Abstract

No abstract available.

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. E. Ives, J. Opt. Soc. Am. 33, 163–166 (1943).
    [Crossref]
  2. Note that we have incidentally derived, from non-relativistic considerations (for this particular problem), the Einstein formula for the composition of velocities, for if w1=w0(1-v2c2)1+vw0c  then v+w0=v+w0(1-v2c2)1+vw0c2=v+w01+vw0c2. Equation (14) derived below has in fact been derived elsewhere [ Becker, Theorie der Electricität (Teubner, Leipzig, 1933), Vol. 2, p. 348] by assuming that the atoms in the absorbing body move so that their velocities conform to the Einstein formula.
  3. Strictly speaking it is the kinetic energy when the particle is brought to rest, but since we have postulated that w0 is the value of velocity when the particle is brought to rest without escape of heat, this value of kinetic energy also applies to the particle in motion.
  4. Abraham, Theorie der Elektrizität (B. G. Teubner, Leipzig, 1905), Vol. 2, p. 383, Eq. (245).
  5. This value for the pressure on a moving absorbing target was obtained by the writer in a previous paper [H. E. Ives, J. Opt. Soc. Am. 32, 32 (1942), in which pertinent references are given] but without the detailed analysis provided by the present paper.
    [Crossref]
  6. There is also involved in this analysis (in evaluating the energy density from the source at the target) the convention that the distance between source and target is always measured at the target, on a scale attached to the source and experiencing the Fitzgerald contraction proper to the velocity of the source.
  7. Since, as pointed out by Epstein [Am. J. Phys. 10, 1 (1942)] the Fitzgerald contraction has been derived from a simple law of attraction, and the variation of clock rate with velocity follows from the variation of mass with velocity, there appears to be no need of a principle of relativity to derive the general invariance of optical phenomena with motion.
    [Crossref]

1943 (1)

1942 (2)

This value for the pressure on a moving absorbing target was obtained by the writer in a previous paper [H. E. Ives, J. Opt. Soc. Am. 32, 32 (1942), in which pertinent references are given] but without the detailed analysis provided by the present paper.
[Crossref]

Since, as pointed out by Epstein [Am. J. Phys. 10, 1 (1942)] the Fitzgerald contraction has been derived from a simple law of attraction, and the variation of clock rate with velocity follows from the variation of mass with velocity, there appears to be no need of a principle of relativity to derive the general invariance of optical phenomena with motion.
[Crossref]

Abraham,

Abraham, Theorie der Elektrizität (B. G. Teubner, Leipzig, 1905), Vol. 2, p. 383, Eq. (245).

Becker,

Note that we have incidentally derived, from non-relativistic considerations (for this particular problem), the Einstein formula for the composition of velocities, for if w1=w0(1-v2c2)1+vw0c  then v+w0=v+w0(1-v2c2)1+vw0c2=v+w01+vw0c2. Equation (14) derived below has in fact been derived elsewhere [ Becker, Theorie der Electricität (Teubner, Leipzig, 1933), Vol. 2, p. 348] by assuming that the atoms in the absorbing body move so that their velocities conform to the Einstein formula.

Epstein,

Since, as pointed out by Epstein [Am. J. Phys. 10, 1 (1942)] the Fitzgerald contraction has been derived from a simple law of attraction, and the variation of clock rate with velocity follows from the variation of mass with velocity, there appears to be no need of a principle of relativity to derive the general invariance of optical phenomena with motion.
[Crossref]

Ives, H. E.

Am. J. Phys. (1)

Since, as pointed out by Epstein [Am. J. Phys. 10, 1 (1942)] the Fitzgerald contraction has been derived from a simple law of attraction, and the variation of clock rate with velocity follows from the variation of mass with velocity, there appears to be no need of a principle of relativity to derive the general invariance of optical phenomena with motion.
[Crossref]

J. Opt. Soc. Am. (2)

Other (4)

Note that we have incidentally derived, from non-relativistic considerations (for this particular problem), the Einstein formula for the composition of velocities, for if w1=w0(1-v2c2)1+vw0c  then v+w0=v+w0(1-v2c2)1+vw0c2=v+w01+vw0c2. Equation (14) derived below has in fact been derived elsewhere [ Becker, Theorie der Electricität (Teubner, Leipzig, 1933), Vol. 2, p. 348] by assuming that the atoms in the absorbing body move so that their velocities conform to the Einstein formula.

Strictly speaking it is the kinetic energy when the particle is brought to rest, but since we have postulated that w0 is the value of velocity when the particle is brought to rest without escape of heat, this value of kinetic energy also applies to the particle in motion.

Abraham, Theorie der Elektrizität (B. G. Teubner, Leipzig, 1905), Vol. 2, p. 383, Eq. (245).

There is also involved in this analysis (in evaluating the energy density from the source at the target) the convention that the distance between source and target is always measured at the target, on a scale attached to the source and experiencing the Fitzgerald contraction proper to the velocity of the source.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (47)

Equations on this page are rendered with MathJax. Learn more.

M ¯ = m ( v ± w ) [ 1 - ( v ± w ) 2 c 2 ] 1 2 ,
M ¯ = 1 2 m ( v + w 1 ) [ 1 - ( v + w 1 ) 2 c 2 ] 1 2 + 1 2 m ( v - w 2 ) [ 1 - ( v - w 2 ) 2 c 2 ] 1 2
M ¯ = 1 2 m v [ 1 - ( v + w 1 ) 2 c 2 ] 1 2 + 1 2 m v [ 1 - ( v - w 2 ) 2 c 2 ] 1 2 + 1 2 m w 1 [ 1 - ( v + w 1 ) 2 c 2 ] 1 2 - 1 2 m w 2 [ 1 - ( v - w 2 ) 2 c 2 ] 1 2 .
w 1 [ 1 - ( v + w 1 ) 2 c 2 ] 1 2 = w 2 [ 1 - ( v - w 2 ) 2 c 2 ] 1 2 .
w 1 = w 0 f 1 ( w 0 , v ) , w 2 = w 0 f 2 ( w 0 , v ) ,
w 0 f 1 ( w 0 , v ) [ 1 - ( v + w 0 f 1 ( w 0 , v ) c ) 2 ] 1 2 = w 0 f 2 ( w 0 , v ) [ 1 - ( v - w 0 f 2 ( w 0 , v ) c ) 2 ] 1 2 .
F 1 [ 1 - ( v + w 0 F 1 c ) 2 ] 1 2 = F 2 [ 1 - ( v - w 0 F 2 c ) 2 ] 1 2 .
1 F 1 - 1 F 2 = 2 v w 0 c 2 ( 1 - v 2 c 2 ) .
1 F 1 = Q + v w 0 c 2 1 - v 2 c 2 , 1 F 2 = Q - v w 0 c 2 1 - v 2 c 2 ,
w 1 = w 0 ( 1 - v 2 c 2 ) Q + v w 0 c 2 = w 0 ( 1 - v 2 c 2 ) 1 + v w 0 c 2 , w 2 = w 0 ( 1 - v 2 c 2 ) Q - v w 0 c 2 = w 0 ( 1 - v 2 c 2 ) 1 - v w 0 c 2 ,
M ¯ = 1 2 m ( 1 + v w 0 c 2 ) v [ 1 - v 2 c 2 ] 1 2 [ 1 - w 0 2 c 2 ] 1 2 + 1 2 m ( 1 - v w 0 c 2 ) v [ 1 - v 2 c 2 ] 1 2 [ 1 - w 0 2 c 2 ] 1 2 + 0
M ¯ = m v [ 1 - v 2 c 2 ] 1 2 [ 1 - w 0 2 c 2 ] 1 2 = M 0 v [ 1 - v 2 c 2 ] 1 2 [ 1 - w 0 2 c 2 ] 1 2 ,
M ¯ = M 0 v [ 1 - v 2 c 2 ] 1 2 + M 0 v [ 1 - v 2 c 2 ] 1 2 [ 1 [ 1 - w 0 2 c 2 ] 1 2 - 1 ] .
M ¯ = ( M 0 + H ¯ c 2 ) v [ 1 - v 2 c 2 ] 1 2 .
K ¯ = ( M 0 + H ¯ c 2 ) c 2 ( 1 [ 1 - v 2 c 2 ] 1 2 - 1 ) .
Energy content of wave packet = E s ( c Δ t ) .
E s ( c Δ t ) = [ M 0 + H t c 2 ] c 2 [ 1 [ 1 - v 2 c 2 ] 1 2 - 1 ] + H t .
E s ( c Δ t ) c 2 + M 0 = M 0 + H t c 2 [ 1 - v 2 c 2 ] 1 2 ,
E s ( c Δ t ) c = ( M 0 + H t c 2 ) v [ 1 - v 2 c 2 ] 1 2 .
E s ( c Δ t ) c 2 + M 0 = E ( c Δ t ) c v
v = E s ( c Δ t ) E s ( c Δ t ) + M 0 c 2 c .
E s ( c Δ t ) = E s ( c Δ t ) c v × [ 1 - v 2 c 2 ] 1 2 c 2 [ 1 [ 1 - v 2 c 2 ] 1 2 - 1 ] + H t
H t = E s ( c Δ t ) [ 1 - c v ( 1 - [ 1 - v 2 c 2 ] 1 2 ) ] ( E s ( c Δ t ) [ 1 - v 2 c ] ) .
E = E s ( 1 + V c 1 - V c ) ,
E s ( c Δ t ) ( 1 + V c ) [ 1 - V 2 c 2 ] 1 2 .
E s ( c Δ t ) c 2 ( 1 + V c ) [ 1 - V 2 c 2 ] 1 2 c + M 0 V [ 1 - V 2 c 2 ] 1 2 = ( M 0 + H t c 2 ) v [ 1 - v 2 c 2 ] 1 2 ,
M 0 + H t c 2 [ 1 - v 2 c 2 ] 1 2 = E s ( c Δ t ) c 2 ( 1 + V c ) [ 1 - V 2 c 2 ] 1 2 + M 0 [ 1 - V 2 c 2 ] 1 2 ;
M 0 = E s ( c Δ t ) c v ( 1 - v c ) .
v = ( 1 + V c ) c + ( 1 - v c ) V c v ( 1 + V c ) c 2 + ( 1 - v c ) c v = V + v 1 + v V c 2 ,
H t = E s ( c Δ t ) [ 1 - c v ( 1 - [ 1 - v 2 c 2 ] 1 2 ) ]
P t = E s ( c Δ t ) c 2 ( 1 + V c ) [ 1 - V 2 c 2 ] 1 2 c - H t ( V + v ) c 2 [ 1 - V 2 c 2 ] 1 2 [ 1 - v 2 c 2 ] 1 2 .
E s ( c Δ t ) { 1 - c v [ 1 - ( 1 - v 2 c 2 ) 1 2 ] }
P t = E s ( c Δ t ) c 2 [ 1 - V 2 c 2 ] 1 2 [ ( 1 + V c ) c - ( V + v ) [ 1 - v 2 c 2 ] 1 2 { 1 - c v [ 1 - ( 1 - v 2 c 2 ) 1 2 ] } ] .
P t = E s ( c Δ t ) c [ 1 - V 2 c 2 ] 1 2
t Δ t [ 1 - V 2 c 2 ] 1 2
P = E s .
P = E ( 1 - V c 1 + V c ) ,
P = Δ M ¯ t = 1 t { M 0 ( V + v ) [ 1 - V 2 c 2 ] 1 2 [ 1 - v 2 c 2 ] 1 2 - M 0 V [ 1 - V 2 c 2 ] 1 2 } = M 0 { v + V ( 1 - [ 1 - v 2 c 2 ] 2 ) } [ 1 - V 2 c 2 ] 1 2 [ 1 - v 2 c 2 ] 1 2 .
P = E s .
E s ( c Δ t ) ( 1 + V c ) [ 1 - V 2 c 2 ] 1 2 + M 0 c 2 [ 1 - V 2 c 2 ] 1 2 = ( M 0 + H t c 2 ) c 2 { V + v 1 + V v c 2 } [ 1 - ( V + v ) 2 c 2 ( 1 + v V c 2 ) 2 ] 1 2 .
E s ( c Δ t ) ( 1 + V c ) [ 1 - V 2 c 2 ] 1 2 = M 0 c 2 { 1 + v V c 2 - [ 1 - v 2 c 2 ] 1 2 [ 1 - V 2 c 2 ] 1 2 [ 1 - v 2 c 2 ] 1 2 } + H t { 1 + v V c 2 - [ 1 - v 2 c 2 ] 1 2 [ 1 - V 2 c 2 ] 1 2 [ 1 - v 2 c 2 ] 1 2 } + H t .
E s ( c Δ t ) ( 1 + V c ) [ 1 - V 2 c 2 ] 1 2 = E s ( c Δ t ) c [ 1 - V 2 c 2 ] 1 2 V + E s ( c Δ t ) [ 1 [ 1 - V 2 c 2 ] 1 2 - 1 ] + E s ( c Δ t ) . Energy in wave packet . Pressure × time × velocity or mechanical work done by radiation on particle . Kinetic energy added to particle by heat motion . Heat motion of atoms , causing rise of temperature .
E s ( c + V ) = P V + E s c [ 1 - V 2 c 2 ] 1 2 × { 1 [ 1 - V 2 c 2 ] 1 2 - 1 } + E s c [ 1 - V 2 c 2 ] 1 2 .
H = E s c ( 1 + V s c 1 - V s c ) ( 1 - V T c 1 + V T c ) [ 1 - V T 2 c 2 ] 1 2 .
H = E s c ( 1 + V c 1 - V c ) ,
H = E s c ( 1 - V c 1 + V c ) .
H = E s c ( 1 - V c 1 + V c ) [ 1 - V 2 c 2 ] 1 2 ,