I Planck's Constant times the speed of light

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The product of Planck's Constant and the speed of light (hc) is significant in physics as it relates photon energy to wavelength, appearing in formulas such as the fine structure constant and Planck's law for black body radiation. It has the physical dimension of energy multiplied by length, which connects to concepts like the de Broglie wavelength and Compton wavelength. Discussions highlight that altering dimensionful constants like the speed of light would not fundamentally change physics but rather redefine measurement units. The conversation touches on the implications of changing the speed of light and its effects on classical physics, suggesting that such changes would require a reevaluation of dimensionless constants. Overall, hc plays a crucial role in understanding the relationship between energy and wavelength in quantum mechanics.
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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.

Thanks in advance.
 
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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}
 
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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? :wink: Other than adjusting units of course.
 
In Wikipedia Plack units https://en.wikipedia.org/wiki/Planck_units I find the formula of Planck charge

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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? :wink: 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).

I'd suggest reading that thread before rehashing it here.
 
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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.
 
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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.
 
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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.
 
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