On Monday 01 March 2010, Ian Tickle wrote:
> 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).
In my experience, f' and f" are given in units of e, just as f itself is,
and "e" is read out loud as "electrons".
Ethan
> 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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