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Module 2
Light and Newtonian Relativity
Three Scenarios
We said in the last module that the laws of mechanics are invariant in Newtonian relativity. By ‘mechanics’, we mean
macroscopic push and pull forces. But what about the laws of electricity and magnetism? Recall that Maxwell’s equations
are a nice summary of these laws and that, from Maxwell’s equations, we can derive the wave equation for the
electromagnetic wave (light wave) in free space. The wave equation for the electric field component of a linearly polarized
wave looks like
 2 E ( x, t ) 1  2 E ( x, t )

0
(2.1)
x 2
c2
t 2
for a wave traveling in the x-direction with its electric field oscillating in the y-direction. The speed of the wave c is found
to satisfy
c  1 / oo
where o and o are the permeability and permittivity of free space, respectively. When the values of these free space
constants are substituted, we find that c = 3x108 m/s.
Now in Newtonian relativity we know that the measured speeds of objects are relative to the motion of the observers. Here
we have a speed c popping out of Maxwell’s equations. But the motion of the observer should affect the value of this speed,
right? Let’s say that it does. Then perhaps this value of c is measured only by the observer for which Eq. (2.1) is valid.
This frame of reference is a special frame in which light travels at c in vacuum. In any other inertial frame, the speed of the
light wave is measured to be different than c. Fig. 2-1 shows one such possibility.
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y’
y
S
S’
v
ux= c
x
O’
O
z
u’x= c - v
z’
x’
Fig. 2-1
Suppose a laser pointer is at rest in frame S and S is the special frame for which Unprime measures the light to travel at c.
Then Prime in frame S’, moving as shown at speed v relative to Unprime, will measure the laser light to travel at c-v
according to Newtonian relativity. Perhaps this is the way things are.
This one special frame for which light is measured to travel at c is called the ether frame. The reason for this is that the
prevalent thought at the time of the development of Maxwell’s equations was that the light wave needed some medium to
support the oscillations of the electric and magnetic fields, much like a water wave needs water or a sound wave needs air.
This medium was called the ether. While similar in function to water or air as a wave medium, the ether is a very different
kind of material. It doesn’t have the usual properties of normal matter but that doesn’t mean it could not exist. We see then
that the frame S Fig. 2-1 is the ether frame. And we say further that Maxwell’s equations (the laws of electricity and
magnetism) as we know them work fine in this ether frame but they change form in any other frame. Thus, perhaps the laws
of electricity and magnetism are not invariant in Newtonian relativity.
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What we have just described is one possible scenario for how the laws of electricity and magnetism behave in a proposed
relativity theory. But there are two other possible scenarios to consider. Perhaps the laws of electricity and magnetism are
invariant under Newtonian relativity but the laws, as written by Maxwell, are incorrect. Or perhaps Maxwell is correct, the
laws of mechanics and the laws of electricity and magnetism are invariant in a relativity theory, but that theory is not
Newtonian relativity. This last scenario implies that the Galilean transformation equations are incorrect. It also implies that
Newton’s laws are most probably incorrect. His laws are invariant in Newtonian relativity and most likely would not be
invariant in a different relativity theory. Let’s summarize these three scenarios* in Table 2-1.
Table 2-1
Scenario 1
Scenario 2
Scenario 3
Newtonian
Newtonian
Non-Newtonian
Laws of Mechanics Correct?
yes
yes
probably not
Laws of Mechanics Invariant?
yes
yes
yes (once corrected)
Laws of Elec. & Mag. Correct?
yes
no
yes
Laws of Elec. & Mag. Invariant?
no
yes (once corrected)
yes
Relativity Theory
Comments
ether frame
Galilean transformation equs. incorrect
* I suppose we could perform another permutation and argue that there is a fourth scenario that goes like this. Maxwell’s
equations are correct and there is a new relativity theory in which the laws of electricity and magnetism are invariant.
Newton is correct and the laws of mechanics are not invariant in the new theory. This has the downside that the laws of
mechanics are invariant. This goes against our observations of mechanical interactions.
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The Michelson-Morley Experiment
We see now that the famous Michelson-Morley experiment was a method to test the validity of Scenario 1. If the
experiment had revealed a fringe shift, then one could have more confidence in stating that the measured speed of light is a
relative quantity and that there is an ether frame.
The details of the experiment are discussed in the supplemental document. Read this document. You will read not only
about the result of the experiment but also about some hypotheses put forth at the time that explained the result and that also
were consistent with the idea of an ether frame. These hypotheses, however, have been abandoned by all but a few and the
general consensus is that Scenario 1 is incorrect.
So what about Scenario 2? Well, the laws of electricity and magnetism seem to work pretty well. Before we roll up our
sleeves and try to fix something that may not be broken, let’s look at Scenario 3. Newtonian relativity sure seems to work in
our everyday world. And the laws of mechanics seem to be okay, too. If there are flaws in these, they must be “minor”
flaws. And who wants to find a new relativity theory? That doesn’t seem trivial.
Well, as you probably know, Scenario 3 is the generally accepted winner. The laws of mechanics and Newtonian relativity
do work well when the relative speed v is small compared to c. That’s why they seem fine in our everyday, macroscopic
world. But they need to be adjusted to a more general form that includes high relative speeds. That’s why they are
“incorrect”. The fix to Newtonian relativity, which boils down to generalizing the Galilean transformation equations, is
made in the next module. The fix to the laws of mechanics follows in subsequent modules.
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