In classical electrodynamics, an extended charge accelerated by a constant electric or magnetic field has all its parts equally accelerated in the laboratory frame, leading to it losing its rigidity in the proper frame of any accelerated part. In effect,
the rest mass of the extended charge increases.

To keep it rigid would require another external field, as in a Rindler space where an additional force is required maintain the rigidness of a hyperbolically accelerated extended body. Is there anything in modern particle physics that requires an
additional external field from somewhere, to maintain the rigidness of say the electron when its accelerated by an EM field? Like the Higgs or vacuum?

Thanks in advance,

John McAndrew

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On 20/02/22 7:47 PM, john mcandrew wrote:

In classical electrodynamics, an extended charge accelerated by a constant electric or magnetic field has all its parts equally accelerated in the laboratory frame, leading to it losing its rigidity in the proper frame of any accelerated part. In

effect, the rest mass of the extended charge increases.

To keep it rigid would require another external field, as in a Rindler space where an additional force is required maintain the rigidness of a hyperbolically accelerated extended body.

You can't always maintain it. (Once you cross the event horizon of
a black hole it's a lost cause..)

Is there anything in modern particle physics that requires an additional external field from somewhere, to maintain the rigidness of say the electron when it's accelerated by an EM field? Like the Higgs or vacuum?

Modern physics is probably the last place to look for it. The electron
in modern physics is a quantum field. A quantum field has quite some
similarity with a classical wave, which is not rigid at all.

Of course a quantum field also has some discreteness, but that is mainly
the existence of certain modes. And those are not rigid at all when they
are accelerated. Most electrons are bound to an atom core, and if that
system is placed in a field it is easily deformated.

Of course you can say that an atom *approximately* keeps it shape, in
the sense that the core and electrons at least tend to stay together,
if the forces don't become too strong at least. For that behavior you
actually need the internal field (regardless whether there's an external
field or not). I'm not sure if that is what you're looking for..

--
Jos

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On Saturday, February 22, 2020 at 7:40:29 PM UTC, Jos Bergervoet wrote:

On 20/02/22 7:47 PM, john mcandrew wrote:

In classical electrodynamics, an extended charge accelerated by a constant electric or magnetic field has all its parts equally accelerated in the laboratory frame, leading to it losing its rigidity in the proper frame of any accelerated part. In

effect, the rest mass of the extended charge increases.

To keep it rigid would require another external field, as in a Rindler space where an additional force is required maintain the rigidness of a hyperbolically accelerated extended body.

You can't always maintain it. (Once you cross the event horizon of
a black hole it's a lost cause..)

Is there anything in modern particle physics that requires an additional external field from somewhere, to maintain the rigidness of say the electron
when it's accelerated by an EM field? Like the Higgs or vacuum?

Modern physics is probably the last place to look for it. The electron
in modern physics is a quantum field. A quantum field has quite some similarity with a classical wave, which is not rigid at all.

Of course a quantum field also has some discreteness, but that is mainly
the existence of certain modes. And those are not rigid at all when they
are accelerated. Most electrons are bound to an atom core, and if that
system is placed in a field it is easily deformated.

Of course you can say that an atom *approximately* keeps it shape, in
the sense that the core and electrons at least tend to stay together,
if the forces don't become too strong at least. For that behavior you actually need the internal field (regardless whether there's an external field or not). I'm not sure if that is what you're looking for..

I had hoped an internal field would be OK, but it doesn't appear to be able to account for EM energy-momentum being permanently ejected from the accelerated extended charge. The problem is that work is done by the increased EM mass on the internal forces
trying to reduce it, which is then transformed into internal mass, without affecting the total mass. Whereas I want this excess EM mass to free itself from the extended charge somehow.

I had thought about using incoming reversed radiation to provide the weird additional external field, but it looks too artificial having to add a boundary condition. I'm hoping I'm missing something subtle going on here.

John McA

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On Saturday, February 22, 2020 at 6:47:31 PM UTC, john mcandrew wrote:

In classical electrodynamics, an extended charge accelerated by a constant electric or magnetic field has all its parts equally accelerated in the laboratory frame, leading to it losing its rigidity in the proper frame of any accelerated part. In

effect, the rest mass of the extended charge increases.

To keep it rigid would require another external field, as in a Rindler space where an additional force is required maintain the rigidness of a hyperbolically accelerated extended body. Is there anything in modern particle physics that requires an

additional external field from somewhere, to maintain the rigidness of say the electron when its accelerated by an EM field? Like the Higgs or vacuum?

Thanks in advance,

John McAndrew

It looks to me that the internal forces aka Poincare stress (PS) are all that's needed in providing a realistic physical picture of the above, if they're applied to the leading edge of the accelerated extended charge, thus opposing its increased
differential acceleration compared to the trailing edge. The net effect is that the PS converts mechanical energy-momentum to field energy-momentum, hence increasing the latter at the expense of the first, and slowing the charge down. So while there isn'
t an EM "radiation reaction force" for constant acceleration, there is one from the PS.

While the extended charge is being accelerated by a constant field, I wonder how the total energy-momentum transforms between different frames, and if it transforms as a four-vector? I'm guessing no for now.

J McA

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