Cavity radiation Friedrich Hasenöhrl

since j. j. thomson in 1881, many physicists wilhelm wien (1900), max abraham (1902), , hendrik lorentz (1904) used equations equivalent to

m

e
m


=


4
3


⋅



e

e
m



c

2






{\displaystyle m_{em}={\frac {4}{3}}\cdot {\frac {e_{em}}{c^{2}}}}

for so-called electromagnetic mass , expresses how electromagnetic energy contributes mass of bodies. , henri poincaré (1900) implicitly used expression m=e/c mass of electromagnetic energy.

following line of thought, hasenöhrl (1904, 1905) published several papers on inertia of cavity containing radiation. entirely classical derivation (no use of special relativity) , used maxwell s equation pressure of light. hasenöhrl associated apparent mass via inertia energy concept through equation:

μ
=


8
3





e

0





b



2






{\displaystyle \mu ={\frac {8}{3}}{\frac {e_{0}}{{\mathfrak {b}}^{2}}}}

,

where μ apparent mass, e0 radiation energy, ,





b




{\displaystyle {\mathfrak {b}}}

speed of light. subsequently, used notation:

m
=


8
3


⋅



h


ε

0




c

2






{\displaystyle m={\frac {8}{3}}\cdot {\frac {h\,\varepsilon _{0}}{c^{2}}}}

,

where hε0 radiation energy. concluded result valid radiating bodies, i.e. bodies temperature > 0°k. result hasenöhrl awarded haitinger prize of austrian academy of sciences. wrote in 1904:

since heat content of every body partly consists of radiating heat, things have demonstrated @ cavity, true mutatis mutandis every body temperature different 0° a.. in particular, every body must have apparent mass determined inner radiation, , therefore above dependent on temperature.

however, shown abraham hasenöhrl s calculation apparent mass incorrect, published paper in 1905, presented abraham s criticism , corrected formula to:

m
=


4
3


⋅



h


ε

0




c

2






{\displaystyle m={\frac {4}{3}}\cdot {\frac {h\,\varepsilon _{0}}{c^{2}}}}

this same relation (as hasenöhrl noted himself) electromagnetic mass formula given above. hasenöhrl s results (concerning apparent mass , thermodynamics) using cavity radiation further elaborated , criticized kurd von mosengeil (1906/7) incorporated albert einstein s theory of relativity in work. broad outline of relativistic thermodynamics , mass-energy equivalence using cavity radiation given max planck in 1907.

in additional papers (1907, 1908) hasenöhrl elaborated further on 1904-work , concluded new results in accordance theories of mosengeil , planck. however, complained fact planck (1907) did not mention earlier 1904-results (like dependency of apparent mass on temperature). in 1908 planck wrote results of hasenöhrl s new approach 1907 indeed equivalent of relativity.

afterwards, several authors gave credit hasenöhrl 1904 achievements on cavity radiation.

explanations

there different explanations result , deviation relativistic formula



e
=
m

c

2




{\displaystyle e=mc^{2}}

. enrico fermi , others argued problem analogous so-called 4/3 problem of electromagnetic mass. is, if hasenöhrl had included shell in calculations in way consistent relativity, pre-factor of 4/3 have been 1, yielding



m
=
e

/


c

2




{\displaystyle m=e/c^{2}}

. not have done this, since did not have relativistic mechanics, model shell.

on other hand, stephen boughn , tony rothman in 2011 (and boughn in 2012), gave historical account of different solutions problem, argued above explanation insufficient. after providing complete relativistic description , solution of cavity problem (in constant velocity case , slow acceleration case ), wrote:

... more reason [hasenöhrl] achieved incorrect result on both occasions wants rigorously equate work performed kinetic energy, work-energy theorem demands. unfortunately, not know how compute energy. in particular, hasenöhrl not conceive of fact if radiators losing energy, must losing mass, contains element of irony because precisely mass-energy relation trying establish. [...]

let end saying fritz hasenöhrl attempted legitimate thought experiment , tackled tools available @ time. working during transition period , did not create new theory necessary allow him solve problem correctly , completely. nevertheless, basic conclusion remained valid , should given credit.

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