Forgotten energy in interactions of particles with opposite charge.

[martillo]

Two particles of opposite charge attract themselves. It is necessary energy to separate them apart. This is something that appear to not be considered in fundamental well known particles interactions like the free neutron beta decay and in the positron-electron pair creation. In the energies' balances are only considered the rest energies of the particles and not the energy between the two particles separated apart. I think this energy is not negligible at all, on the contrary, at subatomic scale the particles can be very close and the electric potential energy between them could be very high. I don't understand why this subject does not appear in any energy balance of experimental particles' interactions anywhere.

From Wikipedia for instance:

1) Free neutron decay (https://en.wikipedia.org/wiki/Free_neutron_decay) :

"For the free neutron, the decay energy for this process (based on the rest masses of the neutron, proton and electron) is 0.782343 MeV. That is the difference between the rest mass of the neutron and the sum of the rest masses of the products."

2) Pair production (https://en.wikipedia.org/wiki/Pair_production) :

"As energy must be conserved, for pair production to occur, the incoming energy of the photon must be above a threshold of at least the total rest mass energy of the two particles created."

Edited October 11, 2023 by martillo

[martillo]

The electric potential energy of the electron-positron pair vary from zero at an infinite distance increasing as they get closer but even at distance about their wavelength the energy would be negligible. I have made the calculation and at such distance the energy is only about one in a thousand of their individual rest energies.

The problem is for instance in the pair production from a gamma ray photon. If a photon is considered a point-like particle how it can produce a pair of electron and positron well separated enough. If they are too close the electric energy between them would be too big. I'm thinking now that actually the process of conversion photon-pair is actually something unknown, is that right? 

Edited October 11, 2023 by martillo

[exchemist]

1 hour ago, martillo said:

The electric potential energy of the electron-positron pair vary from zero at an infinite distance increasing as they get closer but even at distance about their wavelength the energy would be negligible. I have made the calculation and at such distance the energy is only about one in a thousand of their individual rest energies.

The problem is for instance in the pair production from a gamma ray photon. If a photon is considered a point-like particle how it can produce a pair of electron and positron well separated enough. If they are too close the electric energy between them would be too big. I'm thinking now that actually the process of conversion photon-pair is actually something unknown, is that right? 

The photon isn't a pointlike particle.  

[martillo]

2 hours ago, exchemist said:

The photon isn't a pointlike particle.  

What is a photon then? Does it have spatial dimensions? If it has no spatial dimension it is well called "point-like particle".

Edited October 11, 2023 by martillo

[exchemist]

1 hour ago, martillo said:

What is a photon then? Does it have spatial dimensions? If it has no spatial dimension it is well called "point-like particle".

No. It is a quantum mechanical, wave particle entity, so it has some particle-like properties under some conditions and some wavelike properties under other conditions. You must know this, surely?

[martillo]

1 hour ago, exchemist said:

No. It is a quantum mechanical, wave particle entity, so it has some particle-like properties under some conditions and some wavelike properties under other conditions. You must know this, surely?

Of course I know about the called "wave-particle duality". I'm considering the particle-like behavior now. If you know the process of conversion of a photon to a pair of electron and positron integrating some concept of waves please explain. I'm focusing in the electric energy involved in that process. If in the process the electron and the positron get too close then a too big electric energy would be involved.

Edited October 11, 2023 by martillo

[Bufofrog]

12 hours ago, martillo said:

In the energies' balances are only considered the rest energies of the particles and not the energy between the two particles separated apart.

I'm not sure what the issue is.  There is a minimum amount of energy needed for pair production.  At the minimum energy needed the pair will form and immediately annihilate each other.  If the energy is a bit higher than the minimum then the particle pair will have some KE and will move apart before attracting each other and annihilating each other.  If the energy is very high the pair will have enough KE that they never recombine.

[martillo]

47 minutes ago, Bufofrog said:

I'm not sure what the issue is.  There is a minimum amount of energy needed for pair production.  At the minimum energy needed the pair will form and immediately annihilate each other.  If the energy is a bit higher than the minimum then the particle pair will have some KE and will move apart before attracting each other and annihilating each other.  If the energy is very high the pair will have enough KE that they never recombine.

The three particles, the photon, the electron and the positron are currently modeled as point-like particles. The problem arises at considering how, from the one single point of the photon, the other two points fo the electron and the positron surge. If they appear existing in a too close distance the energy needed to separate them apart is too high. Remember that the electric potential energy is inversely proportional to the distance between the pair: kq₁q₂/r = (ke²)/r. A too high energetic photon would be needed to produce the pair in that case. The problem is how two points with opposite charge appear into existence at some proper distance from a single neutral point. At zero distance the separation energy would be infinite. Other subject would be how the charges are created but this is another topic.

Edited October 11, 2023 by martillo

[exchemist]

1 hour ago, martillo said:

Of course I know about the called "wave-particle duality". I'm considering the particle-like behavior now. If you know the process of conversion of a photon to a pair of electron and positron integrating some concept of waves please explain. I'm focusing in the electric energy involved in that process. If in the process the electron and the positron get too close then a too big electric energy would be involved.

You are not at liberty to decide for yourself that these entities behave as point particles during the interaction in question. If such an assumption leads to wrong outcomes then the assumption must be wrong, must it not?

I am not a physicist but I know from quantum chemistry that the interaction between electrons in an atom and photons is not modelled in terms of point particles. 

[martillo]

11 minutes ago, exchemist said:

You are not at liberty to decide for yourself that these entities behave as point particles during the interaction in question. If such an assumption leads to wrong outcomes then the assumption must be wrong, must it not?

Right.

11 minutes ago, exchemist said:

I am not a physicist but I know from quantum chemistry that the interaction between electrons in an atom and photons is not modelled in terms of point particles. 

How they are modeled? Please explain. Not point-like particles lead us to think in particles with possible structures (spatial dimensions, shape, etc.) even for the elementary particles like the photon and the electron.

Edited October 11, 2023 by martillo

[Bufofrog]

11 minutes ago, martillo said:

How they are modeled? Please explain. Not point-like particles lead us to think in particles with possible structures (spatial dimensions, shape, etc.) even for the elementary particles like the photon and the electron.

If an electron and a photon were just 2 points the chances of them 'hitting' each other would be essentially zero.  So clearly the picture in your head of this interaction is incorrect.  

[martillo]

1 minute ago, Bufofrog said:

If an electron and a photon were just 2 points the chances of them 'hitting' each other would be essentially zero.  So clearly the picture in your head of this interaction is incorrect.  

Which is the right picture then? Please explain.

[swansont]

42 minutes ago, martillo said:

If they appear existing in a too close distance the energy needed to separate them apart is too high. Remember that the electric potential energy is inversely proportional to the distance between the pair: kq₁q₂/r = (ke²)/r. A too high energetic photon would be needed to produce the pair in that case. The problem is how two points with opposite charge appear into existence at some proper distance from a single neutral point. At zero distance the separation energy would be infinite. Other subject would be how the charges are created but this is another topic.

The obvious answer is thst they aren’t created at zero distance. Are you familiar with the Heisenberg Uncertainty Principle?

13 hours ago, martillo said:

I think this energy is not negligible at all, on the contrary, at subatomic scale the particles can be very close and the electric potential energy between them could be very high

What you think is far less important than what you can show. I haven’t seen any calculations.

[martillo]

1 minute ago, swansont said:

The obvious answer is thst they aren’t created at zero distance. Are you familiar with the Heisenberg Uncertainty Principle?

I agree they are not created at zero distance and of course I know about Heisenberg uncertainty. I agree in that I don't know how the principle could apply in the determination of the distance and how it can be related to the energy involved to separate them apart. I never saw this subject be treated anywhere. Can you explain that or do you have some reading to suggest?

54 minutes ago, swansont said:

What you think is far less important than what you can show. I haven’t seen any calculations.

The calculation I made is that as the electric potential energy of the pair electron-positron is kq₁q₂/r = (ke²)/r and the energy tends to infinite as the distance tends to zero.

[exchemist]

1 hour ago, martillo said:

Right.

How they are modeled? Please explain. Not point-like particles lead us to think in particles with possible structures (spatial dimensions, shape, etc.) even for the elementary particles like the photon and the electron.

Not at all. It leads us to think in terms of fields and waves.  

But another thing you need to bear in mind is that pair production in general does not lead to a pair that separates. They would be bound together by their mutual electrostatic attraction, cf. positronium: https://en.wikipedia.org/wiki/Positronium

 

 

   

[martillo]

5 minutes ago, exchemist said:

But another thing you need to bear in mind is that pair production in general does not lead to a pair that separates. They would be bound together by their mutual electrostatic attraction, cf. positronium: https://en.wikipedia.org/wiki/Positronium

Production of pairs separating apart have been observed in cloud chambers. See photos below:

 

[exchemist]

9 minutes ago, martillo said:

Production of pairs separating apart have been observed in cloud chambers. See photos below:

 

OK in that case they must have enough extra energy to ionise positronium, then. 

[swansont]

1 hour ago, martillo said:

I agree they are not created at zero distance and of course I know about Heisenberg uncertainty. I agree in that I don't know how the principle could apply in the determination of the distance and how it can be related to the energy involved to separate them apart. I never saw this subject be treated anywhere. Can you explain that or do you have some reading to suggest?

The calculation I made is that as the electric potential energy of the pair electron-positron is kq₁q₂/r = (ke²)/r and the energy tends to infinite as the distance tends to zero.

Do you see the connection between these two statements?

If you can’t determine the distance between the particles, as their location is uncertain, then you can’t make precise claims about the energy. If you can estimate the separation, then you can calculate the potential energy, and see if it’s a problem.

You also have to consider that pair production happens near a nucleus, which has a charge, and that will exert a force on the created charged particles, in opposite directions, which would separate them.

And you haven’t done a calculation that you’ve shared with us.

43 minutes ago, martillo said:

Production of pairs separating apart have been observed in cloud chambers. See photos below:

Because there is a magnetic field present, and the are moving. If you know the strength if the field - in this example it’s 1 T - you can determine their kinetic energy (or the speed), from the radius of curvature.

[martillo]

33 minutes ago, swansont said:

If you can’t determine the distance between the particles, as their location is uncertain, then you can’t make precise claims about the energy. If you can estimate the separation, then you can calculate the potential energy, and see if it’s a problem.

I agree, the only consideration I can make is that the electric potential energy is a constraint in the minimum separation distance at which the pair is created as the energy tends to infinite as the distance tends to zero. At least we agreed in that the pair of charged particles must be created at some distance apart. I just will stay wondering how that can happen starting from a single and neutral photon particle (interacting with an atom, I know).

Edited October 11, 2023 by martillo

[swansont]

24 minutes ago, martillo said:

I agree, the only consideration I can make is that the electric potential energy is a constraint in the minimum separation distance at which the pair is created as the energy tends to infinite as the distance tends to zero. At least we agreed in that the pair of charged particles must be created at some distance apart. I just will stay wondering how that can happen starting from a single and neutral photon particle (interacting with an atom, I know).

The photon is not localized to a point. It has a wavelength.

[martillo]

34 minutes ago, swansont said:

The photon is not localized to a point. It has a wavelength.

Do you mean the photon has size and it would be about its wavelength? The electron and positron also have wavelengths. Would they also have a size about their wavelength? I think that is not currently sustained. If so they would have spatial dimensions, shape, I mean a structure. As far as I know is sustained they are all particles with no dimensions with an associated wave, the De Broglie wave.

Edited October 11, 2023 by martillo

[exchemist]

15 minutes ago, martillo said:

Do you mean the photon has size and it would be about its wavelength? The electron and positron also have wavelengths. Would they also have a size about their wavelength? I think that is not currently sustained. If so they would have spatial dimensions, shape, I mean a structure. As far as I know is sustained they are all particles with no dimensions with an associated wave, the De Broglie wave.

No, it would not follow they have structure. It just means they are fuzzy round the edges, like any quantum entity (uncertainty principle, again). There is no defined "size", just a matter of decreasing probability of interaction, the further from the classical path you get. (Look up "cross section").

The idea of these entities being pointlike particles with "an associated wave" is unhelpful. They are what they are and exhibit both wavelike and pointlike attributes according to circumstances. You need to think in terms of probabilities, not classical exact values.  (For some purposes it can be easier to think of them as waves, which "collapse" to a point only when they interact - but that too can be misleading.)

As Feynman said: "I'm naht gonna fake it, I'm naht gonna tell ya it's like a ball bearing on a spring, when it isn't." 

 

 

[martillo]

1 hour ago, exchemist said:

It just means they are fuzzy round the edges, like any quantum entity (uncertainty principle, again). There is no defined "size", just a matter of decreasing probability of interaction,

Got it. I think this is what @swansont tried to express.

1 hour ago, exchemist said:

They are what they are and exhibit both wavelike and pointlike attributes according to circumstances.

About this and the Feynman video I find them the same as to say "The things are as what we observe and say. Don't ask more questions about.". I'm sorry but I still will continue looking for a more precise better explanation.

Sometimes we arrive at two possible roads. There could be a third way although may be cross country...

Edited October 11, 2023 by martillo

[exchemist]

30 minutes ago, martillo said:

Got it. I think this is what @swansont tried to express.

About this and the Feynman video I find them the same as to say "The things are as what we observe and say. Don't ask more questions about.". I'm sorry but I still will continue looking for a more precise better explanation...

Questions are fine. Nobody says don't ask questions, least of all Feynman. What he is saying is just don't expect nature to behave like classical mechanics, or to be easy to comprehend. Feynman's joke about going "somewhere else, where the rules are simpler, more aesthetically pleasing, more psychologically easy" (my emphasis) contains an important point. Nobody who has studied QM finds it easy to picture. The maths works, but the physical picture it conjures up is murky. At some level one has to accept that struggling to make a consistent physical picture of what is going on is not really possible.

Anyway, to your original question, these entities are fuzzy so trying to apply classical electrostatics, when you can't define the distance of separation, is bound to have limitations.   

[martillo]

9 minutes ago, exchemist said:

Anyway, to your original question, these entities are fuzzy so trying to apply classical electrostatics, when you can't define the distance of separation, is bound to have limitations.

I agree, the classical formula would work at subatomic scale although seems in a "fuzzy" way...

Edited October 11, 2023 by martillo