Dear Gerard
I would certainly agree that in general, provided one takes sufficient
care over dimensions and units, paradoxes can never appear. However,
in this particular case I was pointing out the dimensionality error of
writing equations such as "f = 10e", and equivalent ones for the
structure factor and electron density, given that 'f' is defined as a
dimensionless ratio (as I believe it usually is). Even if you
replaced the 'e' with whatever unit represents an electron's ability
to scatter X-rays (which would be the amplitude of the scattered
wave), you still have the same problem. I only focused on electric
charge because 'e', the elementary unit of charge, was being posited
as the unit of 'f'.
The alternative solution that you suggested of using the word
'electron' as an abbreviation for "an electron's worth of scattering",
is likely to cause just as much confusion and probably would be
further abbreviated to 'e' anyway, thus leading people to believe it
represented the electronic charge! The correct solution, as you, Marc
and myself have pointed out, is to treat f as a pure number, with
corresponding treatment of any other quantity that depends on f.
Cheers
-- Ian
On Mon, Mar 1, 2010 at 1:13 PM, Gerard Bricogne <[log in to unmask]> wrote:
> Dear Ian,
>
> Perhaps I should have made a more explicit connection to your message
> in what I wrote yesterday. I do not think there is any paradox, or apples
> vs. oranges problem, in this situation.
>
> The structure factor is a count of "electrons as X-ray scatterers", so
> that the Fourier synthesis computed from them is a number density for these
> unit scatterers. The density can get clothed with a charge a-posteriori,
> because we know what the charge of an electron is, but it is not that charge
> as such that is sensed by the diffraction experiment: it is the complicated
> combination of charge and mass and various physical constants that ends up
> determining an electron's ability to scatter X-rays.
>
> I think that if one bears this in mind at all times, paradoxes never
> appear.
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