It is a widely accepted fact in physics that the speed of light is the fastest any particles can travel. In 2011, neutrinos appeared to have been found going faster than the speed of light. Although this was later disproved, some physicists believe faster-than-light particles are possible.

## Energy–momentum relation

The energy-momentum relation is an equation which links mass, energy and momentum:

*E ^{2} = (pc)^{2} + (m_{0}c^{2})^{2}*

Where: p = momentum, c = speed of light, m_{0} = rest mass, E = energy

Rearranging this equation to make E the subject, it becomes:

If velocity is greater than the speed of light the fraction inside the radical will have a value larger than one. The radical will therefore be imaginary. Because total energy has to be a real number, the numerator of the fraction has to be imaginary as well.

It can therefore be concluded that particles with a real mass cannot exceed the speed of light, but what about if they have an imaginary mass?

## Tachyons

A tachyon is a theoretical particle which has an imaginary mass, this allows its velocity to exceed the spped of light. The concept of imaginary mass seems bizarre and therefore leads to most physicists believing it is impossible for them to exist.

As well as this, it would be impossible for them to go slower than the speed of light (because the fraction above would have a real denominator and imaginary numerator). Adding kinetic energy to these particles would also cause them to slow down rather than go faster as would be expected.

Another key argument against their existence is that particles moving faster than the speed of light will actually go backwards in time. This would mean a signal sent by a tachyon would be received before it is sent, which logically makes no sense.

## Photon Tunneling

Quantum tunneling is when a particle goes through a barrier even though it doesn’t have enough energy to do so according to classical physics. An example of this would be a ball rolling up a hill. If there wasn’t enough energy then it wouldn’t reach the top. Quantum tunneling would be this particle then passing straight through the hill and reaching the other side despite not having the energy to do so.

This effect occurs due to particles not having a defined location, instead they have a wave function which tells us the probability of finding a particle in a particular place. Therefore the probability of finding a particle on the other side of a barrier is not zero. This effect has real-life applications such as in allowing electrons to jump between semi-conductors in a diode.

During tunneling, the particles cannot be detected which suggests this jump is instantaneous and therefore the particle must travel faster than light speed whilst tunneling.

## Quantum Entanglement

Multiple particles can be linked so that a change made to one particle will instantly also happen to the other particles. This is known as quantum entanglement but for this to occur they must be able to send a signal faster than the speed of light. Because of this many physicists – including Einstein – believed it was impossible. However, it has been observed experimentally and has become a key factor in quantum theory.

## References

http://www.armaghplanet.com/blog/what-ever-happened-to-tachyons.html

https://en.wikipedia.org/wiki/Tachyon

30-second quantum theory by Brian Clegg – *a great book which explains the key concepts in quantum physics in a simple way*