# Calculate, not measure the value of c

• B
Suppaman
Recently I watched a youtube video about the speed of light and how it was not about light. I was wondering if the value of C can be determined instead of measured. Is C a constant in some formula that has well-known parameters and so the value of C can be calculated? I am just a science hobbyist so I will ask questions a degreed person might consider the answer to be self-evident.

rumborak
I am taking your question to mean, "can c be derived from first principles, purely on paper, not relying on measured quantities?", in which case the answer is no. It is considered a fundamental physical constant that is established empirically.

• FactChecker
Mentor
2021 Award
Recently I watched a youtube video about the speed of light and how it was not about light. I was wondering if the value of C can be determined instead of measured. Is C a constant in some formula that has well-known parameters and so the value of C can be calculated? I am just a science hobbyist so I will ask questions a degreed person might consider the answer to be self-evident.
What is the value of c? Scientists usually set c=1 as it depends on length and time, both measured in arbitrary, man made units. The point is, that it does not change its value (in vacuum).

Gold Member
I am taking your question to mean, "can c be derived from first principles, purely on paper, not relying on measured quantities?", in which case the answer is no. It is considered a fundamental physical constant that is established empirically.
That was true until 1983. Then the metre was redefined so that the speed of light is now exactly 299,792,458 m/s, by definition. Or, if you prefer, 1 light-second per second.

Homework Helper
Gold Member
There is a constant that shows up in the electrostatic equations: ## \epsilon_o ## as well as Ampere's law. There is also a constant ## \mu_o ## that shows up in the magnetostatic equations as well as Ampere's law. The speed of light ## c=\frac{1}{\sqrt{\mu_o \epsilon_o}} ##. From the relationships, Faraday's equation ## \nabla \times E=-(\frac{\partial{B}}{\partial{t}}) ##, and Ampere's law in vacuum, ## \nabla \times B=\mu_o \epsilon_o (\frac{\partial{E}}{\partial{t}}) ## , the wave equation is derived which contains the speed of light as ## c=\frac{1}{\sqrt{\mu_o \epsilon_o}} ##. ## \\ ## I do think with measurements involving ## E ## and ## B ## and the effect that the change in one produces in the other, it is possible to generate the result of the a numerical answer for the speed of light without actually measuring the speed of light, but rather, generating the result from indirect measurements. ## \\ ## @vanhees71 might you give an input here please, because I'm not 100% sure that my previous statement is correct.

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• Jehannum
Suppaman
I am taking your question to mean, "can c be derived from first principles, purely on paper, not relying on measured quantities?", in which case the answer is no. It is considered a fundamental physical constant that is established empirically.

Is this true for all "fundamental physical constants?" If that is a fact it seems we can never really know our universe. 1+1 must = 2, not ~2

Staff Emeritus
2021 Award
There is a constant that shows up in the electrostatic equations: ϵo \epsilon_o as well as Ampere's law. There is also a constant μo \mu_o that shows up in the magnetostatic equations as well as Ampere's law.

And because $\mu_0$ is set by the definition of the Ampere, and c is set by the definition of the meter $\epsilon_0$ is a fixed number in SI.

Mentor
Is this true for all "fundamental physical constants?"
No, there are some constants that really are fundamental, in the sense that we have to measure them to know what they are and once we do, they tell us something about how our universe behaves.

These constants will be dimensionless, so their value is independent of how we define our units. Everyone's favorite example is the fine structure constant which is equal to (approximately - it's something we measure and there's always some small uncertainty in our measurements) 1/137 no matter what units we choose. If we were to define the meter to be something other than the distance that light travels in 1/299792458 seconds then ##c## would have a different value - but the values of the other dimensioned constants that appear in the definition of the fine-structure constant would also change, and all the changes would cancel in such a way that the value of the fine structure constant stays the same.

Whenever you hear someone talking about whether the speed of light might change, or what would happen if it did change, they're really talking about the fine structure constant.

• Suppaman
waves and change
Recently I watched a youtube video about the speed of light and how it was not about light. I was wondering if the value of C can be determined instead of measured. Is C a constant in some formula that has well-known parameters and so the value of C can be calculated? I am just a science hobbyist so I will ask questions a degreed person might consider the answer to be self-evident.

The simplest answer would be “c” cannot be derived from any more fundamental parameters. Einstein was willing to throw away the ideas of space and time being fundamentals in order to hold onto only “c” being fundamental and building his theory on that postulate.

m4r35n357
That was true until 1983. Then the metre was redefined so that the speed of light is now exactly 299,792,458 m/s, by definition. Or, if you prefer, 1 light-second per second.
I liked it when it used to be 186,000 miles per second (UK) ;)