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S10i. What happened to the aether?
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The aether as supporting substance for electromagnetic waves
was a standard hypothesis in the 19th century but fell out of 
favor with the successes of relativity theory. 
When in vogue, the aether was the substance filling empty space 
- i.e., the physics of the aether is the physics of empty space.

In a way, the classical background field (also termed the 'vacuum', 
or more neutral a 'coherent state' or - in quantum gravity - 
a 'Hadamard state') around which the quantum field is expanded into 
excitation modes (photons, gravitons, etc.) is the modern equivalent 
of the aether. However nobody uses the term since it it fraught with 
misleading connotations, and not really needed. 
 
In modern language, the aether is called the vacuum, and the properties 
of the aether are the properties of the vacuum. A modern account by
the 2004 Nobel prize winner Frank Wilczek can be found in
   F. Wilczek, 
   The Persistence of Ether, 
   Phys. Today 52N1 (1999), 11-13.

While the 19th century aether was thought to be at rest,
the 20th century aether (= the vacuum in a quantum field theory)
is a Poincare invariant state with zero quantum numbers.
(In a putative quantum gravity, it would even be a diffemorphism 
invariant state, should something like that exist. The Unruh effect
indicates, however, that there is probably no objective vacuum, 
since emptiness is observer dependent.)

Indeed, Poincare invariance is the modern way of saying 
'being at rest' - the momentum of a Poincare invariant state is zero 
in every frame of reference, and the mass of a Poincare invariant 
state must also be zero, which implies that the vacuum is empty
in terms of mass. (It is however allowed to be filled by a constant
nonzero Higgs field, as required in the standard model.)


Identifying the aether and the vacuum is consistent with the way
Einstein thought about the topic, as the following quotes from
Einstein's lecture (in German) at the University of Leyden, 1920, show:

''Da solche Felder auch im Vakuum - d.h. im freien Aether - auftreten, 
so erscheint auch der Aether als Traeger von elektromagnetischen 
Feldern.''

''Man kann hinzufuegen, dass die ganze Aenderung der Aetherauffassung, 
welche die spezielle Relativitaetstheorie brachte, darin bestand, 
dass sie dem Aether seine letzte mechanische Qualitaet, naemlich die 
Unbeweglichkeit, wegnahm.''

''Man kann die Existenz eines Aethers annehmen; nur muss man darauf 
verzichten, ihm einen bestimmten Bewegungszustand zuzuschreiben, 
d.h. man muss ihm durch Abstraktion das letzte mechanische Merkmal 
nehmen, welches ihm Lorentz noch gelassen hatte.''

''Der Aether der allgemeinen Relativitaetstheorie ist ein Medium, 
welches selbst aller mechanischen und kinematischen Eigenschaften 
bar ist, aber das mechanische (und elektromagnetische) Geschehen 
mitbestimmt.''

''Man kann also wohl auch sagen, dass der Aether der allgemeinen 
Relativitaetstheorie durch Relativierung aus dem Lorentzschen Aether 
hervorgegangen ist.''

''... Den Aether leugnen bedeutet letzten Endes annehmen, dass dem 
leeren Raume keinerlei physikalische Eigenschaften zukommen...''

For the complete speech in German and in English translation, see
   http://www.alberteinstein.info/db/ViewCpae.do?DocumentID=34003
(the part with the above quotes is not freely available online).


Note that the QFT vacuum is considered by many as a very dynamical 
entity, being able 
   1. to have excitations, namely single particles and multiparticle 
      states; in particular photons = quantized electromagnetic waves,
   2. to exhibit spontaneous symmetry breaking, and
   3. to generate random particle-antiparticle pairs.
(In some people's imagination, being able to  
   4. allow whole universes to pop up or disappear!) 

Thus the modern vacuum looks much more like the 19th century aether 
(whose excitations were the classical electromagnetic waves) 
than the classical vacuum to which Einstein was referring.