Thread: Questions About the Region of Space Occupied by Quarks and Gluons- Shape Probabilities etc

Okay, I wondered if someone could tell me about the probabilities of finding quarks in a certain region? You know how electrons can be found in certain shaped orbitals depending on their energies? S orbitals, p orbitals, d orbitals, f orbitals etc.

How do the quarks in a proton or neutron relate to each other? Are they equidistantly spaced in a three dimensional sphere? Do the gluons travel in straight lines from quark to quark? or do they think they occupy some weirdly shaped three dimensional space?

As far as I understand it there is no straightforward answer to this; it is not possible to isolate and observe a single quark on its own due to a property called confinement, which is shared by all color-charged particles, therefore making the question of where to find a single quark with which probability rather meaningless.

Gluons are exchanged between quarks when the distance between them changes; it is thought that this exchange is somewhat analogous to a "rubber tube" extending between them. The more you stretch the tube, the more resistance is offered, leading to the well known behavior of the strong force to increase with distance. At some point it becomes energetically more favorable for the system to break apart, at which point a new quark is formed at the end of the gluon "tube". This in turn explains why quarks are never observed in isolation, but only in at least pairs.

well, as the gluons and bosons are the messenger particles for these quarks, are they not different from photons in that they must always hit the quark target? so how if these quarks were NOT stationary but moving around with the other two (or one) quark in some probabilistic manner - how would the gluons and bosons KNOW which velocity to choose to depart one quark and arrive at the neighboring quark? or are the quarks stationary with relation to one another?

also, if a new quark is formed at the end of the "tube" where the departing quark was - doesn't that mean the departing quark is a singlet quark? or does that departing quark also generate a new quark? and how does that happen? does the gluon become a new quark?

I read recently about a meson called a kaon where the quarks can exchange identities (though preserving their matter or antimatter nature) so is there some relation to that interaction?

Originally Posted by ballyhoo

well, as the gluons and bosons are the messenger particles for these quarks, are they not different from photons in that they must always hit the quark target? so how if these quarks were NOT stationary but moving around with the other two (or one) quark in some probabilistic manner - how would the gluons and bosons KNOW which velocity to choose to depart one quark and arrive at the neighboring quark? or are the quarks stationary with relation to one another?

I think someone with a strong background in Quantum Field Theory would be more qualified to answer this than I am. Maybe there is a way to define such a probability, I am really not too sure on this one.
The gist of it is that the situation is analogous to QED in that the vector boson always hit their "target"; I personally imagine them to be like 3-dimensional wave front radiating outwards from the source. In this picture the orientation doesn't matter, only the speed and distance do, and they will always arrive at their target.
No, quarks aren't stationary.

also, if a new quark is formed at the end of the "tube" where the departing quark was - doesn't that mean the departing quark is a singlet quark?

No, because new quarks form at both open ends of the "tube", so what you see is two sets of two quarks each moving away from each other. You never observe a single quark on its own.

I read recently about a meson called a kaon where the quarks can exchange identities (though preserving their matter or antimatter nature) so is there some relation to that interaction?

Yes, quarks can exchange their "flavour" via gluon interactions.

So how exactly do these new quarks originate? From the gluon? or as wikipedia says from the vacuum? and what does that mean? the higgs field? Also, I'm wondering how the quarks can exchange their flavor by gluon interactions, don't the gluons act solely to hold the quarks within the confinement range of each other? What is the situation when the gluon will change the quarks flavor versus hold two or three quarks near each other?

Originally Posted by ballyhoo

So how exactly do these new quarks originate? From the gluon? or as wikipedia says from the vacuum? and what does that mean? the higgs field? Also, I'm wondering how the quarks can exchange their flavor by gluon interactions, don't the gluons act solely to hold the quarks within the confinement range of each other? What is the situation when the gluon will change the quarks flavor versus hold two or three quarks near each other?

Perhaps this may help.

Where did we come from

I have no qualifications in physics, but this seems a fairly comprehensive explanation. Except I do not necessarily agree with the quote of a casual observation by Hawking.

I see from that work and another section of my book that it's the weak force and the W and Z bosons responsible for changing quark flavors, but it still isn't clear how a new quark appears to pair with another quark

In order to stretch the bond between quarks to breaking point, a lot of energy has to be injected into the system. It is this energy that eventually gets "converted" into two new quarks.
As for the exact mechanism - I must freely admit that I am not sure. Again, this would be a matter for someone well versed in QCD.

I'm a bit confused by the idea of the gluon radiating as a wave per your answer to my question to how the gluon hits its' quark target. Isn't QCD like the standard model in that all particles are point particles? If so, how can the gluon radiate as a wave? Also, if that is the case shouldn't the gluon wave hit both (or the other) quark and affect the other quarks equally?

Something still doesn't make sense here. If the quarks are not stationary then they must move in some predictable manner or probabilistic manner. If the latter then how do the gluons choose their velocity? They would need to know where the quark will be at some future point. As the gluons are supposed to be the messengers for the force of confinement and there is no other particle involved - something doesn't make sense!

Originally Posted by ballyhoo

Isn't QCD like the standard model in that all particles are point particles?

My understanding is that they are treated as point particles when it is useful to do so and they are treated as waves when it is useful to do so. In reality, they are not particles and they are not waves (they are whatever they are, with characteristics of both these things).

Gluons are not shot between quarks like little bullets, there is a probability function describing their location. In that sense their position is "fuzzy" and if their probability distribution overlaps that of a quark, they can interact. Or something like that...

something doesn't make sense!

This is quantum mechanics. If it makes sense you haven't understood it.

Originally Posted by Strange

Originally Posted by ballyhoo

Isn't QCD like the standard model in that all particles are point particles?

My understanding is that they are treated as point particles when it is useful to do so and they are treated as waves when it is useful to do so. In reality, they are not particles and they are not waves (they are whatever they are, with characteristics of both these things).

Gluons are not shot between quarks like little bullets, there is a probability function describing their location. In that sense their position is "fuzzy" and if their probability distribution overlaps that of a quark, they can interact. Or something like that...

something doesn't make sense!

This is quantum mechanics. If it makes sense you haven't understood it.

Sure, but "The Study of Quantum Mechanic"s is very much still in its infancy. There is no one who quite understands all of it. Maybe once we get that "Higgs Boson".

Still way too many hypotheticals, so careful.

Does anyone know the difference between the W+, W- and Z bosons? How are they and their effects different? What distinguishes them in their interactions/responsibilities?

Okay, I think I found the answer on wikipedia here - The W and Z bosons (together known as the weak bosons) are the elementary particles that mediate the weak interaction; their symbols are W+ , W− and Z.

The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own antiparticle The two W bosons are best known as mediators of neutrino absorption and emission, where their charge is associated with electron or positron emission or absorption, always causing nuclear transmutation.

The Z boson is not involved in the absorption or emission of electrons and positrons. All three bosons have particle spin s = 1. The emission of a W+ or W− boson either raises or lowers the electric charge of the emitting particle by one unit, and also alters the spin by one unit.

At the same time, the emission or absorption of a W boson can change the type of the particle – for example changing a strange quark into an up quark. The neutral Z boson obviously cannot change the electric charge of any particle, nor can it change any other of the so-called "charges" (such as strangeness, baryon number, charm, etc.).

The emission or absorption of a Z boson can only change the spin, momentum, and energy of the other particle.



My question now becomes - what do they mean by absorption or emission? Do these bosons orbit the quarks in some manner similar to how electrons orbit protons and neutrons?

Yes, but they have such a short lifetime that they're of limited interest.

To go back to your original question, there's maybe a clue about quarks in Topological quantum field theory. Note this bit: "Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory". If you take a look at a trefoil knot you might notice that the crossing-over directions appear to be up, up, and down. And if you had a trefoil knot made of something like a bicycle inner-tube, pulling at the loops is reminiscent of the bag model. Only if you manage to break it, you don't see three free quarks flying apart, instead you see pions. These consist of two quarks, which ties in nicely with the fact that you've broken one of the three loops. In comparison with the electron orbital it sounds like a three-lobed affair, like three spheres melded together. Electron orbitals are mapped out by spherical harmonics, and things have to be different for the proton. Maybe we're dealing with toroidal harmonics because the trefoil is a torus knot, but I'm not sure. This isn't something that's in the textbooks, it's just something I've picked up, so I'd say ask around about TQFT.

How can they have such a short lifetime? Do they convert to neutrinos or photons or something? Also, are you advocating for string theory and that quarks are really intertwined strings in the manner of the trefoil knot? If so, then how to the quarks integrate in your model? Are they not considered separate vibrating strings in string/M theory?

Originally Posted by ballyhoo

How can they have such a short lifetime?

I don't know. But see the wikipedia article W and Z bosons and see the introduction where it says "All three of these particles are very short-lived with a half-life of about 3×10⁻²⁵ s."

Originally Posted by ballyhoo

Do they convert to neutrinos or photons or something?

Something. See for example this article which talks about the W boson decaying into some combination of leptons neutrinos and quarks with percentages. The article also says "This means that within the OPAL detector the W-bosons are never directly observed, only their decay products are measured".

Originally Posted by ballyhoo

Also, are you advocating for string theory and that quarks are really intertwined strings in the manner of the trefoil knot?

No. The "knot" thing is to do with topological quantum field theory, which is much closer to mainstream quantum field theory than string theory is.

Originally Posted by ballyhoo

If so then how to the quarks integrate in your model? Are they not considered separate vibrating strings in string/M theory?

It isn't my model, and I'm not best placed to tell you about string theory. I usually find myself arguing with string theorists.

Recent subatomic particle discovery: New subatomic particle found at super-collider - Technology & science - Science - msnbc.com . The discovery of an excited neutral Xi-b baryon by means of the pattern of its decay into other subatomic particles. Apparently it was too unstable to be directly detected.
This discovery helps to confirm how Quarks bind and the strong interaction [how?]. It also announces that CERN expects the LHC should be able to determine the existence or non-existence of the "Higgs boson" by the end of this year.

Originally Posted by ballyhoo

How can they have such a short lifetime?

It's because they are very massive. In particle physics there is a generally a relationship between mass and lifetime - the more massive a particle is, the more short-lived it tends to be.

Originally Posted by Kalopin

Recent subatomic particle discovery: New subatomic particle found at super-collider - Technology & science - Science - msnbc.com . The discovery of an excited neutral Xi-b baryon by means of the pattern of its decay into other subatomic particles. Apparently it was too unstable to be directly detected. This discovery helps to confirm how Quarks bind and the strong interaction [how?]. It also announces that CERN expects the LHC should be able to determine the existence or non-existence of the "Higgs boson" by the end of this year.

I can't get enthusiastic about particles that can't be directly detected myself. When it comes to the Higgs boson, there's some misleading coverage in the popular press. To get it from the horse's mouth, check out A Zeptospace Odyssey: A Journey into the Physics of the LHC by Gian Francesco Giudice. He's a physicist at CERN with a hundred-plus papers to his name, and he knows what he's talking about. There's a search-inside on Amazon, and if you search on Higgs sector you can read pages 173 through 175. He calls the Higgs sector the "toilet" of the standard model and says it's "frightfully ad-hoc". He castigates the "God particle" nickname and says "The name gives the impression that the Higgs boson is the central particle of the Standard Model, governing its structure. But this is very far from the truth.” He says: “It is sometimes said that the discovery of the Higgs boson will explain the mystery of the origin of mass. This statement requires a good deal of qualification.” He gives a good explanation, and ends up with “In summary, the Higgs mechanism accounts for about 1 per cent of the mass of ordinary matter, and for only 0.2 per cent of the mass of the universe. This is not nearly enough to justify the claim of explaining the origin of mass.”

What do they mean when they say - the helicity of the W boson? What is the 'helicity state'?

Originally Posted by ballyhoo

What do they mean when they say - the helicity of the W boson? What is the 'helicity state'?

Helicity is related to both spin and momentum of a particle; more precisely, the helicity is obtained by projecting the spin vector onto the direction of the particle's momentum. It is s discreet value, just as the spin is.

Originally Posted by Markus Hanke

Originally Posted by ballyhoo

What do they mean when they say - the helicity of the W boson? What is the 'helicity state'?

Helicity is related to both spin and momentum of a particle; more precisely, the helicity is obtained by projecting the spin vector onto the direction of the particle's momentum. It is s discreet value, just as the spin is.

So once you know that information what does it tell you or help you?

I'm wondering also why would a gluon only move along a path that would bring it towards a quark? Are there any examples of gluons escaping the region of the three/two quarks? Maybe as glueballs?

Originally Posted by ballyhoo

So once you know that information what does it tell you or help you?

Not sure about the specifics here myself, but the helicity has some use in the mathematical framework behind the standard model, as it forms a symmetry group whose representations transform in certain ways.
Actually this is a good question. What is the use of it ? Maybe someone with deeper knowledge of the subject can comment...?

All I can find in my book is that that the importance of helicity informs an observer in a different frame of reference than the particles whether the particles is lefthanded or righthanded depending on whether the observer's frame is faster or slower than the velocity of the particles. Not sure why you care which it is though.........

Originally Posted by ballyhoo

I'm wondering also why would a gluon only move along a path that would bring it towards a quark? Are their any examples of gluons escaping the region of the three/two quarks? Maybe as glueballs?

anyone can answer this?

Originally Posted by ballyhoo

I'm wondering also why would a gluon only move along a path that would bring it towards a quark? Are their any examples of gluons escaping the region of the three/two quarks? Maybe as glueballs?

I assume that gluons do not move along "paths" from one quark to another, but rather there is a probability distribution which may overlap the two quarks.

As gluons carry color charge, I assume they are also confined (Color confinement - Wikipedia, the free encyclopedia) either within nucleons or glueballs (if they exist).

Are you sure of that? Simply because something has a probability of being found in a certain region does not mean it winks out in one location and winks into another without traversing the intervening distance. The uncertainty principle is about either knowing position or momentum but not both. So maybe it moves through a path in a certain location only but what about occasionally escaping the region of the nucleon.

Originally Posted by ballyhoo

Are you sure of that?

No.

Simply because something has a probability of being found in a certain region does not mean it winks out in one location and winks into another without traversing the intervening distance.

I wouldn't think of it as "winking out" of one location and appearing in another, but rather that it is spread out in space. In the same way, we can emit a photon from a source and detect it at a detector but, according to QED, we can't assume it went in a straight line between them. Theory doesn't tell us anything about where it was in between (other than as probabilities).

but what about occasionally escaping the region of the nucleon.

It would seem it does. It is the residual strong force that "leaks" out of the nucleons that holds the protons and neutrons together.

Originally Posted by ballyhoo

Originally Posted by ballyhoo

I'm wondering also why would a gluon only move along a path that would bring it towards a quark? Are their any examples of gluons escaping the region of the three/two quarks? Maybe as glueballs?

anyone can answer this?

Yes. You've got the wrong idea about gluons. It isn't your fault, they're portrayed as little particles zipping back and forth when they're not like that. Have a read of the particles and field section of the wikipedia force carrier article and see this sentence: "A force between two particles can be described either as the action of a force field generated by one particle on the other, or in terms of the exchange of virtual force carrier particles between them."

I've underlined the word virtual. Gluons are virtual particles. They're virtual like the virtual photons of QED which mediate the electromagnetic interaction. Think about the hydrogen atom, where virtual photons are said to keep the electron and the proton together. There isn't some blizzard of little flashes of light between them. Instead the underlying reality of virtual photons is the evanescent wave aka near field. It's a standing wave, something like half a photon going nowhere. Not many people seem to know this, but check out Evanescent Waves in Quantum Electrodynamics with Unquantized Sources dating from 1973 and see the bit that says "The identity of these evanescent waves with virtual photons is established, and the result is used to analyze the field due to a uniformly moving charge distribution."

The underlying reality behind gluons is a different type of "near field" to do with the strong interactions rather than the electromagnetic interaction. Hence when you smash a proton, you don't see a whole heap of gluons spilling out.

I'm not sure I understand.

If a virtual particle is -according to wikipedia - a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle.

The degree of uncertainty of each is inversely proportional to time duration (for energy) or to position span (for momentum).Virtual particles exhibit some of the phenomena that real particles do, such as obedience to the conservation laws. - per wikipedia

(assuming wikipedia is accurate about this).

The article continues with this - The strong nuclear force between quarks is the result of interaction of virtual gluons. The residual of this force outside of quark triplets (neutron and proton) holds neutrons and protons together in nuclei, and is due to virtual mesons such as the pi meson and rho meson.


According to that, they exist if only temporarily. So then by that line of thinking the singlet quarks would be virtual particles too?

It seems that when you're talking about fields and standing waves you're relying on mathematics without considering the physicality of such descriptions. How could a standing wave be a physical object?

postscript - your article is behind a paywall but I"m not sure how much I could have followed it anyway.

Originally Posted by ballyhoo

I'm not sure I understand.

If a virtual particle is -according to wikipedia - a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle.

The degree of uncertainty of each is inversely proportional to time duration (for energy) or to position span (for momentum).Virtual particles exhibit some of the phenomena that real particles do, such as obedience to the conservation laws. - per wikipedia

(assuming wikipedia is accurate about this).

It accurately reflects what people tend to say virtual particles are, but IMHO there's something of a myth about this. Virtual particles are nowadays presented as short-lived real particles being spontaneously created like worms from mud. See this bit of the wiki article:

"Virtual particles are viewed as the quanta that describe fields of the basic force interactions, which cannot be described in terms of real particles. Examples of these are static force fields, such as a simple electric or magnetic field, or the components of any field that do not carry information from place to place at the speed of light (information radiated by means of a field must be composed of real particles)."

It mentioned a magnetic field, and magnets don't glow in the dark. Virtual particles are used to describe fields, but they aren't real particles. Also see this bit of the article:

"Virtual photons are also a major component of antenna near field phenomena and induction fields, which have shorter-range effects, and do not radiate through space with the same range-properties as do electromagnetic wave photons. For example, the energy carried from one winding of a transformer to another, or to and from a patient in an MRI scanner, in quantum terms is carried by virtual photons, not real photons".

I underlined near field. The near field is the same thing as the evanescent wave, see wikipedia. It's a standing wave.

Originally Posted by ballyhoo

The article continues with this - The strong nuclear force between quarks is the result of interaction of virtual gluons. The residual of this force outside of quark triplets (neutron and proton) holds neutrons and protons together in nuclei, and is due to virtual mesons such as the pi meson and rho meson.

That's fair enough. But think of those virtual gluons as being something like the virtual photons of a magnetic field. There aren't any actual photons zipping from th North pole of a magnet to the South. In similar vein there aren't any real gluons rattling back and forth between the quarks.

Originally Posted by ballyhoo

According to that, they exist if only temporarily. So then by that line of thinking the singlet quarks would be virtual particles too?

No. In the QED hydrogen atom the messenger particles are virtual - virtual photons, but the electron and proton aren't. The same applies to the quarks that make up the proton. But don't think of them as little billiard-ball things. See what I said above about topological quantum field theory and partons - think of quarks as the parts of the proton.

Originally Posted by ballyhoo

It seems that when you're talking about fields and standing waves you're relying on mathematics without considering the physicality of such descriptions. How could a standing wave be a physical object?

I'm not relying on mathematics, I am considering the physicality. A standing wave is just a field variation that isn't propagating at c. It's not so much a physical object, but it is very real. Google on "evescent wave" to find out more.

Originally Posted by ballyhoo

postscript - your article is behind a paywall but I"m not sure how much I could have followed it anyway.

Sorry, I didn't check, and thought the abstract was enough.

It seems as if you are saying that the crux of the matter is that virtual particles are not real enduring particles but only fields and so on . Is this a mainstream scientific community opinion or simply your view of the matter?

You say that virtual particles are fields etc. But the wikipedia articles say that virtual particles are real though their existence has a brief duration and does not share all the features of real enduring particles. I don't presume to know your education but they seem clear about what virtual particles are.....

I am also unsure what you mean by virtual photons beings messenger particles in a hydrogen atom. I thought photons were real; they certainly can endure well beyond the region of an electronic orbital. Also, simply because virtual particles might not travel at the speed of light does not preclude them from carrying information does it?

The nuances of this wikipedia article cause too much confusion; I can see I have a lot of reading and new mathematics to learn to start comprehending this stuff more clearly.

It is not clear why a field should be interpreted as real without any corresponding physical and observable phenomenon to perform the interaction between components of the physical system.

Originally Posted by ballyhoo

It seems as if you are saying that the crux of the matter is that virtual particles are not real enduring particles but only fields and so on . Is this a mainstream scientific community opinion or simply your view of the matter?

Mainstream. Take a look at Quantum field theory on wiki and see the bit that says In QFT, photons are not thought of as "little billiard balls" but are rather viewed as field quanta – necessarily chunked ripples in a field, or "excitations", that "look like" particles. That's talking about photons rather than virtual photons, but you get the idea.

Originally Posted by ballyhoo

You say that virtual particles are fields etc. But the wikipedia articles say that virtual particles are real though their existence has a brief duration and does not share all the features of real enduring particles. I don't presume to know your education but they seem clear about what virtual particles are.....

There's definitely an underlying reality, but a magnetic field doesn't consist of a host of twinkling photons flashing in and out of existence.

Originally Posted by ballyhoo

I am also unsure what you mean by virtual photons beings messenger particles in a hydrogen atom. I thought photons were real; they certainly can endure well beyond the region of an electronic orbital. Also, simply because virtual particles might not travel at the speed of light does not preclude them from carrying information does it?

Best if you ask around about QED for this. Virtual photons are said to mediate the force that keeps an electron bound to a proton.

Originally Posted by ballyhoo

The nuances of this wikipedia article cause too much confusion; I can see I have a lot of reading and new mathematics to learn to start comprehending this stuff more clearly.

The main thing is to think in terms of waves and fields rather than "billiard ball" particles. A wave is a transient field variation that's moving. If it isn't moving and is a standing wave, then it's just a field. Hence the evanescent wave is also called the near field.

Originally Posted by ballyhoo

It is not clear why a field should be interpreted as real without any corresponding physical and observable phenomenon to perform the interaction between components of the physical system.

A field should be interpreted as real because its effects are detectable. You can feel an electromagnetic field with a couple of magnets in your hands. It's real. As to how the interaction occurs is another matter.

well, leaving that aside for now; I am curious about the interactions that bind protons and neutrons which occur according to wikipedia via -virtual mesons such as the pi meson and rho meson. I wish to know more details about that.

That's the "residual strong force". One way to think of it is via an analogy involving magnetic stix and balls. Electromagnetic force between atoms keeps a stick or a ball as one individual entity that doesn't fall apart. On top of that there's a weaker "residual" electromagnetic force that keeps a stick stuck to a ball. My four-year-old has a set of these, and I confess to playing with them from time to time. Anyway, the original work was done by H Yakuwa in 1935. See http://web.ihep.su/dbserv/compas/src/yukawa35/eng.pdf. It's quite hard going, but it includes sentences like this:

"Now such interaction between the elementary particles can be described by means of a field of force, just as the interaction between the charged particles is described by the electromagnetic field. The above considerations show that the interaction of heavy particles with this field is much larger than that of light articles with it. In the quantum theory this field should be accompanied by a new sort of quantum, just as the electromagnetic field is accompanied by the photon".

Again the messenger particles aren't real particles zipping back and forth so much as field quanta. It's something like you have a field and you divide it up into little squares and say each square is a virtual particle. The field here isn't the electromagnetic field per se, but I'd say that one day unification will demonstrate that all the fields are different aspects of something more fundamental.

To get across what I mean by this, you know how the sinusoidal electric field variation is often portrayed as being orthogonal to the magnetic field variation in the typical depiction of a light wave? There aren't really two fields, there's just one field, the electromagnetic field. And take a look at the Aharonov-Bohm effect on wiki and note what it says about potential vs fields along with this bit:

"In fact Richard Feynman complained^{[citation needed]} that he had been taught electromagnetism from the perspective of E and B, and he wished later in life he had been taught to think in terms of the A field instead, as this would be more fundamental".

There's the electroweak interaction too, but I'm getting ahead of myself here. Sorry, I have to go. Maybe some of the other guys can give you a different slant on all this.

I want to quote a couple passages with sidenotes from my book verbatim and tell me what you think about them.

The first is referencing a feynman diagram which I cannot copy here. quote - " Internal lines (those which begin and end within the diagram) represent particles that are not observed - indeed, that cannot be observed without entirely changing the process. We call them virtual particles.

Only the external lines (those that enter or leave the diagram) represent 'real' (observable) particles. The external lines, then, tell you what physical process is occurring; the internal lines describe the mechanism involved."

Then this other more interesting passage, though again, unfortunately I cannot copy the feynman diagram- "Within a larger diagram, however, these figures are perfectly acceptable, because although energy and momentum must be conserved at each vertex, a virtual particle does not carry the same mass as the corresponding free particle. In fact, a virtual particle can have any mass.*

*In special relativity, the energy E, momentum, p, and mass m of a free particle are related by the equation E squared - p squared times c squared = m squared times c squared.

But for any virtual particle E squared - p squared times c squared can take on any value. Many authors interpret this to mean that virtual processes violate conservation of energy. Personally, I consider this misleading, at best. Energy is always conserved.

"In the business, we say that virtual particles do not lie on their mass shell. External lines by contrast, represent real paritcles, and these do carry the 'correct' mass.**

** Actually, the physical distinction between real and virtual particles is not quite as sharp as I have implied. If a photon is emitted on Alpha Centauri, and absorbed in your eye, it is technically a virtual photon, I suppose.

However, in general, the farther a virtual particles is from its' mass shell the shorter it lives, so a phton from a distant star would have to be extremely close to its' 'correct' mass - it would have to be almost 'real'.

As a calculational matter, you would get essentially the same answer if you treated the process as two separate events ( emission of a real photon by star, followed by absorption of a real photon by eye). You might say that a real particle is a virtual particle that lasts long enough that we don't care to inquire how it was produced, or how it is eventually absorbed."

end really really long quote

Is that Introduction to Elementary Particles by David Griffiths? The excerpts are in quotes:

Internal lines (those which begin and end within the diagram) represent particles that are not observed - indeed, that cannot be observed without entirely changing the process. We call them virtual particles. Only the external lines (those that enter or leave the diagram) represent 'real' (observable) particles. The external lines, then, tell you what physical process is occurring; the internal lines describe the mechanism involved."

This is fair enough. Think about what a photon is. It's an electromagnetic field variation, an electromagnetic wave travelling at c. It can be absorbed by a hydrogen atom whereupon the electron changes orbital. Now take a look at Atomic orbital on wiki and see this bit: "The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves.". That electromagnetic wave isn't apparent any more, its energy has gone into the increased energy of a standing wave. It's "gone virtual".

Within a larger diagram, however, these figures are perfectly acceptable, because although energy and momentum must be conserved at each vertex, a virtual particle does not carry the same mass as the corresponding free particle. In fact, a virtual particle can have any mass.

I know this is what they say, but I don't think it's true in any real sense. We know that photons are massless and that electrons have a rest mass of 511KeV and protons 938MeV. I am not sympathetic to the idea that particles that we cannot see are spontaneously created like worms from mud and can have any mass we like.

*In special relativity, the energy E, momentum, p, and mass m of a free particle are related by the equation E squared - p squared times c squared = m squared times c squared.

E² - p²c² = m²c² can be restated as E² = p²c² + m²c². When we're talking virtual particles we usually start with photons. We can use a real photon to make an electron (and a positron) via pair production. Assuming that the electron and positron end up going very slowly, the p²c² term is essentially converted into the m²c² term. When the electron and positron annihilate, it's the other way around. Photons have no mass, but electrons do because they can be likened to standing waves around the hydrogen atom - a wave going at c is a transient field variation, A standing wave going nowhere is a permanent field. You can say that the absorbed photon has gone virtual and added to the mass, but any mass is not something I'm fond of.

But for any virtual particle E squared - p squared times c squared can take on any value. Many authors interpret this to mean that virtual processes violate conservation of energy. Personally, I consider this misleading, at best. Energy is always conserved.

Yes, energy is always conserved. If there's one golden rule in physics that's it.

In the business, we say that virtual particles do not lie on their mass shell. External lines by contrast, represent real paritcles, and these do carry the 'correct' mass.**

This is what they say.

Actually, the physical distinction between real and virtual particles is not quite as sharp as I have implied. If a photon is emitted on Alpha Centauri, and absorbed in your eye, it is technically a virtual photon, I suppose.

At best you could say it's "gone virtual" because its been absorbed by an atom in your eye. But that photon travelled for four years, and for every second of the way it was a real photon.

However, in general, the farther a virtual particles is from its' mass shell the shorter it lives, so a photon from a distant star would have to be extremely close to its' 'correct' mass - it would have to be almost 'real'.

Cough. Photons are massless.

As a calculational matter, you would get essentially the same answer if you treated the process as two separate events ( emission of a real photon by star, followed by absorption of a real photon by eye). You might say that a real particle is a virtual particle that lasts long enough that we don't care to inquire how it was produced, or how it is eventually absorbed."

Maybe the caculation works out, but IMHO his interpretation that "a real particle is a long-lasting virtual particle" is not actually supported.

Couple brief questions while I ruminate on your answers; you say I should view them as field quanta but the passages say they could have any mass....so are they not particles because they have this variable mass; however briefly or whatever other features of 'real' particles they lack?

Also, I am wondering if there is not some point of dispute in the physicist community about whether photons have mass, however negligible, because I read the works of other physicists who mention the photon as having a negligible mass - and even listened to a bunch of amateur astronomers debating the point.....

Originally Posted by ballyhoo

Couple brief questions while I ruminate on your answers; you say I should view them as field quanta but the passages say they could have any mass....so are they not particles because they have this variable mass; however briefly or whatever other features of 'real' particles they lack?

I don't think the passages say they have a mass that varies, I think the passages say they can have any mass you like. I don't like this at all because when we talk of virtual particles we talk initially of virtual photons and photons are massless. How can it be that "spontaneously created" photons that we can't see have mass when photons don't? A field has mass because a field has energy, and mass is a measure of system energy content. If you trap a massless photon in a box it adds mass to the system, but the photon itself is still going at c and remains massless. IMHO it only works out when you say the virtual photons are sections of the field. Which brings us back to field quanta. I think it's best to to think of virtual photons as the "accounting units" of QED rather than short-lived photons.

Originally Posted by ballyhoo

Also, I am wondering if there is not some point of dispute in the physicist community about whether photons have mass, however negligible, because I read the works of other physicists who mention the photon as having a negligible mass - and even listened to a bunch of amateur astronomers debating the point.....

I'd say that such debate misunderstands mass. If you read Einstein's E=mc² paper Does the inertia of a body depend upon its energy content you'll appreciate that if you open the box (see above) the system loses mass. And you can't make a photon go faster or slower, so mass in the usual sense does not apply to it. That's why the mainstream view, and my view, is that photons are massless. Note though that there's an issue in that the word "mass" is ambiguous. When people say "mass" they usually mean rest mass rather than say relativistic mass, which is a measure of energy. There's also active gravitational mass and inertial mass, and things can get confusing.