Maxwell Views on Relative vs. Absolute Motion & Maxwell's Medium
Rock Brentwood
brief mention was made of Maxwell's views on relative motion and on
the misconception in present-day folklore that Maxwell held to the
idea of relative motion.
He did not.
In part, the misunderstanding come by way of quotes, such as the
following:
Maxwell 1877: "But the phrase 'at rest' means in ordinary language
'having no velocity with respect to that on which the body stands',
as, for instance, the surface of the earth or deck of a ship. It
cannot be made to mean more than this. For the expression 'at rest'
has no scientific meaning, and the expression 'in motion', if it
refers to relative motion, may mean anything..."
(Reference list at the end of the article).
However, it actually means the exact opposite of what you see here,
and has been -- all too frequently -- been taken (i.e., cherry-picked)
out of context.
I've seen this and related out-of-context misconceptions perpeduated
in many places -- by NOVA's bio series on Einstein, in personal
correspondence, even in a recent TWF. So, it's time to set the matter
straight.
First, Maxwell's actual view was as follows:
Electrodynamics has as its foundation an underlying medium which was
approximately isotropic and (therefore) had, associated with it, a
velocity -- that he eventually came to name G.
(Much more context is listed below.)
The larger hope was that eventually a dynamics could be devised for
this, too, on top of a deeper formulation, in which boost-invariance
would indeed hold. That's what the quote is actually referring to.
But, it is largely a vacuous step (pun intended) by Maxwell's own
account, since he repeatedly doubts the existence of any bona fide
vacuum and early on (1864) argues that even "empty space" must be
filled to the brim with energy. Therefore, it would make no sense to
try and formulate a theory of an all-pervasive medium atop a boost-
invariant (but physically unattainable) "perfect vacuum". This is the
underpinning of his point of view, and is what completely negates the
above reference to a boost-invariant substrate.
The exercise of trying to formulate a dynamics to incorporate the key
element of the medium (the vector G) was never fully carried out but
there are clear, systematic ways to approach the issue (1: start with
a Lagrangian that is a function of G and its exterior differential dG,
2: include all the boost-invariants formed of it and the other
quantities in the Lagrangian, and 3: write down the most general
relations involving those invariants). Much of the exercise, in fact,
has already been carried out (in a different setting) by those who
develop Einstein-Aether models, such as Jacobson's recent Einstein-
Aether Lagrangian.
There were 2 reasons for Maxwell to postulate a medium.
One, in a Galilean-invariant theory, it is not possible to have a
finite wave speed, since no finite speed is invariant under the
Galilean transformations. The 1877 quote above is actually part of a
larger context to butress this very point to argue IN FAVOR of a space-
filling medium (and, hence, in favor an absolute velocity and absolute
frame).
Therefore, Maxwell reasons, any theory which predicts wave propagation
must be describing the propagation with respect to a fixed reference.
Thus, the medium served as a reference frame for the velocity vector
G. This vector was introduced early on, and was present in the 1861
paper. It got its own letter name (along with all the other
quantities, A-D, F-J) by the time we reach the 1873 treatise.
The second reason -- which will not enter directly into the
considerations to follow, but which will be discussed in detail in the
following 4 paragraphs -- is (ironically) the far more important
reason and, in fact, is a reason that remains valid to the present
day: the medium was posed as an active dielectric substrate that was
(and still is) required to mediate between the conjugate fields of
this field theory (that is, (D, H) vs. (E, B)), and which would be
required to mediate between the conjugate fields of ANY Lagrangian
field theory. The mediation between (D,H) vs. (E,B) is required in
order to smear out what would otherwise be the two infinities of self-
force (rho E) and self-energy (D.E), if we had adopted a linear
medium, with linear relations between (D,H) and (B,E).
When Lorentz posed the microscopic formulation for electrodynamics, he
ended up throwing out the baby with the bathwater by both (trying to)
remove the G vector (actually he still had a G vector in his
equations) and to turn off the vacuum by making epsilon_0 and mu_0
inert meaningless place-holders or conversion-factors for D vs. E and
B vs. H.
This step, in fact, is unwarranted. On grounds of consistency, alone,
it is self-contradictory since it (like any other linear medium) leads
directly to the contradiction of the self-force and self-energy
infinities -- which would not otherwise be present. Maxwell dedicated
much of the first chapter of his treatise to discussing and resolving
this issue by invoking the 19th century equivalent of the basic
concepts of 20th centory renormalization theory. Lorentz put back the
ininities, and both classical and quantum field theory throughout the
20th century went down this wrong path since then.
This is the true genesis of the Ultraviolet Divergence Problem.
(Not is Lorentz's step actually necessary. The semblance of Lorentz
relations hold for a null field INDEPENDENT of the actual constitutive
relations and Lagrangian used to formulate electrodynamics -- as long
as one only asserts Lorentz invariance.)
So, with these preliminaries out of the way, this is what the actual
quote says, in context ... following by the further references to
place this in the broader context of the 2 decades preceding it.
This is the actual quote:
Maxwell 1877: "the expression 'in motion' ... IF it refers to absolute
motion can only refer to some medium fixed in space. To discover the
existence of a medium and to determine our velocity with respect to it
by observation on the motion of bodies, is a legitimate scientific
inquiry"
IF. Emphasis mine.
The reference to the absolute velocity and related concepts can be
found in numerous places, including the following
Hence, in contrast to the quote
"In all phenomena relating to closed circuits and the current in them,
it is indifferent whether the axes to which we refer the system be at
rest or in motion."
Maxwell's Treatise, 1873.
what we have is:
Maxwell 1873: Article 599:
Refers to G as the velocity relative to the field (i.e. the underlying
medium) and states the addition of the term G x B to the equation for
E, to result in
Equation (10): E = -grad phi - dA/dt + G x B.
Maxwell 1873: Article 600:
The title is: "On the Modification of Electromotive Force [E] when the
Axes to which they are referred to are moving in Space"
(Not "moving in Space, relative to a given reference", but "moving in
Space", absolutely. This is to be taken in context both with the above
1877 quote and the previous article, 599.)
Maxwell 1873: Article 618:
G -- the velocity of a point (i.e. the velocity with respect to the
underlying medium, as was indicated both by context and all throughout
the treatise.)
Maxwell 1861: The discussion above equation (138) in the 1861 paper of
light speed:
"The velocity of transverse undulations IN our hypothetical medium..."
i.e. an absolute speed; that is, speed with respect to the all-
pervasive underlying medium that is being hypothesized here.
Maxwell 1861: In the opening paragraphs of section 4
Maxwell refers the the differences that would occur in the speed of
light for the frame where "the medium [is] at rest" vs. where "the
medium is in rotation"
Maxwell 1861: Equation 77 (in vector form):
Prop XI: To find the electromotive forces [that is, E] for a MOVING
BODY
E = G x B - dA/dt - grad phi.
i.e. the field-potential relation for a body in absolute motion
(meaning: motion with respect to the underlying medium).
Maxwell 1864: The discussion in section (4) explicitly links the
motion for waves as being with respect to the all-pervasive medium.
Maxwell 1864: Article (5) distinguishes the case of the moving frame
(that is, where the medium is in motion, or G != 0) from the
stationary frame (that is, where G = 0 and the medium is at rest).
Maxwell 1864: Article (8) relates the motion of the waves to the frame
of reference defined by the all-pervasive medium.
Maxwell 1864: Article (18) indicates that the equation (D) will also
include a term which accounts for the absolute motion of the body (the
motion, that is, relative to the underlying medium)
Maxwell 1864: Article (22) discusses the possibility that the motion
of the medium will also have a dependence on the magnetic field. (This
dependence is listed by Thomson in the 1892 version of Maxwell's
treatise as the addition of the -G x D term to H, or equivalently of
the modification of the B vs. H constitutive law to B = mu (H - G x D)
from B = mu H).
Maxwell 1864: Article (47) is a verbal discussion surrounding the G x
B term. The thought experiment here is the one Einstein also described
(critically) in the opening section of his 1905 paper on special
relativity.
Maxwell 1864: Article (64) re-introduces the medium velocity which he
later named G.
Maxwell 1864: Article (65) generalizes the field-potential law (E = -
grad phi - dA/dt) to moving frames, resulting in
Equation (D): E = -grad phi - dA/dt + G x B.
The 1877 quote cited thus, actually, means the exact opposite of what
it appears to say, to someone just glossing over it! It's the argument
Maxwell used to explain why he thought there MUST be a medium -- as he
clearly stated at the very end of the quote.
To further clarify this, I've taken the parts of the 1877 quote and
have further elaborated on them:
Maxwell 1877: "But as there is nothing to distinguish one portion of
time to another except the different events which occur in them, so
there is nothing to distinguish one part of space from another except
its relation to the place of material bodies. We cannot describe the
time of an event except by reference to some other event, or the place
of a body except by reference to some other body. All our knowledge,
both of time and place is essentially relative."
Meaning: "since my equations involve an explicit reference to
velocity, G, they cannot be taken as fundamental but representative of
a deeper substrate in which the medium, with respect to which the
velocity G is being taken, is also included as part of the dynamics.
The overall dynamics, in which both the field and its substrate are
included, should respect the boost-invariance of the the Galilei
group."
Maxwell 1877: "But as it is impossible to define the position of a
body except with respect to the position of some point of reference,
so it is impossible to define the velocity of a body, except with
respect to the velocity of the point of reference. The phrase absolute
velocity has as little meaning as has absolute position."
Meaning: "My earlier references to velocities fixed relative to an
medium pervading all of space cannot be taken as the final word -- for
that would then imply the return of the notion of an absolute state of
rest. Therefore, this medium must be a mechanical system in its own
right; itself subject to laws that make no reference to any fixed
velocities."
Maxwell 1877: "It is true that when we say that a body is at rest we
use a form of words which appears to assert some thing about that body
consider in itself, and we might imagine that the velocity of another
body, if reckoned with respect to a body at rest, would be its true
and only absolute velocity."
Meaning: "I'm speaking, in particular, of my earlier tendencies toward
doing that very thing. Despite my own reference to a fixed sense of
stationarity vs. motion, this cannot be referring to the vacuum of a
space devoid of matter. For such a space cannot have any landmarks to
identify whether one is at rest or moving. THEREFORE, since my
equations, in fact, DO have such a reference -- and a reference that
seems to pervade even "empty" space -- then there can be no such thing
as a vacuum at all. Hence my reference, articulated at several places
in the 1873 treatise, to a skepticism of the so-called vacuum even
being a vacuum."
Meaning, further: "In fact, not only can there be no vacuum in the
usual sense of the word, but space must be literally FILLED to the
brim with HUGE amounts of energy arising from that which provides a
substrate to the field. The medium pervading all of space has enormous
positive energy."
Maxwell 1861: Article (82): "The assumption, therefore, that
gravitation arises from the action of the surrounding medium in the
way pointed out, leads to the conclusion that every part of this
medium possesses, when undisturbed, an enormous intrinsic energy, and
that the presence of dense bodies influences the medium so as to
diminish this energy wherever there is a resultant attraction."
The energy density is given as bounded below by the whatever value, a_
{Max}, the largest possible gravitational acceleration has
(explicitly, in our notation: Density >= a_{Max}^2/(8 pi G)).
Maxwell 1877: "But the phrase � at rest � means in ordinary language �
having no velocity with respect to that on which the body stands �,
as, for instance, the surface of the earth or deck of a ship. It
cannot be made to mean more than this."
In fact, that's precisely what he did by making explicit reference,
all throughout the previous 16 years to such a fixed frame. This is
therefore meant to demote the all-pervasive medium from its lofty
aetherial heights, to the more mundane level of just another
mechanical system or just another body or assemblage of objects.
Maxwell 1877: "It is therefore unscientific to distinguish between
rest and motion, as between two different states of a body in itself,
since it is impossible to speak of a body being at rest or in motion
except with reference, expressed or implied, to some other body."
Which does not bode well for his earlier work, where he did exactly
that ...
Maxwell 1877: "For the expression � at rest � has no scientific
meaning, and the expression � in motion �, if it refers to relative
motion, may mean anything, and if it refers to absolute motion can
only refer to some medium fixed in space."
BINGO. Note the last IF. Basically, he just flat-out did a 180
turnabout from where he had just been 2 lines before, flat-out
contradicted himself, and snapped back to his earlier premise.
Maxwell 1877: "To discover the existence of a medium and to determine
our velocity with respect to it by observation on the motion of
bodies, is a legitimate scientific inquiry, but supposing all this
done we should have discovered, not an error in the laws of motion,
but a new fact in science . and the effect of a given force on a body
does not depend on the motion of that body. �"
(Which completely contradicts his earlier remark about this very thing
being unscientific)
Now, you may say it wasn't a flat-out contradiction because it was
intended to demote the space-filling medium to the level of a
mechanical system.
But a moment's consideration shows that, indeed, it does have the
import of a self-contradiction. For, given the other references,
replete throughout the 1861-1873 works, questioning the very existence
of a vaccum; then to turn around and say that this mechanical system
is built atop the motion-relative underpinning of a (non-existent)
vacuum is to speak vacuously, pun intended.
Therefore, on technical grounds, this counts as Maxwell 1877 totally
contradicting Maxwell 1861-1873 (and, in fact, contradicting Maxwell
1877 all the way up to 2 paragraphs before this final statement).
He flip-flopped in the last 2 paragraphs. [1]
References:
Maxwell 1861: J.C. Maxwell, "On Physical Lines of Force",
Philosophical Magazine, S. 4
Part I: Vol. 21, No. 139, 1861 March, 161-175.
Part II: Vol. 21, No. 140, 1861 April, 281-291; 338-348.
Part III: Vol. 23, No. 151, 1862 January, 12-24.
Part IV: Vol. 23, No. 151, 1862 January, 85-95.
Maxwell 1864: J.C. Maxwell, "A Dynamic Theory of the Electromagnetic
Field"
Royal Society Transactions V, 1864 December 8, 459-512
Maxwell 1873: J.C. Maxwell, "A Treatise on Electricity and Magnetism",
1873
Maxwell 1877: J.C. Maxwell, "Matter and Motion", 1877.
Links:
http://federation.g3z.com/Physics/index.htm#Maxwell
Includes:
* Transcribed, annotated copies of Maxwell 1861 and Maxwell 1864;
* A summary, "Maxwell's Original Equations", partly based on an
article by Andre Waser,
* Maxwell 1865 (http://federation.g3z.com/Physics/Maxwell1865.htm), a
rewriting of a Wikipedia article to correct for the misconceptions
regarding the velocity vector and equation (D).
The Wikipedia article misunderstood the meaning of the velocity vector
and said equation (D), in the list of equations (A-H), was an
embryonic form of the Lorentz force law. In fact, it had nothing to do
with it. Instead, the force law Maxwell used was listed as equations
(J) and (K). An formula slightly different from this was used in the
treatise, and no final form for the force law was ever consistently
settled on. (Equation (I) was the energy law).
harry
news:f037b50b-0a24-46d3...@v17g2000vbb.googlegroups.com...
[..]
> When Lorentz posed the microscopic formulation for electrodynamics, he
> ended up throwing out the baby with the bathwater by both (trying to)
> remove the G vector (actually he still had a G vector in his
> equations) and to turn off the vacuum by making epsilon_0 and mu_0
> inert meaningless place-holders or conversion-factors for D vs. E and
> B vs. H.
Thanks for the interesting quotes from Maxwell! However, I don't understand
your remarks about Lorentz. I happen to know Lorenztz's texbook, for example
in the discussion of Neuman's ether theory he puts for the stored potential
energy in the ether:
1/2 * D*E = 1/(2*epsilon)*D^2
Why do you call that a "meaningless placeholder"? Can you give a reference
where Lorentz "threw out the baby with the bath water"?
Thanks,
Harald