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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

velocity. - 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

(1858-1947).

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

assistant. - 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

Predictions)

Technical Details for Non-Physics People. (Like

Myself)

- 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

dependent.

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

electron? - 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

- 3 MAIN ISSUES
- 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

data. - Most Important Kaufmann Experiments are no

longer an obstacle in the path of the Theory of

Relativity

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.

Neumann

- 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.

Neumann

- The best-fit graph favored Lorentzs theory.

It showed that Lorentzs numbers were more

accurate.

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

result.