# Planck's Constant times the speed of light

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• LarryS
LarryS
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TL;DR Summary
Does hc have any special significance in physics?
Does the product of Planck's Constant and the speed of light, hc, have any significance in physics other than an arbitrary product of two constants? I noticed that it appears in one formula for the fine structure constant. It also appears in Planck's formula for black body radiation.

hc has physical dimension of energy*length. de Beloglie wave length of super relativity
$$\lambda=\frac{hc}{E}$$
Compton wave length
$$\lambda=\frac{hc}{E}=\frac{hc}{mc^2}$$

LarryS and DrClaude
LarryS said:
Does the product of Planck's Constant and the speed of light, hc, have any significance in physics

Does any dimensionfull constant have any significance in physics? Other than adjusting units of course.

In Wikipedia Plack units https://en.wikipedia.org/wiki/Planck_units I find the formula of Planck charge

LarryS said:
Does the product of Planck's Constant and the speed of light, hc, have any significance in physics other than an arbitrary product of two constants?
It relates photon energy to wavelength.
Photon energy, in eV; E = h c / λ

weirdoguy said:
Does any dimensionfull constant have any significance in physics? Other than adjusting units of course.
Not sure. What if the speed of light was one millimeter per second? I would think that would have a profound effect on our everyday, classical/macro world. Would Newtonian physics, as we know it today, ever have been developed?

anuttarasammyak said:
hc has physical dimension of energy*length. de Beloglie wave length of super relativity
$$\lambda=\frac{hc}{E}$$
Compton wave length
$$\lambda=\frac{hc}{E}=\frac{hc}{mc^2}$$
Not familiar with the term "super relativity". Did you mean to say "special relativity"?

LarryS said:
Not sure. What if the speed of light was one millimeter per second? I would think that would have a profound effect on our everyday, classical/macro world. Would Newtonian physics, as we know it today, ever have been developed?
There's an ongoing thread explaining why you cannot change just the speed of light, and if you mess around with dimensionful constants it all ends up being just a redefinition of what "1m" means. You need to change the (dimensionless) fine structure constant to get the effect you are thinking of, which may or may not involve changing the speed of light (depending on your unit system).

DaveE, Vanadium 50, PeterDonis and 1 other person
LarryS said:
Not sure. What if the speed of light was one millimeter per second? I would think that would have a profound effect on our everyday, classical/macro world.
I would have a very long beard, that's for sure.

LarryS said:
Not familiar with the term "super relativity". Did you mean to say "special relativity"?
I mean the case that velocity v is almost light speed c so
$$E = \sqrt{p^2c^2+m^2c^4} \approx pc$$
Photons m=0 are the case exactly.

LarryS
anuttarasammyak said:
I mean the case that velocity v is almost light speed c....
"Ultra-relativistic" will be one of the better ways of describing this case.

LarryS and anuttarasammyak

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