A flaw in Larmor’s formula?
Posted: Sat May 09, 2015 12:09 am
Poynting flux in the neighborhood of a point charge in arbitrary motion and the raditive power loss
http://arxiv.org/abs/1505.01737
http://arxiv.org/abs/1505.01737
a discussion forum for Polywell fusion
https://talk-polywell.org/bb/
His point is that the standard Larmor's formula gives a nonzero radiated energy from a static particle given a nonzero acceleration at t=0, when it has not yet attained a nonzero velocity/kinetic energy.(emphasis added)
VII. CONCLUSIONS
We showed that Larmor’s formula for the radiative
loss from a point charge gives the power only in a time-averaged
sense and does not always yield an instantaneous
radiative loss. In particular, even from an instantly
stationary accelerated charge, according to Larmor’s formula,
there should be a finite rate of radiation proportional
to the square of acceleration of the charge, in violation
of energy conservaion as the charge has no kinetic
energy that could be go into radiated power. However,
a proper examination of the elecromagnetic fields in the
neighborhood of the point charge and the Poynting flux
across a surface surrounding the point charge shows the
absence of any such radiation in the instantaneous rest
frame. Further, we showed that, contrary to the view
in the literature, the radiation loss derived even from
Poynting flux is in complete agreement with that derived
hitherto from radiation reaction due to the self-force for a
charges sphere of vanishing small radius. In this way we
not only showed the conformity of the two result, from
Poynting flux and from the radiation reaction, but also
established that the radiated power being proportional to
the first time derivative of the acceleration, indeed is the
exact formula for an instantaneous radiative loss from a
point charge with an arbitrary motion.
Percisely. My laymans point is that they are describing dT as zero. That is a zero in the denominator. It is meaningless. But, I suppose this is like saying the time dimension has shrunk to such a small size it is effectively zero for all practical purposes. It is like string theory. you can create extra dimensions to describe something mathematically, and use the dodge that the extra dimensions are so small they cannot be detected. This is interesting for theoretical work but has yet to show any practical/ predictable consequence on experienced reality- it is not testable.hanelyp wrote:A particle at V=0 has no kinetic energy. But if it is being accelerated there is a dE/dT > 0 for that particle as seen from that rest frame. So long as the dE/dT of radiation is less I see no problem in where the energy may come from.