## A flaw in Larmor’s formula?

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DeltaV
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Joined: Mon Oct 12, 2009 5:05 am

### A flaw in Larmor’s formula?

Poynting flux in the neighborhood of a point charge in arbitrary motion and the raditive power loss
http://arxiv.org/abs/1505.01737

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

### Re: A flaw in Larmor’s formula?

In the abstract, they say in the relative rest frame of a charged particle, in motion- somewhat of a nonsense statement by itself. The radiated energy loss is zero (Bremsstruhlung, I assume), even though the particle is being accelerated. They use the dodge that in instantaneous time- which I think means zero seconds of elapsed time. Without any time , there can be no radiation as the photons cannot move .

http://arxiv.org/abs/1505.01737

[qoute/]"...in the instantaneous rest-frame of the accelerated charge, the charge has no kinetic energy of motion that could be lost into radiation."[/quote]

It sounds like a clever mathematical manipulation that has no relation to reality, ie four dimensional space. Bremsstruhlung certainly exists and a mathematical derivation that says otherwise, despite proper book keeping, is flawed. It is sort of like the arguement that a bullet fired from a gun will never hit you because the bullet travels 1/2 the distance per a unit of time, and travels 1/2 the remaining distance in 1/2 of a unit of time... The bullet arguably would never reach you because the unit of time in the denominator never reaches zero. It is mathematically consistent, but obviously flawed as a description of reality.

Admittedly, this is only from the abstract of the paper. What is described in the body of the paper is unknown. They may not be challenging reality so much as proposing some subtle modification of the mathematical derivation that would more accurately define a formula. Such, without some correlation to reality (will it more accurately match measurement with theory?) still remains only a mathematical exercise. I suppose if the 'correction' is extended to further systems, it might eventually allow for some subtle change in predictions that would resolve some measured discrepancy. They do not mention any such speculation in the abstract.

Dan Tibbets.
To error is human... and I'm very human.

DeltaV
Posts: 2245
Joined: Mon Oct 12, 2009 5:05 am

### Re: A flaw in Larmor’s formula?

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
.

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.

In the first sentence quoted above, "does not always yield an instantaneous radiative loss" should probably read "does not always yield the correct instantaneous radiative loss".

For such a particle, at t=0 the "instantaneous rest-frame of the accelerated charge" would be an inertial frame.

hanelyp
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Joined: Fri Oct 26, 2007 8:50 pm

### Re: A flaw in Larmor’s formula?

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.
The daylight is uncomfortably bright for eyes so long in the dark.

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

### Re: A flaw in Larmor’s formula?

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.

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.

Dan Tibbets
To error is human... and I'm very human.