“Relativistic” particle dynamics without relativity

Feynman gave an extremely concise pedagogical derivation of the momentum of light:

Richard P.

 

Feynman

,

Robert

 

Leighton

, and

Matthew

 

Sands

, (, , ), Vol. , Chap. 34, pp. –.

Albert

Einstein

, “,”  , – ().

English translation in , translated by Anna Beck (, , ), Vol. , pp. –.

A 1905 thought experiment of Einstein, involving the emission of oppositely directed pulses of light from a free body, also apparently establishes the mass equivalent of energy independently of the relativity postulates. Feigenbaum and Mermin offer a purely mechanical version in which the light pulses are replaced by particles:

Mitchell J.

 

Feigenbaum

and

N.

 

David Mermin

, “,”  (), – (). Their version relies on the relativistic velocity addition formula, which does derive from the relativity postulates.

A. P.

 

French

, (, , ), pp. –.

More rigorously, the recoil speed and light travel time are $V=E/(M−δm)c, t=(L−δs)/c$ where $δs=Vt$⁠, so the condition of stationary center of mass, $(M−δm)δs=δm(L−Vt)$⁠, can be written as $(M−δm)Vt=δm⋅ct$⁠. Dividing through by t and substituting for V, we find δm = E/c² as before.

Max

 

Von Laue

, “,” in , 3rd ed., edited by

P. A.

 

Schilpp

(, , ), pp. –.

Reference 3, pp. –.

William C.

 

Davidon

, “,”  (), – ().

J. M.

Levy Leblond

, “,” in , edited by

A.

Janner

 et al., Lecture Notes in Physics 50 (, , );

J. M.

 

Levy Leblond

“,” in , Paris, July, 2002, edited by

J. P.

 

Gazeau

, et al. (, , ), pp. –.

Adel F.

 

Antippa

, “,”  (), – ().

Eugene

 

Feenberg

, “,”  (), – ().

Reference 3, pp. –.

Examples: Ref. 1, Chap. 16, pp. 6–7; Ref. 3, pp. 169–175;

Edwin F.

Taylor

and

John

Archibald Wheeler

, (, , ), pp. –;

See also

P. C.

 

Peters

, “,”  (), – () for a variant of the approach.