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The Kaufmann Experiments


Series of experiments aimed to determine the variation of an electron's mass with its velocity. ... mapparent = (1/v)(dW/dv), which is the longitudinal mass. ... – PowerPoint PPT presentation

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Title: The Kaufmann Experiments

The Kaufmann Experiments
  • Cathy Huml
  • Yao McCormick

The Kaufmann Experiments
  • Walter Kaufmann (1871-1947)
  • Series of experiments aimed to determine the
    variation of an electrons mass with its
  • Deals with Electron Theory of Matter, and the
    possible Electromagnetic origin for part or all
    of the mass of an electron.

Equation Variation of Mass with Velocity
Electromagnetic Mass of Electron
  • Competing Electromagnetic Mass Theories of the
    early 1900s.
  • The contenders Walter Kaufmann (1871-1947), Max
    Abraham (1875-1922), Alfred Bucherer (1863-1927),
    Hendrik Lorentz (1853-1928), Max Planck

Walter Kaufmann
  • Studied at the University of Berlin and Munich.
  • 1897-performed experiments on cathode rays and
    confirmed there existed negatively charged
    particles, but he didnt believe that he was
    justified in calling them electrons.

Max Abraham (1875-1922)
Max Abraham
  • Studied at University of Berlin as Plancks
  • In 1902 proposed his own model of the electron
    with charge uniformly distributed over the
    surface of a rigid sphere.
  • Opposed to Relativity, strong believer in the
    existence of the aether.
  • 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.

Alfred Bucherer (1863-1927)
Alfred Bucherer
  • Studied at Johns Hopkins, Cornell, Strasbourg.
  • Bucherers model of the electron was deformed as
    it moved through the aether, but in a fashion
    that its volume remained constant.
  • Kaufmanns experiments could not distinguish
    between the models of Bucherer and Abraham.

Hendrik Lorentz (1858-1923)
Hendrik Lorentz
  • Lorentz model of the electron was based on a
    uniform spherical charge throughout the electron.
  • As an electron was set in motion through the
    ether its transverse dimensions remained
    unchanged but its length in the direction of
    motion contracted.
  • FitzGerald-Lorentz Contraction and the Special
    Theory of Relativity (Einstein-Lorentz

Technical Details for Non-Physics People. (Like
  • Central Idea
  • Charge Q moving at a velocity of v which is small
    compared to the speed of light (c)
  • When v moves toward c, mass becomes very velocity

Kaufmanns Experiments
  • Between 1901-1906, Kaufmann published a series
    of experiments that measured the variation of the
    charge to mass ratio of the electron.
  • From his experiments, Kaufmann discovered that
    the charge e of electron does not change with its
    velocity, v.
  • Decrease in the ratio e/m relates to the increase
    in m.

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Kaufmanns Experiments
  • Now e/m can be expressed in terms of coordinates
    ( y, z ).
  • y (e/m)(A/v2) (e/m0)(A/c2)1/(ß?(ß))z
    (e/m)(A/v) (e/m0)(A/c)1/(ß?(ß))With a
    function ?(ß) where m(v) m0 ?(ß).

Kaufmanns First Results
  • Kaufmann published his first results of e/m
    values for high-speed ß rays ( 0.787 ß 0.945
    ) in his 1901 paper.

Kaufmanns First Results
  • In his paper, Kaufmann tried to calculate the
    mechanical mass (true mass) and electromagnetic
    mass (apparent mass) of an electron.mtotal
    Mtrue mapparent
  • Kaufmann used Searles equation for total energy
    of a moving spherical electron to find mapparent
    (1/v)(dW/dv), which is the longitudinal mass.
  • From his data points, Kaufmann calculated the
    true mass is about 3 times larger than the
    apparent mass.

Kaufmanns 1902 Paper
  • Kaufmanns 1901 analysis was incorrect because he
    used longitudinal mass rather than transverse
    mass. As well, his data points did not support
    relativity theory.
  • In 1902, Kaufmann published more data and
    analyzed in term of Abrahams transverse mass.
  • Kaufmann corrected an algebraic error in his
    formula, and made some geometric change in the
    dimensions of his apparatus.

Kaufmanns 1902 Paper
  • Because of rapid vibration in ?(ß), a small error
    in determining ß would cause a huge uncertainty
    in m. Kaufmann declared that 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 electron is purely of an
    electromagnetic nature.

Kaufmanns 1903 and 1905 Data
  • Kaufmann published more data in 1903
  • In 1905, he published a set of 9 famous data
    points later Planck used to in his analysis

Kaufmanns 1905 Paper
  • Kaufmann concluded his 1905 paperThe prevalent
    results decidedly speak against the correctness
    of Lorentzs assumption as well as Einsteins.
    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
    ?(ß). Whether Bucherers formula for the optics
    of movie bodies in the realm of possible
    observation can yield the same results as
    Lorentzs, still has yet to be proven.

Plancks Analysis
  • Does Kaufmanns data really give conclusive
    support of Abrahams theory and equation for the
    variation of the electromagnetic mass of the
  • Lorentz challenge and conclusion.
  • Plancks challenge and conclusion.

Plancks Analysis
  • Reversed interpretation of Kaufmanns data.
  • To be sure, this question of the acceptability
    of the relativity principle appears to be
    already answered through the recent and important
    measurements of W. Kaufmann, that is, however in
    the negative sense so that every further
    investigation seems to be unnecessary. In the
    meantime I would still like to consider it
    possible, in view of the extremely complex theory
    of these experiments, that the principle of
    relativity could be reconciled with these
    observations if one would more carefully
    elaborate them.

Plancks Analysis
  • How?
  • Planck computed the expected deflection on the
    basis of the Abraham and Lorentz theories.

Plancks Analysis 1906
  • Planck used Kaufmanns 9 data points to compute a
    value u.
  • um0c/p

Plancks Analysis
  • 1. Had value of e/m from Kaufmann.
  • 2. Obtain expression for p ( the radius of the
    spherical electron).
  • 3. Obtained values of Bv/c for each theory.
  • 4. Obtain values for y.
  • 5. Use his own equations for z and y to calculate
    B independently.

Plancks Analysis
  • 1. Uniform Electric Field
  • 2. Maintaining the Vacuum
  • 3. Kaufmanns analysis Begs the Question

Plancks Analysis
  • Reanalyze Kaufmanns Data (1907)
  • Make Changes
  • Detect electric field at each distinct data point
    (y, z)
  • Found that Lorentz Theory more accurate detection
    of electric field, therefore favored by Kaufmann
  • Most Important Kaufmann Experiments are no
    longer an obstacle in the path of the Theory of

Subsequent Determinations of e/m0
  • It was still not clear whether Abrahams or
    Lorentzs theory was more correct, even after
    Planks reanalysis of Kaufmanns data.
  • To prove the more favorable theory, other
    scientists Bestelmeyer, Bucherer, and Neumann did
    their own experiments.

Adolf Bestelmeyer
  • 1907, Adolf Bestelmeyer (1875-1954) used the
    secondary cathode rays ejected from a metal by
    incident X rays.
  • He measured the e/m for those electrons that were
    sent through the velocity selector (acted by
    crossed electric and magnetic fields), then
    deflected by magnetic field.

Adolf Bestelmeyer
  • These data still did not show the clear favorite
    of these two theories, Abrahams and Lorentzs.

Alfred Bucherer
  • Like Bestelmeyer did, in 1909, Alfred Bucherer
    used ß rays from a radium fluoride source through
    the velocity selector of crossed electic and
    magnetic fields.

Alfred Bucherer
  • Bucherer discovered that as ß varies, the values
    for e/m0 stay nearly constant.
  • His data showed e/m0 is more constant for
    Lorentzs theory than Abrahams, but there were
    still some controversies about his conclusion.

  • 1914, Neumann finally found Lorentzs theory has
    the most constant e/m0 values for different ß.
  • Using am improved Bucherers method, he found 26
    data points from 0.39152 ß 0.80730, and did a
    best-fit graph of the points for both theories.

  • The best-fit graph favored Lorentzs theory.
    It showed that Lorentzs numbers were more

Mr. Einsteins Thoughts
  • On the Theories of Abraham and Bucherer
  • On his Theory of Relativity

In Conclusion
  • The Kaufmann experiments were a case study to
    illustrate the development and acceptance of
    scientific theory.
  • Experiment does not always yield a definitive