Why does the speed of light in vacuum have no uncertainty?

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Solution 1

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 in vacuum? for more info.

Solution 2

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.

Solution 3

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.

Solution 4

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.

Solution 5

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.

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Comments

  • The Quantum Physicist
    The Quantum Physicist over 1 year

    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 Quantum Physicist
    The Quantum Physicist almost 10 years
    It's a very weird convention to take the error to be in length... Thank you.
  • Michael
    Michael almost 10 years
    Channeling Adrian Monk here, but why couldn't they have defined a meter to be exactly 1/300,000,000 light-second?
  • Brian S
    Brian S almost 10 years
    @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.
  • Isidore Seville
    Isidore Seville almost 10 years
    @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.
  • Gabe
    Gabe almost 10 years
    @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.
  • v.oddou
    v.oddou almost 10 years
    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
    v.oddou almost 10 years
    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.
  • mikhailcazi
    mikhailcazi almost 10 years
    @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!
  • The Quantum Physicist
    The Quantum Physicist almost 10 years
    @mikhailcazi The embarrassing part in this question is that it makes me look like a beginner in physics, while I'm a PhD :)
  • mikhailcazi
    mikhailcazi almost 10 years
    @TheQuantumPhysicist Haha, sorry then! My bad. :)
  • Anixx
    Anixx almost 10 years
    -1. This is wrong. The speed of light indeed fluctuates. The c is the MEAN speed of light over large distances.
  • user12262
    user12262 almost 10 years
    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".
  • Incnis Mrsi
    Incnis Mrsi about 9 years
    Respectfully disagree that this piece of fringe science pertains to this question. The speed of light in vacuum directly arise from so named light cone, that is a crucial element of structure of the spacetime. Although there might be hypotheses challenging an established wisdom, if would be unwise and off-topical to discuss this matter in the thread focused on units of measurement.
  • Anixx
    Anixx about 9 years
    @Incnis Mrsi what do u call "established wisdom"? Established wisdom is that in Special Recativity transfer of information faster than light is impossible. Here is no transfer of information faster than light, so where it contradicts "established wisdom"?
  • Anixx
    Anixx about 9 years
    @Incnis Mrsi I agree the link is wrong though, I removed it.
  • Incnis Mrsi
    Incnis Mrsi about 9 years
    Not a question of the concrete paper, but of an idea that a thing, on which a definition of the spacetime depends, can fluctuate over the spacetime. Ī mean, the wisdom that we live in a Lorentzian manifold. Actually Ī do not deem myself this paradigm good for 21st-century physics, but any reasonable attempt to subvert it requires theoretical speculations certainly beyond the scope of a little nice discussion around the units of time and length.
  • Anixx
    Anixx about 9 years
    @Incnis Mrsi spacetime depends on some constant c, in certain circumstances objects can move faster than c, if this does not break causality. For instance, quantum tunnelling is possible with speeds faster than c (again due to quantum uncertainty). en.wikipedia.org/wiki/…
  • Incnis Mrsi
    Incnis Mrsi about 9 years
    Ī’m not competent enough to discuss less-than-1 refraction index, but this is not about the vacuum. A vacuum without gravity is Poincaré-invariant (an established wisdom), whereas all these plates and gaps have a preferred reference frame.
  • Jay
    Jay almost 9 years
    He said based on the geometry. I would say noy onlt is it correct its the easiest to understand answer here.