Re: [Phys-l] Inertia? - Reprise

[Brian Whatcott <betwys1@sbcglobal.net>]

> At 07:34 AM 11/13/2008, David Bowman, you wrote:

[Q.]
> > >>...In the bending of starlight around massive stars, are the shorter
> > >>wavelength photons bent more than longer, or is the bending the same
> > >>for all wavelengths?
> >...

[A]
> > >I suppose that the higher energy photons are bent more, using that
> > >old didactically discredited equivalence of energy and mass.
> >

[Much Better A]
> >All wavelengths are bent the same amount if they have the same impact
> >parameter.  The photon's energy is irrelevant as long as that energy
> >remains a tiny fraction of the rest energy of the gravitating star,
> >(which is a pretty good approximation for all the photons I know of)....
> >David Bowman

Hmmm....looking over this thread once more, I find myself
disappointed for missing an opportunity for a little exploration
 at a junior high level - so that I consider that I snatched
 defeat from the jaws of victory, as sometimes happens.
   Let me try again.

It is reasonable when answering the question about the
 influence of a photon's frequency on its angular  deflection
 during a grazing trajectory to mention the kind of
 equivalence that Einstein so memorably used.
 You could put it like this:
the photo electric effect shows the influence of frequency on
photon energy.  Using a relation between energy and mass
 provides a certain relation between frequency and mass.
 e = h.f    e = m.c^2, so  m = h.f / c^2

So a higher frequency photon has more effective mass.

This kind of connection led to a prediction for the
deflection of starlight at grazing incidence to the Sun,
 by considering the effective mass of the light rays,
[let us say]  which an eclipse expedition confirmed,
 at least to within +- 50% .
 (And recall that another Physics Nobel laureate could
later make an error in writing the magnitude of energy
 needed to lift a mass with a screw-jack - so numeric
 errors are not the central issue, but rather just a detail)

I called this equivalent mass of a photon idea into view,
dismissing it as didactically out of favor.
Out of favor certainly, but still a usable idea.

So now, it's easy to model a small effective mass
quickly skirting the Sun,and being deflected by it.
   So far, so good (at least at the student level in mind).
  But then, I leaped immediately to  the idea that large
 masses are more attracted than small masses to a
 nearby massive object.

And so they are, but I imagine it was quite obvious to
 all except me, that the parallel question would be
 this one:
 " If you drop a cannon ball and a feather together in a
vacuum, which accelerates more?"
[ Same acceleration, even though the more massive
cannon ball sees a larger attractive force?
                                         Yes of course!]

As David diplomatically pointed out, the mass ratio of photon
and Sun is so asymmetric, whether it is a 'light' microwave photon,
or a 'heavy' X-ray photon that the larger reaction at the
 massive body is all but incalculably small so that any difference
 in acceleration would truly be so minuscule as to be negligible.

But how about de Broglie's celebrated diffraction of masses?
 Mass wavelength being related to its inverse speed as well as its
proximity to a half slit ( or its "impact parameter",
to put it another way)    that this kind of diffraction  is not
 consequential for such a fast moving and tiny"equivalent mass" ,
 and may similarly dismissed.

There: at least I feel better now.....    :-)


Brian Whatcott    Altus OK    Eureka!