[Paper Review] Variation of Mass with Velocity: "Kugeltheorie" or "Relativtheorie"

Galina Weinstein|arXiv (Cornell University)|May 27, 2012

Relativity and Gravitational Theory3 citations

TL;DR

This paper examines the historical development of mass-velocity variation in electron theory, contrasting Lorentz's 'Kugeltheorie' (spherical electron model) with Einstein's 1905 relativity theory. It analyzes Einstein's derivation of longitudinal and transverse mass using relativity and light-speed invariance, clarifies his distinction from Lorentz's approach, and evaluates experimental tests by Kaufmann and Bucherer, concluding that Bucherer's results confirmed both Lorentz's and Einstein's formulas.

ABSTRACT

This paper deals with four topics: The first subject is Abraham's spherical electron, Lorentz's contracted electron and Bücherer's electron. The second topic is Einstein's 1905 relativity theory of the motion of an electron. Einstein obtained expressions for the longitudinal and transverse masses of the electron using the principle of relativity and that of the constancy of the velocity of light. The third topic is Einstein's reply to Ehrenfest's query. Einstein's above solution appeared to Ehrenfest very similar to Lorentz's one: a deformed electron. Einstein commented on Ehrenfest's paper and characterized his work as a theory of principle and reasoned that beyond kinematics, the 1905 heuristic relativity principle could offer new connections between non-kinematical concepts. The final topic is Kaufmann's experiments. Kaufmann concluded that his measuring procedures were not compatible with the hypothesis posited by Lorentz and Einstein. However, unlike Ehrenfest, he gave the first clear account of the basic theoretical difference between Lorentz's and Einstein's views. Finally, Bücherer conducted experiments that confirmed Lorentz's and Einstein's models; Max Born analyzed the problem of a rigid body and showed the existence of a limited class of rigid motions, and concluded, "The main result was a confirmation of Lorentz's formula".

Motivation & Objective

• To clarify the theoretical distinctions between Lorentz's spherical electron model ('Kugeltheorie') and Einstein's 1905 relativity framework.
• To analyze Einstein's derivation of longitudinal and transverse mass using the principle of relativity and constancy of light speed.
• To examine Einstein's response to Ehrenfest's comparison of his theory to Lorentz's, emphasizing the role of the relativity principle in connecting non-kinematical concepts.
• To assess the experimental validity of Lorentz's and Einstein's models through Kaufmann's and Bucherer's experiments.
• To evaluate Max Born's analysis of rigid body motions and its implications for confirming Lorentz's formula.

Proposed method

• Historical analysis of Abraham's spherical electron, Lorentz's contracted electron, and Bucherer's electron model.
• Examination of Einstein's 1905 derivation of mass-velocity dependence using the principle of relativity and light-speed invariance.
• Comparison of Einstein's and Lorentz's theoretical frameworks through Einstein's correspondence with Ehrenfest.
• Evaluation of Kaufmann's experimental results and his conclusion that his data conflicted with both Lorentz's and Einstein's hypotheses.
• Analysis of Bucherer's experimental confirmation of Lorentz's and Einstein's models, including Born's theoretical treatment of rigid body motions.
• Use of historical and philosophical analysis to distinguish between 'principle theories' (Einstein) and 'constructive theories' (Lorentz) in the context of electron theory.

Experimental results

Research questions

• RQ1 How did Einstein's derivation of mass-velocity dependence in 1905 differ from Lorentz's approach in terms of theoretical foundations?
• RQ2 Why did Ehrenfest perceive Einstein's 1905 model as similar to Lorentz's contracted electron model despite Einstein's emphasis on the relativity principle?
• RQ3 What were the key theoretical differences between Lorentz's 'Kugeltheorie' and Einstein's 'Relativtheorie' as identified by Kaufmann?
• RQ4 How did Bucherer's experiments confirm both Lorentz's and Einstein's models, and what did Max Born's analysis of rigid body motions contribute to this?
• RQ5 To what extent did Einstein's 1905 theory go beyond kinematics to connect non-kinematical concepts through the relativity principle?

Key findings

• Einstein derived expressions for longitudinal and transverse mass using the principle of relativity and the constancy of light speed, establishing a foundation for relativistic mechanics.
• Einstein characterized his 1905 theory as a 'theory of principle,' emphasizing its broader explanatory power beyond kinematics, unlike Lorentz's constructive approach.
• Kaufmann's experiments initially appeared to contradict both Lorentz's and Einstein's models, but he clearly identified the theoretical divergence between them.
• Bucherer's experiments confirmed both Lorentz's and Einstein's formulas, supporting the consistency of their predictions for electron mass-velocity variation.
• Max Born's analysis of rigid body motions confirmed the existence of a limited class of rigid motions and concluded that the main result supported Lorentz's formula.
• Despite initial experimental ambiguity, Bucherer's results ultimately validated both Lorentz's and Einstein's models, with Einstein's framework gaining broader theoretical acceptance.