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archive:fun:time
                          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)

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