Secular, non-secular mathematics

[viator]

You are making assumptions which we cannot prove.

The Boltzmann constant is based upon "conditions" and it has an experimentally determined value. The value used in the CODATA is close enough to be useful. You might be interested in Max Planck's Nobel Lecture.

http://nobelprize.org/nobel_prizes/phys ... cture.html

Max Planck stated in his lecture,

This constant is often referred to as Boltzmann's constant, although, to my knowledge, Boltzmann himself never introduced it - a peculiar state of affairs, which can be explained by the fact that Boltzmann, as appears from his occasional utterances, never gave thought to the possibility of carrying out an exact measurement of the constant.

For example the velocity of light is a peculiar velocity, it is the same whenever and wherever in the universe and it is likely to be known to any civilization in the universe. Hence it is a natural unit for velocities.

The velocity of light has been measured only on the earth's surface, thus we cannot assume the value we use as a constant is exactly the same "everywhere".

[angel]

Well, to present understanding the speed of light in vacuum with no gravitational field IS a universal constant.

If tomorrow we shall discover it is not true then the velocity of light will loose its fundamental character.

I suppose I don't need to say that everything we know in science is relative to the current understanding, do I?

PS: There are a lots of tests which are equivalent to measuring the speed of light in places we see (eg far galaxies).
For examples the light spectra shape depends on that parameter.

The value of the speed of light is the same within experimental accuracy.

[viator]

Well, to present understanding the speed of light in vacuum with no gravitational field IS a universal constant.

Where has the speed of light been measured in a vacuum with no gravitational field?

Where has the speed of light been measured other than on the earths surface?

[angel]

Where has the speed of light been measured in a vacuum with no gravitational field?

The photons we received from stars or planets have travelled for minutes, years or billion of years in vacuum; since they are free falling they are in fact not feeling the gravitational field (as astronauts on the shuttle).

If the light speed were different we shall see anomalies in Jupiter's moons eclipses, for example.

And GPS would not work. Nor Galileo positioning system will.

Moreover, when we say "in vacuum" we mean "almost in vacuum" as well. The same for gravitational field. Jupiter or Earth gravitational field could be considered no gravitational field. It is the same when you say that a body falls according to a law which is independent of its weight.
That is true in vacuum with no friction. Nobody can reach "no friction" but you can quantify frinction and the less friction one has, the less weight influences body fall.

Where has the speed of light been measured other than on the earths surface?

As I mentioned above, when an hydrogen atom emits a photon it can emit it just at discrete frequencies. The spacing between the possible emission frequencies does in fact depend on the velocity of light in vacuum.

If we observe a photon emitted by a quasar in the line of hydrogen, we are in fact checking that the value of the velocity of light is the same where and when the photon has been emitted as we measure on Earth now.

If you accept that we have plenty of measurements of the velocity of light around the universe (from everything we see) and at any time along the universe history.

That is far not the only methods, but it is enough for a good start.