Re: On Planck's constant

From: Todd (nope_at_nospam.com)
Date: 01/10/05 

Date: Mon, 10 Jan 2005 03:28:10 GMT

----- Original Message -----

From: "RP" <no_mail_no_spam@yahoo.com>

Newsgroups: sci.physics

Sent: Sunday, January 09, 2005 8:45 PM

Subject: On Planck's constant

>
> Going back over "On the Electrodynamics of Moving bodies" I noticed
> that a spherical wave has energy E wrt the source and energy E' wrt a
> moving observer and that these are related by
>
> E'/E = sqrt((1 - v/c)/(1 + v/c)).
>
> Einstein then notes that
>
> "[...] It is remarkable that the energy and frequency of a light
> complex vary with the state of motion of the observer in accordance
> with the same law [...]"
>
> Now I'm not the brightest crayon in the box, having only recently
> signed a truce with special relativity, as most of you already know,
> but doesn't it follow from this that:
>
> E'/E = f'/f
>
> and that
>
> E' = Ef'/f
>
> and that if we let
>
> E/f = h
>
> we get
>
> E' = hf'
>
> and reciprocally that
>
> E = hf
>
> for any spherical light bundle?

Unfortunately no (although I also wondered about this the first time I read
this part of the paper). Einstein is here considering a volume element of a
plane wave. The size of the volume element is arbitrary. If you double the
size of the volume element, then the value of both E and E' will double; but
f and f ' will stay the same. So, in this context, E/f cannot be considered
a fundamental constant that relates energy and frequency of light.

However, this does show that Einstein's introduction of the light quantum
(photon) in another paper is consistent with SR. Planck's constant relates
the energy and frequency of a single photon, not the energy and frequency of
an arbitrary volume element of a plane wave.

> And since E and F can be found, wouldn't it follow from this that h
> can be calculated directly from Maxwell/Lorentz?
>

There is no way to calculate h from Maxwell's equations.

> Is this the very knowledge that led Einstein to his derivation of the
> photoelectric effect?
>
> The reason that I ask, is that if the above is correct, then for the
> first time I'll have gained some understanding of the natural
> relationship between QM and special relativity.
>
> BTW, this is a great paper when not being read with preconceptions :)
>

Yes indeed!

Todd

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