The speed of light is the speed at which lightwaves propagate through different materials. In particular, the value for the speed of light in a vacuum is now defined as exactly 299,792,458 metres per second.
The meter is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second.
Which one is derived from other one?
Which one is derived from other one?
The meter is defined in terms of the speed of light. So in that sense the meter is derived from the speed of light. I would use the word “defined” rather than “derived” since it is not a logical proof but rather an authoritative statement of the meaning of the meter.
However, the order of definition is not particularly important. Currently the s, m, kg, A, K, cd, and mol are defined in terms of $c$, $h$, $N_A$, $e$, $k_B$, $K_{cd}$, and $\Delta \nu_{Cs}$. But it could easily have been done the other way around. Either way would lead to the same set of equations and the same size of all the units.
The meter is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second.
Note, this is no longer the definition of the meter. The meter is now defined as “The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum $c$ to be 299792458 when expressed in the unit m⋅s−1, where the second is defined in terms of the caesium frequency ΔνCs.”
While there seems to be a circularity in the definitions there isn't one- the definitions are just two expressions of a ratio. It is just like saying that an inch is a twelfth of a foot and a foot is twelve inches.
If you define an Ocram as a third of the distance light travels in a second then the speed of light is likewise 'defined' as three Ocrams per second.
The seeming circularity arises from saying that the speed of light is defined. That is misleading. The speed of light is not defined by anyone- it is a physical constant. The definition applies to the choice of unit in which the speed of light is expressed, which is just a ratio.
To expand on Dale’s answer: the speed of light is defined as a particular immutable value. The second is defined as some specified number of periods of the electromagnetic wave emitted when a certain type of atom undergoes a particular transition. These together define the meter.
This means that if a more accurate measurement of the speed of light were made, (say it’s a tiny bit faster than previous measurements suggested) the numerical value of that speed would remain the same, and the distance corresponding to one meter would be a tiny bit larger than it was before. However, there is no other way to measure distances with as much precision as by timing the travel of light, so there would be no practical effect of such an adjustment.
The definition of the speed of light is independent of its numerical value when it is measured in different media. And the exact/approximate numerical value is influenced by the system of units for distance and time.
So the value of the speed of light in vacuum in the MKS system of SI units follows trivially from the 1983 definition of meter.
On the other hand, if you say: the speed of light in vacuum is exactly 299.792.458 meters per second, then, in order to avoid circularity, you need a definition of a meter independent from the speed of light. This was the status before 1983. Since then, the definition of a meter places 0 error on speed of light in vacuum.
Since the speed of light in a vacuum is a constant, both are true. As long as we know what a second is. As for which came first, the speed of light in a vacuum was established to be 299,792,458 metres per second in 1975, and in 1983 the International System of Units (SI) redefined the metre as the distance light in a vacuum travels in 1/299,792,458 of a second. This redefining did away with the margin of error in the speed of light.
I would like to add a few words regarding the meter. Originally, its length was exactly 1/40,000,000 of the circumference of the planet. So it was not more arbitrary than the speed of light in a vacuum. However I suppose the life expectancy of the planet is not long enough nor its sphericity round enough to make for a SI definition sustainable in the long run so we got this fancy definition of the meter based on flashlights and precious stones.
