Is the quantum field an aether?
ptam...@yahoo.co.uk
I don't understand: On the one hand with special relativity Einstein
got rid of the aether - the medium which electromagnetic waves use to
travel and which can be used as an absolute reference system. On the
other hand in quantum field theory quantum fields are invented which
fill all space and which are the "medium" for particle waves. Isn't
this reinventing the aether? In what way is this 'aether' bettern than
the one Einstein got rid?
Thanks for help,
Pedro
Timo Nieminen
Why bring quantum field theory into it? Even in classical field theory,
the electromagnetic field fills all space and time, and is the "medium"
for electromagnetic waves. Now, recall that the electromagnetic field is
simply a function of time and space that tells you the field at a given
point at a given time, and _can be equal to zero_ over some space and
time. Can you really call something that can be equal to zero somewhere a
"medium"? Recall that electromagnetic waves are essentially perturbations
of this field from zero. When there is no wave (or static field) there,
there is noting there except for a mathematical entity. No energy, no
momentum, basically nothing. Hardly a medium in the sense that
aether/ether was intended.
That said, Pauli and other writers have used "ether" as a synonym for
electromagnetic field.
The advantage that such an entity has over the earlier material medium
ether is that (a) it doesn't result in the various difficulties that came
out of material medium ether theories and (b) it doesn't leave a material
medium that we have to explain the properties of.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
Roman Werpachowski
reality. It has the same status as the wavefunction, or probability
distribution in statistical mechanics.
Arnold Neumaier
It is just better defined. 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.
See the entry ''What happened to the aether?'' in my theoretical physics
FAQ at
http://www.mat.univie.ac.at/~neum/physics-faq.txt
Arnold Neumaier
ptam...@yahoo.co.uk
great, your FAQ answered my question fully. Congratulations for this
very nice web page!
Thanks.
Pedro
DRLunsford
The ether was sidestepped, because the geometry went from rotationally
invariant, to Lorentz invariant. The Laplace operator went over to the
wave operator, and so propagation was built into the geometry, and did
not require a factitious cause. The ether is thus an artifact of
contracting the Lorentz group by letting c->infinity. The lost symmetry
is assigned to the "stiffness" of the vacuum. See here:
http://www.physics.gatech.edu/people/faculty/finkelstein/Emptiness031215.pdf
http://arxiv.org/abs/hep-th/0106273
-drl
-drl
Dirk Bruere
describing reality. However, assigning some mathematical features 'more
reality' than others can only be done on either experimental or
philosophical grounds neither of which have their grounding in the
formalism itself.
Dirk
mark...@yahoo.com
This reply, in full (below), originally intended for someone else, is
eminently suitable here.
Some of what follows is discussed in greater depth in the "Yang-Mills
Equations in Maxwell Form" article in http://federation.g3z.com/Physics
where more detailed cited from Maxwell's treatise are provided.
The reply to follow:
> Bilge said: The causal structure of spacetime is determined by the
> geometry.
>
> I'm getting confused. What really is an ether?
Aether.
The causal structure of spacetime is determined by the constitutive
relations of the electromagnetic field. For Minkowski spacetime they
are:
D = epsilon_0 E; B = mu_0 H.
For Galilean spacetime they would be (to use Maxwell's "G"):
D = epsilon_0 (E + G x B); B = mu_0 (H - G x D)
where "G" would indicate the velocity relative to a certain
distinguished frame where wave propagation is of equal velocity in all
directions.
> What is your understanding of ether?
A lot of it is historical revisionism and mythology built up by people
who never read the originals (much less, transcribed and copy-edited
them, as I have done).
Maxwell never talked about any "aether". Instead, the central premise
of his theory was that the vacuum was a dielectric capable of
charge-screening, vacuum polarization, with a non-trivial relation
between (D,H) and (B,E) holding, particularly, in the close vicinity of
point-like and line-like sources. He believed that infinities in the
classical field theory are avoided because the vacuum polarizes near
such sources, thus leading to a distinction between "bare" and
"dressed" charges (which, in turn, he briefly discussed in Chapter 1).
All of this eventually came to be adopted as the central features
(after the 1940'/s) of what came to be known as renormalization theory.
His relations were the Galilean invariant ones above (as far as any
relations were set out explicitly); not the Lorentz relations.
It's because Lorentz relations were found to hold in all frames, that
you no longer see the "G" in the alphabet soup comprising Maxwell's
nomenclature (A, B, C = total current = J + dD/dt, D, E, F = force
density, (G), H, I = magnetization, J).
The biggest misconception cast, in the way of historical revisionism,
was that relativity did away with an *otherwise equivalent* "aether"
theory. What it did away with is NOT equivalent -- it did away with the
"G" and the Galilean invariant relations posed above, which Maxwell
originally surmised. The difference between the Lorentz and Galilean
relations *is* the difference between Minkowski and Galilean spacetime.
And the instant you write down (D = epsilon_0 E; B = mu_0 H), you're in
Relativity, not Galilean physics.
So, Relativity began (whether its participants realized it or not) as
soon as the G was dropped and (what are today known as) Maxwell's
equations were first written down .. after Maxwell died.
.. which gets back to the original point: the constitutive relations
determine the causal structure of spacetime; in particular,
distinguishing causal structure of Galilean spacetime from that of the
Minkowski spacetime; distinguishing Galilean relativity from Poincare
relativity.
The punchline comes at the very end ... in the presence of point-like
sources, *no* linear relations can hold between the (D,H) and (B,E)
fields. For a singularity in the sources (rho, J) mean a singularity in
(D,H) via the relations (div D = rho; curl H - dD/dt = J). In the
presence of a linear relation that would entail a singularity in (E,B),
which would make the force law (F = rho E + ...) ill-defined --
contradiction. Therefore, a linear (D,H) vs. (E,B) breaks down near
point sources.
Given the foregoing, about constitutive relations reflecting the causal
structure that nature already puts there, this is then a clear
indication that the causal structure, itself, breaks down near
point-like sources and is being reflected as such by the break down of
the linear relations between (D,H) and (B,E).