[alancalverd]

BC: I'm not sure how the uncertainty principle applies to E = mc2,

That's OK, lots of people don't.
http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html

And not a single mention of mass-energy equivalence. Though it is indeed an excellent discussion of indeterminacy and its implications for atomic structure.

[Bored chemist]

And not a single mention of mass-energy equivalence.

They probably expect you to work that out for yourself.
If E is uncertain, so is M.
How uncertain depends on the lifetime of the particle. For stable particles it's... not a big effect.

[alancalverd]

The E they are talking about is binding energy or kinetic energy, not the energy released when a mass is annihilated. For instance they quite reasonably calculate the binding energy of an electron in an atom as 9.4 eV, whilst we know the annihilation energy of a free electron is 511 keV

[Bored chemist]

These things often turn out to be remarkably general.
If that gamma is released from positronium  then I think you can calculate the effect of its lifetime(s) on the linewidth,
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/parlif.html

it's not a big effect.

[hamdani yusuf (OP)]

How do we know that?

It works.

What works? Assuming that momentum of electron is not an exact quantity?
Why assuming that it has exact quantity, but we can't measure precisely, doesn't work as well?

[hamdani yusuf (OP)]

Nothing to do with Planck or a closed system. ε+-ε- annihilation is a single event in which a fixed mass is converted into electromagnetic energy.

How do you count the number of electrons and positrons before and after the annihilation?

[hamdani yusuf (OP)]

I wonder how these experiments would be explained using particle models.

[alancalverd]

Nothing to do with Planck or a closed system. ε+-ε- annihilation is a single event in which a fixed mass is converted into electromagnetic energy.

How do you count the number of electrons and positrons before and after the annihilation?

We know the mass and charge of each species. We know the energy of the emitted photons. E = mc² and opposite charges annihilate.

It's clear that we can't capture all the emitted photons, but the simultaneous capture of two 511 keV photons at 180 degrees is excellent evidence that 2m_e has been annihilated, and the net charge of the patient remains stubbornly at zero.

[Bored chemist]

How do you count the number of electrons and positrons before and after the annihilation?
Re

Broadly the same way chemists count atoms.

[alancalverd]

I wonder how these experiments would be explained using particle models.

It would be foolish to try, which is why we use wave models for low energy electromagnetic radiation. Above about 100 keV the particle model is more useful, and in the diagnostic x-ray range (10 - 100 keV) you need to be aware of both models. Crystallographers, for instance, rely on the particle model to collect their data and the wave model to interpret their results.

[alancalverd]

How do you count the number of electrons and positrons before and after the annihilation?
Re

Broadly the same way chemists count atoms.

By weighing the patient? Neat trick, my friend!

[hamdani yusuf (OP)]

We know the mass and charge of each species. We know the energy of the emitted photons. E = mc2 and opposite charges annihilate.

I think you know how neutrino was discovered. How do you make sure that no neutrino is produced in the process?

[hamdani yusuf (OP)]

It's clear that we can't capture all the emitted photons, but the simultaneous capture of two 511 keV photons at 180 degrees is excellent evidence that 2me has been annihilated, and the net charge of the patient remains stubbornly at zero.

Are they always detected simultaneously in the opposite direction? Detector's efficiency is typically less than 100%. Some of the incoming energy are turned into heat. Do those detectors on opposite sides always fail and succeed concurrently? Is it possible for one detector to fail to capture the photon while its counterpart succeed?

[alancalverd]

As I said, we don't catch them all, but

(a) the frequent capture of two simultaneous 511 keV  photons at 180 degrees corresponds exactly with the theoretical prediction of pair annihilation
(b) it only happens (at least in a PET scanner) when a positron emitter is present 
(c) occasional absence of evidence (failed detector) is not evidence of absence (no positrons).

If you found your fingerprint on a sheet of glass, wouldn't you conclude that you had touched it? The fact that you had touched several other things and several other people had touched the glass, is irrelevant. In nuclear physics, finding the predicted particle at the predicted time and place is considered definitive.

[Bored chemist]

In nuclear physics, finding the predicted particle at the predicted time and place is considered definitive.

Strictly speaking, doing that once is just suggestive.
Once you get a few dozen events, the odds are pretty solid that you have a real effect.
Perhaps you can help us out here. Roughly how many events go into a typical PET scan image?

[alancalverd]

Around 10⁸ to 10⁹. I find that fairly convincing evidence that we are indeed looking at positronium annihilation!

 

[acsinuk]

511 keV is the energy of an electron not a photon.   E=mc^2       Electron mass= 9x10^-31 x 3x10^8 x3x10^8= 8.1x10-13 joules which is 511.68 keV.
Photons are massless spinning volumes of magnetic inertia and each unit contains the power = hf Cos ϴ.of energy per second.

[Bored chemist]

511 keV is the energy of an electron not a photon. 

Denial of reality is not a good symptom.

Photons are massless

Yes and no.
The photons Alan is talking about have a mass equal to that of an electron (or positron, if you like)

each unit contains the power = hf Cos ϴ.of energy per second.

That's gibberish.

[Bored chemist]

Around 10⁸ to 10⁹. I find that fairly convincing evidence that we are indeed looking at positronium annihilation!

 

Thanks
And roughly how many  PET scans are there in the world each day?
And how many have there been in total.
I think we are talking "beyond reasonable doubt" here.

[alancalverd]

Not sure about the world, but there is a practical limit because positron emitters tend to have very short halflives, so you need to have a neighborhood cyclotron radiopharmacy. And a hell of a lot of concrete. AFAIK there are about 80  PET scanners in the UK, say each one doing 6 scans per day for maybe the last 10 years....   So we have probably captured around 10¹⁹ annihilations to date in clinical applications.

Long before PET-CT imaging, we used the 1.02 MeV threshold for pair production to calibrate small linear accelerators, and photonuclear pair production and subsequent annihilation photons are part of the routine correction factors for all sorts of radiation dosimetry including radiotherapy.

I think the experimental facts are pretty well established.  And I can't explain them with a wave model.