Virtual photons as force carriers

[ergo]

TL;DR Summary

Multiple questions about virtual photons as force carriers, including how many are created per unit time with what frequencies.

(My multipart question is from a very naive perspective, so sorry if it is rife with misunderstandings. Please answer conceptually, with as few & as simple equations as possible. I think that all of the answers to these questions should be understandable to a high schooler, though maybe the derivations of some of the answers would be too complex for them.)

From what I’ve heard, virtual photons are the force carriers for both electrostatic & magnetostatic fields.

A) Are virtual photons actually emitted from a charged particle? Or are they just a convenient modeling of the interaction between two charged particles, but they don’t actually propagate from one particle to another?

B) If virtual photons are actually emitted:

1) what are their frequencies? Does a target charged particle get hit by a variety of virtual photon frequencies, all of the frequencies being low enough to survive long enough to travel from the source the target within the Heisenberg uncertainty time limit?

2) how many of them are emitted per unit time (and of which wavelengths, if multiple wavelengths emitted)?

3) could they be prevented from propagating their force by some interposed object that absorbs, reflects, scatters, or otherwise impedes non-virtual photons of the same frequency?

4) are they emitted in all directions, or are they somehow only emitted towards other charged particles?

I) If the former, what is the 2-dimensional density of emitted virtual photons at various distances?

II) If the former, how do magnets only react to virtual photons from a magnetic field, and how do charged bodies only react to virtual photons from an electric field? Is this related to spin?

III) If the latter, how do the charged particles detect each other?

C) If virtual photons are not really emitted, but are rather just a misleading conceptualization of the effects of electric & magnetic fields, then how is electromagnetic force actually transmitted?

D) Do virtual photons between two oppositely charged bodies provide an attractive force by somehow having negative momentum, or is there some other mechanism at work / some other way of conceptualizing attractive forces? Is this related to spin?

 

[Nugatory]

A) Are virtual photons actually emitted from a charged particle?

No

Or are they just a convenient modeling of the interaction between two charged particles, but they don’t actually propagate from one particle to another?

yes (to the very limited extent that this can be explained using natural language instead of math).

C) If virtual photons are not really emitted, but are rather just a misleading conceptualization of the effects of electric & magnetic fields, then how is electromagnetic force actually transmitted?

Try this link: https://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html and also our Insights articles on virtual particles.

 

[PeroK]

A) Are virtual photons actually emitted from a charged particle? Or are they just a convenient modeling of the interaction between two charged particles, but they don’t actually propagate from one particle to another?

The latter. Virtual means not real in this case.

C) If virtual photons are not really emitted, but are rather just a conceptualization of the effects of electric & magnetic fields, then how is electromagnetic force actually transmitted?

There is no "how" other than the mathematical model, which can be described diagrammatically as an exchange of virtual photons.

Note that I deleted the word "misleading" from your question.

D) Do virtual photons between two oppositely charged bodies provide an attractive force by somehow having negative momentum ...

Not negative momentum. It comes out in the calculations that opposite charges effectively attract and like charges effectively repel.

 

[ergo]

Noyes (to the very limited extent that this can be explained using natural language instead of math).
Try this link: https://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html and also our Insights articles on virtual particles.

Thanks for info & link. How frequently are the virtual photons exchanged? If they were exchanged twice as frequently, then the electrostatic force should be twice as much, right? Unless there’s a specific reason for the frequency of exchange, could this be evidence for the quantization of time, with the exchanges occurring every quantum?

If virtual photons are exchanged between electrostatics and between magnetostatics, why aren’t any effects seen form an electrostatic exchanging virtual photons with a magnetostatic? Are they not exchanged, or are they exchanged but net effects average out to zero?

Why is the momentum distribution of the virtual photons what it is? Why is it so different from that of normal photons? Don’t normal photons never impart an attractive force?

 

[ergo]

The latter. Virtual means not real in this case.

There is no "how" other than the mathematical model, which can be described diagrammatically as an exchange of virtual photons.

Note that I deleted the word "misleading" from your question.

Not negative momentum. It comes out in the calculations that opposite charges effectively attract and like charges effectively repel.

Thanks for the info. Please see my response to the other answer for follow up questions.

 

[PeroK]

Thanks for the info. Please see my response to the other answer for follow up questions.

I think you have an unhelpful picture of virtual photons. Let me describe a scenario.

We fire two beams of electrons at each other and watch them scatter. In classical EM there is Coulomb's law and everything is all very nice and simple. Look up Rutherford scattering. Although, that may usually describe electron-proton scattering classically it all works the same.

In QED, which is the quantum upgrade of classical EM things are not at all nice and simple. First, QED is probabilistic. What you calculate ultimately is the probability that one electron is scattered at a certain angle. And that calculation involves an infinite series of difficult integrals. Basically, you do as many integrals as you are capable of and stop there with the best approximation. Thankfully, even doing just the first integral gives a good approximation.

Richard Feynman, however, found a way to represent each integral as a Feynnan diagram. The first integral is represented by the exchange of a single virtual photon ( of all possible momenta) - so there is still integration to be done.

Subsequent integrals are represented by the exchange of more and more virtual photons.

For each scattering interaction - electron-electron, electron-positron, electron-muon and, with a struggle, electron-proton - QED throws up a different series of integrals requiring a different set of Feynman diagrams and different resulting probabilities.

At low energy, of course, Coulomb's law approximates QED. But, at high energy QED makes different predictions. And, in actual experiments, QED proves the right calculation.

All the questions you ask of virtual photons are, I'm sorry to say, misguided and not part of the theory of QED.

 

[PeroK]

And, if a high-school student cannot understand that then blame mother nature and not me!

 

[hutchphd]

Thanks for info & link. How frequently are the virtual photons exchanged? If they were exchanged twice as frequently, then the electrostatic force should be twice as much, right? Unless there’s a specific reason for the frequency of exchange, could this be evidence for the quantization of time, with the exchanges occurring every quantum?

The interaction, as with most things quantum mechanical, is described by a probability amplitude. There is no frequency associated in the way you think.

If virtual photons are exchanged between electrostatics and between magnetostatics, why aren’t any effects seen form an electrostatic exchanging virtual photons with a magnetostatic? Are they not exchanged, or are they exchanged but net effects average out to zero?

All photons are electromagnetic. The separation into magnetic and electric fields is useful for us atlarge scale.

Why is the momentum distribution of the virtual photons what it is? Why is it so different from that of normal photons? Don’t normal photons never impart an attractive force?

To what distribution do you refer?
I second @PeroK admonition. As already discussed, these virtual photons are largely intermediate calculational devices. And "actual" photons are not at all as depicted by popular literature.
Unfortunately you need to understand Quantum Fields to meaningfully discuss these questions.

 

[ergo]

I think you have an unhelpful picture of virtual photons. Let me describe a scenario.

We fire two beams of electrons at each other and watch them scatter. In classical EM there is Coulomb's law and everything is all very nice and simple. Look up Rutherford scattering. Although, that may usually describe electron-proton scattering classically it all works the same.

In QED, which is the quantum upgrade of classical EM things are not at all nice and simple. First, QED is probabilistic. What you calculate ultimately is the probability that one electron is scattered at a certain angle. And that calculation involves an infinite series of difficult integrals. Basically, you do as many integrals as you are capable of and stop there with the best approximation. Thankfully, even doing just the first integral gives a good approximation.

Richard Feynman, however, found a way to represent each integral as a Feynnan diagram. The first integral is represented by the exchange of a single virtual photon ( of all possible momenta) - so there is still integration to be done.

Subsequent integrals are represented by the exchange of more and more virtual photons.

For each scattering interaction - electron-electron, electron-positron, electron-muon and, with a struggle, electron-proton - QED throws up a different series of integrals requiring a different set of Feynman diagrams and different resulting probabilities.

At low energy, of course, Coulomb's law approximates QED. But, at high energy QED makes different predictions. And, in actual experiments, QED proves the right calculation.

All the questions you ask of virtual photons are, I'm sorry to say, misguided and not part of the theory of QED.

Thanks again for the info. If you have more time, I’d really like to try to ask more questions that will help clarify things for me.

When a virtual photon is exchanged and its effects are calculated, is it always calculated for a specific instant, or is it used to summarize the effects of the electrostatic field over a non-instantaneous period of time that you integrate over?

A virtual photon has a frequency, right? If so, what gives rise to the frequency of a virtual photon that is exchanged to transmit the electrostatic force?

e.g., I understand that when an electron in an excited state in an atom drops to a lower state, a photon is emitted with frequency E/h, where E is the energy difference between the 2 states.

But I don’t know the cause for the frequency of a virtual photon.

 

[ergo]

The interaction, as with most things quantum mechanical, is described by a probability amplitude. There is no frequency associated in the way you think.

Thanks for the info. I think we are somehow accidentally taking past each other. The issue that I was trying to understand with my question about frequency of virtual photon exchange is that the electrostatic force is something that doesn’t just happen once (unlike an excited electron emitting a photon when it fails to a lower energy state). At least classically, the electrostatic force is continuously applied.

But a virtual photon exchange is a single interaction. If the virtual photon exchange summarizes the effects of the electrostatic force over a chosen period of time (which would also have to deal with the source & target charged bodies having moved due to the electrostatic field), then it seems that virtual photons don’t exist, because you could choose to summarize the effects of the electrostatic force over each half the time separately, which would require analyzing 2 virtual photons rather than 1.

If the virtual photon exchange models the electrostatic force at one instant in time, however, then you have to analyze another virtual photon for the next instant. Then the next. Then the next. … How could you progress to the next instant to analyze without time being quantized (in which case you’d just progress to the next quantum)?

Since I haven’t heard of time having been shown to be quantized, I assume that the virtual particles just summarize effects over an integrated time, but then there are no such things a virtual photons. They’re just an abstraction to explain electrostatic force for an arbitrary period of time.

 

[PeroK]

When a virtual photon is exchanged and its effects are calculated, is it always calculated for a specific instant, or is it used to summarize the effects of the electrostatic field over a non-instantaneous period of time that you integrate over?

A virtual photon has no definite energy-momentum. Instead, the integration is over all possible energy-momentum values.

Note that energy-momentum is used instead of frequency.

A virtual photon has a frequency, right? If so, what gives rise to the frequency of a virtual photon that is exchanged to transmit the electrostatic force?

Not really. It's not a real photon with a single frequency. It represents all possible photon exchanges. Of all possible frequencies, if you like. We're not kidding when we say it's not a real photon and just a calculation tool.

e.g., I understand that when an electron in an excited state in an atom drops to a lower state, a photon is emitted with frequency E/h, where E is the energy difference between the 2 states.

That's a real photon.

 

[PeroK]

But a virtual photon exchange is a single interaction.

It's not an interaction, because it doesn't actually happen. Interaction describes what happens to real particles.

If the virtual photon exchange summarizes the effects of the electrostatic force over a chosen period of time

Time is not directly involved. There are input particles and output particles. What happens where and when within the interaction itself is outside the theory. Virtual particles are an aid to calculating the probabilities of all possible outputs.

If the virtual photon exchange models the electrostatic force at one instant in time, however, then you have to analyze another virtual photon for the next instant.

You are just guessing what the theory says. Wrongly

Since I haven’t heard of time having been shown to be quantized, I assume that the virtual particles just summarize effects over an integrated time, but then there are no such things a virtual photons. They’re just an abstraction to explain electrostatic force for an arbitrary period of time.

It's more complicated than that. The basic idea is that you imagine one virtual photon exchange within the interaction. That's your first approximation. Then you imagine either one or two virtual photon exchanges. The calculation for the case of two exchanges becomes a small correction to your first approximation.

Then you consider three exchanges and this becomes a further even smaller correction.

This is similar to the "sum over all paths" idea.

The strange idea is to imagine everything that could possibly happen and add up the contributions from each to get your answer for the probability of what is measured as output from an interaction.

I notice from your posts you don't appear to have digested the probabilistic nature of quantum theory. Which gives many people indigestion, it seems.

 

[PeroK]

PS this is where the popular science idea that an electron "takes all possible paths" comes from. It doesn't take all possible paths as it doesn't take any well-defined path.

Instead, you imagine it takes each possible path and do a probabilistic calculation for each path. The sum of all these calculations gives you the total probability for the electron to be measured somewhere.

Again, these ideas are for calculations and not part of what one can measure, which is what quantum theory is really about.

 

[ergo]

I notice from your posts you don't appear to have digested the probabilistic nature of quantum theory. Which gives many people indigestion, it seems.

I understood the probabilistic nature of an actual particle with defined characteristics like charge, mass, spin, frequency, etc. moving through space. I didn’t understand the nature of some calculations being made for particles that don’t exist requiring you to imagine all possible values for all possible combinations of particles. That’s a completely different thing.

 

[ergo]

It's not an interaction, because it doesn't actually happen. Interaction describes what happens to real particles.
…
What happens where and when within the interaction itself is outside the theory.

I’m confused. It seems like you said that virtual photon exchange is “not an interaction”, but later said that “what happens where and when within the interaction is outside the theory”, seemingly about virtual photon exchange. I’m honestly trying to understand your terminology, but it seems contradictory to me. Am I misreading / misunderstanding something? Did you misspeak?

 

[hutchphd]

I understood the probabilistic nature of an actual particle with defined characteristics like charge, mass, spin, frequency, etc. moving through space.

With respect, you do not. Even this description is fraught for a photon

I didn’t understand the nature of some calculations being made for particles that don’t exist requiring you to imagine all possible values for a particle.

OK

That’s a completely different thing.

No it is not. If you truly wish to understand this subject, you will need to speak a new language and it is not easy and it is not English. Even then you will likely be confused...trust me.
Your questions are not foolish, but they are not answerable in the framework you demand. Quantum mechanics is fundamentally different from classical mechanics

 

[ergo]

With respect, you do not. Even this description is fraught for a photon

Can you explain what is wrong with my description for a photon so that I can understand quantum better?

 

[PeterDonis]

Can you explain what is wrong with my description for a photon so that I can understand quantum better?

We can explain what is wrong with it pretty easily: everything you think you know about photons, particularly virtual photons, is wrong.

The "understand quantum better" part is not so easy. You're basically asking for a course in quantum field theory, and that is well beyond the scope of what PF can provide. There is no shortcut to that kind of understanding, unfortunately.

 

[PeterDonis]

From what I’ve heard, virtual photons are the force carriers for both electrostatic & magnetostatic fields.

First, "from what I've heard" is much too vague as a reference. Specifically, where have you "heard" whatever it is you've heard about virtual photons and force carriers?

Second, while the statement "virtual photons are force carriers for the electromagnetic interaction" is not wrong, exactly, it is also not useful, because you can't reason from it the way you are trying to do. It is not the kind of statement that let's you infer further things about how the electromagnetic interaction works (for example by asking how frequently virtual particles are exchanged--that question doesn't even make sense in the actual mathematical framework of quantum field theory). Nor is it intended to be. Physicists who are actually trying to teach people how quantum field theory works don't use statements like that. They teach the actual mathematical framework that is used to make predictions. And if you want to understand this topic, that is what you are going to end up having to learn.

 

[ergo]

I think I might have been thrown by some of the language in the linked primer whose link was provided above: https://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

Is that primer flawed?

I’m trying to triangulate between different people’s descriptions, each of which probably confused me in a different way, so my understanding of each individually might have been working at cross purposes.

If I understand correctly:

In an interaction, there may be zero to infinity virtual photon exchanges.

Zero-exchange interactions won’t have any effect.

Each additional exchange is increasingly less likely, so they each provide an ever diminishing adjustment to the outcome relative to scenarios with fewer exchanges. Thus the contribution of the single-exchange scenario provides a good deal (if not most) of the probability amplitude. For practicality, you can stop calculating the contributions of possible additional exchanges after the marginal contributions drop off quickly.

In an exchange, each virtual photon’s energy-momentum can only be understood as a probability amplitude, because you don’t a priori know exactly what energy-momentum any of them will have.

Is the above anywhere close to the correct concept?

If so, a part that I’m still hung up on is the timing.

Does each exchange completely occur in an instant (emission from source occurs at same instant as collision with target), or over time (emission from source occurs before or after collision with target)? From what I read in the primer, it seems like exchanges occur over a duration of time:

“Actually calculating the photon's wave function is a little hairy; I have to consider the possibility that the photon was emitted by the other particle at any prior time.”

&

“all I have to do is include situations in which the photon is ‘emitted on the right’ in the future and goes ‘backward in time’”

Similarly, does an interaction occur all at one instant, or over a duration of time?

If each exchange [sic] occurs over a duration, how are any of them included in an interaction? Is it if the collision occurs during the interaction, the emission occurs during the interaction, both occur during the interaction, etc.?

Thanks again for the help.

 

[PeterDonis]

Is the above anywhere close to the correct concept?

No.

The general descriptions you are reading of virtual particles are not describing actual processes that are taking place "under the hood", so to speak, in a real electromagnetic interaction. They are describing, as best it can be described in vague ordinary language, a mathematical procedure that has been found to be helpful in organizing the calculations one has to do to make predictions using quantum field theory. (Even this is more limited than it sounds, because this procedure only works for certain types of calculations, the ones that can be done in what is called perturbation theory. Many phenomena in QFT cannot be calculated this way.) The term "virtual particle" refers to a particular element of this mathematical procedure. But it has to be taken highly heuristically. You are trying to take it way, way, way too literally, as though the "virtual particles" were real things that were actually being exchanged, and that does not work. They're not.

 

[haushofer]

How frequent virtual photons are exchanged between charged particles is like asking how many angels fit on the tip of a needle.

 

[PeroK]

I’m confused. It seems like you said that virtual photon exchange is “not an interaction”, but later said that “what happens where and when within the interaction is outside the theory"

That just means quantum theory has nothing to say about what "really goes on" when two charged particles interact. Quantum theory tells you how to calculate the probability of each possible result of such an interaction, such as scattering angle.

The calculation is based on the exchange of all possible numbers of virtual particles each with all possible energy-momentum. But, in no way can this be interpreted as "what really goes on".

 

[PeroK]

I think I might have been thrown by some of the language in the linked primer whose link was provided above: https://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

Is that primer flawed?

I only read the first couple of paragraphs, but the author stresses that virtual particles are not to be taken literally. Which is what we are saying.

If so, a part that I’m still hung up on is the timing.

Timing doesn't come into it. There is nothing in the calculations corresponding to the timing of the exchange of virtual particles. That's taking things too literally.

 

[ergo]

Is my usage of variants of “emit”, “emission”, “collision”, etc., one of the problems that you guys seem to have with my description? I was using those words because the primer that was provided above also uses variants of “emit”; “collision” (or “absorption”) seemed to be the appropriate word as the counterpart of “emission”.

Is my usage of “exchange” and/or “interaction” a problem? The primer also uses them.

When I use these words, I’m trying to use them in a manner that just means they’re describing the calculations used to model the whole process.

Can I try this with baby steps instead of discussing nearly the whole shebang to see where I’m going astray?

Given that the primer uses the following words (or variants of them), can you tell me if any of them should not be used when describing this process (and if so, why it was OK or not OK for the primer to use them), or, if they can be used, what their meanings and relationships are? I’ll provide my guesses, which might be wholly inaccurate, but it’s the best I can do with the info provided so far (instead of just saying that my definitions are wrong, can you provide correct definitions, if the terms are applicable to this issue?):

Interaction: a calculation model of the process of the transmission of the force that we are attempting to calculate, limited to the electrostatic (or electromagnetic, if that’s more correct) force between exactly 2 particles for this discussion. Can be comprised of zero to infinity exchanges.

Exchange: a constituent component of an interaction that models a transmission of energy-momentum between the 2 particles participating in the interaction. Each exchange is modeled using one virtual photon.

Emission: a part of the modeling process in which a virtual photon is added to the calculation process associated with one of the 2 particles

Collision: a part of the modeling process in which a virtual photon emitted by one of the particles is calculated as affecting the other particle

Thanks again everyone for continuing to help. I think that by more rigorously defining things, we’ll obtain better building blocks for understanding these concepts.

 

[vanhees71]

The problem is that people think about photons as particles. This is errorneous idea of the "old quantum mechanics" is long overcome by modern quantum theory.

It is important to learn to think in terms of fields first. In relativistic physics the fundamental mathematical description is in terms of fields and even in the classical (i.e., non-quantum) theory point particles, which are a concept very successful in non-relativistic classical mechanics, are very problematic. The field concept instead is very natural, because it describes not interactions at a distance (like Newtonian theory of the gravitational interaction) but as local interactions of fields.

Now in the quantum realm each field also has some particle interpretation but only in a very specific sense of asymptotic free states, i.e., only for non-interacting fields there are states that admit a particle interpretation. That's why as the most simple (and also most important) application of non-relativistic particles one describes scattering processes, where two particles, which are initially so far distant from each other that you can neglect their interaction, are colliding. When they come close enough to each other such that interactions become relevant, a particle interpretation is impossible, but after some time the state goes again to an asymptotic free state, where a particle interpretation makes sense, and you can ask for the probability that the initial asymptotic free particles reacted into some particles in the final asymptotic free state. In relativistic physics it's pretty natural that in such reactions the original particles get entirely destroyed and new ones are formed (inelastic collisions), although with some probability you just get back the same two particles you started with running in other directions (elastic collisions).

The corresponding transition probabilities for the reaction of some asymptotic free initial to some other asymptotic free final state is what's the primary goal in doing calculations using quantum field theory, which is the kind of mathematical description of quantum theory, where creation and destruction processes of particles are important.

There is a very intuitive notation to perform such calculations in the evaluation of these transition probabilities (or more formally scattering-matrix (S-matrix) elements), known as Feynman rules. They are graphical pictures of scattering processes in a space-time diagram, but they have to read in the right way, and their true meaning is to be a very concise and efficient notation for a mathematical formula to calculate S-matrix elements (in an approximation called perturbation theory).

Some lines go into the graph and some go out, and only these lines have the mathematical meaning of the wave functions that describe the asymptotic free particles. Then there are given rules, derived from the underlying mathematical quantum field theory describing the interactions among the particles. On the most simple level there are just points where some lines meet, the socalled vertex, and these stand for a certain expression describing an interaction. Usually there is more than 1 vertex in a diagram describing a certain scattering process, and the internal lines connecting two vertices are often called "virtual particles", but that's just slang. It's better to understand them as describing a field mediating the interaction between the asymptotic free particles. Mathematically these internal lines stand for socalled propagators, i.e., mathematical functions that describe the creation and propagation of fields, like e.g. an electromagnetic field is there due to the existence of some charged matter, which itself is describing the electromagnetic interactions within the matter (or, in the specific sense of asymptotic free states, particles). Since these internal lines don't depict observable asymptotic free particles they do not have certain properties like such an observable particles has, i.e., they have no specific mass and also cannot even be interpreted as moving particles, because that would violate causality, and a great deal of the necessity to describe these scattering processes in pretty complicated quantized fields is just to finally have a causal theory for all observable facts described by this theory.

 

[Vanadium 50]

You are just guessing what the theory says. Wrongly

This.

 

[mattt]

My advice: learn the mathematics of quantum field theory, up to a point where you are able to correctly calculate things with it ( this will take you possibly years, depending on what your current level is).

After that, ask yourself (if you wish) "why" does Nature behave like that?

But don't try to start the house from the roof!

 

[PeterDonis]

Can I try this with baby steps instead of discussing nearly the whole shebang to see where I’m going astray?

Apparently not, since even your first baby steps are wrong.

Interaction: a calculation model of the process of the transmission of the force that we are attempting to calculate, limited to the electrostatic (or electromagnetic, if that’s more correct) force between exactly 2 particles for this discussion.

So far so good, but this is not even a baby step, just a specification of the scenario.

Can be comprised of zero to infinity exchanges.

Wrong. And so is everything else after it.

Go back and read my post #21 over and over again until it sinks in. You cannot learn how quantum field theory works the way you are trying to do it.

 

[Drakkith]

Perhaps this article will help: https://profmattstrassler.com/artic...ysics-basics/virtual-particles-what-are-they/

An excerpt from the article:
Physicists often say, and laypersons’ books repeat, that the two electrons exchange virtual photons. But those are just words, and they lead to many confusions if you start imagining this word “exchange” as meaning that the electrons are tossing photons back and forth as two children might toss a ball. It’s not hard to imagine that throwing balls back and forth might generate a repulsion, but how could it generate an attractive force? The problem here is that the intuition that arises from the word “exchange” simply has too many flaws. To really understand this you need a small amount of math, but zero math is unfortunately not enough. It is better, I think, for the layperson to understand that the electromagnetic field is disturbed in some way, ignore the term “virtual photons” which actually is more confusing than enlightening, and trust that a calculation has to be done to figure out how the disturbance produced by the two electrons leads to their being repelled from one another, while the disturbance between an electron and a positron is different enough to cause attraction.