Download Einstein`s Electrodynamic Pathway to Special Relativity

Einstein’s
Electrodynamical
Pathway
to Special Relativity
John D. Norton
Department of History
and Philosophy of Science
University of Pittsburgh
1
“…the seven and more years that the development of
the Special Theory of Relativity had been my entire life.”
Einstein’s tribute to A. A. Michelson, Dec. 19, 1952.
7 and more years
= 364 and more weeks
…
1898
1899
1900
1901
“The step”
5-6 weeks
before
“On the electrodynamics...”
received by Annalen der Physik,
Jun. 30, 1905
What was Einstein doing for the
remaining 364 - 5.5 = 358.5 and
more weeks?
…reflecting on electrodynamics
in the context of Newtonian
space and time.
1902
1903
1904
1905
new considerations of
space and time enter
2
We know...
The Michelson-Morley experiment had no decisive presence in his
deliberations. (Holton) Its importance was to affirm the principle of relativity, not
the light postulate (Stachel).
Einstein’s early deliberations were driven by the magnet
and
conductor thought experiment, which brought him the device of
field transformations well before the Lorentz transformation of space and
time. (Rynasiewicz et al.)
Einstein seriously investigated an emission
covariant) akin to Ritz’s approach. (Stachel)
theory of light (= Galilean
…and very little more can be said if we demand
unequivocal foundation in documentary evidence.
3
This talk will try nonetheless to answer…
What could Einstein recover from
the device of field transformations?
What was Ritz’s emission
“theory”?
How might Einstein have used a
Ritz type approach?
What thought experiment shows
its failure most cogently?
How did Einstein make “the step”?
Two partial theories of electrodynamics,
jointly not adequate to the principle of
relativity.
Part polemic against Einstein and part program
for finding Galilean covariant force laws.
To construct a promising, Galilean
covariant electrodynamics.
Einstein’s chasing-a-light-beam
thought experiment.
Several possibilities; it may not have been
by reflecting on light signals and clock
synchronization.
4
Read all about it in:
"Einstein's Investigations of Galilean
Covariant Electrodynamics prior to
1905," Archive for History of Exact
Sciences, forthcoming.
"Einstein's Special Theory of Relativity
and the Problems in the Electrodynamics
of Moving Bodies that Led him to it." in
Cambridge Companion to Einstein, M.
Janssen and C. Lehner, eds., Cambridge
University Press.
Links at www.pitt.edu/~jdnorton
5
The Magnet and
Conductor Thought
Experiment
and the Device of Field
Transformations
6
A device that reveals motion through the ether?
H
A magnet at rest in the
ether is surrounded by a
pure magnetic field H,
but no electric field E.
IMPROVED
VERSION
conductor moves
with magnet
E
H
A magnet moving through
the ether creates in addition
an induced magnetic field.
Is this induced magnetic field the detectible mark of motion through the ether?
7
What is observable?
no
current
no
current
conducto
r
Einstein
1905
current due
to electric
field
Observables obey principle of relativity.
Theoretical account should as well.
exactly
balanced
by
current due to
motion of
conductor in
magnetic field
…but how?
8
Einstein’s 1920 recollection of his reaction:
“The idea, however, that these were two, in principle different cases was
unbearable for me.
The difference between the two, I was convinced, could only be a difference
in choice of viewpoint and not a real difference.
Judged from the magnet, there was certainly no electric field present.
Judged from the [resting observer], there certainly was one present.
Thus the existence of the electric field was a relative one, according to the
state of motion of the coordinate system used, and only the electric and
magnetic field together could be ascribed a kind of objective reality, apart
from the state of motion of the observer or the coordinate system.
The phenomenon of magneto-electric induction compelled me to postulate
the (special) principle of relativity.”
9
The device of field transformations.
“Judged from
the magnet,
there was
certainly no
electric field
present.”
H
E’ = - (1/c)vxH
H’
“Judged from the
[resting observer],
there certainly was
one present.”
Pure magnetic
field H
change observer’s
velocity by v
Magnetic field H’ = H and
Electric field E’ = - (1/c)vxH
10
Which transformation for the general case?
Lorentz transformation (First order)
E = E’ + (1/c) uxH’
H = H’ - (1/c) uxE’
Simplified transformation
E = E’ + (1/c) uxH’
H = H’
Unusable without Lorentz’s
local time. Einstein is still
years from “the step.”
Unique, linear field transformation
law under which Lorentz force law
f/e = E + (1/c) uxH
is covariant
11
Maxwell’s electrodynamics splits into two partial theories
(“two charges partial theory”)
(“magnet and conductor partial theory”)
(M1) .E = 4pr
(M2) .H = 4pr
(M3) xH = (4p/c)j + (1/c)(∂E/∂t)
(M4) xE = - (1/c)(∂H/∂t)
(L) f/e = E + (1/c) uxH
is covariant under
is covariant under
t=t’ r=r’-ut
E = E’ H = H’ - (1/c) uxE’
t=t’ r=r’-ut
E = E’ + (1/c) uxH’ H = H’
Full theory of Föppl’s (1894) two
charges thought experiment, which
violates the principle of relativity.
Full theory of the magnet and
conductor thought experiment.
BUT
A moving magnet does not induce
an electric field.
Lorentz force law not included.
BUT
A moving charge does not
induce a magnetic field
12
August Föppl’s Two Charges Thought Experiment
from Einführung in die Maxwell’sche Theorie der Elektricität. Leipzig:
B. G. Tuebner, 1894, Part 5, Ch.1.
To what extent is the
principle of relativity
respected in
electrodynamics?
It fails in the
+
case of the two
charges thought
experiment.
-
It holds in the case of the
magnet and conductor
thought experiment.
Force
between
charges at
rest in the
ether is f.
+
-
Force between
same charges
when they share a
common motion
in the ether is
f’ = (1-v2/c2)f.
13
What now?
(“two charges partial theory”)
(“magnet and conductor partial theory”)
(M1) .E = 4pr
(M2) .H = 4pr
(M3) xH = (4p/c)j + (1/c)(∂E/∂t)
(M4) xE = - (1/c)(∂H/∂t)
(L) f/e = E + (1/c) uxH
modify
this?
The two partial
theories jointly entail
the constancy of the
velocity of light.
How can it be
extended to
cover all electrodynamics?
Supports an account of the
magnet and conductor thought
experiment fully in accord with
the principle of relativity.
Einstein concluded his 1920 recollections:
“The difficulty to be overcome lay in the constancy of the velocity of light in a
vacuum, which I first believed had to be given up. Only after years of groping did
I notice that the difficulty lay in the arbitrariness of basic kinematical concepts.”
14
keep
this?
Ritz’s Emission
“Theory” of Light
15
Ritz’s
Emission
“Theory”
A modified
electrodynamics in which
the velocity of the light
emitter is added vectorially
to the velocity of light.
Einstein to Ehrenfest,
June, 1912 and elsewhere
Reasons to
take Einstein’s
remark
seriously.
All Galilean covariant theories of
light must be emission theories
(but not conversely).
Synonym for a Galilean
covariant theory?
“…Ritz’s conception, which incidentally
was also mine before rel. theory.”
Closeness of 1912 to actual events.
Einstein was defending his relativity theory from Ritz’s
theory. Ehrenfest was proposing experimental tests.
Einstein knew Ritz and had co-authored a note with him.
Einstein won his first job in Zurich in 1909 only after the
first choice, Ritz--Einstein’s critic, fell ill.
16
Ritz’s Negative Program
“Recherches Critique sur l’Électrodynamique Génénerale,”
Annales des Chimie et de Physique,” 13 (1908), pp. 145-275.
(and other works)
Died July 1909, aged 31,from tuberculosis.
We should be skeptical about many quantities used in electromagnetic theory, especially
electric and magnetic fields.
Fields laws should be eliminated in favor of action at a distance laws such as due to
Weber and others.
The ether should be eliminated from electrodynamics and the principle of relativity
restored.
The principle of relativity should not be restored by means of Einstein’s strange
kinematical notions.
Presentations of electrodynamics should be given in terms of retarded potentials. The
advanced potentials admitted by Maxwell’s equations are unphysical.
17



Ritz’s Positive Program
To reconfigure and reformulate all of electrodynamics in terms of Galilean
covariant, Weber-like action at a distance force laws. The program was not
completed. Ritz developed many examples of such laws for special cases.
The force F between two charges e, e’, moving with velocity u and acceleration w is
given by:

u u2  u u u u2  rw u u2 
ee
Fx 
cos(r,x)  r , 2  x2 r   r , 2  2x   r , 2 
 rw
 c c  c
 c c  c
 c c 

r2 1  2r 
 c 
Fy = …
3 k u 2 3(1 k) u r2
u4
 1

 a1

2
2
4
4 c
4
c
c
u r2
k 1
u2

 b1
 b2

2
2
2
c
c
  1  c1
u2
2
c
 c2
u r2
2
c

Note the many
undetermined
constants!
18
Ritz’s Theory as reported in Pauli’s 1921 Relativitätstheorie
Formulate electrodynamics in terms of
scalar and vector potentials , A
E =   - (1/c)∂A/∂t
H = xA
[ r]
 (x,y,z,t)  
d
r
[ rv ]
A(x,y,z,t)  1c 
d
r
Replace
the propagating
retardation time
t’=t-r/c
by
“[…]” means a quantity is
evaluated at event (x’,y’z’,t’)
where the retardation time t’is
t’ = t - r/c
This time delay encodes the
propagation of electromagnetic
action at speed c in the ether.
a Galilean covariant,
projected retardation time
t’=t-r/(c+vr)
vr=speed of source in
direction of point at
r=(x,y,z).
19
Propagation versus Projection
Propagation
Electromagnetic
action propagates
from fixed point in
space that is left
behind by a moving
source.
Projection
The apparent source
of electromagnetic
action is boosted,
and moves with
uniformly moving
source.
Ritz imagined that charges emit fictitious particles that are
projected by ordinary rules of Galilean kinematics.
20
Propagation versus Projection
Propagation
Electromagnetic
action propagates
from fixed point in
space that is left
behind by a moving
source.
Projection
The apparent source
of electromagnetic
action is boosted,
and moves with
uniformly moving
source.
21
My conjecture:This is also the theory Einstein hit upon and
associated with Ritz’s name.
“Ritz’s ideas on electrodynamics and optics are not so far developed
that one can call them a ‘theory.’ What is special in them is that there
does not exist a definite speed for light propagation at a position and in
a given direction, but that this [speed] depends on the state of motion
of the light source. Then one cannot trace light propagation back to
differential equations, but one must introduce “retarded potentials,”
which is a kind of action at a distance.
Before setting up the special theory of rel., I had myself thought of
investigating such a possibility.”
Draft of a response written on the back
of a letter dated 1 February 1952 to
Einstein from C. O. Hines.
(Einstein Archive 12 250, 12 251.)
22
Why Einstein might think of “investigating such a possibility”:
Galilean covariant, magnet and
conductor partial theory
Necessary and sufficient for existence of
scalar and vector potentials
E =   - (1/c)∂A/∂t
(M2) .H = 4pr
(M4) xE = - (1/c)(∂H/∂t)
H = xA
Retarded integrals capture content of
remaining Maxwell equations (M1) and (M3).
(L) f/e = E + (1/c) uxH
t=t’ r=r’-ut
E = E’ + (1/c) uxH’ H = H’
 (x,y,z,t)  
[ r]
d
r
A(x,y,z,t)  1c 
[ rv ]
d
r
Might we render the theory
Galilean covariant
 by replacing

propagating retardation times by projected retardation times?
Promising, BUT…
H = H’ still precludes
magnetic fields induced by
charge currents.
Transformations for A must
conform, so A=A’ under which
A(x,y,z,t)  1c 
[ rv ]
d
r
is not covariant.
Might some other variant ofthis theory escape these troubles?
Is any Galilean covariant electrodynamics admissible?
23
Einstein’s Objections to All Emission Theories of Light.
Collected from remarks in many places.
The physical state of a light ray is determined
completely by its intensity and color [and polarization].
“ I decided [against an emission theory], since I was convinced that each
light [ray] should be defined by frequency and intensity alone, quite
independently of whether it comes from a moving or a resting light source.”
Einstein to Ehrenfest, mid June 1912
The theory cannot be formulated in
terms of differential equations.
Different velocities entail that
light can back up on itself (later
parts overtakes earlier).
e.g. Einstein to Shankland, 1950s; to
Hines Feb. 1952
e.g. Einstein to Shankland, 1950s
Problems with shadow
formation by a moving screen.
e.g. To Mario Viscardini, April 1922
24
Einstein Chases a
Beam of Light
25
Einstein, Autobiographical Notes, 1946
“After ten years of reflection such a principle
resulted from a paradox upon which I had
already hit at the age of sixteen:
If I pursue a beam of light with the velocity c
(velocity of light in a vacuum),
I should observe such a beam of light as an electromagnetic field at rest
though spatially oscillating. There seems to be no such thing, however,
neither on the basis of experience nor according to Maxwell’s equations.
From the very beginning it appeared to me intuitively clear that, judged
from the standpoint of such an observer, everything would have to happen
according to the same laws as for an observer who, relative to the earth,
was at rest. For how should the first observer know or be able to
determine, that he is in a state of fast uniform motion?
One sees in this paradox the germ of the special relativity theory is
already contained.”
26
Albert Einstein, “Autobiographical Sketch”
published 1956
“During this year in Aarau the following question came to me:
if one chases a light wave with the speed of light, then one
would have before one a time independent wave field. But
such a thing appears not to exist! This was the first child-like
thought experiment related to the special theory of relativity.
Discovery is not a work of logical thought, even if the final
product is bound in logical form.”
As recounted to Max Wertheimer in 1916
“The problem began when Einstein was sixteen years old, a pupil in the Gymnasium
(Aarau, Kantonschule)…
The process started in a way that was not very clear, and is therefore difficult to
describe—in a certain state of being puzzled. First came such questions as: What if one were to run
after a ray of light? What if one were riding on the beam? If one were to run after a ray of light as it
travels, would its velocity thereby be decreased? If one were to run fast enough, would it no longer
move at all?…[W’s ellipses] To young Einstein this seemed strange.
…When I asked him whether, during this period, he had already had some idea of the
constancy of light velocity, independent of the movement of the reference system, Einstein answered
decidedly: ‘No, it was just curiosity. That the velocity of light could differ depending upon the
movement of the observer was somehow characterized by doubt. Later developments increased that
doubt.’”
27
The Thought
A frozen waveform!
28
The thought experiment generates no trouble for an ether based Maxwell
electrodynamics.
“…I should observe such a beam of light
as an electromagnetic field at rest though
spatially oscillating.
There seems to be no such thing,
however, neither on the basis of
experience
nor according to Maxwell’s equations.
From the very beginning it appeared to me
intuitively clear that, judged from the standpoint of
such an observer, everything would have to happen
according to the same laws as for an observer who,
relative to the earth, was at rest. For how should
the first observer know or be able to
determine, that he is in a state of fast
uniform motion?”
…but only because we have
no experience of moving at
the speed light in the ether.
…but it is allowed by
Maxwell’s equations through
the simplest transformation.
…but the observer would know
he is moving rapidly because the
light would appear frozen.
29
Why does the thought experiment merit pride of
place in Einstein’s defining autobiography?
Is it merely the recording of the
visceral hunches of a precocious
sixteen year old, who did not study
Maxwell’s theory until two years later?
Or does it have
a cogency that
extends beyond
Einstein’s final
high school
year?
Einstein (16yrs) in 1896 in the cantonal school of Aarau
30
The Thought Experiment succeeds against an emission theory of light.
i.e. a theory that conforms to the principle of relativity
using Newtonian notions of space and time.
Frozen lightwaves? “…There seems
to be no such thing, however, neither
on the basis of experience...”
A light source receding at c
leaves a frozen wave behind.
We should expect to experience these frozen waves
if there are rapidly receding light sources. There is
no need for us to move at c.
31
“…or according to Maxwell’s equations…”
Frozen electromagnetic
waves are possible in
any inertial frame of
reference.
Frozen electromagnetic
waves must be admissible
in electrostatics and
magnetostatics.
Electrostatics and magnetostatics
of an emission theory should
agree with the electrostatics and
magnetostatics of Maxwell’s
theory. (Oldest and most secure part of
theory.)
BUT Maxwell’s equations
prohibit frozen waves.
32
“…For how should the first observer know or
be able to determine, that he is in a state of fast
uniform motion?”
A light wave of
definite color,
amplitude,
polarization.
Is it a
propagating
wave?
Or a frozen
wave?
An extra property is needed to
separated the two cases.
(Equivalent to:Is the observer moving
rapidly with respect to the source?)
But color, amplitude and
polarization are the only
properties light has.
33
An emission theory of light cannot be formulated in terms of
differential field equations.
Field theory formulated with
differential equations: present, local
state of the field determines its future
time development.
Precluded in an emission theory of
light. An extra property is needed to
distinguish frozen from propagating
waves.
Example: Maxwell’s theory
xH =
(1/c)(∂E/∂t)
xE = - (1/c)(∂H/∂t)
Present
state of
field
Rate of
change of
field
Future time
development
of field.
34
The obvious
escape…
A field theory in which the color of a
wave fixes its velocity of propagation.
Example:
The differential field equation
(∂2/∂t2 - ∂2/∂x2 -m2) (x,t)= 0
admits waves
(x,t)= exp i (wt-kx)
where m2=k2-w2
Color (wave number k)
fixes velocity
v = w/k = (1- m2/ k2) 1/2
k = m --> v=0
“But the strongest argument [against an emission theory] seemed
to me: If there is no fixed velocity for light at all, then why should
it be that all light emitted by “stationary” bodies has a velocity
completely independent of the color? This seemed absurd to me.
Therefore I rejected this possibility as a priori improbable.”
Einstein to Hines, Feb. 1952,
35
Pathways to
“the Step”
36
Did Einstein actually discover
Or was the celebrated analysis of
the relativity of simultaneity by
reflecting on clocks and their
synchronization by light signals?
clock synchronization a convenient
way to present a result already
found by other means?
Light enters virtually
everywhere as an
electromagnetic waveform and
not a spatially localized signal.
Other pathways are possible:
e.g. aberration, Einstein unaware
that Fresnel drag coefficient can be
derived by velocity addition on
light pulses.
The aberration of starlight and the
Fresnel drag in Maxwell-Lorentz
electrodynamics is a manifestation
of Lorentz’s local time. Reverse the
derivation to read relativity of
simultaneity from observations.
Simple thought experiments show
how field transformations can force
the relativity of simultaneity.
37
Conclusion
38
What could Einstein recover from
the device of field transformations?
What was Ritz’s emission
“theory”?
How might Einstein have used a
Ritz type approach?
What thought experiment shows
its failure most cogently?
How did Einstein make “the step”?
Two partial theories of electrodynamics,
jointly not adequate to the principle of
relativity.
Part polemic against Einstein and part program
for finding Galilean covariant force laws.
To construct a promising, Galilean
covariant electrodynamics.
Einstein’s chasing-a-light-beam
thought experiment.
Several possibilities; it may not have been
by reflecting on light signals and clock
synchronization.
39