SITEMAP
2008
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The
Speed of Light1:
HistoryThe
approximate speed of light was already known to
us back
in the time of Isaac Newton. Astronomers
were able to use the rotation of planets and their moons as an
incredibly precise system of "clockwork", and the precision of these
measurements was so exact that they could identify the changes in
apparent timings caused by light taking longer to reach us
from more
distant parts of the solar system. The critical measurement was that of
the eclipse of the moons of Jupiter -- Roemer
noted that the
eclipses
were seen slightly earlier when Jupiter was nearer to us, and
slightly later when the planet was further away. Newton's
quoted estimates in Opticks of light taking seven or eight minutes to
reach us from the Sun, along with an estimated distance of the Sun of
seventy million miles, would have given an estimated
speed of light of 150,000-160,000 miles per second. More
modern
values of a bit over eight minutes (~500 seconds) and just
over 93
million miles give us a speed of around 186,000 miles per second, so
the old figures weren't that far off. [1] [2] James
Maxwell's work on electricity and
magnetism in the mid-Nineteenth Century then led to
a prediction of the existence of electromagnetic
waves that just happened to propagate at the same speed as light.
Maxwell argued that light was
an electromagnetic wave, and that visible light consisted of
electromagnetic radiation whose wavelengths happened to be in a
suitable range for human eyes to be able to detect it. Maxwell's
work suggested that the speed of light should be constant, but didn't
tell us exactly what sort of lightspeed constancy
ought to be involved.
2:
"Global" lightspeed constancy, and special relativityG.
F.Fitzgerald
and H.A. Lorentz pointed out, around the
turn of the Twentieth Century, that
if lightspeed was absolutely fixed with respect to
a background frame, but observers moving with respect to that
background frame contracted (and perhaps time-dilated)
in a particular way, then it'd be impossible for them to use round-trip
measurements of the speed of light to work out whether they were
"moving" or "stationary". [3]
Einstein then took this
system of "Lorentzian electrodynamics" and rederived it in
more minimal
form to produce his special theory of relativity [4].
If we said that light
was globally constant for all
inertial observers, then the effects associated with Lorentz's "special
factor" would absorb the disagreements that we'd otherwise expect
between these observers, over whose frame was the "real" frame for the
propagation of light. Although it seemed impossible for the same
lightbeam to have the same totally-constant speed in everybody's
different frames, special relativity's redefinitions of distances and
times created a system in which this could work. [5]
If
a lightbeam links two agreed events, special relativity says that
two differently-moving observers can disagree as to the
distance that they believe the lightbeam "really" traveled and the
amount of time that it "really"
took to do it, but
the combination of those two things, modified by the appropriate
Lorentz
factors, would combine to produce the same nominal value for the
speed of the lightbeam for both observers. For this system to
work, we
need the lightbeam to travel in a simple way that isn't disturbed by
the motion of any nearby objects ... we say that the geometry of
spacetime, as defined by lightbeams, is "flat" for all observers with
simple inertial motion.
3:
"Local"
lightspeed constancy, and general relativityWhen
Einstein wanted to extend the principle of relativity to deal with all
forms of motion, he immediately ran into a problem. Gravity bends
lightbeams, and a lightbeam that seems straight and constant for an
inertial observer can appear to mark out a variable-speed curved path
for an accelerating observer. So special relativity's concept
of lightspeed constancy didn't work in a more ambitious theory that
also had to be
able to deal with accelerations and gravitational effects. Gravity
didn't just appear to alter light-distances, it mangled
clockrates too [6], so for two different
observers drifting in deep space
in different gravitational environments, their different rates of
timeflow could lead them to assign different speeds to the same
lightbeam. These effects also cause a lightbeam to
take longer to cross a more "gravitationally-dense" region than one
in which
the background
gravitational field intensity is weaker ("Shapiro
effect"). [7] Under
general
relativity, the user can respond to these variations by
deciding to define distances and times locally.
It's no longer necessary for us to apply the earlier SR idea
that lightspeed has to be globally constant across
the region, it
turns out that Nature is happy to violate that rule, as long as
lightspeed is still locally constant. So if
an observer is drifting in a
strong-gravity region where gravitational time dilation is causing
their
clocks to run at half the speed that we'd otherwise
expect, then the same slowing effect should make
light move across the region at half the usual speed as well. Someone
far outside
the region might argue that light is appearing to cross the region more
slowly than usual, but to a local observer, whose local references are
warped by the same degree as the propagation of light, the speed of
adjacent light seems to
be exactly right. If it seems to have a different speed somewhere else,
well, that's someone else's problem.
4:
Combining descriptionsIt could
now be
argued that since we had learnt that only local
c-constancy was necessary (and that SR's "law" of the propagation of
light wasn't a law after all), perhaps the geometrical basis
of
the earlier and more restricted"special"
theory wasn't valid. Einstein preempted this argument by
designing his general theory to
reduce to the special theory over small regions of spacetime. He then
argued that the special theory wasn't invalidated
by general
relativity, but instead lived on within it as a limiting case.
[8] Towards
the end of his life, Einstein
wrote that he
no longer considered the
decision to construct general relativity as a two-stage model, with
"curvature" arguments built on top of a flat-spacetime "SR"
foundation, as justifiable. It had been the best that could be achieved
at the time, but with the benefit of hindsight it didn't deem to be
defensible. [9]
Quite what Einstein may have meant by this, what the alternative might
have been, and what the implications might be of having a general
theory that didn't have a forced reduction
to special relativity, still seem to be unresolved questions. [10]
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References:- I.
Newton, Principia, Book I
(based on the
1729 Motte translation from the original Latin)
"
For
it is now certain from the phenomena of Jupiter's satellites, confirmed
by the observations of different astronomers, that light is propagated
in succession, and requires about seven or eight minutes to travel from
the sun to the earth. ... ... Therefore because of the
analogy
there is between the propagation of rays of light and the motion of
bodies, I thought it not amiss to add the following Propositions for
optical uses; not at all considering the nature of the rays of light,
or inquiring whether they are bodies or not; but only determining the
curves of bodies which are extremely like the curves of the rays.
"
- I.
Newton, Opticks, Definitions II,
and Query 21"
... But by an argument taken from the equations of the times of the
eclipses of Jupiter's satellites it seems that light is propagated in
time, spending in its passage from the Sun to us about seven minutes of
time ... And therefore I have chosen to define rays and refractions in
such general terms as may agree to light in both cases. "
"
Light
moves from the Sun to us in about seven or eight minutes of time, which
distance is about 70,000,000 English miles, supposing the horizontal
parallax of the Sun to be about 12 ' ' "
- H. A.
Lorentz, "Electromagnetic Phenomena in a System
moving with any
Velocity less than that of Light", Proc. Acad Sci
Amsterdam 6
1904[on
"aether drift" results]: " The first example of
this kind is Michelson's well-known interference-experiment, the
negative result of which has led Fitzgerald and myself to the
conclusion that the dimensions of solid bodies are slightly altered by
their motion through the aether. "
- A. Einstein, "On
the
Electrodynamics of Moving Bodies" ("Zur
Elektrodynamik
bewegter Körper"), Annalen der Physik 17
1905"
If we imagine the electric charges to be invariably coupled to small
rigid bodies (ions, electrons), these equations are the
electromagnetic basis of the Lorentzian electrodynamics and optics of
moving bodies. "
- A. Einstein, Relativity, the
Special
and the General Theory section 7, "The
apparent
incompatibility of the Law of Propagation of Light with the Principle
of Relativity""
At this juncture the theory of relativity entered the arena. As a
result of an analysis of the physical conceptions of time and space, it
became evident that in reality there is not the least
incompatibility between the principle of relativity and the law of
propagation of light,
and that by systematically holding fast to both these laws a logically
rigid theory could be arrived at. This theory has been called the special
theory of relativity ... "
- A. Einstein, "On the influence of
Gravitation on the Propagation of Light" ("Über
den
Einfluss der Schwerkraft auf die Ausbreitung des Lichtes")
Annalen der Physik 35 1911"
The principle of the constancy of the velocity of light holds good
according to this theory in a different form from that which
usually underlies the ordinary theory of relativity. "
- For
a good discussion of the Shapiro effect, see:
Clifford Will, Was Einstein Right,
ch.6: "The time
delay of light: better late than never", pp 108-134
- A. Einstein, Relativity, the
Special
and the General Theory section 22, "A
few
inferences from the General Principle of Relativity""
... according to the general
principle of relativity, the law of the constancy of the velocity of
light in vacuo,
which constitutes one of the two fundamental
assumptions in the special theory of relativity and to which we have
already frequently referred, cannot claim any unlimited validity. A
curvature of rays of light can only take place when the velocity of
propagation varies with position. Now we might think that as a
consequence of this, the special theory of relativity and with it the
whole theory of relativity would be laid in the dust. But in reality
this is not the case ... ... No fairer destiny could be allotted to any
physical theory, than that it should of itself point out the way to the
introduction of a more comprehensive theory, in which it lives on as a
limiting case. "
- A.
Einstein, Scientific American, April
1950
"
I do not see any reason to assume
that ... the principle of general relativity is restricted to
gravitation and that the rest of physics can be dealt with separately
on the basis of special relativity ... I do not think that such an
attitude, although historically understandable, can be objectively
justified ... In other words, I do not believe that it is justifiable
to
ask: what would physics look like without gravitation? "
- E. Baird, Relativity in
curved
spacetime (2007), section 12, "What's
wrong with
General relativity?"
"
Almost all of the problems and potential problems that we've identified
here with Einstein's general theory seem to be consequences of the
theory's incorporation of special relativity, and its assumption that
the relationships of SR have to apply as a limiting case of the theory.
..."
all original material
copyright © Eric Baird 2007/2008 |
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