# Measuring the speed of light and defining the metre - absolute or relative?

If the metre is now defined as the distance light travels in vacuum in $1/299\,792\,458^{\textrm{th}}$ of a second and the speed of light is accepted to be $299\,792\,458\ \textrm{m}\,{\rm s}^{-1}$, doesn't this seem like the chicken and egg problem?

I remember reading somewhere (in the context of uncertainity principles):

...the more precisely one property is measured, the less precisely the other can be measured.

So how, then, do physicists claim to have accurately measured the speed of light? Does this mean the definition of the metre is dependent on our ability to accurately measure the speed of light?

After all, to determine speed (distance traveled/time taken) you must first choose some standards of distance and time, and so different choices can give different answers?

What about so many other factors that affect these measurements? I do not claim to understand the theories of relativity entirely, but what about the chosen frame of reference? Spacetime curvature?

Does this mean that our measurements are only relative and not absolute?

• The uncertainty principle (UP) only applies to certain specific pairs of physical properties (specifically, those that are represented by noncommuting operators in QM). The speed of light is not one of those properties. So the UP is pretty much irrelevant here. Also, your reference frame doesn't matter because the speed of light is invariant, and spacetime curvature on the Earth's surface is so weak it doesn't have a noticeable effect on the measurements. (At least I think so, although I don't have the data to back that up offhand.) – David Z Nov 28 '10 at 22:09
• Spacetime curvature isn't so weak, since time computaton have to take it into account to get correct time synchronization in GPS system. I would like to understand how the second, the meter and the speed of light will (or will not) change in a satellite orbiting the Earth. – dan May 5 '19 at 21:51

## 5 Answers

There are three relevant quantities involved here: the length of a meter, the duration of one second, and the speed of light. You only need to absolutely measure one of them, after which the other two can be defined in terms of the one that is measured.

For technological reasons, we have chosen to make the measured reference quantity the length of one second, which is defined in terms of the number of oscillations of radiation associated with the transition between the hyperfine ground states in cesium (specifically, it's 9,192,631,770 oscillations of that light). This is basically because there are experimental techniques that allow incredibly precise measurements of the frequency of radiation, at a level that really can't be matched by length or speed measurements. (The best frequency measurements in the world use trapped aluminum ions as the "clock," and are good to something like one part in $10^{18}$.)

Having defined the second in terms of some physically measurable quantity, we are then free to define the speed of light as having some particular value in meters/second, and then define the meter in terms of the distance traveled by light in one second. The size of a meter is merely a matter of convention, not anything fixed in the physical world, so as long as we have anchored the second to something fundamental, we can make the meter be whatever we want.

The particular values of the meter and the speed of light that we choose are based on older measurements using a meter defined in terms of the circumference of the Earth. We've chosen to keep that value, because it would be a hassle to make a wholesale change.

• ""The best frequency measurements in the world use trapped aluminum ions as the "clock," "" Is this a Mössbauer line? – Georg Feb 2 '11 at 21:48
• This is an optical transition in the UV range. The work is done in the NIST Time and Frequency Division by Dave Wineland's group-- a searchable database of their papers, with freely available copies of most, is at: tf.nist.gov/general/publications.htm The recent Science article "Relativity and Optical Clocks" is a good place to start looking. – Chad Orzel Feb 3 '11 at 12:29
• The 1983 definition render the relationship between unit of space and unit of time completely fixed: [unit of space] = (1 m / 299792458 s) . [unit of time] (at the speed of light in vacuum on earth surface). [return] in many situations, approaching the speed of light, approaching a gravitational well, space shrinks and time expands (GR). Space and time aren't don't follow a constant relationship, they rather follow a rotation. [return] How may we conciliate these non-linear space-time deformations with a relationship of strict proportionality? [..../....] – dan May 8 '18 at 10:05
• [cont...] How may we detect physical deviations around this strict proportionality rule ? [return] How may we take into account the distorsion on space and the distorsion on time components entering in the red shift due to the space-time "expansion"? [return] For example, how may we detect that this space-time "expansion" could be a space expansion and a time shrinking, as is the case upon exiting a gravitational well or slowing speed? – dan May 8 '18 at 10:09
• You are saying that "Having defined the second in terms of some physically measurable quantity, we are then free to define the speed of light as having some particular value in meters/second". The problem is that the physical measured quantity we used to define the second is based on electromagnetism causality speed which is the speed of light itself, so changing the speed of light will also change the definition of the second. It is like saying c=m(c)/s(c) this looks like a circular logic to me. – Marios Mourelatos Apr 10 at 22:54

Basically, what happened is that we managed to measure time very accurately with the advent of atomic clocks. Einstein's theory of relativity predicts, or rather posits, that the speed of light is an invariant. So measuring time accurately implies we can measure distances accurately too. We only have to check that light is indeed an invariant and there are also easily reproducible and precise lab techniques to check that, for instance by interferometry. This allows then to define the meter. The number 299,792,458 is then chosen so to make the meter agree with the old definition which used a standard rod.

It seems that in practice, the meter is often determined by measuring wavelengths of certain atomic transitions, read further on:

http://en.wikipedia.org/wiki/Metre

The speed of light is not a fundamental constant and it does not represent a measured quantity. It is a conversion factor that creeps in due to the use of a clumsy system of units that uses different units for distance depending on direction (spatial vs temporal) in spacetime.

In a way,'speed of light' is akin to 'right angle': the concept itself is important but the associated value is void of real meaning as it is based on a rather arbitrary convention. A right angle is agreed (not measured!) to equate to 90 degrees, and similarly the speed of light is agreed (not measured!) to equate to 299792458 meters per second.

The agreed value of speed of light, combined with the definition of the second, results in an unambiguous unit of length. In other words, by defining the unit of speed, units for both length and time are defined based on a frequency standard. There is no circular reasoning involved in this.

• Maybe the down-voters care to elaborate? The above should be undisputed and is absolutely mainstream physics. Strangely enough, some consider the above simple insight ("dimensionfull constants are not fundamental") worthy of publication: arxiv.org/abs/1412.2040 – Johannes Dec 8 '14 at 17:05
• Now which tools may we use to proove that what we think to be 90° between x and y axis isn't exactly 90° but slightly distorted? Which tools may we use to proove that what we think to be an angle of 299972458 m/s betweeen x and t axis isn't exactly this but slightly distorted (near the BB, near any gravitational well, nearly everywhere)? – dan May 8 '18 at 10:27

I just complete @Chad Orzel's response by point : you seem to be worried on the effect of chosen frame of reference and space-time curvature. One of the reasons to redefine the meter in term of speed of light is because the speed of light is independent of the frame of reference and the space time curvature, while distance and time are not. That the whole point of Einstein relativity theories.

• You just have to be careful that your stopwatch is in a rest frame with respect to you when you measure a second. – Peter R Jun 27 '16 at 1:02

The speed of light is invariable but the number or ratio of the frames of reference are variable as determined by the amount of gravity, the result of which is gravitational lensing.