## Ask a Scientist: Why is the speed of light what it is?

Otago Daily Times, 5 May 2017

Alan Crighton, of Ohoka, asked:-

Why is the speed of light the value it is?

David Wiltshire, a theoretical physicist at the University of Canterbury responded:

Your question contains at least 3 questions.

1. Why is the speed of light in vacuum 299,792.458 kilometres per second rather than (say) 1,000,000 kilometres per second?

Well, we don't know. The speed of light in vacuum is a fundamental constant of nature which is independent of the other four fundamental constants: Newton's gravitational constant, Boltzmann's constant which arises in statistical physics, Planck constant which arises in quantum physics, and the vacuum permittivity which refers to electromagnetism. A fundamental constant is something we can measure but not derive. So to know something more precise about the value of the speed of light would need a revolutionary change to our laws of physics that reduced the number of fundamental constants.

2. Why is the speed of light in materials like air, water or glass slower than the speed of light in vacuum?

Light is an electromagnetic wave just like radio waves or x-rays. That means it interacts with, and is scattered by, any electric or magnetic field created by charged particles in atoms or any material. That slows light down and bends its path when the medium changes, making possible untold pieces of technology, starting with humble spectacles.

3. Why is the speed of light in vacuum a universally constant finite value?

The answer to this is related to the fact that the speed of light in vacuum, c, is an upper bound to all possible locally measured speeds of any object.

This follows from Einstein's 1905 Principle of Relativity. This Principle demands that the laws of physics do not depend on arbitrary choices of the values we give to independent spatial positions (x,y,z) and to time.

For example, the physical law about how light is travelling from the page to your eye right now should not depend on whether you set your clock exactly by the radio pips this morning, or whether it is 5 minutes slow. Likewise it should not depend on whether you choose to rotate both yourself and the page by exactly the same angle relative to the room in which you are sitting. Furthermore, as long as the distance between you and the page is the same, then the calculation about how light gets from the page to your eye is exactly the same whether you are sitting in your living room at home or whether you are travelling in a jet above the Pacific Ocean. The same goes for any law of physics other than gravity, and gravity is not important as long as we only consider small regions.

Formally, we demand that the non-gravitational laws of physics should be the same regardless of how we choose the origin of our local coordinates in space and time up to translations, spatial rotations and finite changes of local velocity. By some elegant steps of pure logic - which we teach at third year in university - you can then show that there are only two possibilities for the laws of physics: (i) the relativity of Galileo and Newton in which any speed is possible and ideal clocks keep a universal time independent of their motion in space; or (ii) Einstein's special relativity in which there is an upper speed limit. Experiment shows that we live in a Universe obeying the second possibility and that the speed limit is the speed of light in vacuum.

If the speed of light in vacuum was anything other than a finite absolute speed limit, then all the laws of physics, and the whole Universe, would be utterly different to the one we live in.

Professor David Wiltshire
Department of Physics and Astronomy
University of Canterbury
Homepage: http://www2.phys.canterbury.ac.nz/~dlw24/