How do scientists measure the speed of light? by Jack Fraser

Answer by Jack Fraser:

We don't.

No, seriously, we don't measure the speed of light (which

alwaysrefers to the speedin a vacuum).We know

exactlywhat the speed of light is.It is:

[math]c = [/math][math]299792458[/math][math] ms^{-1}[/math]

And that is absolutely 100% accurate, with no measurement errors.

But Jack, I hear you say,

what the bloody hell are you talking about?The reason we know that that's

exactlythe speed of light, is thatwe defined it to be that number.We then take our definition of a second (the length of time for a certain number of periods of the radiation emitted in hyperfine transitions in caesium-133), and from that

we define a metre.So the thing we would be measuring

is what a metre is!We use the speed of light as a fixed velocity, from which all observers can define their own length scale.

To

measurethe speed of light would require an external definition of what a metre is – and since about the 1970s, we don't have one!And if you

didwant to measure the speed of light using this external distance reference, it's easy to test – you just release a light pulse at t=0, towards a mirror – and then time how long it takes to get back to you. This is the exact principle that Radar/Sonar work on (although again, they measure thedistanceknowing thespeed– but it works either way round).

Some background:The metre was originally defined after the French Revolution, in about 1799. It was defined as [math]\frac{1}{10,000,000}[/math] the distance between the equator and the pole.

The “metre” was formally defined from 1889 as the length of a platinum rod, held in a vault in Paris.

From this definition of a metre (and an old definition of a second – I forget what that was), we measured (using the mirror-timing method, or based on astronomical observations) the speed of light to be

about[math]299792458[/math], plus a non-integer bit, and error bars from the measurement errors.Eventually, we realised that having a metre defined by

something there was only one ofwas a bit annoying. So, we attempted to define it in a way thatanyonecould replicate – without having to refer to a “standard object”.Therefore, we

redefined the metre– using the speed of light.The official definition of a metre today is:

[math]\frac{1}{299792458} [/math]of the distance travelled by light in a vacuum, in 1 second[math].[/math]

Using the caesium definition of a second.

Therefore, this was

exactlyequivalent to defining the speed of light to be the number given above.We chose that number (and not a more convenient number like 300,000,000), because that number changed the definition of a metre by only a fraction of a fraction of a percent – but made everything all nice and integer-y.

A consequence of using this definition is that

any attempt to measure the speed of light is cyclical –youmustuse a “metre” to measure it at some point – which relies on the speed of light.Therefore what you

actuallydo now, when you “measure” the speed of light (in a vacuum), is actually “measure how accurate your measuring instruments are”!

How do scientists measure the speed of light?