Exploring the Weak Interaction: Is it a Force?

[michael879]

weak "force"

this is really just a question about terminology, so I am not expecting any overly complex answers. I am familiar with the weak interaction, but in what sense is this a force? It is unlike anything that we would consider a force..

The only sense in which I can see it being called a force is that it is identical to the electromagnetic force (which is clearly a force) at high energies. However, since this is the case, what exactly does an electro-weak interaction look like? Does it resemble a classical force?

The definition of "classical force" I am using here is basically just a force whose feynman diagram involves particles either repelling or attracting each other and being unchanged at the end. Another possible definition would be that U = gradiant(F dot r) (I might have the equation slightly wrong, I am kind of tired and don't remember the exact format equation but the point is the same). Even with this definition I don't see how the weak interaction can be called a force.

Can anyone clear this up for me?

 

[humanino]

You have a classical non-relativistic notion of force. There does not seem to be a lot of hope from that remote corner of physics from weak interaction. Do you even know how to produce attraction with a virtual photon ?

 

[michael879]

actually yea, I've read about that. The actual quantum E&M force is not described well by the feynman diagram "analogy" that works with repulsive forces. HOWEVER, the one I've seen involves a virtual photon coming out of each particle opposite the vector to the other one. The explanation is that since the virtual photon has no defined position it "tunnels" behind the other particle. Its a pretty crappy explanation but it does illustrate that the quantum force resembles a classical force. Also, the E&M force has a term in the hamiltonian which is identical to its classical one (using my second definition).

 

[michael879]

also, the other 2 quantum force (and gravity) can be described by repulsion or attraction between particles. This may be accomplished with virtual particles, but the result is still attractive or repulsive. The weak force is nothing like this.

 

[humanino]

The actual quantum E&M force is not described well by the feynman diagram "analogy" that works with repulsive forces.

The Feynman diagram technology is not an analogy. It is more of a Taylor expansion. Every term of the expansion is a topological class of elementary processes in space-time.

HOWEVER, the one I've seen involves a virtual photon coming out of each particle opposite the vector to the other one.

Two-photon exchange is a big deal. Most of the time one-photon exchange is enough. Only recently has it been suggested that two-photon exchange might have been observed.

The explanation is that since the virtual photon has no defined position it "tunnels" behind the other particle.

This is really lame.

I'd suggest the infamous Some Frequently Asked Questions About Virtual Particles. It is much more correct in that it is actually closer to what you get when you do the calculation.

also, the other 2 quantum force (and gravity) can be described by repulsion or attraction between particles. This may be accomplished with virtual particles, but the result is still attractive or repulsive. The weak force is nothing like this.

The way I see it, the problem with the strong and weak "forces" is that they have no classical counterparts at our scales, contrary to EM and gravity.

But it's true that on the one hand, one reads everywhere how the strong force should supposedly be understood in terms of a "potential", the reason for that being that heavy quark systems are indeed non-relativistic and their spectrum can be well-described using such schemes. On the other hand, there are indeed such things as attractive and repulsive sectors in quark-quark interactions via one gluon exchange. However, it is not clear to me where this is useful beyond the non-relativistic potential I mentionned earlier for heavy quark systems.

Anyway, let us forget for one second about the charged current sector of the weak force. You'll admit that Z exchange is pretty similar to photon exchange. In fact, they are indistinguishable and interfere with one another.

Let me also say that I agree with you, the term "force" is not well-suited to the weak interaction altogether, unless one takes for granted that a "generalized force" can turn one particle into another (with which I personally don't have a problem). And as you said, the electroweak interaction is an additional reason to accept this idea.

 

[michael879]

This is really lame.

haha that's exactly what I said when I heard it. I was just quoting a previous answer I got on this site. All I know about QFT is from what I've read on wikipedia and this site. Apparently its too advanced for undergrad?

The way I see it, the problem with the strong and weak "forces" is that they have no classical counterparts at our scales, contrary to EM and gravity.

Well the strong force (from the little I know, I wouldn't be suprised if I am wrong), does act like a classical force. A weird force, but still a force. It acts like a spring that has a breaking point.

But anyway, whether or not it can be understood in terms of potentials, the way every force but the weak force is setup is the following:
when particles exert these forces on each other, they react with some change in acceleration.

This doesn't remotely work with the weak force, because there's no particle that accelerates. The two original particles "change" into new particles!

 

[merryjman]

At the scale where weak interactions are observed, the term "force" has no meaning. Neither do terms like "velocity" since they're all moving at practically c. In its classical definition, a force acts on a point particle. But at those energies and sizes, you don't have point particles, you have resonant excitations ("waves") in quantum fields. So instead, they use the term "interaction." Rather than particle A exerting a force on particle B, you have wave/particle A interacting with wave/particle B through a mediator W.

As to your comment about the strong force: quark A interacts with quark B through the mediator G. The interaction strength is large for small distances and vanishingly small for distances larger than the nuclear size. On our scale this does appear to be like a spring.

All 3 of the "forces" in the Standard Model are described this way: as interactions through some mediator. For the EM the mediator (or gauge boson) is the photon, for the weak the W and Z, for the strong the gluon. The only other "force" we know of is gravity and although there's no evidence yet for a gravitational gauge boson, there are theories which allow them or even insist on them.

 

[humanino]

But at those energies and sizes, you don't have point particles, you have resonant excitations ("waves") in quantum fields.

Can you remind me at which scale does an electron cease to be pointlike ?

On our scale this does appear to be like a spring.

Can you remind me at which scale does the string break (0.5 inverse fermi) and compare it with the two-pion mass scale at which it should occur in the "spring model" ? Why do you say the potential grows ? How do you know ?

 

[merryjman]

Humanino, you sound more learned than I, so I defer. Your questions seem designed to attack my understanding rather than help the OP, since he seemed not to want overly technical answers, but I'll play along. (1) I know that electrons are still considered pointlike. What I meant was that in conventional Newtonian mechanics, forces are envisioned as acting on the center of mass of an object, so the object is treated as a point. Plus, the high-energy people I know always speak about leptons as being waves at those energies and scales. (2) I can't answer this question. All I know is that in the dumbed-down explanations of the strong interaction that I can comprehend, it is likened to a spring or rope. Is this a poor analogy? (3) I didn't say this. (4) I don't.

 

[humanino]

Your questions seem designed to attack my understanding rather than help the OP, since he seemed not to want overly technical answers

I do attack whenever I read "the QCD potential grows, therefore quarks are confined, therefore QCD is solved and boring". The potential does grow and it is a sufficient condition for quark confinement. However, it is not a necessary condition. The failure to recognize this subtlety leads to a generally low interest in QCD. Unfortunately, the rising of the potential seems irrelevant to explain the confinement of light quarks and especially its link with the dynamical breaking of chiral symmetry. Interestingly enough, the rising of the QCD coupling "constant" stops around the confinement scale, around where the string breaks, which is not where it is supposed to break from two-pion creation, indicating that indeed something else happens before the naive dual-superconducting model of the vacuum.

Electrons are pointlike down to scales much above the vector boson mass scale.

 

[michael879]

can someone answer my other question too? Ok, I get what you guys are saying about the main question: force is a bad word to use because no quantum interactions meet the definition of force at that scale. humanino, thanks a lot for that link. I thought it was something I read a while ago but it actually cleared up a lot for me.

Anyway, my other question was what would the weak interaction look like at the energy scales where the electromagnetic and weak forces unify? Rotating the standard picture of the weak interaction (beta decay), it looks like at those energy scales:
W = photon
neutron = proton (up quark = down quark maybe?)
neutrino = electron (since anti-neutrino = positron)

This actually seems very plausible to me (i.e. if the bosons, quarks, and leptons were all to unify into 3 particles), but I am wondering if its actually predicted or not?

 

[enotstrebor]

can someone answer my other question too? Ok, I get what you guys are saying about the main question: force is a bad word to use because no quantum interactions meet the definition of force at that scale.?

The weak force is a bad term but not for the reasons given. Given, the V-A theory and associate coupling constants, the weak coupling constant is a unitless constant and used in the same manor as the fine structure constant. The fine structure constant is unitless because it is the ratio of two particle level forces (charge and spin) which are vector (V) and axial vector (A) forces.

Thus via its use in the V-A theory, the weak coupling constant associated with the weak effect (or weak force) should actually be a ratio of two particle level forces just like the fine structure constant.

The theory does not and can not say what these two forces are, but they can not both be charge and spin, so there must be at least one other (unidentified) particle level force in the weak coupling force ratio.

But, the term weak force is badly named as it (weak) can only be a adjective termed ``weak'' for its association with the weak effect, not an adverb for the strength of this unidentified force. From the theory, the unidentified force's weak effect stems from the fact that the two competing forces are of approximately the same magnitude (Weak coupling =.23). (The fine structure constant is small because of the difference in force magnitude is large resulting in a large effect, thus electromagnetic decay is quick while weak decay is slow).

Thus potentially, if one of the weak coupling constant forces is spin, this unidentified force must be almost as large as spin, if one of the weak coupling constant forces is charge, this unidentified force must be almost as large as charge, if one of the forces is neither charge or spin, then one has two unidentified forces in the weak coupling constant.

Take a course with the V-A theory, and look how the coupling constants are used.

 

[michael879]

well Ill admit that I really have virtually no knowledge of the mathematics behind the weak force (Ive only taken 2 years of QM so far). However, I don't understand why some unitless constant associated with the weak interaction implies that there is some underlying force whose ratio is that constant.. Plenty of things can produce unitless constants, and just because the E&M force has two components (electric/charge, magnetic/spin) doesn't mean all forces must, right?

This stuff actually sounds pretty interesting, and I plan to read up on it when I get some time. Does anyone have an answer for my second question though (reposted 2 posts up)?

 

[enotstrebor]

Plenty of things can produce unitless constants, and just because the E&M force has two components (electric/charge, magnetic/spin) doesn't mean all forces must, right?

You are correct. However the assumption is that the V-A theory is fundamentally correct.

If the ``coupling constants'', as used in the V-A theory, are coupling constants (couplings of vector and axial vector forces), then as the weak coupling constant is used in the same manor as the fine structure coupling constant, then if the theory is fundamentally correct, then the weak coupling constant is the coupling of two forces (or more correctly force like effects, as spin [spin angular momentum] is not truly a force in the sense of a field force like charge).

If the V-A theory is phenomenological in some manor then the coupling can be a A-V coupling rather than a V-A coupling, or not even a coupling of two forces.

All implications taken from the Standard Model and QM assume that they are fundamentally correct rather than being phenomenological and only fundamentally accurate.

 

[enotstrebor]

Anyway, my other question was what would the weak interaction look like at the energy scales where the electromagnetic and weak forces unify? Rotating the standard picture of the weak interaction (beta decay), it looks like at those energy scales:
W = photon
neutron = proton (up quark = down quark maybe?)
neutrino = electron (since anti-neutrino = positron)

This actually seems very plausible to me (i.e. if the bosons, quarks, and leptons were all to unify into 3 particles), but I am wondering if its actually predicted or not?

I have never seen a prediction of equality of charged particles to non-charged particles (and I wouldn't know how this could happen, the neutrino can't suddenly gain charge or electron loose charge). And what ever you read can't be implying mass because the photon does not have mass.

Force equivalence does not imply particle equality, only interaction magnitude equality.

 

[michael879]

I have never seen a prediction of equality of charged particles to non-charged particles (and I wouldn't know how this could happen, the neutrino can't suddenly gain charge or electron loose charge). And what ever you read can't be implying mass because the photon does not have mass.

Force equivalence does not imply particle equality, only interaction magnitude equality.

I didnt read anything, I made those equivalences up. What I read was that at some energy level the E&M, weak, and strong forces are supposed to unite into a single force. Looking at the feynman diagrams for E&M and weak, that was the only way I could see to unite them.

As for conservation of charge, at those energy levels charge is pretty much meaningless. Charge is what determines the E&M force, but at those energy levels the E&M force is completely different and has united with the weak force. What I was saying was that the electron and neutrino at those energy levels appear identical (although I am guessing neither would resemble what we call an electron or neutrino now).

As for mass, its the same thing. Who knows how the bosons interact with the higgs field at those energy levels. The W/Z bosons could lose their mass, or the photon could gain mass. I have no idea.

As for force equivalence just referring to relative strength, do you have a source on that? From what I've read the current theory is that all the forces were originally one. They split into separate forces at different times due to spontaneous symmetry breaking.. Also, you can't deny the beauty of all the leptons unifying into 1 lepton, all the quarks unifying into 1 quark, and all the bosons unifying into 1 boson.

Anyway, like I said I pretty much made up those equivalences so if you give me some type of reference Id be happy to drop it and believe you. Otherwise, from the bits I've read on the subject what I said makes sense to me..

 

[michael879]

You are correct. However the assumption is that the V-A theory is fundamentally correct.

If the ``coupling constants'', as used in the V-A theory, are coupling constants (couplings of vector and axial vector forces), then as the weak coupling constant is used in the same manor as the fine structure coupling constant, then if the theory is fundamentally correct, then the weak coupling constant is the coupling of two forces (or more correctly force like effects, as spin [spin angular momentum] is not truly a force in the sense of a field force like charge).

If the V-A theory is phenomenological in some manor then the coupling can be a A-V coupling rather than a V-A coupling, or not even a coupling of two forces.

All implications taken from the Standard Model and QM assume that they are fundamentally correct rather than being phenomenological and only fundamentally accurate.

ah cool, thanks. That really sounds interesting. Do you have anything I can read about this? I've never heard of it before.

 

[enotstrebor]

As for force equivalence just referring to relative strength, do you have a source on that? .

Actually it is the equivalence of the couplings (force ratios) which is not the same as the equivalence of the forces (unless the couplings go to 1 which is not the case).

Wikipedia is generally a good broad back ground (see GUT - Grand Unification Theory). Green has a book which has a picture of the running of the couplings, but I do not have the reference with me.

To quote Wikipedia "If we look at the renormalization group running of the three-gauge couplings have been found to nearly, but not quite, meet at the same point if the hypercharge is normalized so that it is consistent with SU(5)/SO(10) GUTs, ... However, if the supersymmetric extension MSSM is used instead of the Standard Model, the match becomes much more accurate. It is commonly believed that this matching is unlikely to be a coincidence. "