                            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)