From: Dejan Vucinic (dejan@mit.edu)
Date: Mon Jul 07 1997 - 11:52:19 MDT
The Low Golden Willow wrote:
> How do gamma rays through vacuum go slower than light?
That is an interesting question. The interesting part is about
the "rays" being gamma, meaning they are above the threshold for
conversions into e+e- pairs.
To partially answer your question, light does travel "slower than
light" in interstellar space because it is not travelling through
a perfect vacuum, but rather through a diluted gas, mostly hydrogen.
In engineering terms, that gas has a dielectric constant slightly
different from 1, so the speed of light changes accordingly
(c=sqrt(epsilon*mu)). Since the cross-sections for various
scattering processes change with wavelength, so does the dielectric
constant (i.e. if you hit an absorption line, tough luck). I
vaguely remember a discussion about estimating the density of
interstellar matter by measuring the delay between the arrival of
neutrinos and visible light from a supernova, neutrinos being the
"control sample" since they don't significantly interact with matter.
Now to the interesting part. I admit I've never given any thought
to what happens as you cross the e+e- threshold. A back of the
proverbial envelope calculation tells me that the elastic
cross-section goes down with energy so the velocity of wavefront
propagation goes to c, but you get conversions which snatch photons
from the beam and so reduce intensity. Therefore, to first
approximation gammas travel at c, and lose intensity; visible
light (and infrared, etc.) travels at c minus epsilon and doesn't
get much dimmer unless it matches an absorption line of whatever
it goes through. Corrections anyone?
Regards,
--dv
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