On 19/10/26 11:57 PM, john mcandrew wrote:
Suppose a charge is accelerated by an external field, hence radiating irreversible energy-momentum given by the Lienard-Wiechert fields.
Why do you call it "irreversible"? It can just as well go the other way.
.. We
can time reverse this
Exactly what I said! SO why did you call it "irreversible"?
so that the radiation instead converges upon the
charge causing it to "absorb" the radiation. If I'm not mistaken, this
is physically interpreted as the incoming radiation converging to a singularity at the point charge,
Until now you just called it a "charge", now suddenly it has become
a "point charge". So indeed there is then a singularity (and it is not
a completely realistic case any more).
then propagating outwards again but
Why do you believe it will be "propagating outwards" again? Was there anything propogating inwards in the original (non-time-reversed) case?
phase reversed and now *exactly* cancelling the radiation emitted by
the accelerated charge.
Which radiation emitted?! The emitted radiation in the original (non- time-reversed) case is now absorbed radiation, so what are you referring
to? You are mixing up the time-reversed and non-reversed cases.
Is this exact cancelling a consequence of the standard Maxwell's
You are mixing up the time-reversed and non-reversed cases, so of course there will be some things in one case which are equal but opposite to
the corresponding things in the other case. That is just due to your own construction of a time-reversed case.
equations, or is it an additional postulate?
No, there is no postulate in classical ED that specifies anything about time-reversed solutions. They are by definition just what you obtain
by changing t to -t. That's a complete description which does not leave
any room for postulating anything more.
On Friday, November 1, 2019 at 8:25:18 PM UTC, Jos Bergervoet wrote:an accelerating charge irreversible.
On 19/10/26 11:57 PM, john mcandrew wrote:
Suppose a charge is accelerated by an external field, hence radiating
irreversible energy-momentum given by the Lienard-Wiechert fields.
Why do you call it "irreversible"? It can just as well go the other way.
I'm using the most common definition of EM radiation given by the 1/r fall off term in the LW equations which is used to then calculate radiation power at large distances via Lamor's formula. This is always positive making the EM radiation generated by
model by reversing the order of events, so that this radiation is now interpreted as a boundary condition and externally generated radiation incoming towards the charge... We
can time reverse this
Exactly what I said! SO why did you call it "irreversible"?
The radiation generated by the accelerating charge is irreversible as in we can't alter the motion of the charge so that this radiation can reverse in direction towards the charge. However, it is reversible in that we can create another valid physical
me when treating the incoming radiation as independent of the charge it's now going to accelerate. The effect of the incoming radiation + its effect on accelerating the charge must combine to give zero net outward radiation because this was zero incomingso that the radiation instead converges upon the
charge causing it to "absorb" the radiation. If I'm not mistaken, this
is physically interpreted as the incoming radiation converging to a
singularity at the point charge,
Until now you just called it a "charge", now suddenly it has become
a "point charge". So indeed there is then a singularity (and it is not
a completely realistic case any more).
then propagating outwards again but
Why do you believe it will be "propagating outwards" again? Was there
anything propogating inwards in the original (non-time-reversed) case?
No, there was nothing propagating inwards in the original case. I'm trying to physically interpret the time reversed case by splitting the reversed model into physical processes that combine to give a coherent model.
In the original case, the charge is accelerated and generates outgoing radiation. Time reverse this and the radiation that was outgoing now converges onto the charge which to me looks physically odd -- where does it go? Things become more sensible to
match the state of the deformed charge when it emitted the radiation, to exactly time reverse events which would be extremely unlikely.phase reversed and now *exactly* cancelling the radiation emitted by
the accelerated charge.
Which radiation emitted?! The emitted radiation in the original (non-
time-reversed) case is now absorbed radiation, so what are you referring
to? You are mixing up the time-reversed and non-reversed cases.
Staying with the time reversed case, the now incoming radiation will accelerate the charge causing it to emit outgoing radiation.
Is this exact cancelling a consequence of the standard Maxwell's
You are mixing up the time-reversed and non-reversed cases, so of course
there will be some things in one case which are equal but opposite to
the corresponding things in the other case. That is just due to your own
construction of a time-reversed case.
I disagree, I hope I've made things clearer in my above replies.
equations, or is it an additional postulate?
No, there is no postulate in classical ED that specifies anything about
time-reversed solutions. They are by definition just what you obtain
by changing t to -t. That's a complete description which does not leave
any room for postulating anything more.
I agree after thinking about this over the past few days. The key for me was realizing that the charge is rigid in a sense so that it appears the same towards both incoming and outdoing radiation. Otherwise, the incoming radiation would have to exactly
John McAndrew
On Friday, November 1, 2019 at 8:25:18 PM UTC, Jos Bergervoet wrote:
On 19/10/26 11:57 PM, john mcandrew wrote:
Suppose a charge is accelerated by an external field, hence radiating
irreversible energy-momentum given by the Lienard-Wiechert fields.
Why do you call it "irreversible"? It can just as well go the other way.
I'm using the most common definition of EM radiation given by the 1/r fall off term in the LW equations which is used to then calculate radiation power at large distances via Lamor's formula.
This is always positive making the EM radiation generated by an accelerating charge irreversible.
Why do you believe it will be "propagating outwards" again? Was there
anything propogating inwards in the original (non-time-reversed) case?
No, there was nothing propagating inwards in the original case. I'm trying to physically interpret the time reversed case by splitting the reversed model into physical processes that combine to give a coherent model.
In the original case, the charge is accelerated and generates outgoing radiation. Time reverse this and the radiation that was outgoing now converges onto the charge which to me looks physically odd -- where does it go?
Things become more sensible to me when treating the incoming radiation as independent of the charge it's now going to accelerate. The effect of the incoming radiation + its effect on accelerating the charge must combine to give zero net outwardradiation because this was zero incoming radiation in the original case. So the reverse accelerated charge will generate outgoing radiation that must be cancelled by another outgoing field,
Is this exact cancelling a consequence of the standard Maxwell's
You are mixing up the time-reversed and non-reversed cases, so of course
there will be some things in one case which are equal but opposite to
the corresponding things in the other case. That is just due to your own
construction of a time-reversed case.
I disagree, I hope I've made things clearer in my above replies.
On 19/11/02 1:45 AM, John McAndrew wrote:
On Friday, November 1, 2019 at 8:25:18 PM UTC, Jos Bergervoet wrote:
On 19/10/26 11:57 PM, john mcandrew wrote:
Suppose a charge is accelerated by an external field, hence radiating
irreversible energy-momentum given by the Lienard-Wiechert fields.
Why do you call it "irreversible"? It can just as well go the other way.
I'm using the most common definition of EM radiation given by the 1/r fall off term in the LW equations which is used to then calculate radiation power at large distances via Lamor's formula.
This common definition does not make any claim of irreversibility.
This is always positive making the EM radiation generated by an accelerating charge irreversible.
It's a bit of an illogical use of the term. Sunlight is always coming
from the sun towards us, but that doesn't make it irreversible. You
just need a mirror..
Irreversible in my view is better reserved for cases where
thermodynamics is involved. (Of course you could argue that we're
already at that transition here. For a large collection of charges
that might be true..)
Why do you believe it will be "propagating outwards" again? Was there
anything propogating inwards in the original (non-time-reversed) case?
No, there was nothing propagating inwards in the original case. I'm trying to physically interpret the time reversed case by splitting the reversed model into physical processes that combine to give a coherent model.
Than it is a mathematical approach of choosing between equivalent descriptions of what happens..
In the original case, the charge is accelerated and generates outgoing radiation. Time reverse this and the radiation that was outgoing now converges onto the charge which to me looks physically odd -- where does it go?
Its energy goes into the force field (whichever it is) that in the
original case did accelerate the particle. In the reversed case this
force absorbs energy, in the original case it had to donate energy
to the [particle + EM field] system.
radiation because this was zero incoming radiation in the original case. So the reverse accelerated charge will generate outgoing radiation that must be cancelled by another outgoing field,Things become more sensible to me when treating the incoming radiation as independent of the charge it's now going to accelerate. The effect of the incoming radiation + its effect on accelerating the charge must combine to give zero net outward
Not really, the decelerated charge can simply absorb the incoming
radiation, and that's already a solution of the CED equations. Let's
call that solution 1.
But, as you prefer, you can consider the same decelerated charge in a
space where there is no incoming radiation, let's call this solution 2.
In that case of course it will radiate (like any decelerated or
accelerated charge will do if there is not this precisely tuned incoming radiation of solution 1).
To go from solution 2 back to solution 1, you have to add solution 3:
the case of *only* incoming radiation, no particle present at all!
And the incoming radiation will contract to the position where the
particle is in solutions 1 and 2, but which is now empty. And there
it will just bounce back (without any singularity) and become outgoing radiation. This outgoing radiation has a minus sign compared to that
of solution 2, so adding solutions 3 and 2 gives you zero outgoing
radiation, it is solution 1. This addition also gives you exactly one particle (from solution 2) because solution 3 doesn't have one.
The fact that solution 3 has no singularity can be understood by
looking at the case of a purely spherical incoming wave, which will
bounce back in the origin as an outgoing wave, but will *not* become
become infinite. Only regular spherical Bessel functions are needed
to describe this wave. (The irregular ones, the Neumann functions,
would be needed if there actually is a point source, like a rotating
point dipole, but not in the free-space case of solution 3).
On Saturday, November 2, 2019 at 5:25:55 PM UTC, benj wrote:accelerated by a uniform electric field E from a to b, then to get it to move from b to a we just reverse the velocity of the charge keeping E the same. It's "time reversed" compared to the original in that the order of the events have been reversed.
On 11/1/2019 8:45 PM, John McAndrew wrote:
[snipped]
Feynman and others have already been through this loop. Great theory! I
John McAndrew
have no doubt it will become widely accepted just as soon as someone
demonstrates a working time machine.
Wheeler–Feynman absorber theory https://authors.library.caltech.edu/11095/1/WHErmp45.pdf
I've never read it in detail because I found the idea of radiation needing an absorber bizarre. That is, an accelerated charge wouldn't radiate if it was alone in the universe according to Tetrode and then Feynman.
What I'm talking about doesn't have anything to do with this. "Reversing in time" here just means creating a physical model via added boundary conditions if necessary that is a backward running version compared to the original. So if a charge is
Likewise with a charge moving in a circle in a constant magnetic field B from a to b. To reverse the events and hence "time reverse the model" we reverse the velocity and also the magnetic field to -B. Any idea as to why we need to reverse B?to me to be time-asymmetric, and that's what I find interesting. Maybe that's what Feynman and Wheeler were getting at, but I haven't fully appreciated yet?
It turns out that the accelerated charge also radiates away energy-momentum, so we have to add incoming radiation to compensate for the original loss, which wasn't there in the original model as outgoing radiation. In this sense, classical EM *appears*
John McAndrew
On 11/1/2019 8:45 PM, John McAndrew wrote:
John McAndrew
Feynman and others have already been through this loop. Great theory! I
have no doubt it will become widely accepted just as soon as someone demonstrates a working time machine.
On 11/3/2019 6:40 PM, John McAndrew wrote:...
On Saturday, November 2, 2019 at 5:25:55 PM UTC, benj wrote:
On 11/1/2019 8:45 PM, John McAndrew wrote:
... Classic
EM mathematically allows time reversal but reality does not.
On 11/4/2019 4:02 AM, Jos Bergervoet wrote:
On 19/11/04 1:03 AM, benj wrote:
On 11/3/2019 6:40 PM, John McAndrew wrote:...
On Saturday, November 2, 2019 at 5:25:55 PM UTC, benj wrote:
On 11/1/2019 8:45 PM, John McAndrew wrote:
...
... Classic EM mathematically allows time reversal but reality does
not.
Where does it show that?
An EM wave absorbed in resistive material clearly is the 'time-
reversed' case of chares emitting outgoing radiation. They
absorb incoming radiation.
I think on that part we agree. But why do you restrict it to
*classical* EM and why do you say it is only *mathematically*?
These EM waves really are absorbed. And the description of the
process does not need the classical theory, in fact QED does a
better job, usually.
So you are saying ...
On 19/11/04 1:03 AM, benj wrote:
On 11/3/2019 6:40 PM, John McAndrew wrote:...
On Saturday, November 2, 2019 at 5:25:55 PM UTC, benj wrote:
On 11/1/2019 8:45 PM, John McAndrew wrote:
...
... Classic EM mathematically allows time reversal but reality does
not.
Where does it show that?
An EM wave absorbed in resistive material clearly is the 'time-
reversed' case of chares emitting outgoing radiation. They
absorb incoming radiation.
I think on that part we agree. But why do you restrict it to
*classical* EM and why do you say it is only *mathematically*?
These EM waves really are absorbed. And the description of the
process does not need the classical theory, in fact QED does a
better job, usually.
On Saturday, November 2, 2019 at 8:55:35 PM UTC, Jos Bergervoet wrote:...
Irreversible in my view is better reserved for cases where
thermodynamics is involved. (Of course you could argue that we're
already at that transition here. For a large collection of charges
that might be true..)
"Irreversible" radiation emitted by a charge has been used since at least Dirac in 1938: http://ivanik3.narod.ru/EMagnitizm/JornalPape/ParadocCullwick/Dirac/Proc1938v167Dirac148.pdf
page 155: "The third term -2/3 e^2 a^2 v_0 corresponds to irreversible emission of radiation and gives the effect of radiation damping on the electron".
There's this more recent paper 2010 from Gron: The significance of the Schott energy for energy-momentum conservation of a
radiating charge obeying the Lorentz-Abraham-Dirac equation
page 6 claims Schott and Rhorlic used it: “The radiation rate is always positive (or zero)
and describes an irreversible loss of energy; the Schott
I suppose context matters here so that people don't end up confused over what's actually meant.
My intention was to understand the physics of what's going on with the mathematics coming secondary. I find the incoming radiation disappearing into the charge as "absorbed" unsatisfactory to my understanding which admittedly is probably down to me notconsidering others factors.
Its energy goes into the force field (whichever it is) that in the
original case did accelerate the particle. In the reversed case this
force absorbs energy, in the original case it had to donate energy
to the [particle + EM field] system.
To help me understand your point, consider a charged particle m entering a uniform magnetic field B at right angles.
It spirals towards some point from a to b from dp/dt = evxB + radiation loss term. The magnetic field accelerates m but doesn't do any work on it so that the radiation is donated by the loss of kinetic energy of m IMO.
Time reversing this so that m travels from b to a, the incoming radiation raises the kinetic energy of m.
The only way I can think of energy going in and out of the applied field causing the charge to accelerate
is by changing the configuration of the sources generating it. But I don't see this taking place in this example.
Not really, the decelerated charge can simply absorb the incoming
radiation, and that's already a solution of the CED equations. Let's
call that solution 1.
In this picture, how do you physically interpret the charge as "absorbing" the incoming radiation? eg. does the radiation just accelerate the charge so there's no energy left to radiate?
But, as you prefer, you can consider the same decelerated charge in a
space where there is no incoming radiation, let's call this solution 2.
In that case of course it will radiate (like any decelerated or
accelerated charge will do if there is not this precisely tuned incoming
radiation of solution 1).
To go from solution 2 back to solution 1, you have to add solution 3:
the case of *only* incoming radiation, no particle present at all!
And the incoming radiation will contract to the position where the
particle is in solutions 1 and 2, but which is now empty. And there
it will just bounce back (without any singularity) and become outgoing
radiation. This outgoing radiation has a minus sign compared to that
of solution 2, so adding solutions 3 and 2 gives you zero outgoing
radiation, it is solution 1. This addition also gives you exactly one
particle (from solution 2) because solution 3 doesn't have one.
The fact that solution 3 has no singularity can be understood by
looking at the case of a purely spherical incoming wave, which will
bounce back in the origin as an outgoing wave, but will *not* become
become infinite. Only regular spherical Bessel functions are needed
to describe this wave. (The irregular ones, the Neumann functions,
would be needed if there actually is a point source, like a rotating
point dipole, but not in the free-space case of solution 3).
"bouncing back" is one way of putting it since that's what it looks like.
What I think really happens is that all parts of the incoming wavefront pass straight through the minimum region occupied by the charge, swapping places with one another at a fixed point.
On 19/11/03 3:20 AM, John McAndrew wrote:
not considering others factors.My intention was to understand the physics of what's going on with the mathematics coming secondary. I find the incoming radiation disappearing into the charge as "absorbed" unsatisfactory to my understanding which admittedly is probably down to me
For me it isn't "just" disappearing, but is converted to other fields,
since I don't see charged particles as anything else than configurations
of quantum fields of some type.
And you'll surely agree that fields interact, the E-field also can be converted into B-field (in a resonating cavity it happens every half
period). So fields disappearing while other fields gain energy seems
fine to me.
Its energy goes into the force field (whichever it is) that in the
original case did accelerate the particle. In the reversed case this
force absorbs energy, in the original case it had to donate energy
to the [particle + EM field] system.
To help me understand your point, consider a charged particle m entering a uniform magnetic field B at right angles.
That doesn't help. In that case you already have given the energy to
the particle (so it is not a case where any external force is needed
to donate energy. It is actually simpler than what I described.)
It spirals towards some point from a to b from dp/dt = evxB + radiation loss term. The magnetic field accelerates m but doesn't do any work on it so that the radiation is donated by the loss of kinetic energy of m IMO.
So everything is balanced. (No external forces of non-EM type needed).
Time reversing this so that m travels from b to a, the incoming radiation raises the kinetic energy of m.
Again nicely balanced. So what is your question?
The only way I can think of energy going in and out of the applied field causing the charge to accelerate
Which energy? Which field? Before the particle entered the region
you described there may have been a force field (EM or other) that accelerated it, but you don't specify that. During its spiraling
in the B-field region the energy exchange is zero (both in the time-
reversed and non-reversed case). So what is the question?
is by changing the configuration of the sources generating it. But I don't see this taking place in this example.
Exactly, there is no energy exchange with the B-field. In this special
case it's not positive, not negative, but simply zero.
Still you could look at the self-field of the particle (its eletro-
magnetic mass contribution, so to say). Part of the 'kinetic energy'
you mention is actually EM field energy in the self-field. And if
your particle has the classical EM radius, its mass and kinetic energy
are even 100% EM.
So whenever the kinetic energy s=changes, the EM part of the kinetic
energy changes as well, so there you have exchange of energy between
the self-field and the radiated (or incoming) waves.
On 11/4/2019 4:02 AM, Jos Bergervoet wrote:
On 19/11/04 1:03 AM, benj wrote:
On 11/3/2019 6:40 PM, John McAndrew wrote:...
On Saturday, November 2, 2019 at 5:25:55 PM UTC, benj wrote:
On 11/1/2019 8:45 PM, John McAndrew wrote:
...
... Classic EM mathematically allows time reversal but reality does
not.
Where does it show that?
An EM wave absorbed in resistive material clearly is the 'time-
reversed' case of chares emitting outgoing radiation. They
absorb incoming radiation.
I think on that part we agree. But why do you restrict it to
*classical* EM and why do you say it is only *mathematically*?
These EM waves really are absorbed. And the description of the
process does not need the classical theory, in fact QED does a
better job, usually.
So you are saying that any absorbed wave is a result of exact
cancellation by waves coming from the future? That makes a mathematical theory, but we need some data showing present events can be influenced
by future actions. If you have a time machine, I'd like to take a ride!
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate
for the original loss, which wasn't there in the original model as
outgoing radiation. In this sense, classical EM *appears* to me to
be time-asymmetric, and that's what I find interesting.
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate
for the original loss, which wasn't there in the original model as
outgoing radiation. In this sense, classical EM *appears* to me to
be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed
case the charge as to respond in a manner that also self-consistently time-reverses the original specification of its motion.
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away energy-momentum, so we have to add incoming radiation to compensate
for the original loss, which wasn't there in the original model as
outgoing radiation. In this sense, classical EM *appears* to me to
be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed
case the charge as to respond in a manner that also self-consistently time-reverses the original specification of its motion.
On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate
for the original loss, which wasn't there in the original model as
outgoing radiation. In this sense, classical EM *appears* to me to
be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed
case the charge as to respond in a manner that also self-consistently time-reverses the original specification of its motion.
If the forward case is easy (as you claim) the time-reversed case
is equally easy. t --> -t solves it all.
On Monday, November 11, 2019 at 12:55:53 PM UTC, Jos Bergervoet wrote:
On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate
for the original loss, which wasn't there in the original model as
outgoing radiation. In this sense, classical EM *appears* to me to
be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed
case the charge as to respond in a manner that also self-consistently
time-reverses the original specification of its motion.
If the forward case is easy (as you claim) the time-reversed case
is equally easy. t --> -t solves it all.
I don't think it's that easy. In a uniform magnetic field B, a charged particle radiates energy-momentum from a to b.
Reversing everything including B and the charge loses further energy-momentum from b to c
while gaining some from the now incoming time reversed outgoing a -> b emitted radiation.
It's not enough to get the charge back to a:
the radiation loss from b to c
has to be added as additional energy-momentum
to make the time reversed case physically possible,
which wasn't in the original a -> b case.
On 19/11/11 5:34 PM, John McAndrew wrote:
On Monday, November 11, 2019 at 12:55:53 PM UTC, Jos Bergervoet wrote:
On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate
for the original loss, which wasn't there in the original model as
outgoing radiation. In this sense, classical EM *appears* to me to
be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed
case the charge as to respond in a manner that also self-consistently
time-reverses the original specification of its motion.
If the forward case is easy (as you claim) the time-reversed case
is equally easy. t --> -t solves it all.
I don't think it's that easy. In a uniform magnetic field B, a charged particle radiates energy-momentum from a to b.
You mean it's going from a to b (the particle).
Reversing everything including B and the charge loses further energy-momentum from b to c
No. If you reverse *everything* then the particle goes from
b to a. It simply returns.
while gaining some from the now incoming time reversed outgoing a -> b emitted radiation.
Of course. the same amount that it lost in the forward case. (Since
you reverse *everything*, you can't escape that conclusion.
It's not enough to get the charge back to a:
Yes, It absolutely is. All B-fields have a minus sign, the velocity
is reversed, so the vxB Lorentz term is the same. The E-fields are
unchanged so the force from the E-field is also the same. So the
particle feels the same force while traveling in the other direction,
which means:
1) Its energy loss (or gain) is exactly opposite than in the forward
case.
2) Its acceleration d/dt v(-t) is the same, which proves that following
this 'exactly reverse' trajectory is indeed a solution (after all
d^2/dt^2 x(-t) at time=-t, is equal to d^2/dt^2 x(t) at time=t,
so x(-t) exactly obeys Newton's law.)
the radiation loss from b to c
The point c is exactly a.
has to be added as additional energy-momentum
But it is a negative loss, i.e. a radiation gain, not a loss!
to make the time reversed case physically possible,
Aha! There we are. You *reject* the solution, even though t --> -t
exactly obeys Newton, and Maxwell, you *still* claim that it isn't
a solution (because your 'feelings' tell you so, perhaps?)
I cannot help you if you reject the laws of CED while claiming to
discuss CED. You may think it is not 'physically possible', but
you simply are wrong. Within CED this time reversed solution is
an exact and perfectly valid solution. (It will not often occur
in nature, of course. It requires a very special incoming wave
to get exactly this case.)
which wasn't in the original a -> b case.
Everything definitely *was* in the original case. If you just
reverse t --> -t, you're not throwing anything away.
On Monday, November 11, 2019 at 8:46:13 PM UTC, Jos Bergervoet wrote:
On 19/11/11 5:34 PM, John McAndrew wrote:
On Monday, November 11, 2019 at 12:55:53 PM UTC, Jos Bergervoet wrote:
On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate >>>>>> for the original loss, which wasn't there in the original model as >>>>>> outgoing radiation. In this sense, classical EM *appears* to me to >>>>>> be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed >>>>> case the charge as to respond in a manner that also self-consistently >>>>> time-reverses the original specification of its motion.
If the forward case is easy (as you claim) the time-reversed case
is equally easy. t --> -t solves it all.
I don't think it's that easy. In a uniform magnetic field B, a charged particle radiates energy-momentum from a to b.
You mean it's going from a to b (the particle).
Reversing everything including B and the charge loses further energy-momentum from b to c
No. If you reverse *everything* then the particle goes from
b to a. It simply returns.
while gaining some from the now incoming time reversed outgoing a -> b emitted radiation.
Of course. the same amount that it lost in the forward case. (Since
you reverse *everything*, you can't escape that conclusion.
It's not enough to get the charge back to a:
Yes, It absolutely is. All B-fields have a minus sign, the velocity
is reversed, so the vxB Lorentz term is the same. The E-fields are
unchanged so the force from the E-field is also the same. So the
particle feels the same force while traveling in the other direction,
which means:
1) Its energy loss (or gain) is exactly opposite than in the forward
case.
2) Its acceleration d/dt v(-t) is the same, which proves that following
this 'exactly reverse' trajectory is indeed a solution (after all
d^2/dt^2 x(-t) at time=-t, is equal to d^2/dt^2 x(t) at time=t,
so x(-t) exactly obeys Newton's law.)
the radiation loss from b to c
The point c is exactly a.
has to be added as additional energy-momentum
But it is a negative loss, i.e. a radiation gain, not a loss!
to make the time reversed case physically possible,
Aha! There we are. You *reject* the solution, even though t --> -t
exactly obeys Newton, and Maxwell, you *still* claim that it isn't
a solution (because your 'feelings' tell you so, perhaps?)
I cannot help you if you reject the laws of CED while claiming to
discuss CED. You may think it is not 'physically possible', but
you simply are wrong. Within CED this time reversed solution is
an exact and perfectly valid solution. (It will not often occur
in nature, of course. It requires a very special incoming wave
to get exactly this case.)
which wasn't in the original a -> b case.
Everything definitely *was* in the original case. If you just
reverse t --> -t, you're not throwing anything away.
The time reversibility of CED for continuous charges where all forces are long range EM makes sense to me for the reasons you've given above.
The bit I'm skeptical about is then imposing a rigidness on all the charges making up the system via short range local EM forces,
and claiming time reversibility still holds when emitted radiation is reversed back onto the rigid charge.
When the rigid charge (RC) is accelerated by a constant E field, the short range EM forces (Poincare stresses) balance the internal field of the continuous charge and the effect of the external E, while radiating.
Reversing this, we now have an additional reversed radiation field acting on the RC, causing the Poincare stresses having to change in magnitude compared to the non-reversed case. I therefore still remain unconvinced.
On 19/11/13 12:23 AM, John McAndrew wrote:
On Monday, November 11, 2019 at 8:46:13 PM UTC, Jos Bergervoet wrote:
On 19/11/11 5:34 PM, John McAndrew wrote:
On Monday, November 11, 2019 at 12:55:53 PM UTC, Jos Bergervoet wrote: >>>> On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate >>>>>> for the original loss, which wasn't there in the original model as >>>>>> outgoing radiation. In this sense, classical EM *appears* to me to >>>>>> be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed >>>>> case the charge as to respond in a manner that also self-consistently >>>>> time-reverses the original specification of its motion.
If the forward case is easy (as you claim) the time-reversed case
is equally easy. t --> -t solves it all.
I don't think it's that easy. In a uniform magnetic field B, a charged particle radiates energy-momentum from a to b.
You mean it's going from a to b (the particle).
Reversing everything including B and the charge loses further energy-momentum from b to c
No. If you reverse *everything* then the particle goes from
b to a. It simply returns.
while gaining some from the now incoming time reversed outgoing a -> b emitted radiation.
Of course. the same amount that it lost in the forward case. (Since
you reverse *everything*, you can't escape that conclusion.
It's not enough to get the charge back to a:
Yes, It absolutely is. All B-fields have a minus sign, the velocity
is reversed, so the vxB Lorentz term is the same. The E-fields are
unchanged so the force from the E-field is also the same. So the
particle feels the same force while traveling in the other direction,
which means:
1) Its energy loss (or gain) is exactly opposite than in the forward
case.
2) Its acceleration d/dt v(-t) is the same, which proves that following
this 'exactly reverse' trajectory is indeed a solution (after all
d^2/dt^2 x(-t) at time=-t, is equal to d^2/dt^2 x(t) at time=t,
so x(-t) exactly obeys Newton's law.)
the radiation loss from b to c
The point c is exactly a.
has to be added as additional energy-momentum
But it is a negative loss, i.e. a radiation gain, not a loss!
to make the time reversed case physically possible,
Aha! There we are. You *reject* the solution, even though t --> -t
exactly obeys Newton, and Maxwell, you *still* claim that it isn't
a solution (because your 'feelings' tell you so, perhaps?)
I cannot help you if you reject the laws of CED while claiming to
discuss CED. You may think it is not 'physically possible', but
you simply are wrong. Within CED this time reversed solution is
an exact and perfectly valid solution. (It will not often occur
in nature, of course. It requires a very special incoming wave
to get exactly this case.)
which wasn't in the original a -> b case.
Everything definitely *was* in the original case. If you just
reverse t --> -t, you're not throwing anything away.
The time reversibility of CED for continuous charges where all forces are long range EM makes sense to me for the reasons you've given above.
Even if the particle collides with some (non-electrical) object it
would still be valid, despite short-range forces during the collision.
No reason to exclude any forces, EM or otherwise.
CED as a theory only describes the EM forces anyway, so other forces
would just be a 'given' for the calculation, and in the reverse
situation they should be present as well (with -t substituted as
time dependence of course).
The bit I'm skeptical about is then imposing a rigidness on all the charges making up the system via short range local EM forces,
But whatever your 'rigidness' description is, you can always mirror
it in time. If the particle has some elastic deformation then that
also can be mirrored in time. Please note, however, that you cannot
describe a stable particle with only EM forces! It would either blow
up or collapse. I'm not even sure whether you can easily describe
stable matter with any combination of classical forces. (In QM, the
fact that there is Pauli-exclusion for fermions makes it much easier, classically you probably need some ad-hoc repulsive short-range force, perhaps becoming attractive at larger range.. But anyhow it's outside
the realm of CED.) <https://duckduckgo.com/?q=stability+of+classical+matter>
and claiming time reversibility still holds when emitted radiation is reversed back onto the rigid charge.
You would have to assume that the (ad hoc) repulsive force that you
add is time reversible, if not then of course the total system isn't.
(Also in QM it isn't, it's only TCP-invariant.)
When the rigid charge (RC) is accelerated by a constant E field, the short range EM forces (Poincare stresses) balance the internal field of the continuous charge and the effect of the external E, while radiating.
I don't think so. The charge would blow apart if there is nothing
else then EM Poincare stress, you need to add non-EM! (But we can
of course assume that there is such a force, whatever it is..)
Reversing this, we now have an additional reversed radiation field acting on the RC, causing the Poincare stresses having to change in magnitude compared to the non-reversed case. I therefore still remain unconvinced.
Pure EM forces won't give you stable particles, so you're right.
But combined with other (time-reversible, non-EM) forces you could
still have a time reversible solution! Whether you would really
get a stable solution is doubtful, but that has nothing to do
with acceleration. Even the static configuration of a stationary
particle is not stable with only EM forces, acc. to Earnshaw's
theorem. And the theorem does not say that with other (reasonable)
forces it *would* become stable!
(NB: if you include GR as part of CED, then a simple way out is
to define a extremal Kerr-Newton black hole as your particle..
But that solution is already quite, eh.. extreme.)
On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate
for the original loss, which wasn't there in the original model as
outgoing radiation. In this sense, classical EM *appears* to me to
be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed
case the charge as to respond in a manner that also self-consistently time-reverses the original specification of its motion.
If the forward case is easy (as you claim) the time-reversed case
is equally easy. t --> -t solves it all.
Jos Bergervoet <jos.bergervoet@xs4all.nl> wrote:
On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate
for the original loss, which wasn't there in the original model as
outgoing radiation. In this sense, classical EM *appears* to me to
be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed
case the charge as to respond in a manner that also self-consistently
time-reverses the original specification of its motion.
If the forward case is easy (as you claim) the time-reversed case
is equally easy. t --> -t solves it all.
It's been a while, but I wanted to come back to this, just to make it
clearer why - and on what grounds - I said the reversed case was
different.
If I want to generate an outgoing field, I can do this by waving a
charge around according to some specification. It may, as you say, be
hard to calculate what the exact resulting outgoing field is, but in principle it can be done. The generated field travels away, and that
is it.
Cancelling an incoming field by waving a charge is a different
problem; because *UNLESS PREARRANGED* the charge-waver cannot know
when when the incoming field will arrive, and will also not know what waveform it will take.
In this not-pre-arranged case, the charge-waver therefore will have to
detect the field as it arrives, infer on the basis of that necessarily partial information what the field is going to do next, and try to
wave their charge to achieve their goal of cancelling the whole field.
It will be impossible, on grounds of causality, to achieve perfect cancellation. As soon as the leading edge of the incoming field
arraives and is detected, it is too late for that part to be
cancelled; the cancellation process will always lag the arriving
field; and the cancellation will never be perfect (although it might
be good enough).
#Paul
On 1/27/2020 5:09 AM, p.kinsler@ic.ac.uk wrote:
Jos Bergervoet <jos.bergervoet@xs4all.nl> wrote:... > I'd say you pretty much have described the situation. What was the question? From the Jefimenko equations it is seen that all fields are
On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, ...
created by charges and currents (charges moving). In Jos' world of mathematics +t and -t are totally the same and interchangeable.
.. However
as you point out, in our meat universe causality creates problems
because unlike Jos the rest of us are not constantly getting messages
from the future.
However, the reverse time cancelling thing is so
appealing people try to take advantage of it by approximating knowing
the future as I've mentioned before. One way is to use delays to give
the impression you can know the future and the other way is simply to
use an educated guess
as to what sort of information you expect to be
coming from the future.
It does indeed sort of work and a certain amount
of success has been found with things like cancelling the modulations of atmospheric turbulence on laser beam transmissions.
Jos Bergervoet <jos.bergervoet@xs4all.nl> wrote:
On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate
for the original loss, which wasn't there in the original model as
outgoing radiation. In this sense, classical EM *appears* to me to
be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed
case the charge as to respond in a manner that also self-consistently time-reverses the original specification of its motion.
If the forward case is easy (as you claim) the time-reversed case
is equally easy. t --> -t solves it all.
It's been a while, but I wanted to come back to this, just to make it
clearer why - and on what grounds - I said the reversed case was
different.
If I want to generate an outgoing field, I can do this by waving a
charge around according to some specification. It may, as you say, be
hard to calculate what the exact resulting outgoing field is, but in principle it can be done. The generated field travels away, and that
is it.
Cancelling an incoming field by waving a charge is a different
problem; because *UNLESS PREARRANGED* the charge-waver cannot know
when when the incoming field will arrive, and will also not know what waveform it will take.
In this not-pre-arranged case, the charge-waver therefore will have to
detect the field as it arrives, infer on the basis of that necessarily partial information what the field is going to do next, and try to
wave their charge to achieve their goal of cancelling the whole field.
It will be impossible, on grounds of causality, to achieve perfect cancellation. As soon as the leading edge of the incoming field
arraives and is detected, it is too late for that part to be
cancelled; the cancellation process will always lag the arriving
field; and the cancellation will never be perfect (although it might
be good enough).
#Paul
Jos Bergervoet <jos.bergervoet@xs4all.nl> wrote:
On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate
for the original loss, which wasn't there in the original model as
outgoing radiation. In this sense, classical EM *appears* to me to
be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed
case the charge as to respond in a manner that also self-consistently
time-reverses the original specification of its motion.
If the forward case is easy (as you claim) the time-reversed case
is equally easy. t --> -t solves it all.
It's been a while, but I wanted to come back to this, just to make it
clearer why - and on what grounds - I said the reversed case was
different.
If I want to generate an outgoing field, I can do this by waving a
charge around according to some specification. It may, as you say, be
hard to calculate what the exact resulting outgoing field is, but in principle it can be done. The generated field travels away, and that
is it.
Cancelling an incoming field by waving a charge is a different
problem; because *UNLESS PREARRANGED* the charge-waver cannot know
when when the incoming field will arrive, and will also not know what waveform it will take.
In this not-pre-arranged case, the charge-waver therefore will have to
detect the field as it arrives, infer on the basis of that necessarily partial information what the field is going to do next, and try to
wave their charge to achieve their goal of cancelling the whole field.
It will be impossible, on grounds of causality, to achieve perfect cancellation.
As soon as the leading edge of the incoming field
arraives and is detected, it is too late for that part to be
cancelled;
the cancellation process will always lag the arriving
field; and the cancellation will never be perfect (although it might
be good enough).
On Monday, January 27, 2020 at 10:24:01 AM UTC, p.ki...@ic.ac.uk wrote:defined incoming reversed radiation that requires knowing how this will affect the energy-momentum of the charge exactly. At the very least we can say it will increase the "rest" energy-momentum, but then what?
Jos Bergervoet <jos.bergervoet@xs4all.nl> wrote:
On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate
for the original loss, which wasn't there in the original model as
outgoing radiation. In this sense, classical EM *appears* to me to
be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed
case the charge as to respond in a manner that also self-consistently
time-reverses the original specification of its motion.
If the forward case is easy (as you claim) the time-reversed case
is equally easy. t --> -t solves it all.
It's been a while, but I wanted to come back to this, just to make it
clearer why - and on what grounds - I said the reversed case was
different.
If I want to generate an outgoing field, I can do this by waving a
charge around according to some specification. It may, as you say, be
hard to calculate what the exact resulting outgoing field is, but in
principle it can be done. The generated field travels away, and that
is it.
Cancelling an incoming field by waving a charge is a different
problem; because *UNLESS PREARRANGED* the charge-waver cannot know
when when the incoming field will arrive, and will also not know what
waveform it will take.
In this not-pre-arranged case, the charge-waver therefore will have to
detect the field as it arrives, infer on the basis of that necessarily
partial information what the field is going to do next, and try to
wave their charge to achieve their goal of cancelling the whole field.
It will be impossible, on grounds of causality, to achieve perfect
cancellation. As soon as the leading edge of the incoming field
arraives and is detected, it is too late for that part to be
cancelled; the cancellation process will always lag the arriving
field; and the cancellation will never be perfect (although it might
be good enough).
#Paul
I think your previous point is far more relevant where you pointed out that in one picture you can arbitrarily define the trajectory of the charge and then assume an incoming field exists for this; whereas in the reversed case you now have a well
In classical EM, it looks to me that point charges requires a relativistic rigidness;
so I'd tend to go for the above increased "rest" energy-momentum being re-radiated in addition to the radiation from the charge being accelerated by the original applied field. Hence the charge wouldn't reverse its original trajectory IMO; whereas themainstream view is that it would and the two radiations exactly cancel.
On 20/01/27 8:32 PM, benj wrote:
On 1/27/2020 5:09 AM, p.kinsler@ic.ac.uk wrote:
Jos Bergervoet <jos.bergervoet@xs4all.nl> wrote:... > I'd say you pretty much have described the situation. What was the >> question? From the Jefimenko equations it is seen that all fields are
On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, ...
created by charges and currents (charges moving). In Jos' world of
mathematics +t and -t are totally the same and interchangeable.
Not the same, benj. +Infinity and -infinity are the same (and
you know that very well, it's the most right-hand point on the
Smith chart) but of course +t and -t are by no means the same,
althi=ough they are interchangeable.
.. However as you point out, in our meat universe causality creates
problems because unlike Jos the rest of us are not constantly getting
messages from the future.
Really? You never told me that! (But I knew you were going to
say it, of course..)
However, the reverse time cancelling thing is so appealing people
try to take advantage of it by approximating knowing the future as
I've mentioned before. One way is to use delays to give
Yes! Like the big delay lines after RF power amplifiers to allow
a bypass path to be faster and cancel the distortion before it
comes out.
the impression you can know the future and the other way is simply to
use an educated guess
benj you are over-educated, I'm afraid..
as to what sort of information you expect to be coming from the
future.
I always use the reverse mode of those transmission lines (Just
try it! See you at Mathew's meeting: http://youtu.be/pGnMiGrYmPE ).
It does indeed sort of work and a certain amount of success has been
found with things like cancelling the modulations of atmospheric
turbulence on laser beam transmissions.
Canceling incoming radiation can be done very accurately with only
slightly futuristic methods: <https://www.theverge.com/2019/8/20/20813054/vantablack-ultrablack-black-material-surrey-nanosystems-carbon-nanotubes-science-materials>
On 20/01/27 10:59 PM, john mcandrew wrote:defined incoming reversed radiation that requires knowing how this will affect the energy-momentum of the charge exactly. At the very least we can say it will increase the "rest" energy-momentum, but then what?
On Monday, January 27, 2020 at 10:24:01 AM UTC, p.ki...@ic.ac.uk wrote:
Jos Bergervoet <jos.bergervoet@xs4all.nl> wrote:
On 19/11/11 11:10 AM, p.kinsler@ic.ac.uk wrote:
John McAndrew <johnmcandrew66@gmail.com> wrote:
It turns out that the accelerated charge also radiates away
energy-momentum, so we have to add incoming radiation to compensate >>>>> for the original loss, which wasn't there in the original model as >>>>> outgoing radiation. In this sense, classical EM *appears* to me to >>>>> be time-asymmetric, and that's what I find interesting.
It seems to me you also need a model for the motion of the charge
under the influence of the EM fields (ie Lorentz force law plus
some kinematics). It's easy - in the outgoing (forward) case - to
specify "the charge accelerates like this"; but in the time reversed >>>> case the charge as to respond in a manner that also self-consistently >>>> time-reverses the original specification of its motion.
If the forward case is easy (as you claim) the time-reversed case
is equally easy. t --> -t solves it all.
It's been a while, but I wanted to come back to this, just to make it
clearer why - and on what grounds - I said the reversed case was
different.
If I want to generate an outgoing field, I can do this by waving a
charge around according to some specification. It may, as you say, be
hard to calculate what the exact resulting outgoing field is, but in
principle it can be done. The generated field travels away, and that
is it.
Cancelling an incoming field by waving a charge is a different
problem; because *UNLESS PREARRANGED* the charge-waver cannot know
when when the incoming field will arrive, and will also not know what
waveform it will take.
In this not-pre-arranged case, the charge-waver therefore will have to
detect the field as it arrives, infer on the basis of that necessarily
partial information what the field is going to do next, and try to
wave their charge to achieve their goal of cancelling the whole field.
It will be impossible, on grounds of causality, to achieve perfect
cancellation. As soon as the leading edge of the incoming field
arraives and is detected, it is too late for that part to be
cancelled; the cancellation process will always lag the arriving
field; and the cancellation will never be perfect (although it might
be good enough).
#Paul
I think your previous point is far more relevant where you pointed out that in one picture you can arbitrarily define the trajectory of the charge and then assume an incoming field exists for this; whereas in the reversed case you now have a well
the mainstream view is that it would and the two radiations exactly cancel.In classical EM, it looks to me that point charges requires a relativistic rigidness;
Yes, but can any consistent definition of this "rigidness" exist
for classical EM? I'd expect you run into inconsistencies if you
stick to special relativity (because of the accelerations involved),
and if you merge it with general relativity you can't have rigidness
in any meaningful way for at least some cases. (The singularities,
with the simple black hole collapse the most well-known).
so I'd tend to go for the above increased "rest" energy-momentum being re-radiated in addition to the radiation from the charge being accelerated by the original applied field. Hence the charge wouldn't reverse its original trajectory IMO; whereas
It seems to become philosophical if there is a choice of relativistic rigidness definition. (We can never find out experimentally what is the correct choice, since classical EM does not exist in our universe.)
--
Jos
Suppose a charge is accelerated by an external field, hence radiating irreversible energy-momentum given by the Lienard-Wiechert fields. We can time reverse this so that the radiation instead converges upon the charge causing it to "absorb" theradiation. If I'm not mistaken, this is physically interpreted as the incoming radiation converging to a singularity at the point charge, then propagating outwards again but phase reversed and now *exactly* cancelling the radiation emitted by the
Is this exact cancelling a consequence of the standard Maxwell's equations, or is it an additional postulate?
Thanks in advance,
JMcA
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