## The Guest Star

```When a star explodes as a supernova, material is flung out at high
speeds in all directions, and this material emits enormous amounts
of radiation over a wide range of frequencies, including x-rays,
gamma rays, and so on.  Based on the broad range of spectral shifts
(resulting from the Doppler effect), it's clear that the sources of
this radiation have a range of speeds relative to the Earth of over
10000 km/sec. This is because we are receiving light emitted by
some material that was flung out from the supernova in the direction
away from the Earth, and by other material that was flung out in the
direction toward the Earth.

If the supernova was located a distance D from us, then the time
for the "light" (i.e., EM radiation of all frequencies) to reach
us should be roughly D/c, where c is the speed of light.  However,
if we postulate that the actual speed of the light as it travels
through interstellar space is affected by the speed of the source,
and if the source was moving with a speed v relative to the Earth
at the time of emission, then we would conclude that the light
traveled at a speed of c+v on it's journey to the Earth.  Therefore,
if the sources of light have velocities ranging from -v to +v, the
the first light from the initial explosion to reach the Earth would
arrive at the time D/(c+v), whereas the last light from the initial
explosion to reach the Earth would arrive at D/(c-v).  Hence the
arrival times for light from the initial explosion event would be
spread out over an interval of length D/(c-v) - D/(c+v), which
equals (D/c)(2v/c) / (1-(v/c)^2).  The denominator is virtually 1,
so we can say the interval of arrival times for the light from the
explosion event of a supernova at a distance D is about (D/c)(2v/c),
where v is the maximum speed at which radiating material is flung
out from the supernova.

However, in actual observations of supernovae we do NOT see this
"spreading out" of the event.  For example, the Crab supernova was
about 6000 light years away, so we had D/c = 6000 years, and with
a range of source speeds of 10000 km/sec (meaning v = +-5000) we
would expect a range of arrival times of 200 years, whereas in fact
the Crab was only bright for less than a year, according to the
observations recorded by Chinese astronomers in June-July of
1054 AD.  For a few weeks the "guest star" (as they called it) in
the constellation Taurus was the brightest star in the sky, and was
even visible in the daytime.  Within two years it had disappeared
completely (to the naked eye).  The event was also recorded by
Islamic observers, but (oddly) it seems to have passed unnoticed
(or at least unrecorded) in Europe.  In the time since the star
went supernova the debris has expanded to it's present dimensions
of about 3 light years, which implies that this material was moving
at only (!) about 1/300 the speed of light.  Still, even with this
value of v, the bright explosion event should have been visible on
Earth for about 40 years (if the light really moved through space
at c+-v).  Hence we can conclude that the light actually propagated
through space at a speed essentially independent of the speed of
the sources.

This source independence of light speed is obvously consistent with
Maxwell's equations and special relativity, but we should be careful
proof that the speed of light in a vacuum is independent of the speed
of the source, because for visible light (which is all that was noted
on Earth in 1054 AD) the extinction distance in the gas and dust of
interstellar space is much less than the 6000 light year distance
of the Crab nebula.  Hence it's possible to argue that even if the
initial speed of light in a vacuum was c+v, it would have slowed
to c for most of its journey to Earth.  Admittedly, the details of
such a counter-factual argument are lacking (because we don't really
know the laws of propagation of light in a universe where the speed
of light is dependent on the speed of the source, nor how the frequency
and wavelength would be altered by interaction with a medium, so we
don't know if the extinction distance is even relevant), but it's
not totally implausible that the static interstellar dust might
affect the propagation of light in such as way as to obscure the
source dependence, and the extinction distance seems a reasonable
way of quantifying this potential effect.

One way of strengthening the case for source-independence of light
speed based on astronomical observations is to use light from the
high-energy end of the spectrum.  The extinction distance is
proportional to 1/(rho*lambda) where lambda is the wavelength of
the light and tho is the density of the medium.  For x-rays and
gamma rays the extinction distance in interstellar space is enormous,
mcuh greater than the distances to many supernova events, as well as
binary stars and other configurations with identifiable properties.
By observing these events and objects it has been found that the
arrival times of light are essentially independent of frequency, e.g.,
the x-rays associated with a particular identifiable event arrive at
the same time as the visible light for that event, even though the
distance to the event is much less than the extinction distance for
x-rays.  This gives strong evidence that the speed of light in a
vacuum is actually invariant and independent of the motion of the
source.

With the aid of modern spectroscopy we can now examine supernovae
events in detail, and it has been found that they exhibit several
characteristic emission lines, particularly the signature of atomic
hydrogen at 6563 angstroms.  Using this as a marker we can determine
the Doppler shift of the radiation, from which we can infer the
speed of the source.  It's remarkable that the energy emitted by
a star going supernova is comparable to all the energy that it
emitted during millions or even billions of years of stable evolution.
Three main categories of supernovae have been identified, depending
on the mass of the original star and how much of its "nuclear fuel"
remains.  In all cases the maximum luminosity occurs within just
the first few days, and drops by 2 or 3 magnitudes within a month,
and by 5 or 6 magnitudes within a year.  The initial shock wave moves
outward in just seconds, and this elevates the temperature of the
material to such a high level that fusion is initiated, and much of
the lighter elements are fused into heavier elements, including some
even heavier than iron.  This process yields most of the interesting
elements that we find in the world around us.
```