

Furthermore Newton's laws are invariant for Galilean transformation, and so work only at relatively low speed. To make them invariant for Lorentz transformations a new idea of mass is needed. The mass we are used to is the rest mass, or invariant mass, but the real relativistic mass increases with speed. In fact, according to the famous equation, mass is just a defined form of energy:

If we try to accelerate a body its energy will increase, and so will do his mass as well. So we must take this in account, changing the inertial mass in Newton's laws with the relativistic one, that is:

Problems rise at light-speed. In fact if we consider the following limit, it gives infinite as result:

This mean that no object with inertial mass different from zero will ever reach the speed of light. Increasing speed will increase also mass, and the work to bring it to the speed of light is infinite if the mass is infinite.

Here we can see why the discovery of a particle with mass travelling over the speed of light is incredible. This evidence, if confirmed, requires a new formulation of laws of motion, similar to the one done by Einstein in 1905.

In this post I tried to explain the main theoretical problems caused by this experiment. In the following one i will explain more about neutrino, focusing on its nature and on the history of its discovery.