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