Why is the speed of light exactly exactly 299 792 458 meters per second ?

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122 replies · 26K views
neopolitan,

It's true that the caesium 133 radiation has a wavelength, but the point is that you don't need to have measured that wavelength in order to define a second. You could define your unit of length to be anything at all you liked but the second's definition would still be valid and unaltered.

In fact, you could define a metre to be 299792458/9192631770 wavelengths of caesium 133 radiation, and in some ways that would be a better definition because all you have to do is count wavelengths without needing to have a definition of time-units. This would make length "independent" of time in terms of its definition considered in isolation. Of course, considering this definition of distance and the definition of time simultaneously shows the two are linked, but logically you can arbitrarily choose either one to be independent and then the other becomes dependent.

To put it another way, you have one degree of freedom in choosing how to measure either time or distance, but once you've made that choice then the method of the other measurement is effectively fixed apart from a conversion factor c.

The spacetime view is that time and space are just different dimensions of a unified structure and c is just the conversion factor that links the two together.
 
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Before this ends up in the bleachers and to ease my guilt for taking this beyond the lucidity of DaleSpam's and D H's answers (#14, #26, #55), let me attempt to redeem myself with what appears to me to be a consensus.

First a point of clarification: a, the, any "definition" of a second does not require any reference to the dimension Length.

A definition of any quantity of dimension can be expressed in two ways: as a portion or sum of some other predefined quantity of the same dimension - an hour is sixty minutes, a minute is sixty seconds, etc.- or, as a portion or sum of a physical "action" of known (experimentally verified) value which again need not have any reference to any other dimension.
For a unit Time, the latter is a repeatable, finite and extremely accurate definition when it is defined as the atomic "action" corresponding to the transition between the two hyperfine levels of the ground state of cesium 133 and the second is the sum of 9 192 631 770 periods of the radiation of this action.
It is important to note that the temporal constancy of this action is irrelevant to the "definition" of the unit second, but crucial to the validity of theory of the action.

With respect to my comments regarding a "measure" of time being a comparative measure of Length, I will give way to DrGreg's far more concise and enlightening post above regarding degrees of freedom.(#121)

Now, at the risk of this going out of the park, I will offer one more point that is crucial to understanding the role of dimensionless constants in the development of physics.
A point that comes back to the OP question regarding "Why" light or any physical constant is in fact - Constant. We can rationalize the numerical values associated with a constant and make every possible representation that proves, empirically, its constancy. But this does not answer Why.
To answer Why, we must look beyond kinematical descriptions of dimensions to dynamics. What is the dynamic law, theory or model from which constancy arises as a natural indeed necessary consequence? This is a/the fundamental quest of physics. Until a theory can "give rise" to the dimensionless constants, we are still dealing with shadows.
 
DrGreg said:
The spacetime view is that time and space are just different dimensions of a unified structure and c is just the conversion factor that links the two together.

That's the one I would go with then :smile:

cheers,

neopolitan