sci.physics.research

On the Electrodynamics of Moving Bodies
/Physics/#Einstein1905a

About 17 pages in PDF, derived ultimately from a translation of
Einstein's 1905 original landmark paper on Special Relativity, the
notation has been updated and additional commentary (as well as
corrections) provided. The version currently on-line is working off a
compilation from 1999 that, in turn, came from a 1923 English
translation. I'm set to go back to the 1905 original and do the
translation myself.

Two sets of comments: first on the "abstract" (or introductory
paragraphs) of the 1905 original and second on the paper, itself, and
problematic features in the approach it adopted.

(1) The Abstract
Seriously, this needs to be completely reworked relative to the 1923
and 1999 translations, because much has been lost in the way of
context over the intervening time (even by the 1920's). Because of the
lost context, the completely wrong take is generally had by modern
consensus on what was purportedly said in that passage, versus what
was ACTUALLY said. In particular, the focus was NOT on the issue of
whether an ether exists. The ether remark, often cited and quoted,
when put back in context is little more than an anciliary note
following on the main topic of that passage -- which was Maxwell's G
vector and the assertion that G = 0 can be made to apply to all frames
of reference.

I'm therefore still deciding whether to go idiomatic with this, or
literal. Literal sounds too stinted and completely misses the feel of
the original (as well as missing the crucial context as just alluded
to). Therefore, though this may not actually appear in the
retranslation and reformatting of the paper linked above, when I'm
through; this is what the opening passages actually say, when more
explicitly written out and written in more idiomatic form in modern
American English.

"As usually understood at present, Maxwell's electrodynamics, when
applied to moving bodies, is known to entail an asymmetry that does
not appear to be inherent to the situation. For example, consider the
interaction of a magnet with a wire. What is observed depends only on
how the two are moving with respect to one another. In contrast, a
sharp distinction is customarily drawn based on which of the two is
deemed to be the body in motion, and which one, the body at rest. If
the magnet is taken to be the one moving, and the wire the one at
rest, then in the vicinity of the magnet appears an electric field, of
a certain definite energy, that produces a current along the wire. On
the other hand, if the magnet is taken to be the one at rest, and the
wire the one in motion, then there is no electric field around the
magnet. Instead, we find an electromotive force, which is associated
with no energy, but which - assuming the equality of relative motion
of the two cases - leads to electric currents along the wire with the
same path and intensity as would have been produced by the electric
forces in the former case."

"These kinds of examples, along with the failure to discern any motion
of the earth with respect to the 'light medium', suggest that neither
electrodynamics nor mechanics possess any means to distinguish a state
of absolute rest. Rather, as has already been shown to the first order
of small quantities, they suggest that the same laws of
electrodynamics and optics hold in whatever frames of reference the
equations of mechanics hold good. We shall raise this conjecture
(henceforth to be called the Principle of Relativity) to the level of
postulate, while also introducing a second, seemingly irreconcilable,
postulate that light always moves in empty space at the same speed c,
independent of the motion of the body emitting it."

"While Maxwell asserted the following relations between the electric
displacement and electric field
D = epsilon E, E = -del phi - dA/dt + G x B
whose consistent extension to the magnetic force and magnetic
intensity would have entailed
B = mu(H + G x D),
epsilon mu = (1/c)^2 in vacuuo,
we shall now find that from the two postulates it is possible to
consistently formulate a theory of electrodynamics, based on Maxwell's
stationary theory, where G = 0, that nonetheless applies to bodies in
motion."

"Whereas Maxwell required a vector G to assign a velocity for
electromagnetic processes in empty space; the point of view to be
developed here will neither require G, nor the specially distinguished
'absolutely stationary space' identified by it. In turn, the
introduction of a 'luminiferous ether' as the putative basis for such
a distinguished frame shall be rendered superfluous."

"Instead, the theory to be developed is based - like all
electrodynamics - on the kinematics of the rigid body, since the
assertions of any such theory have to do with the relationships
between rigid bodies (systems of coordinates), clocks, and
electromagnetic processes. It is the failure to properly consider this
circumstance that lies at the root of the difficulties presently
encountered by the electrodynamics of moving bodies."

(2) The Paper
Some comments on the problematic features of the original paper. This
is speaking as an editor, had I been assigned the task of refereeing
the paper.

As I noted in the paper, the functional argument needed serious
reworking. First, at some point the assumption of linearity is simply
deposited in. There are plenty of ways to realise the light hypothesis
non-linearly, examples can be seen (and illustrated) under

/Physics/#Alexandroff

These are the conformal transformations. More to the point: one does
not need to assume the functions are even differentiable, let alone
linear. The conformal nature of the transformations follows by a
purely geometric argument. From this, in turn, one gets
differentiability and, finally by assuming the "plane at infinity" is
fixed, and the "affine space" preserved, one gets linearity. The
result are the Poincare' transformations. Assuming the origin is fixed
(as was pointed out in the paper), the Poincare' transformations drop
down to the Lorentz transformations.

At one point, he references the "time" when "t = 0 = t'" -- completely
missing the point of the paper, itself! This is not a time, it's a
plane at an instant. Namely, it's the YZ plane at the instant it meets
the Y'Z' plane.

The second major issue is the use of the Maxwell-Hertz variant of
electrodynamics (or, for that matter, even Maxwell-Lorentz theory).
The point would have been better made by going back to the so-called
"macroscopic" Maxwell equations, thereby also unclouding the issue. In
fact, Einstein consistently kept out the 4th equation of each set and
at one point (the t = 0 = t' "time" comment), was caught in the
process of thinking in the Newtonian mould.

The Maxwell equations written out in their full glory CLEARLY show the
regularity that Einstein was trying to capture, but which was obscured
in his paper:
0 + dD^x/dx + dD^y/dy + dD^z/dz = rho
-dD^x/dt + 0 + dH_z/dy - dH_y/dz = J^x
-dD^y/dt - dH_z/dx + 0 + dH_x/dz = J^y
-dD^z/dt + dH_y/dx - dH_x/dy + 0 = J^z
and
0 + dB^x/dx + dB^y/dy + dB^z/dz = 0
-dB^x/dt + 0 - dE_z/dy + dE_y/dz = 0
-dB^y/dt + dE_z/dx + 0 - dE_x/dz = 0
-dB^z/dt - dE_y/dx + dE_x/dy + 0 = 0

It gets even more obvious (in the process also paving the way to the
mass energy relations) when the force and power laws are joined onto
these relations,
F_x = e (E_x + 0 + v^y B^z - v^z B^y)
F_y = e (E_y - v^x B^z + 0 + v^z B^x)
F_z = e (E_z + v^x B^y - v^y B^x + 0)
-P = e (- v^x E_x - v^y E_y - v^z E_z)
And also with the field-potential relations
E_x = -dA_x/dt + d(-phi)/dx, B^x = dA_z/dy - dA_y/dz
E_y = -dA_y/dt + d(-phi)/dy, B^y = dA_x/dz - dA_z/dx
E_z = -dA_z/dt + d(-phi)/dz, B^z = dA_y/dx - dA_x/dy
In particular, when the potentials are substituted in the force and
power laws, writing the force and power, respectively, as derivatives
of the momentum and kinetic energy
F_x = dp_x/dt, F_y = dp_y/dt, F_z = dp_z/dt, P = dT/dt,
one gets something that screams out the regularity:
d(p_x + e A_x)/dt = d/dx (A_x v^x + A_y v^y + A_z v^z - phi)
d(p_y + e A_y)/dt = d/dy (A_x v^x + A_y v^y + A_z v^z - phi)
d(p_z + e A_z)/dt = d/dz (A_x v^x + A_y v^y + A_z v^z - phi)
d((-T) + e (-phi))/dt = d/dt (A_x v^x + A_y v^y + A_z v^z - phi)
where the partial derivatives on the right are with v^x, v^y, v^z kept
fixed.

A flaw in the derivation of the transformation law can be seen from
the field equations, when written correctly, as above. Einstein did
not write down the most general transformation law. In the absence of
sources (rho = 0, (J^x, J^y, J^z) = (0,0,0)), one has cross-
transformations between (D,H) and (E,B):

D' = D + theta B; H' = H - theta E.
E' = E - lambda H, B' = B + lambda D.

In fact, ONLY the latter can be ruled out in the presence of sources.
One STILL has the former set. This cannot be ruled out. It's a
surviving residual of complexity transformation that resides in the
little group of the field equations-with-source.

Had the analysis been done right, one would have posed the following
question, instead. What is the most general relation between (D,H) and
(B,E) that accords with the light hypothesis? In fact, the answer is
MORE general than Maxwell-Hertz theory or Maxwell-Lorentz theory and
is of the form

D = epsilon E + theta B, H = epsilon c^2 B - theta E.

This leads to a different symplectic structure (and different
Lagrangian and Hamiltonian dynamics) than usual, and (when the
constitutive coefficients are not constant) a non-trivial dynamics
with respect to theta.

There is nothing that theoretically mandates either of the
coefficients be constant. The only requirement that Lorentz invariance
makes -- assuming the electrodynamic theory comes out of a Lagrangian
form (another oversight of the 1905 paper, not to tie this or anything
else to a Lagrangian formulation, when even Maxwell wrote part of his
treatise in the language of Lagrangian dynamics) -- is that the
Lagrangian be functions of the Lorentz invariants,
L = L(I, J)
I = 1/2 (E^2 - B^2 c^2), J =
with coefficients
epsilon = dL/dI, theta = dL/dJ
likewise functions of I and J. That's all that one can say from
Lorentz invariance.

But none of this could even be addressed, because it's filtered out by
the stipulation of Maxwell-Hertz dynamics, where the (equivalent of
the) Lorentz relations (D = epsilon_0 E, B = mu_0 H) are built into
the very notation, itself.