Date: Sun, 26 Jul 2020 13:11:14 -0500 (CDT)
From: "Stephen A. Fulling" <fulling@math.tamu.edu>
To: Acceleration Radiation Community: ;
Subject: Two more sets of comments

==============================================================

1. Date: Sat, 25 Jul 2020 08:57:06 -0700 (PDT)
From: Bill Unruh <unruh@physics.ubc.ca>
Subject: Re: More comments, and a new query by Don Page

>> [BILL:]
>> My proposal is as above. boosted static before t0, and retarded 
> thereafter.
>
> [DANIEL] Probably I am misunderstanding something in the above proposal: In 
> the boosted frame where the charge is static util t_0 you want $ E= ( q/r^2 ) 
> \hat r $ , $ B=0$ on all spacetime to the past and including the hypresurface 
> t_0, and then to the future of that hypersurface, you want to consider the 
> world-line of the charge staring at t_0 as the source of the retarded 
> solution. Is that correct?

No, that was not what I meant. I meant that the boosted coulomb field is the
intial data that was desired for the t=0 hypersurface.  Basically this
solution is the retarded solution for all times.

>
> If that is the proposal then it seems that in the region to the future of the 
> t_0 hypersurface , but outside the future light come starting at the location 
> of the charge in the t_0 hypersurface we would have E=B=0.  That does not 
> seem right!

That would certainly not be right.


>
> ...
>
>> [BILL:]
>> Physics does not depend on coordinates.
>
> [DANIEL] It seems to me that in varios parts of the discussion one is 
> dealing with two notions of energy fluxes: one associated to inertial 
> observers and a second one associated to Rindler observers. And those do not 
> necessarily coincide. In particular if one wants to compare results must 
> recall that the region covered by Rindler observes is not spherically 
> symmetric.


The energy momentum tensor is a tensor. That tensor does not change when one
changes coordinates (the components of course do). 
You might if you wish, define "energy flux" in a way which does explicitly
depend on the coordinates, but that way lies madness. 
>
> ...
>
>>  3.  The problem of the sudden onset of acceleration is =
> pre-acceleration, much discussed over the decades, and the need to add =
> an additional boundary condition because of the third derivative in the =
> equations of motion. There is an extensive ancient literature on it.

In the case of uniform acceleration, one assumes that the motion is
determined, not by the equations of motion for the charge only under the
influence of EM, but by fiat. That gets rid of the "preacceleration" problem
(since the external force needed to keep the particle on track of course has
to be adjusted to take care of that radiation reaction force, but that is easy
for a theorist.)


....
>
> 2. From: Don Page <profdonpage@gmail.com>
> Date: Thu, 23 Jul 2020 12:45:09 -0600

...
>
> P.S.  There was some mention in a comment I received today of a possible 
> divergence if the acceleration of the charge worldline changed suddenly. 
> However, the 4D form F = (e/r^3) N ^ [(1 - a.N) V + r a] does not show any 
> divergence in F, but just a discontinuity between different finite values of 
> F if a jumps suddenly.

I was basing my comment on the belief that The vector potential had a
discontinuity in that case which would give a delta function in the EM field.
For example the field at the charge goes as the time derivatative of a which
is a delta function if the acceleration is a step function.


===========================================================

2. From: Ashok Kumar Singal <ashokkumar.singal@gmail.com>
Date: Sun, 26 Jul 2020 07:43:28 +0530
Subject: Re: More comments, and a new query by Don Page

  Taking the acceleration to begin suddenly at t = - \tau (with \tau -->
infinity!), is not really problematic, and one can easily calculate the
resulting delta-function and the energy in that (as an analytic function of
\tau, the energy may though  -->  infinity as  \tau -->  infinity ). In
fact, it has been shown that because of a rate of change of acceleration at
time t= - \tau, an event with which the delta-field has a causal relation,
the charge undergoes radiation losses, owing to the Lorentz-Dirac radiation
reaction, which neatly explains the total energy in the \delta-field [ref:
``A discontinuity in the electromagnetic field of a uniformly accelerated
charge,'' arXiv:2006.09169 (2020).]

As for the stoppage of the acceleration at the end (say, at t  --> +
infinity), since it will still be a future event at any finite time, when
we might  be examining the fields of the charge under a uniform
acceleration, it should not affect our results or conclusions in any way.


Ashok Singal

===============================================================