1 April 2002
Physics Letters A 295 (2002) 318–319
www.elsevier.com/locate/pla
Comment
Qualitative properties of an equation of motion of a classical point
charge
✩
Marijan Ribari
ˇ
c, Luka Šušterši
ˇ
c
∗
Jožef Stefan Institute, p.p. 3000, 1001 Ljubljana, Slovenia
Received 1 November 2001; received in revised form 29 January 2002; accepted 14 February 2002
Communicated by P.R. Holland
Abstract
We point out three unusual qualitative properties of the equation of motion of a classical point charge recently proposed by
Rohrlich.
2002 Elsevier Science B.V. All rights reserved.
PACS: 03.20.+i; 41.70.+t
Keywords: Electrodynamics; Point charge; Equation of motion
1. Introduction
Motivated by serious qualitative defects of the
Lorentz–Abraham–Dirac equation as an equation of
motion, Rohrlich [1] recently gave arguments in sup-
port of the following relativistic equation of motion of
a classical point charge:
(1)m
0
d
dτ
v
µ
= F
µ
ext
+ τ
0
d
dτ
F
µ
ext
+ τ
0
v
µ
v
α
d
dτ
F
α
ext
,
where τ
0
= 2e
2
/3m
0
; c = 1; v
µ
is the particle velocity,
v
µ
v
µ
=−1; F
µ
ext
is the external force, v
µ
F
µ
ext
= 0; and
τ is the proper time.
✩
PII of original article: S0375-9601(01)00264-X
*
Corresponding author.
E-mail address: luka.sustersic@ijs.si (L. Šušterši
ˇ
c).
2. Some qualitative properties
If the particle is moving along a straight line,
say x
1
, then the equation of motion (1) implies the
following relation between the particle velocity and
the external force:
(2)
F
1
ext
(τ ) = F
1
ext
(τ
i
)
v
0
(τ )/v
0
(τ
i
)
e
−(τ −τ
i
)/τ
0
+ m
0
τ
−1
0
τ
τ
i
v
0
(τ )/v
0
(τ
)
dv
1
(τ
)
dτ
× e
(τ
−τ)/τ
0
dτ
,
(3)F
2
ext
(τ ) = F
2
ext
(τ
i
)e
−(τ −τ
i
)/τ
0
,
(4)F
3
ext
(τ ) = F
3
ext
(τ
i
)e
−(τ −τ
i
)/τ
0
,
(5)F
0
ext
(τ ) = v
1
(τ )F
1
ext
(τ )/v
0
(τ ).
Thus according to the equation of motion (1): (a) there
is an infinity of external forces that correspond to
any given motion along a straight line, and (b) under
0375-9601/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved.
PII:S0375-9601(02)00161-5