ELECTROMAGNETISM & RELATIVITY - Chapter 7, Exercise 1 Solution
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Conceptual: The Ether's Contradictory Required Properties

PROBLEM
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Explain, in your own words, why the luminiferous ether needed to
have genuinely contradictory physical properties - name both
properties directly, and explain why each was necessary for the
ether theory to work at all.

SOLUTION
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The two contradictory required properties were:

  1. FRICTIONLESS / UNDETECTABLE: The ether had to offer essentially
     zero resistance to any object moving through it - planets,
     comets, and everyday objects on Earth all needed to pass through
     it completely unimpeded, with no measurable drag or slowing
     effect at all. If the ether had any real friction, it would have
     visibly disrupted planetary orbits and everyday motion long
     before the 19th century, which was never observed.

  2. RIGID / STIFF: At the very same time, the ether had to be dense
     and stiff enough to support a wave propagating through it at the
     genuinely enormous speed of light, roughly 3 x 10^8 m/s. In
     general, a wave travels faster through a STIFFER medium (sound
     travels faster through steel than through air, for example), so
     supporting a wave at such an extreme speed implied the ether
     would need to be an almost unimaginably rigid substance.

These two requirements are genuinely in tension: everyday physical
substances that are extremely rigid (like steel) also tend to offer
real resistance to objects moving through them, while substances
offering little to no resistance (like a very thin gas) tend to be
far too "soft" to support waves at anything close to the speed of
light. The ether needed to combine the frictionlessness of empty
space with the rigidity of a solid, all at once - a combination no
known real substance could plausibly satisfy.

ANSWER: The ether needed to be simultaneously frictionless (to allow
planets and objects to move through it completely undetected) and
extremely rigid (to support light waves travelling at their real,
enormous speed) - two properties that, in every other known real
substance, work directly against each other.

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WHY THIS WORKS AS AN ANSWER

Naming this contradiction directly (rather than just saying "the
ether had weird properties") shows exactly why physicists were
already somewhat uneasy about the ether concept even before Michelson
and Morley's own real 1887 experiment - the theory demanded a
substance with no known real-world analogue, making it a genuinely
fragile idea even on paper, well before any experimental test
actually failed to detect it.