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The Kaufmann Experiments:
Data and Interpretation in
by Matt Cook
Walter Kaufmann
• 1871 – 1947
• Studied mechanical
engineering at the
Universities of Berlin and
Munich (1891)
• Began study of physics in
1892; completed doctorate
in 1894
• Performed cathode ray
experiment in 1897;
confirmed that they were
negatively charged particles,
but did not call them
“I predict, along with the
varying mass of the electron
with speed, that a scientist’s
street cred varies proportionally
with the size of his moustache.”
-Kaufmann (probably)
Walter Kaufmann
• On faculties at Berlin, Gottingen, Bonn, and
Konigsberg before retiring in 1935 to lecture in
• Experiments we will discuss conducted at
• While on faculty, Kaufmann becomes close with
Max Abraham
Max Abraham
• 1875-1922
• Born in what is now
• Studied under Planck in
Berlin, graduated in 1897,
then worked as Planck’s
assistant for three years
• Developed model of the
electron as a rigid sphere
with charge distributed
uniformly over the surface
• Opposed relativity; clung
to model of the aether
Max Abraham, the only one of the
physicists mentioned in this
presentation who did not have some
form of ridiculous facial hair
Max Abraham
• Later on the faculty at Gottingen, Illinois, Milan,
and Aachen
• Cushing says his death was a “tragic and
protracted affair”; diagnosed with a brain tumor
• Died in 1922
“He loved his absolute aether, his field equations, his rigid electron just as a youth
loves his first flame, whose memory no later experience can extinguish.”
Max Born and Max von Laue
Alfred Bucherer
• 1863-1927
• Born in Cologne; studied at
five universities over fifteen
years, including at Johns
• Habilitated in Bonn and
taught there until 1923
• His own model of the
electron predicted that the
electron’s shape, but not
volume, changed with
velocity through the aether
• Kaufmann’s data could not
determine whether
Bucherer’s or Abraham’s
model was correct
“They try to make me go to pre-hab,
but I said no, no, no.”
– Alfred Bucherer (slight paraphrase)
Hendrik Lorentz
• 1853-1928
• Studied physics and
math at Leiden
• Electron model: uniform
spherical surface charge
• Transverse dimensions
of electron in motion are
unaffected, but contracts
in direction parallel to
Hendrik Lorentz, demonstrating his
signature look, Blue Steel
• Inertial mass: a
measure of a body’s
resistance to
acceleration, or
consequently, a
measure of the work
necessary to set the
body in motion
• Classical
predicts an
electromagnetic energy
that increases rapidly
with velocity for a
charged body
Basis for Models of Electron
For a moving charge q, moving at a velocity v, mass is velocity dependent
The total work needed to bring a particle up to speed v: m = e²/6πc²a (a being
the radius of the electron)
The above expression is valid only for small velocities and represents the
electromagnetic mass of the electron under these conditions
When v approaches c appreciably, then m itself becomes highly dependent on
Abraham wanted to provide an electromagnetic model for mechanics,
essentially the opposite of models like Maxwell’s that proposed a tangible,
physical explanation of electromagnetic phenomena via the aether
The Experiments
• 1901-1906: Kaufmann published results from a
series of experiments to measure the variation of
the charge to mass ratio (e/m) of the electron
• Should be no change in e with velocity, so any
alteration of the ratio can be explained by an
increase in m
Apparatus and Method
Cylindrical container with
condenser plates separated by
quartz insulators
Grains of radium chloride (obtained
from the Curies) at O produce highspeed  rays
Whole apparatus surrounded by
magnets supplying a continuous and
uniform horizontal magnetic field
everywhere in the cylinder
A potential difference across the
condenser plates maintained a
horizontal electric field as well
Electrons with proper velocity
emerged through diaphragm D, then
hit a photographic plate
Many experiments, but apparatus
was essentially the same
Within the Apparatus
Mathematical Outcomes
• When all is said and done, e/m can now be
expressed in terms of coordinates ( y, z ):
y = (e/m)(A’/v2) = (e/m0)(A/c2)[1/(βψ(β))]
z = (e/m)(A/v) = (e/m0)(A’/c)[1/(βψ(β))]
Initial Experiment (1901)
• Produce the following results of e/m values for β
rays traveling between 78.7% and 94.5% of c
• Quickly followed up in 1902 with corrected data
(he discovered an algebraic error) that was
analyzed in terms of Abraham’s mass
Initial Experiment (1901)
• Despite the fact that Kaufmann knew that a small
experimental error in β would lead to huge
uncertainty in m, he still declared:
“The mass of the electrons that constitute the
Becquerel rays is dependent on velocity. The
dependency can be demonstrated exactly by the
formula of Abraham. Therefore the mass of electrons
is purely of an electromagnetic nature.”
Take Two
• Kaufmann published further data in 1903
• In 1905, he attempted to definitively choose
between Abraham, Bucherer, and Lorentz’s models
using nine (now famous) data points
Conclusions, 1905
“The prevalent results decidedly speak against the correctness
of Lorentz’s assumption as well as Einstein’s. If on account of
that one considers this basic assumption refuted, then one
would be forced to consider it a failure to attempt to base the
entire field of physics, including electrodynamics and optics,
upon the principle of relative movement. A choice between the
theory of Abraham and Bucherer for the time being is
impossible and does not seem to be attainable by observations
of the type described above due to the largely numerical
identity of the values of ψ(β). Whether Bucherer’s formula for
the optics of moving bodies in the realm of possible observation
can yield the same results as Lorentz’s still has to be proven.”
Planck’s Reversal of the Data
• Planck applied strict logic to a “confused situation”
• Seeks to reconcile Kaufmann’s data with relativity
• Using a different method of analysis but
Kaufmann’s own data, he arrived at a data point
that yielded a value for β greater than 1.0
(Kaufmann’s 1903 data also yielded a β above 1.0)
• First defined a quantity u = mc/p (where p is the
radius of a spherical electron)
• Able to obtain a theoretical expression for p using
Kaufmann’s value for e/m.
• He extracted values of β = v/c via his expression
for the value of u (all of this done without using
the experimental values for y).
• Obtained values for y using β.
• Essentially, predictive data points to be compared
to each theory’s predictions
Planck’s Results
Planck: Round Two
• Planck took issue with Kaufmann’s apparatus and
methods, namely that he could not have kept the value of
his electric field very constant run to run on the
• Planck also thought that it was likely Kaufmann’s
apparatus provided a poor seal and a bad vacuum
• Came up with a changing α value that dictated the electric
field at any given point along the particle’s arc within the
• Found that Lorentz’s theory fit the data more accurately
and with a narrower α range than Abraham’s; concluded
that the data favored Lorentz and Einstein’s theory of
• True or not, it meant that Kaufmann’s data were no longer
a stumbling block to relativity
Subsequent Experiments
• Adolf Bestelmeyer (1875-1954) subjected cathode
rays to crossed E and B fields, then to a B field
alone; neither theory was definitively favored
based on his data
• Bucherer used β rays and used much the same
process Bestelmeyer had; extracted the value for
e/m that followed. The theory was favored that
most closely held to a constant e/m value.
• Seemed to favor Lorentz over Abraham, but results
were statistically insignificant
1914: The Issue is Settled
• Refinement of Bucherer’s method was employed
by Neumann to obtain 26 new data points for
• The superiority of Lorentz’s theory over
Abraham’s was clear
• Kaufmann’s data were first used to disprove, then
support, the theory of relativity
• Planck held onto relativity even as Kaufmann’s data
seemed to refute it – sometimes theories ‘ proved’
false are worth a second look
• Science does not always yield a definitive result
• Science does not always operate along the typical
pattern of:
hypothesis  prediction  refutation  rejection of
• Can you think of any other experiments, theories,
or hypotheses whose initial conclusions were later
thrown out?
• It is clear from the story of the Kaufmann
experiments that reevaluation is crucial in science.
Do you think that, in the future, theories or
hypotheses we hold to be true today will be