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From: valls on 3 Jun 2010 09:46
The conversion of a pair positron-electron into photons (and vice
versa) is a common experimental fact of today Physics. If the
particles are considered initially at rest infinitely separated, the
final photons total energy results equal to the initial total rest
energy. Then, to where the initial electrostatic field energy goes
after the conversion?
From: eric gisse on 3 Jun 2010 12:46
valls(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. If the
> particles are considered initially at rest infinitely separated, the
> final photons total energy results equal to the initial total rest
> energy. Then, to where the initial electrostatic field energy goes
> after the conversion?

Photons don't have electro*static* fields.
From: valls on 3 Jun 2010 14:05
On 3 jun, 11:46, eric gisse <jowr.pi.nos...(a)gmail.com> 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. If the
> > particles are considered initially at rest infinitely separated, the
> > final photons total energy results equal to the initial total rest
> > energy. Then, to where the initial electrostatic field energy goes
> > after the conversion?
>
> Photons don't have electro*static* fields.
You are very right, photons don't have electrostatic fields (neither
rest mass). But that doesn't answer the question at all. The
experimental fact is that entities with rest mass and electrostatic
fields convert into ones not having both. When making the energy
balance in the conversion, with only the energy of the rest mass we
obtain the total energy of the photons. I repeat my question:what
occurs then with the electrostatic field energy of the positron-
electron pair? If somebody says that the energy of the electrostatic
field is tranformed in the energy of the photons, then the question
must be changed to [what occurs then with the rest energy of the
positron-electron pair?]. It seems here ocurring a violation of the
Conservation Principle of Energy. I take for granted that must exist
in this group some person that can offer and adequate answer.

RVHG (Rafael Valls Hidalgo-Gato)
From: Tom Roberts on 3 Jun 2010 18:34
valls(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).


Tom Roberts
From: eric gisse on 3 Jun 2010 20:25
valls(a)icmf.inf.cu wrote:

> On 3 jun, 11:46, eric gisse <jowr.pi.nos...(a)gmail.com> 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. If the
>> > particles are considered initially at rest infinitely separated, the
>> > final photons total energy results equal to the initial total rest
>> > energy. Then, to where the initial electrostatic field energy goes
>> > after the conversion?
>>
>> Photons don't have electro*static* fields.
> You are very right, photons don't have electrostatic fields (neither
> rest mass). But that doesn't answer the question at all. The
> experimental fact is that entities with rest mass and electrostatic
> fields convert into ones not having both. When making the energy
> balance in the conversion, with only the energy of the rest mass we
> obtain the total energy of the photons. I repeat my question:what
> occurs then with the electrostatic field energy of the positron-
> electron pair?

Huh, that was a spectacular display of 'not reading for comprehension' on my
part.

My guess based on classical E&M would be 'poof' because when the two charges
come together there is no more charge to maintain the field.

>If somebody says that the energy of the electrostatic
> field is tranformed in the energy of the photons, then the question
> must be changed to [what occurs then with the rest energy of the
> positron-electron pair?]. It seems here ocurring a violation of the
> Conservation Principle of Energy. I take for granted that must exist
> in this group some person that can offer and adequate answer.
>
> RVHG (Rafael Valls Hidalgo-Gato)

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