# How do we know the precise speed of light in a vacuum? [duplicate]

From Wikipedia - "Its exact value is 299792458 metres per second"

I'm wondering how we can be so precise as to the speed of light given that we cannot create a true vacuum on Earth and as I understand it the interstellar vacuum is a lot more active than we used to think with particles and anti-particles appearing and annihilating each other constantly. Is there a caveat here that should say "Exact value as measured at vacuum density x"?

Apologies if this is a duplicate, I did find several questions regarding the speed of light, the type of vacuum and whether it's a constant but couldn't find one that dealt with the precision of the measurement.

• Good question, but that value cannot be exact. It is only accurate to 9 decimal places. – Mike Dunlavey Sep 13 '16 at 21:54

As stated, there is no uncertainty of the definition because the standard was reversed, the meter was redefined in terms of the speed of light in a vacuum as opposed to the speed of light begin defined relative to a meter. c, the constant is the standard so is by definition exact. If c is more accurately measured in the future, the accepted length of a meter will be what changes, not he number used for c.

As to how c is measured, there are a number of ways, some mentioned, but the accepted number was basically reached from extrapolating different methods and reaching a common answer. For instance, air has a know, measured index of refraction which effects the speed of light. If the speed is measured at one standard atmosphere, then again at 0.5 atmospheres, at 0.1 atmospheres, at 0.01 atmospheres, etc., and the graph is found to be accurately linear, then one can extrapolate to 0 atmospheres. If this technique is used with high accuracy measurements for multiple different methods of measuring the speed of light in different media, different wave lengths, etc. and they all agree to measurable limits, then the number is assumed correct to within measurable limits.

The speed of light in a vacuum is now a fixed constant used to define the SI unit of length - the metre:

The metre is the length of the path travelled by light in vacuum during a time interval of $\left (\dfrac {1}{299 792 458}\right)$ of a second

It follows that the speed of light in vacuum is exactly 299 792 458 metres per second and there is no caveat to this statement.
As with the definition of the second quoting the speed of light to that number of significant figures means that the old definition of the metre using the light form Krypton 86 and the new definition of the metre agree to the uncertainties of the apparatus used to produce the practical realisation of the metre.
In other words in practical terms the old metre and the new metre are the same to the limit of the accuracy of the apparatus used to measure them so you will not have to recalibrate your metre rule.

Other constants have an exact value in the SI system such as the permeability of a vacuum being $4 \pi \times 10^{-7}$ H m$^{-7}$ and the triple point temperature of water $273.1600$ K.

The answer to your question is contained in Resolution 1 of the 17th CGPM (1983).

• This is all very interesting and useful but the question was how we measure the speed of light in a vacuum precisely, the linked resolution uses the distance travelled by light in a vacuum as the measure. For this reason I have accepted dlb's answer, I do really appreciate this information as well though. Thank you – LiamRyan Sep 13 '16 at 22:48

Actually, we don't know.

Wikipedia has put the cart before the horse here. The speed of light in a vacuum ($c$) isn't really known in terms of other units, but instead, other units are defined in terms of $c$ (because it is constant).

It's more accurate (and less misleading) to say that one meter is the distance light travels (in a vacuum) in $\dfrac{1}{299792458}$ s, instead of saying that light travels $299792458 \text{ m}$ in one second.