# Why does the speed of light have no uncertainty?

I could understand that the definition of a second wouldn't have an uncertainty when related to the transition of the Cs atom, so it doesn't have an error because it's an absolute reference and we measure other stuff using the physical definition of a second, like atomic clocks do.

But why doesn't the speed of light have uncertainty? Isn't the speed of light something that's measured physically?

Check out that at NIST.

-

The second and the speed of light are precisely defined, and the metre is then specified as a function of $c$ and the second. So when you experimentally measure the speed of light you are effectively measuring the length of the metre i.e. the experimental error is the error in the measurement of the metre not the error in the speed of light or the second.

It may seem odd to treat the metre as variable and the speed of light as a fixed quantity, but it's not as odd as you may think. The speed of light is not just some number, it's a fundamental property of the universe and is related to its geometry. By contrast the metre is just a length that happens to be convenient for humans. See What is so special about speed of light? for more info.

-
It's a very weird convention to take the error to be in length... Thank you. –  The Quantum Physicist Jan 9 at 10:38
@TheQuantumPhysicist The speed of light was actually calculated (precisely) from Maxwell's Equation: $c = \frac{1}{\sqrt{\epsilon_o\mu_o}}$. This is constant for every frame (intertial or not). We found out that even if we go faster and faster, the speed of light remains to be $c$, it is our perception of length and time which keeps changing. Normal Newtonian Mechanics aren't valid! –  mikhailcazi Jan 12 at 6:53
@mikhailcazi The embarrassing part in this question is that it makes me look like a beginner in physics, while I'm a PhD :) –  The Quantum Physicist Jan 12 at 6:56
@TheQuantumPhysicist Haha, sorry then! My bad. :) –  mikhailcazi Jan 12 at 7:02
-1. This is wrong. The speed of light indeed fluctuates. The c is the MEAN speed of light over large distances. –  Anixx Jan 15 at 4:58

To repeat Wikipedia:

The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its value is exactly 299,792,458 metres per second, a figure that is exact because the length of the metre is defined from this constant and the international standard for time.

In other words, it's exact because we have a definition of the second:

the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom

and the metre is the distance light travels in $1/299,792,458$ of a second.

That leaves no room for error in the definition of the speed of light.

-
no you are biting your own tail. you say the metre is defined from the speed of light, then the speed of light is known to be [this constant] * 1m/1s. this constant must have been rounded for convenience, and the metre redefined from its original definition to fit the rounding. originally it was a fraction of earth's arc, so it cannot have anything to do with the speed of light. I doubt that it is the definition of the second that was rounded to fit this constant. But it doesn't answer the OP. the OP speaks of uncertainty, and speed of light, IS uncertain. –  v.oddou Jan 10 at 3:36
the measurements are said to ought to be the same whatever the direction of the light for example, and whatever the speed of the emitting particle. but, measurments are noisy, and some experiments even go as far as to measure statistical elements on this noise, like variance, according to directions. and I recall seeing some results where 1 direction had more variance. the conclusion being that maybe the universe is not isotropic. I think this is this kind of talk that OP expects. –  v.oddou Jan 10 at 3:38

As you can read in this Wikipedia article, it was decided recently to base all SI units on seven constants of nature. To be able to do so, these constants have to be set to absolute values. Therefore it was decided, that these constants are fixed without error margin at their commonly accepted values to derive all other SI units from those now fundamental constants.

-

In SI system, a meter is defined to be 1/299,792,458 light-second (in other words, the distance traveled by light in vacuum in 1/299,792,458 second), and the speed of light in vacuum therefore is defined to be 299,792,458 m/s.

-
Channeling Adrian Monk here, but why couldn't they have defined a meter to be exactly 1/300,000,000 light-second? –  Michael Jan 9 at 15:18
@Michael, The meter was originally defined as 1/10,000,000 of the distance from the equator to the north pole. The definition changed in 1983. –  Brian S Jan 9 at 15:22
@Michael Technically, they (CGPM) can. But meter is a widely used unit and therefore it is highly desirable to make the new definition as close to the historical definition as possible. –  Isidore Seville Jan 9 at 16:19
@Michael: It is only a coincidence that the meter is so close to 1/300k light-sec. The first proposal for the meter was the length of pendulum needed to have a period of 2 seconds (to make clock that can tick every second). Due to the variations in the Earth's gravity, it was ultimately decided to make it based on the circumference of the Earth. It is just luck that all three of these definitions are within rounding error of each other. –  Gabe Jan 9 at 20:28

The reason is that measurements of speed of light became very, very precise. Much more than measurements of Earth's diameter or any physical object like 1 metre rod. So it is better to settle on some fixed value of metres per second in c. Something has to be fixed, let it be something we can easily measure in any laboratory.

-

$c$ is a fundamental constant, so it has no uncertainty. I fact, lengths are defined using time and $c$.

It's important to note that defining the light speed to be a fixed number is not just a matter of convention. It's a property of spacetime. Physicists take $c$ to be a fundamental constant because nature suggests so. You should read some introductory book on special relativity to understand how this property arises. I recommend Russel's ABC of Relativity and the first chapters of Rindler's Relativity. Of course you should have some background in newtonian mechanics and galilean relativity to understand it better.

-
$c$ is not a fundamental constant of nature. if the meter was defined independently of $c$ as was done before 1959, then $c$ would be a quantity to measure and there would be measurement error. the only truly fundamental constants of nature are the dimensionless ones, like $\alpha$ or $\frac{m_p}{m_e}$. but dimensionful constants are really only about the units used to express them. –  robert bristow-johnson Jan 10 at 2:11
GabrielF: "I[n] fact, lengths are defined using time and $c$." -- Right on!, +1. Just a nitpick concerning terminology: In fact, distance values (or also: values of quasi-distances) are defined using durations (namely: ping durations between participants who find constant ping durations between each other) and $c$. "not just a matter of convention. It's a property of spacetime." -- In order to characterize "spacetime" at all (especially, by geometric relations between participants, such as their (quasi-)distance ratios) it must be defined how to measure geometric relations. –  user12262 Jan 15 at 19:21

The speed of light indeed fluctuates in vacuum. A single photon can propagate slightly faster or slower than light. This can be interpreted as appearance of virtual photons ahead of the propagating one and consequent annihilation of the first one with one of the appeared. Only statistically the speed of light is constant.

-

In order to answer this question, one has to realize that the term "speed of light" has two components. There is the actual physical speed of light (electromagnetic radiation), and the value associated with it.

It should be readily apparent that the value is not a constant because it depends on the system of units used. It is 186,000 miles per second in one system, 299,792,458 m/s in another system, etc.. If we redefine the length and/or the time, we obtain different values.

However, since the actual speed of light depends only on the properties of the medium through which it propagates, therefore, the speed of light is "constant" (or absolute) in a homogeneous medium.

-
Guill:"[...] the value is not a constant because it depends on the system of units used." -- This statement appears inconsistent with common usage of this terminology, e.g. "to obtain the same physical value expressed in terms of a different unit" or "the value of a physical quantity Z is expressed as the product of a unit ... and a numerical factor". Maybe you're just missing the notion "numerical factor". –  user12262 Jan 15 at 19:10