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The modern view of time
1. Introduction
In the late 19th century, there were two theories of light.
The first, held by Isaac Newton, among others, was that
light was composed of tiny luminous "corpuscles", and that
different colours were corpuscles of different masses. The
second, held by Christiaan Huyghens, among others, was that
light was a wave phenomenon, and that different colours were
different frequencies. Both theories were supported by a
large body of evidence, but both of them had trouble
explaining some phenomena. However, the wave theory was more
successful at explaining most phenomena, and by the end of
the 19th century had won the support of most physicists.
2. The Michelson-Morely Experiment
By 1887, the wave theory of light was more or less accepted
by everyone, despite the problem of how light propogates in
vacuum (how can a WAVE exist without a medium in which to
propogate?). An explanation was proposed, namely that a
vacuum wasn't a true vacuum, but contained a substance with
very strange properties, called Ether (don't confuse with
the chemical).
Two American physicists, Michelson and Morely, attempted to
detect the medium in which the light waves were propogating.
They reasoned as follows:
The Ether is (presumably) stationary, and the Earth is
moving relative to it. If so, a beam of light trasmitted
back and forth along the direction of the Earth's motion
should take longer to cover the same distance than a beam
transmitted across the direction of the Earth's motion (For
proof, see apppendix A). All we have to do is compare the
time it takes two light beams to go along/across the Earth's
orbit.
They set up the experiment, but could not detect ANY
difference in the transit times. Subsequent experiments
confirmed their results. This, of course, threatened to
shake physics to its foundations.
3. The Lorentz-Fitzgerald contractions
In order to keep the foundations of physics from toppling,
Lorentz and Fitzgerald proposed that the clocks on all
moving particles slow down when measured by a outside
observer. They also suggested a similar contraction for
masses and distances in the direction of movement, to keep
things consistent.
2
v 0.5
t' = (1 - ---) t time
2
c
2
v 0.5
x' = (1 - ---) x
2 distance
c
m
______________
2
v -0.5
m' = (1 - ---) mass
2
c
These were "ad-hoc" corrections, and had no theoretical
basis at the time, but they "saved the day".
4. The Theory of Relativity
In 1905, a 26 year old physicist, Albert Einstein publish
his special theory of relativity, which put the
Lorentz-Fitzgerald transformations on a sound theoretical
ground. Einstein made only one assumption - that the speed
of light is measured as being exactly the same by all
observers. This enabled him to explain the Michelson-Morely
experiment, confirm the Lorentz-Fiztgerald contraction
formulae, and also integrate electromagnetic theory and
mechanics. It also derived the formula that is usually all
most people know of physics:
2
E = mc
This theory set the upper speed limit at the speed of light.
No attempts to break this speed have succeeded as of now.
The special theory was incomplete, in that it did not take
into account the effects of gravity. In 1915, Einstein
published an extension to his theory, the General Theory of
Relativity, which incorporated a CURVED four-dimensional
space-time. It is NOT neccesary to assume a 5th dimension in
which the other four are curved, as it is possible to deduce
the curvature from observations inside a four-dimensional
space. Therefore, space-time is a curved FOUR-DIMENSIONAL
continuum.
5. Current theories
In the attempt to "marry" general relativity, quantum
mechanics and elementary partical physics, more dimensions
HAVE been postulated. However, these dimensions only show
up at enormous energies (where 1 PROTON has an energy
measured in joules!!) therefore, these theories are pure
speculation at the moment, until some experimental evidence
comes along or until some of the predicted low-energy
phenomena are discovered.
Appendix A
In the classical view, light and sound waves travel in a
manner similar to that of a swimmer through water. The
Michelson-Morely experiment was essentially this:
Take two equally good swimmers. One will swim a distance L
downstream and back, and the other will swim the same
distance perpendicular to the first (not allowing the
current to drag him downstream). We shall call:
v - the speed of the stream (the Earth's speed in the
ether)
c - the speed of the swimmers (the speed of light)
For the first swimmer:
Downstream:
d = L distance
V = v+c velocity
t = L/(v+c) time
Upstream:
d = L distance
V = c-v velocity
t = L/(c-v) time
Total:
2 2
T1 = 2Lc/(c - v )
For the second swimmer:
Both ways:
d = L distance
2 2 0.5
V = (c - v ) velocity (don't forget
the current)
t = L/V time
Total:
2 2 0.5
T2 = 2L/(c -v )
2 2 0.5
T1/T2 = c/(c - v ) >=1 ratio of times
Therefore, the beam traveling up/downstream ALWAYS takes
longer than the beam traveling cross-stream. It is this
effect that Michelson and Morely looked for.
References
==========
Fundamental University Physics / Alonso & Finn
A Second Course of Light / McKenzie
Suggested Reading
=================
The Weitzman Institute high-school physics books (Hebrew)