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