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From: Edward Green on 3 Jun 2010 21:03
On Jun 3, 6:34 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
> va...(a)icmf.inf.cu wrote:
> > The conversion of a pair positron-electron into photons (and vice
> > versa) is a common experimental fact of today Physics.
>
> Yes.
>
> > If the
> > particles are considered initially at rest infinitely separated, the
> > final photons total energy results equal to the initial total rest
> > energy.
>
> No. And this error is why you are confused about overall energy conservation.
>
> If the particles are initially at rest with ZERO separation, the final gammas'
> total energy is equal to the initial total rest energy (= 2 m_e c^2, the total
> rest mass). Of course for this situation the external electrostatic field is
> zero, and the question you ask does not apply.
>
> The situation you described is VERY complicated -- the electron and positron
> will accelerate toward each other, radiating as they go (remember they initially
> have a very large potential energy, represented by the energy in the
> electrostatic field). They will meet with non-zero kinetic energy, making it
> unlikely they will annihilate, so they'll pass each other and be re-accelerated
> back toward each other, radiating more energy away. This will continue until
> they have radiated essentially all of their kinetic energy away, and then they
> will annihilate, essentially at rest. Thus the initial energy in the
> electrostatic field is converted to energy in the radiation (not counting the
> annihilation gammas, which again have a total energy equal to the total rest
> mass of the pair).
>
> That is the most likely scenario. It is rare but possible for them to annihilate
> at higher energy (e.g. as in the e+ e- colliders). Then the reaction products
> are usually more than just a pair of gammas, and the total energy of the
> reaction products equals the total energy of the pair (which is necessarily more
> than their rest masses). In this case the initial energy in the electrostatic
> field is converted to energy in the radiation and the reaction products.
>
>         This classical description is inaccurate in several details; one
>         really needs a quantum description.
>
> We know the above description is reasonably accurate, because when a few MeV
> positron beam hits a material object (full of electrons), the vast majority of
> the annihilation gammas are emitted with energies very close to 511 keV, and are
> accompanied by lots of bremsstrahlung radiation, which is broad-band and much
> lower energy. There are occasional higher-energy gammas, interpreted as
> annihilation at higher energy. The 511 keV peak is very prominent (IIRC ~99% of
> all annihilations emit two gammas).

Very interesting. ITIT that the "theory" that the energy of an
electron is totally equivalent to the energy of its field is dead in
the water, since 511 keV is apparently what you get by annihilation of
a particle whose electrostatic field has already been nulled out by
its anti-particle. There is a residual energy which seems to be
associated with the death of the structural core of the electron (and
of course another equal one for the positron), after the external
field has given up its energy to bremsstrahlung (I'll pretty much copy
that word in context to give the illusion I know what it is ;-).
From: valls on 9 Jun 2010 17:24
On 3 jun, 17:34, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
> va...(a)icmf.inf.cu wrote:
> > The conversion of a pair positron-electron into photons (and vice
> > versa) is a common experimental fact of today Physics.
>
> Yes.
>
> > If the
> > particles are considered initially at rest infinitely separated, the
> > final photons total energy results equal to the initial total rest
> > energy.
>
> No. And this error is why you are confused about overall energy conservation.
>
> If the particles are initially at rest with ZERO separation, the final gammas'
> total energy is equal to the initial total rest energy (= 2 m_e c^2, the total
> rest mass). Of course for this situation the external electrostatic field is
> zero, and the question you ask does not apply.
>
> The situation you described is VERY complicated -- the electron and positron
> will accelerate toward each other, radiating as they go (remember they initially
> have a very large potential energy, represented by the energy in the
> electrostatic field). They will meet with non-zero kinetic energy, making it
> unlikely they will annihilate, so they'll pass each other and be re-accelerated
> back toward each other, radiating more energy away. This will continue until
> they have radiated essentially all of their kinetic energy away, and then they
> will annihilate, essentially at rest. Thus the initial energy in the
> electrostatic field is converted to energy in the radiation (not counting the
> annihilation gammas, which again have a total energy equal to the total rest
> mass of the pair).
>
> That is the most likely scenario. It is rare but possible for them to annihilate
> at higher energy (e.g. as in the e+ e- colliders). Then the reaction products
> are usually more than just a pair of gammas, and the total energy of the
> reaction products equals the total energy of the pair (which is necessarily more
> than their rest masses). In this case the initial energy in the electrostatic
> field is converted to energy in the radiation and the reaction products.
>
>         This classical description is inaccurate in several details; one
>         really needs a quantum description.
>
> We know the above description is reasonably accurate, because when a few MeV
> positron beam hits a material object (full of electrons), the vast majority of
> the annihilation gammas are emitted with energies very close to 511 keV, and are
> accompanied by lots of bremsstrahlung radiation, which is broad-band and much
> lower energy. There are occasional higher-energy gammas, interpreted as
> annihilation at higher energy. The 511 keV peak is very prominent (IIRC ~99% of
> all annihilations emit two gammas).
>
First of all, thanks a lot for your very detailed answer. I remain
with some doubts.
The case I present is supposed to be the one with the highest possible
initial potential energy (kinetic energy zero and infinite distance
between the particles). You refer the potential energy as “very
large”. It is clear that with the two particles at rest, the potential
energy will increase if we increase the distance between them. How
great can be this potential energy? It tends to infinite when the
distance tends to infinite? Or it will tend to some finite maximal
value? As the attraction force tends to zero when the distance tends
to infinite, it seems to me logical the existence of a maximal finite
limit for the potential energy. But then this maximal value must be a
characteristic constant of the particles. Do you know what is that
value for the positron-electron pair that we are addressing? Almost
sure must be some relationship with the well-know 511keV value. What
do you think about?

> Tom Roberts

RVHG (Rafael Valls Hidalgo-Gato)
From: Sue... on 9 Jun 2010 20:41
On Jun 3, 9:03 pm, Edward Green <spamspamsp...(a)netzero.com> wrote:
> On Jun 3, 6:34 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
>
>
>
> > va...(a)icmf.inf.cu wrote:
> > > The conversion of a pair positron-electron into photons (and vice
> > > versa) is a common experimental fact of today Physics.
>
> > Yes.
>
> > > If the
> > > particles are considered initially at rest infinitely separated, the
> > > final photons total energy results equal to the initial total rest
> > > energy.
>
> > No. And this error is why you are confused about overall energy conservation.
>
> > If the particles are initially at rest with ZERO separation, the final gammas'
> > total energy is equal to the initial total rest energy (= 2 m_e c^2, the total
> > rest mass). Of course for this situation the external electrostatic field is
> > zero, and the question you ask does not apply.
>
> > The situation you described is VERY complicated -- the electron and positron
> > will accelerate toward each other, radiating as they go (remember they initially
> > have a very large potential energy, represented by the energy in the
> > electrostatic field). They will meet with non-zero kinetic energy, making it
> > unlikely they will annihilate, so they'll pass each other and be re-accelerated
> > back toward each other, radiating more energy away. This will continue until
> > they have radiated essentially all of their kinetic energy away, and then they
> > will annihilate, essentially at rest. Thus the initial energy in the
> > electrostatic field is converted to energy in the radiation (not counting the
> > annihilation gammas, which again have a total energy equal to the total rest
> > mass of the pair).
>
> > That is the most likely scenario. It is rare but possible for them to annihilate
> > at higher energy (e.g. as in the e+ e- colliders). Then the reaction products
> > are usually more than just a pair of gammas, and the total energy of the
> > reaction products equals the total energy of the pair (which is necessarily more
> > than their rest masses). In this case the initial energy in the electrostatic
> > field is converted to energy in the radiation and the reaction products..
>
> >         This classical description is inaccurate in several details; one
> >         really needs a quantum description.
>
> > We know the above description is reasonably accurate, because when a few MeV
> > positron beam hits a material object (full of electrons), the vast majority of
> > the annihilation gammas are emitted with energies very close to 511 keV, and are
> > accompanied by lots of bremsstrahlung radiation, which is broad-band and much
> > lower energy. There are occasional higher-energy gammas, interpreted as
> > annihilation at higher energy. The 511 keV peak is very prominent (IIRC ~99% of
> > all annihilations emit two gammas).
>
> Very interesting. ITIT that the "theory" that the energy of an
> electron is totally equivalent to the energy of its field is dead in
> the water, since 511 keV is apparently what you get by annihilation of
> a particle whose electrostatic field has already been nulled out by
> its anti-particle.

<<an electron and a positron, each with a mass of
0.511 MeV/c2, can annihilate to yield 1.022 MeV of energy.>>
http://en.wikipedia.org/wiki/Electronvolt#As_a_unit_of_energy

eliza... :-))


> There is a residual energy which seems to be
> associated with the death of the structural core of the electron (and
> of course another equal one for the positron), after the external
> field has given up its energy to bremsstrahlung (I'll pretty much copy
> that word in context to give the illusion I know what it is ;-).

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