This is in response to the question, "So the speed of light differs
depending on medium, right? Is this also true for neutrinos?"
Actually, there is an important sense in which one can (and should)
say that the speed of light does NOT depend on the medium! See my
article
http://matterandinteractions.org/Content/Articles/Refraction.pdf
If you accelerate charges, they radiate light. Light consists of
traveling waves of electric and magnetic fields; you can see a video
about electromagnetic waves titled "Electric Fields, Cell Towers, and
Wi-Fi", a presentation I made to Santa Fe city government staff:
http://www4.ncsu.edu/~basherwo
There is an extremely important though underrated property of charges
and fields called the "superposition principle": The value of the
electric or magnetic field at a location in space is the vector sum of
all the fields contributed by all the charges in the Universe, AND THE
CONTRIBUTION OF ANY PARTICULAR CHARGE IS UNAFFECTED BY THE PRESENCE OF
OTHER CHARGES.
It is the capitalized portion of the principle that despite its
innocent-sounding content leads to quite counterintuitive
consequences. For example, you've probably heard that a metal
container shields out electric fields made by charges outside the
container. False! There is no such thing as "shielding". By the well
validated superposition principle, the field at any location inside
the metal container includes the field contributed by external
charges. However, it LOOKS as though the metal prevents the field from
getting in, because the external charges "polarize" the metal by
shifting the mobile electrons in the metal, and the polarized metal
contributes an additional electric field inside the container that is
equal in magnitude but opposite in direction to the field contributed
by the external charges. The effect is indeed as though the metal
"shielded" the interior, but the actual mechanism has nothing to do
with "shielding", and the field due to the external charges is most
definitely present inside the container.
Consider a cubical box with metal walls, and there's a positive charge
to the right of the box. That positive charge makes an electric field
through the region, and that field causes (negatively charged) mobile
electrons in the metal to move to the right, toward the external
positive charge. That makes the right side of the box have an excess
negative charge, and it leaves the left side with a deficiency of
electrons, hence a positive charge.
By convention, the direction of electric field is said to be in the
direction that a positive charge would be pushed, so the electric
field inside the box due to the external positive charge is to the
left. Note that the "polarization" charges, negative on the right side
of the box and positive on the left side of the box, contribute a
field inside the box to the right. The 1/r squared character of the
electric field of point charges leads to the surprising result that
the field inside the box contributed by the polarization charges is
exactly equal in magnitude and opposite in direction to the field
contributed by the external charge, so the vector sum of the field
contributions of all the charges is in fact zero inside the box, as
though the metal "shielded" the interior.
In fact, if one claims that the box "prevents the field of external
charges getting into the box", there's an flaming inconsistency, since
the polarization charges would make a nonzero electric field inside
the box, uncompensated for by the field due to the external charge,
and in violent disagreement with measurements that show that the
electric field inside the box is zero.
Back to the case of light, which is produced by accelerated charges.
If you accelerate charges for a short time, they radiate a short pulse
of light. Let's accelerate some charges somewhere off to the left, for
a short time. Light (electric and magnetic fields) propagates in all
directions, but we're interested in the light traveling to the right,
toward a detector (which could be a camera) some known distance from
the "source" (the accelerated charges). We measure the time from when
we briefly accelerated the charges to when we detect the light a known
distance away. Divide distance by time and get the speed of light in
air, 3e8 m/s.
Now let's repeat the experiment, except that there's a thick slab of
glass between the source and the detector. You've surely heard that
"light travels much slower in glass than in air", so you would expect
the light to take significantly longer to reach the detector now that
the glass is in place. But that's not what happens! You find the same
time interval between the emission and the first light reaching the
detector, and you determine the same 3e8 m/s speed as before! And you
must, because the field at any location in space is the vector sum of
the field contributions of all the charges in the Universe, unaffected
by the presence of other charges (in this case, the electrons and
protons in the glass). The fields radiated by the accelerated charges
are unaffected and reach the detector in the same amount of time as
before.
However, there is an effect. As the electric field passes through the
glass, it accelerates the electrons and protons (it accelerates the
electrons much more than the protons, due to their very low mass).
These accelerated electrons radiate electromagnetic radiation, like
any accelerated charges. The traveling fields of this re-radiation
also come to our detector, so that the shape of the pulse we receive
is altered from what we saw without the glass, because there are now
additional field contributions that were not present in the absence of
the electron-containing glass. The first bit of light shows up on
time, but then the situation becomes quite complicated.
An important special case is that where the source charges off to the
left are accelerated not for a short time, but continuously,
sinusoidally up and down (which involves accelerations as the charges
move faster and slower and turn around). If you turn on this
sinusoidal radiation abruptly, of course you'll first see some light
at the detector on time, with or without the glass being present. But
let the sinusoidal acceleration of those source charges continue for a
long long time. It can be shown that the vector sum of this radiation
and the re-radiation from electrons accelerated in the glass leads to
a detection of sinusoidal radiation, and that sinusoidal radiation has
a phase which is shifted. That is, the peaks come at a different time
than they did without the glass. In fact, in the "steady state", the
peaks come later than they used to, and the lateness is proportional
to how thick the glass is. It is a useful shorthand to say that the
"light travels more slowly in the glass", as that description is
consistent with the phase delay of peaks in the sinusoid, in the
steady state, even though the speed of light in the glass is the usual
3e8 m/s. (The initial transient is messy, and not a simple sinusoid.)
Richard Feynman in the famous Feynman Lectures on Physics discusses
this quantitatively in Chapter 31 on "The Origin of the Refractive
Index".The "refractive index" is usually denoted by n, and it is
common practice to say that "the speed of light in a medium with
refractive index n is 3e8/n m/s". But in fact the speed of light is a
universal quantity. Although it is very often convenient to pretend
that the speed of light is slower in glass, that's just a
calculational convenience -- it's a misleading description of what's
really going on. In fact, the refractive index and "speed of light" in
glass is different for different frequencies of the sinusoidal
radiation, because different frequencies of electric field affect the
motion of the electrons differently in the glass.
Bruce
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