Photonic Properties Determining Charge

[13thDoctor]

Beforehand, please excuse my ignorance in this field, as I am only beginning to delve into its astounding depths.

So, as I understand it, Photons are the force carrier particles (gauge bosons) for the electromagnetic interaction (electromagnetic force). This given, one could pretty much say that EM fields are comprised of these photons and that all interactions which involve electric charges are entirely dependent on, and determined by, these photons (even if said photons are virtual particles as would be the case with perturbation theory-something my understanding of is extremely limited).

With this in mind, when an electron repels another electron it is due to photon exchange between the electrons. Or when an electron is attracted to a proton it is also due to photon exchange.

My question is this: What properties of a photon determine whether or not the particles between which it is being exchanged repel or attract each other, and to what degree that repulsion/attraction is?

Additionally, I would very much like to improve my comprehension of perturbative models and how they explain fundamental interaction through virtual particle exchange, and so would be endlessly grateful if someone knowledgeable in such things would help me in this endeavor.

Thank you all in advance.

 

[andrien]

I would very much like to improve my comprehension of perturbative models and how they explain fundamental interaction through virtual particle exchange,

well it is not simple at least mathematically.In two lines,you draw a feynman diagram.More vertices it has,higher the order in perturbation.you calculate with certain rules the amplitude for that process and takes it absolute square which is used for many purposes like calculating cross-sections.Also one can directly use amplitudes also with some unitarity,analyticity condition to get some results but it is of less use now.

 

[Bill_K]

What properties of a photon determine whether or not the particles between which it is being exchanged repel or attract each other

In a word, polarization.

The electromagnetic field is described by a polarization vector, which is a 4-vector A_μ with components (A, φ). In ordinary terms, φ is the electrostatic potential and A is the magnetic vector potential. A charged particle is described by a current 4-vector J^μ with components (J, q). Again in ordinary terms, q is the charge and J is the current. The interaction between them is the energy J^μA_μ. For a charge that's sitting still, the interaction energy is just qφ.

All this is a fancy way of describing the Coulomb energy of a charge in an electrostatic field. But here's the point: in terms of photons, φ is the 4th component of its polarization vector. If you have two like charges (say both of them are positive) one produces a field φ that is positive, and then the interaction energy qφ between the two charges is also positive. If the charges are unlike, then qφ is negative. Positive interaction energy means the two charges will tend to repel, negative energy would mean they tend to attract.

 

[Naty1]

Welcome to physicsforums 13th doctor

for a start:

Try reading Wikipedia on PERTURBATION THEORY and STANDARD MODEL of particle physics. I have skipped much of the math myself, but utilize interpretations from such sources and experts in these forums to get a view of what science thinks is happening.

 

[13thDoctor]

Welcome to physicsforums 13th doctor

for a start:

Try reading Wikipedia on PERTURBATION THEORY and STANDARD MODEL of particle physics. I have skipped much of the math myself, but utilize interpretations from such sources and experts in these forums to get a view of what science thinks is happening.

Thank you for the welcome. I did indeed read those Wikipedia entries. As I still needed more clarification, I posted here.

 

[Naty1]

I would very much like to improve my comprehension of perturbative models and how they explain fundamental interaction through virtual particle exchange, and so would be endlessly grateful if someone knowledgeable in such things would help me in this endeavor.

This post may be at the edge of you interest, hard to tell...but if you want to know how particles and virtual particles come into being, read on.

If you think 'virtual particles' are perhaps a bit vague, wait til you come across the fact that so are 'real' particles...perhaps you have and that's why you are here. They are NOT so easy to define either locally nor globally. Quick suggestion: Search 'Perturbation' or similar in these forums...some related discussions below...

My limited understanding is that perturbative models equate to a non zero vacuum expectation value. These non zero vev occur during the inflationary phase of the universe, just after the Big Bang, in the 'slow roll' found by Steinhardt and also in Standard Model of Particle physics. The commonality used to be different types of Higgs fields, but apparently Higgs during inflation is now superseded at least in the minds of some theorists...

Virtual particles can become real particles if the proper separation distance expands at the same rate or faster than the light signal distance... then the particle pair will never annihilate and the local particle becomes observable. In a nutshell, a horizon is essential to particle production during the inflation of geometry, that is, the inflation of spacetime. [If you are familiar with string theory, this becomes an even more fascinating statement.]

Virtual particles, or vacuum fluctuations, are features of both models. But I don't know the mathematics of how they arise. In the Inflationary phase of the universe, Particles emerge as a result of the evolution of a scalar field fluctuation during inflation...associated with cosmological horizons! You'll have to decide whether this interests you or not...

Also, the Unruh effect and Hawking Radiation arise due the nonzero vev. I do not know if these are considered 'perturbative' models or not, but I do know the phenomena is fascinating because of horizon effects analogous to those of the inflationary moment of the universe. Here are some of my summary notes on Perturbation Theory...from these forums and Wikipedia...I include references where I kept them. Synopsis:

Non-vanishing vacuum state

If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator (or more accurately, the ground state of a QM problem). In this case the vacuum expectation value (VEV) [no condensates] of any field operator vanishes.

For quantum field theories in which perturbation theory breaks down at low energies (for example, Quantum chromodynamics [QCD] or the BCS theory of superconductivity) field operators may have non-vanishing vacuum expectation values [vev] called condensates. In the Standard Model, the non-zero vacuum expectation value of the Higgs field, arising from spontaneous symmetry breaking, is the mechanism by which the other fields in the theory acquire mass.

http://en.wikipedia.org/wiki/Vacuum_...g_vacuum_state

also:
A vacuum state is observer dependent. [This refers to the Unruh effect and Hawking radiation, for example.]

Perturbative Vacuum

[vanishing vev {vacuum expectation value}]

The perturbative vacuum is the true ground state of a system.

It contains only virtual particles.

In a certain sense the perturbative vacuum is 'empty'; it's annihilated by typical field operators, so the result for counting particles in the vacuum is zero (after normal ordering) [NO PARTICLES];

It does have energy…as the cosmological constant negative energy pressure.



Non perturbative vacuum.

[non vanishing vev {vacuum expectation value}]

“…The Standard Model is an … example of a quantum field theory, of … non-perturbative behavior…” It has a non zero vev: the Higgs field.
Typically a non-perturbative vacuum is not 'empty'. For example in QCD ….in the phase where chiral symmetry is broken the 'vacuum' is not 'empty' but 'contains quark-antiquark pairs'.

Condensates [non zero vev] like BCS, QCD ground state, non-vanishing vev for Higgs, ...) are all examples for non-perturbative vacuum states.I read Rovelli's Introduction and this caught my attention:

..uniquely-defined particle states do not exist in general, in QFT on a curved spacetime. ... in general, particle states are difficult to define in a background-independent quantum theory of gravity

You should find this discussion interesting:

What is a particle
https://www.physicsforums.com/showthread.php?t=386051

and maybe

Big Bang Theory and Matter
https://www.physicsforums.com/showthread.php?p=3847806#post3847806

 

[Naty1]

While reviewing my notes on black holes came across this interesting description...
sorry, no source:

Quantum foam is theorized to be created by virtual particles of very high energy. Virtual particles appear in quantum field theory, where they arise briefly and then annihilate during particle interactions, in such a way that they affect the measured outputs of the interaction even though the virtual particles are themselves never directly observed. They can also appear and annihilate briefly in empty space, and these "vacuum fluctuations" affect the properties of the vacuum, giving it a nonzero energy known as vacuum energy, a type of zero-point energy (however, physicists are uncertain about the magnitude of this energy)

I think 'zero point energy', 'vacuum expectation energy and 'energy of the vacuum' are used interchangeably...but the first is the energy of the lowest, ground state.

and this excerpt According to the book Quantum Fields in Curved Space by Burrell and Davies, pages 268-269,

These considerations resolve an apparent paradox concerning the Hawking effect. The proper time for a freely-falling observer to reach the event horizon is finite, yet the free-fall time as measured at infinity is infinite. Ignoring back-reaction, the black hole will emit an infinite amount of radiation during the time that the falling observer is seen, from a distance to reach the event horizon. Hence it would appear that, in the falling frame, the observer should encounter an infinite amount of radiation in a finite time, and so be destroyed. On the other hand, the event horizon is a global construct, and has no local significance, so it is absurd too conclude that it acts as physical barrier to the falling observer.

The paradox is resolved when a careful distinction is made between particle number and energy density. When the observer approaches the horizon, the notion of a well-defined particle number loses its meaning at the wavelengths of interest in the Hawking radiation; the observer is 'inside' the particles. We need not, therefore, worry about the observer encountering an infinite number of particles. On the other hand, energy does have a local significance. In this case, however, although the Hawking flux does diverge as the horizon is approached, so does the static vacuum polarization, and the latter is negative. The falling observer cannot distinguish operationally between the energy flux due to oncoming Hawking radiation and that due to the fact that he is sweeping through the cloud of vacuum polarization. The net result is to cancel the divergence on the event horizon, and yield a finite result, ...

[PS: Soon you'll be wondering "WHY did I ever ask this??" [LOL]

 

[13thDoctor]

Thank you for your replies, Naty1. I am indeed very interested in what you have mentioned so far. As you may have expected I have come across virtual particles, the inruh effect, and hawking radiation countless times. I have even done pretty extensive research on them. One of the most interesting things I found is that "vacuum cherenkov radiation" would be mediated by virtual particles. I find it interesting how, in the case of hawking radiation, one of the particles in the particle/antiparticle pair might get sucked in releasing the other, which is emitted away from the event horizon.

I have most certainly done a great deal on the string theories and M-theory, as I not only find them to be extremely intriguing but I also wish to write a novel which involves physics of that level.

Yes I have indeed become fairly well acquainted with the ambiguity of particle definition. At the moment this is slightly irrelevant to my questions.

Yes, as far as I can tell "zero-point energy" and "vacuum expectation energy" are referring to the same thing. I came across the two multiple times when researching into the casimir effect.

Quantum Foam is another thing that I am endlessly interested. Albeit strings may never be small enough to fit into it (the bounce off effect), it is certainly an intriguing idea, especially when there exist theories which expand the microwormholes which exist within this foam.

Yes, I've also come across the observer paradox on numerous occasions, but I actually haven't heard of that resolution to it before. Thank you for providing that.

At the moment, I simply wish to have a greater understanding of how fundamental interaction itself (more specifically the electromagnetic interaction) functions. This is partially due to the fact that, in my novel, I wish to utilize fictional physics which would actually fit into the current standard model of real physics, and thus be a scientific possibility. The particular area of the fictional physics that I am currently having a problem with involves the electromagnetic interaction extensively.

As to why I asked this question. I know very well why I asked it. I simply wish to know the answer to these things (impart due to my insatiable lust for knowledge). I don't care how overwhelmingly difficult to comprehend these answers might be. I'm either going to understand them eventually, or die trying. I realize that the answers to some questions have yet to be solved, but I at least wish to know many of those which have been (or have probably been, given that much of it is still theoretical).

 

[Naty1]

Sounds like you have a good background... you can consider getting some inexpensive used books from places like Amazon books and use this link...which provides some money to these forums: https://www.physicsforums.com/showthread.php?t=473931

At Amazon, just pick a topic like cosmology, particle physics,or relativity...and up pop lots
of suggestions...textbooks [expensive] as well as books for the general public [not expensive]...

 

[13thDoctor]

Sounds like you have a good background... you can consider getting some inexpensive used books from places like Amazon books and use this link...which provides some money to these forums: https://www.physicsforums.com/showthread.php?t=473931

At Amazon, just pick a topic like cosmology, particle physics,or relativity...and up pop lots
of suggestions...textbooks [expensive] as well as books for the general public [not expensive]...

Thank you. You yourself seems to have at least as good a background if not better.

Hmm... Thanks for the advice. I'll certainly look into it. I suppose sometimes going back to textbooks as a platform for education is useful.

 

[Polyrhythmic]

In a word, polarization.

The electromagnetic field is described by a polarization vector, which is a 4-vector A_μ with components (A, φ). In ordinary terms, φ is the electrostatic potential and A is the magnetic vector potential. A charged particle is described by a current 4-vector J^μ with components (J, q). Again in ordinary terms, q is the charge and J is the current. The interaction between them is the energy J^μA_μ. For a charge that's sitting still, the interaction energy is just qφ.

All this is a fancy way of describing the Coulomb energy of a charge in an electrostatic field. But here's the point: in terms of photons, φ is the 4th component of its polarization vector. If you have two like charges (say both of them are positive) one produces a field φ that is positive, and then the interaction energy qφ between the two charges is also positive. If the charges are unlike, then qφ is negative. Positive interaction energy means the two charges will tend to repel, negative energy would mean they tend to attract.

But doesn't your argument break down in temporal gauge, where you set A₀=0?