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LIGHT and SPECIAL
RELATIVITY ETHER MICHELSON-MORLEY
EXPERIMENT EJECTION OF ETHER
HYPOTHESIS |
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SUMMARY Classical
physics postulate for the propagation of light through space Michelson-Morley experiment attempted
to measure the relative velocity of the Earth through the ether. Null result. Maxwell
– electromagnetic radiation propagates at the speed of light
independent of the frame of reference.
Einstein’s postulates of Special Relativity 1.
The laws of
physics are valid in all inertial frames of reference. 2.
Space and
time are relative quantities. Speed of light is a constant and does not
depend upon the motion of the source or observer. There is no frame of
reference in which the light of light is measured. |
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Learning strategies My
notes are often long and complex. But I believe that you cannot do well in
physics by using notes that give a superficial view of the content. So, how to make the best of my
resources? You need to make visual mindmaps on each topic.
Then you can use your visual mindmaps to transfer knowledge from your short
term to long term memory. Why do I use the work visual? It is difficult to recall words, but it is
very easy to recall a picture. When you view my images and animations, you
need to “process them into your brain”. Hence, it is an easy task
to recall the image and then it is not so difficult to add the words to the
picture. |
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ETHER MODEL FOR THE TRANSMISSION OF LIGHT In
the well-established laws of classical physics, the concept of velocity only
has meaning when it is measured with respect to a frame of reference. Thus,
the measured value of a velocity depends upon the motion of an observer. To
illustrate this principle, we will consider a simple example. Mary is in a
river boat, while Steve is on a bank of the river observing Mary. What is
Mary’s speed? This question is
not meaningful. We need to state the frame of reference in which
the speed is to be measured. In our example, we can define three frames of
reference.
1.
Steve’s
frame of reference on the river bank (S) 2.
Mary’s
frame of reference in the boat (M) 3.
The water
as a frame of reference (W) We
then can define the velocities The
animation below shows Mary in a boat and the water flowing from the left to
the right at 2.0 m.s-1. The three
animations show Mary moving at 10 m.s-1 w.r.t the water but in
different directions.
Fig. 1. The
speed at which Mary travels is only meaningful by stating the frame of
reference of the observer. So,
in terms of the principles of classical physics, relativity involves an
analysis of how measurements are made depend upon the observer as well as
what is observed. Just as the measurement of the speed of the boat depends
upon the observer, this principle was believed to apply to all types of waves
including light (figure 2).
Fig.
2. Classical picture for
the speed of light. The speed of light is relative to the motion of the
observer, and so the speed of light is c + v or c - v.
But this is not correct. The correct answer is
that the person will measure the speed of light to be the constant value c and it does not matter how fast or slow they are approaching or
receding from the light beam or the speed of the light source. But, what is the
frame of reference to measure the speed of light? It seemed inconceivable to 19th Century physicists
that light and other electromagnetic waves, in contrast to all other kinds of
waves, could propagate without a medium (frame of reference). It seemed to be
a logical step to postulate such a frame of reference, called the ether (or aether),
even though it was necessary to assume unusual properties for it, such as zero density and perfect
transparency, to account for its undetectability. This ether was assumed to fill all space
and to be the medium with respect to which electromagnetic waves propagate
with the speed c. It
followed, using Newtonian relativity, that an observer moving through the
ether with speed v would measure the speed of the light beam to be (c + v) if they were directly approaching
the light source and (c - v) if moving away from the light source (figure 2).
When
19th Century physicists selected the ether as the medium for the propagation of
electromagnetic waves they were merely borrowing and adapting an existing
concept. The fact that certain physical events propagate themselves through
space led to the hypothesis that space is not empty but is filled with an
extremely fine substance, the ether, which is the carrier or medium of these
phenomena. Indeed, the ether was
proposed as the carrier of light in Rene Descartes’ Dioptrics,
which in 1638 became the first published scientific work on optics. In this work, Descartes proposed that
the ether was all-pervasive and made objects visible by transmitting a
pressure from the object to the observer’s eye. Robert
Hooke in 1667 developed pressure wave theories that allowed for the
propagation of light. In these
theories, luminous objects set up vibrations that were transmitted through
the ether like sound waves through air. The
Dutchman Christiaan Huygens published a full theory on the wave nature of
light in 1690. According to
Huygens, light was an irregular series of shock waves that proceeded with
great speed through a continuous medium – the luminiferous ether. This ether consisted of minute
elastic particles uniformly compressed together. The movement of light through the
ether was not an actual transfer of these particles but rather a compression
wave moving through the particles.
It was thought that the ether particles were not packed in rows but
were irregular in their orientation so that a disturbance at one particle
would radiate out from it in all directions In
1817 the French engineer Augustine Fresnel and the English scientist Thomas
Young independently deduced that light was a transverse wave motion. This
required a rethink of the nature of the ether, which until this time had been
considered by most scientists to be a thin fluid of some kind. Transverse waves can only travel
through solid media (or along the surface of fluids). Clearly, the ether had to be a
solid. The solid also had to be
very rigid to allow for the high velocity at which light travelled. Clearly,
this posed a problem, since such a solid would offer great resistance to the
motion of the planets and yet no such resistance had been noted by
astronomers. In 1845 George Stokes
attempted to solve the dilemma by proposing that the ether acted like pitch
or wax which is rigid for rapidly changing forces but is fluid under the
action of forces applied over long periods of time. The forces that occur in light
vibrations change extremely quickly (600´1012
times per second) compared with the relatively slow processes that occur in
planetary motions. Thus, the
ether may function for light as an elastic solid but give way completely to
the motions of the planets. In
1865 the great Scottish physicist James Clerk Maxwell published his theory of
electromagnetism, which summarised the basic properties of electricity and
magnetism in four equations.
Maxwell also deduced that light waves are electromagnetic waves and
that all electromagnetic waves travelled at 3´108 m.s-1 relative to the ether. The ether was now called the electromagnetic ether rather
than the luminiferous ether and became a kind of absolute reference frame for
electromagnetic phenomena.
Fig. 3. Ether proposed as the medium for
the propagation of electromagnetic waves. Classical concept: the speed of
light depends on the relative motion of the Earth through the ether. ETHER
– proposed medium for the propagation of electromagnetic waves Property of ether
Evidence Fills space, permeates all
matter
Light travels everywhere Stationary
Light travels in straight lines Transparent
Can’t see it Extremely low density
Can’t be detected Great
elasticity
Medium must be elastic otherwise
energy dissipated MICHELSON-MORLEY EXPERIMENT If the ether
exists, an observer on Earth should be able to measure changes in the
velocity of light due to the Earth’s motion through the ether. The Michelson-Morley
experiment attempted to do just this. In 1887, Albert Michelson &
Edward Morley performed a very careful experiment to measure the motion of
the Earth relative to the ether and thereby demonstrate that the ether
existed. Their method involved using the phenomenon of the interference of
light to detect small changes in the speed of light due to the Earth’s
motion through the ether. The apparatus was mounted on a
solid stone block for stability and was floated in a bath of mercury so that
it could be rotated smoothly about a central axis. The apparatus is assumed
to be travelling through the ether with a uniform velocity v of about 30 km.s-1,
equivalent to the Earth at rest with the ether streaming past it at a
velocity –v.
A beam of light from the source
S is split into two beams by a half-silvered mirror K, half of the beam
travels from K to mirror M1 and is then reflected back to K - the other half
reflected from K to mirror M2 and then reflected from M2 back to K. At K part of the beam from M1 is
reflected to the observer O and part of the beam from M2 is transmitted to O.
Fig. 4. Michelson – Morley Interferometer. The light from reflected by
the two mirrors produces an interference pattern at the location of the
observer. Although the mirrors M1 and M2
are the same distance from K, it is virtually impossible to have the
distances travelled by each beam exactly equal, since the wavelength of light
is so small compared with the dimensions of the apparatus. Thus, the two beams would arrive at O
slightly out of phase and would produce an interference pattern at O. There
is a difference in the time taken by each beam to traverse the apparatus and
arrive at O, since one beam travels across the ether stream direction while
the other travels parallel and then anti-parallel to the ether stream
direction. This difference in time taken for each beam to arrive at O would
also introduce a phase difference and would thus influence the interference
pattern. Now if the apparatus were to be
rotated through 90o, the phase difference due to the path
difference of each beam would not change. However, as the direction of the light
beams varied with the direction of flow of the ether, their relative
velocities would alter and thus the difference in time required for each beam
to reach O would alter. This
would result in a change in the interference pattern as the apparatus was
rotated (changes in the patterns of bright and dark fringes).
Fig. 5. Interference patterns
recorded at location O. The pattern on the right was expected where a fringe
shift occurs but a null result was obtained as shown by the interference
pattern on the left. The Michelson-Morley apparatus
was capable of detecting a phase change of as little as 1/100 of a
fringe. The expected phase change
was 4/10 of a fringe. However, no
such change was observed - the result of the Michelson-Morley experiment was
that no motion of the Earth relative to the ether was detected. Since the experiment failed in its
objective, the result is called a null result. The
Michelson-Morley experiment is an excellent example of a critical experiment
in science - the fact that no motion of the Earth relative to the ether was
detected suggested quite strongly that the ether hypothesis was incorrect and
that no ether (absolute) reference frame existed for electromagnetic
phenomena – this opened the way for a whole new way of thinking that
was to be proposed by Albert Einstein in his Theory of Special Relativity.
The null result of the Michelson-Morley experiment was such
a blow to the ether hypothesis and to theoretical physics in general that the
experiment was repeated by many scientists for more than 50 years. A null result has always been obtained. REJECTION OF THE ETHER HYPOTHESIS The
negative result of the Michelson-Morley experiment had three consequences. 1.
It rendered
untenable the hypothesis of the ether by demonstrating that the ether had no
measurable properties – an ignominious end for once had been a respect
idea. 2.
It
suggested a new physical principle: the speed of light is the same
everywhere, regardless of any motion of source or observer. 3.
Acceptance
of the prediction of Maxwell’s equation that the speed of light in free
space depends only on the electrical and magnetic properties of a vacuum and
not on the motion of the source of motion of any observer. The speed of light
was given by the equation
where
The
propagation of water waves and the propagation of light as see by two
observers is contrasted in the animations shown in figures 6 and 7.
Fig. 6. The
observers Steve and Mary
observe different ripple patterns when a stone was dropped into the water.
The water acts as the frame of reference. From the circular ripple pattern,
Steve knows that he is stationary w.r.t to the water. Mary knows that she is moving
through the water from the left to the right because of the asymmetrical
ripple pattern.
Fig. 7. Mary and Steve both
see a sphere of light expanding with themselves at the centre even though
they may be changing their position with respect to the point where the flare
went off. They must both see identical phenomena according to the 1st
and 2nd postulates of special relativity. The
remarkable fact that the speed of light in free space does not depend upon
any inertial frame of reference or the motion of source or observer leads to
dramatic consequences such as two events may be simultaneous to one observer
but not to other, time and space are relative quantities and not absolute
ones, and mass and energy are equivalent quantities.
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