Photons are massless. Gluons also are thought to be massless, but they are not free particles, so their velocity or locus of interaction generally is assumed to be unobservable.

What is the nature of the Higgs field?

Well, because it determines rest mass, its effects must be Lorentz invariant. Therefore, it must be a differential field in which position is undefined. A similar "field" is that of the vacuum permittivity, which is everywhere and which, with the vacuum permeability, determines the

speed of light c, which of course is the same in all inertial frames.

Here's my question: If we don't need a "permittivity particle" to describe electrical properties of the vacuum, why should we need a "mass particle" to describe the mass-giving properties of the vacuum?

The "mass particle" in question is the Higgs boson -- a scalar to account for the differential nature of the Higgs field, and a boson to account for its assumed zero (or maybe unit) spin. By analogy, the electromagnetic forces are mediated by exchange of photon bosons, the weak

force by exchange of W or Z bosons, the strong force by gluons -- and, the mass force (as it were) by Higgs bosons.

The Higgs boson is calculated from Standard Model consistency not to be massless, but rather to have a mass probably between 100 and 200 GeV/c^2, as much as twice the mass of the weak force bosons. According to this model, the Higgs boson may possibly have a mass as great as 1000 GeV/c^2, but not more than this.

One of the goals of current work with the Large Hadron Collider at CERN is to observe the Higgs boson. But, if it represents a nonpositional field, why should energy concentrated at a certain position, the collision point, make any difference?

And, should the "mass particle" have mass? If so, it must react on itself in an illogical way. Also, if the Higgs boson is massive, and if it mediates mass by vacuum virtual exchanges, the exchange rate must be subject to Lorentz time dilation. Because other forces grow with boson exchange rate, time dilation would suggest that the rest mass of all particles should decrease with

increasing relativistic velocity, possibly cancelling the observed increase in particle momentum.

Thus, it appears that there may exist a Higgs vacuum field, but there may not exist a Higgs particle. And if there is a Higgs boson, it should be massless.

How can these objections be answered? The Standard Model apparently is wrong about the mass of neutrinos, so why should it be accepted uncritically in regard to the mass of the Higgs boson?

## Comments

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Photons are the only particle confirmed massless by measurement of their velocity. Gluons are observed only by inference, and gravitons, if they exist, have not yet been observed.

I'll try to answer these points in the same order you asked.

Gluons are known to be massless. They mediate the color force, in the same way that the photon mediates the electromagnetic force. Color is an exact symmetry, and this requires gluons to be massless. Although they interact strongly with quarks and with each other, they do live long enough for their position and velocity to be meaningful. For example a high-energy gluon produced in a collision can be observed to decay into a "jet" of other particles.

The "permittivity of vacuum" is not a property of anything. It's just a defined constant that is used to convert between different sets of electromagnetic units.

The Higgs is not a "mass particle." The purpose of the Higgs field is to break electroweak symmetry. If electroweak symmetry were exact, the electromagnetic force and the weak force would have the same strength. And if it were not for the Higgs field, the photon, W-meson and Z-meson would all have the same properties. Indirectly, the existence of the Higgs field allows the fermions (quarks and leptons) to have a nonzero mass in a manner consistent with electroweak symmetry. But the Higgs particle does not couple to all particles through their mass -- the graviton plays that role.

(Note that the Higgs boson is not the same as the Higgs field. The Higgs boson is an excitation of the Higgs field. The Higgs field is uniform throughout space, while of course a Higgs boson is localized, the same as any other particle.)

Finally, it's not fair to say the Standard Model is "wrong" about neutrino masses. We now know these masses must be nonzero, and they may very easily be added to the model, but for most purposes they're ignored.

I disagree on permittivity: The vacuum permittivity is a property of the vacuum, just as is the Higgs field. The mass of the electron is assumed determined by the Higgs, and this is no different that saying that the speed of light is determined by the vacuum permittivity (and permeability). I would agree that it might be possible to use some other approach than Maxwell's to handle electromagnetic fields; nevertheless, the speed of light is determined by properties of the vacuum, and there is no essential reason why the speed of light (c) could not be some different value, were the vacuum itself different.

Maybe I was ambiguous on the objection to Higgs mass: I agree that the graviton, if it exists, is what couples massive particles by their mass. However, what determines the rest masses to be coupled is the Higgs field. If there is a Higgs boson, and it works by virtual exchange, and it is itself massive, then the REST masses of particles relativistically in motion should decrease because of time dilation. This in turn would alter graviton exchange, which was not intended to be my main point.

Yes, the Standard Model might be enhanced to accommodate massive neutrinos; however, at present, it has not been so (in a widely accepted way). Perhaps I should suggest that it be changed to eliminate the Higgs boson or at least define it to be massless?

I just don't think it is enough to BELIEVE in a graviton or a Higgs boson to make it exist; there has to be experimental evidence directly supporting such beliefs. At present, they may be reasonable hypotheses . . ..

All of these statements are incorrect. First of all, the Higgs field has a uniform value everywhere, and since it is a scalar field it is also the same in every rest frame. So all particles see the same value of the Higgs field regardless of their motion. This value is usually denoted v.

The Higgs field permits each fermion to have a mass, but does not "determine" it. The mass will be Gv (G times v) where G is a coupling constant different for each type of fermion. No one knows what determines the G values, but it is certainly not the Higgs or anything else within the standard model. There is no "virtual exchange of Higgs bosons" going on!

As far as the Higgs mass goes, if it were anything small it would have been seen long ago. Experiments at the previous CERN collider (the LEP) ruled out a Higgs mass below 115 GeV,

I disagree with the hair you are splitting with the rest: If other particles "couple" with the Higgs field, then standard application of field theory implies that this coupling is mediated by virtual particle exchange. It doesn't matter what determines each particle's coupling constant; that wasn't the point. If coupling to the Higgs field is required to determine the mass, then my point is as presented.

Look at a simpler analogy: The (nonrelativistic) momentum of a particle is given by m*v, m the rest mass and v the velocity. Therefore, one can assert that m determines the momentum, even though changing v (read, varying Higgs G across different particles) changes the momentum, too. If m is allowed to go to zero, the momentum goes to zero, regardless of v (of course, I am not trying to make an issue of how the singularity of EXACTLY zero mass could be reached). For a specific v, m determines the momentum of a particle.

If there were no Higgs field, then, accepting the theory, there could not be a mass for any of those particles, regardless of its particular G. Thus, coupling to the Higgs field determines the mass. Naturally, various particles have different masses; I did not intend to say that all particles had the same mass because the mass was determined by the one Higgs field.

OK. Let me ask you, what mediates the coupling of the Higgs field to a particle?

My answer is that it must be virtual exchange of Higgs bosons. Do you know this to be incorrect? Even if the Higgs bosons didn't couple to anything, but merely popped in and out of the vacuum, if they were massive, they would be associated with an inertial rest frame and thus would experience time dilation relative to other particles in relativistic motion. One can not have a scalar boson which fails to break symmetry (as would a scalar field) and is "massive" in any meaningful way. Mass is equivalent to failure of Lorentz invariance.

The illogic which I see here is the idea of a massive scalar particle. This contradicts special relativity, which has been confirmed in all other contexts.

As for your final point, you are begging the question that the Higgs exists, just because some thing can be calculated for it in the Standard Model. As I mentioned before, the Standard Model is known to be defective with regard to neutrino masses. It is just a model which provides a consistent analogical framework for much of particle physics. So, at least in my opinion, one can not assume that it is so correct as to be allowed to contradict special relativity.

1) "Gluons also are thought to be massless, but they are not free particles, so their velocity or locus of interaction

generally is assumed to be unobservable."

According to wiki, experimental limit of the gluon is < 20 MeV/c^2

2) The part about vacuum permittivity

I don't understand how vacuum permittivity can be thought of as a field?

According to wiki, vacuum permittivity = permittivity of free space, which is a constant. Combine with vacuum permeability, it gives the speed of light in vacuum.

3) "mass force (as it were) by Higgs bosons"

I don't think mass is a force?

3) "why should energy concentrated at a certain position, the collision point, make any difference?"

Higgs couples to mass, I think the process they are mainly looking for in LHC is gluon-gluon fusion, which gives top quarks in the immediate stage and see if this will produce the Higgs. In order for this to happen often, it requires high energy.

4) "And, should the "mass particle" have mass? If so, it must react on itself in an illogical way. Also, if the Higgs boson is massive, and if it mediates mass by vacuum virtual exchanges, the exchange rate must be subject to Lorentz time dilation. Because other forces grow with boson exchange rate, time dilation would suggest that the rest mass of all particles should decrease with increasing relativistic velocity, possibly cancelling the observed increase in particle momentum."

I don't really understand this paragraph at all.

Higgs is not a "mass particle" (covered by Bill)

What is "vacuum virtual exchanges"? Why the exchange rate must be subject to Lorentz time dilation?

"Because other forces grow with boson exchange rate"

Are you saying, the strength of a force is proportional to the corresponding rate of boson exchange? If so, I think that is wrong, strength of a force is proportional to the coupling. It is the rate of a process that is proportional to the rate of boson exchange.

Rest mass by defination should not change, no matter what velocity it is travelling at.

Finally, you are correct about the neutrino having mass. Physicists know the Standard Model is not complete. There are actually quite a lot of different models beyond the Standard Model but we don't know which one is correct, that is one of the reason why we want to conduct experiments such as in the LHC and gives us hints which direction to head towards. If they can't find the Higgs in the LHC, then theorists might start to consider other mechanisms for the electroweak symmetry breaking.

"In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction."

I still don't quite understand your steps about Lorentz invariant.

From wiki again

"The invariant mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations. When the system as a whole is at rest, the invariant mass is equal to the total energy of the system divided by c^2, which is equal to the mass of the system as measured on a scale. If the system is one particle, the invariant mass may also be called the rest mass"

Which quantity are you saying is not Lorentz invariant? (Rest mass is Lorentz invariant)

Strictly speaking, everything moving with respect to (wrt) an observer will experience time dilation compare to the observer. This effect is barely noticable unless travelling at speed close to c.

So are you purposing the Higgs boson would be a free massless particle? If so, experiments would be able to detect it already. (as Bill said)

I personally think that, in order to talk about physics formally, it might be a good idea to study the actual physics, go through the mathematics. Then discuss possible mistakes in the physics (or maths). If you want to convince me with your theory, I think you will need to show me some maths.

"In physics, a fundamental interaction or fundamental force is a process by which elementary particles interact with each other. An interaction is often described as a physical field, and is mediated by the exchange of gauge bosons between particles. For example, the interaction of charged particles takes place through the mediation of electromagnetic fields, whereas beta decay occurs by means of the weak interaction. An interaction is fundamental when it cannot be described in terms of other interactions. There are four known fundamental interactions in Nature: The electromagnetic, strong, weak, and gravitational interactions. The weak and electromagnetic interactions are unified in electroweak theory, which is unified with the strong force in the Standard Model."

Are you saying the coupling constant is not Lorentz invariant if the exchange particle (boson) is not massless?

"What is the logical conclusion here? There is no Higgs boson. Or, maybe the massless search has not been performed adequately. Two rights make a wrong."

I don't know if there are Higgs boson exists or not, but that's not really the point of discussion. We are discussing if there are any flaws in the theory (Higgs mechanism) that tells us Higgs is not massless (rather heavy instead).

"Here' an analogy: The electromagnetic field couples to charged particles. The coupling is by massless photons. Now, when the electric and vector potentials couple, the result IS Lorentz invariant; however, coupling to a charged (massive) particle never is Lorentz invariant. My understanding from this is that if the Higgs were massless, it could mediate rest mass; but, if it were massive, than its effect on particles (rest mass) would not be Lorentz invariant. If there is a Higgs boson, it must be massless."

What RESULT are you talking about?

What do you mean by "mediate rest mass"?

If you don't mind, can you cite some sources where you get this information from?

"Is it possible that doing the math could convince you of something? I don't know, but jumpng into equations before understanding the problem often solves the wrong problem. As I have shown, the problem here is logical inconsistency of the assumption that the Higgs may be massive. How can anyone do any math describing a logical inconsistency?"

Other people might disagree with me. The language for physics is mathematics, when discussing physics purely using languages, it makes things very confusing/inconsistent and loses quite a lot of deep meanings. Mathematics itself is logical, so unless there is inconsistency in the maths, I wouldn't really call it an logical inconsistency. What you refer to "logical inconsistency" could just be your misunderstanding to physics?!

I agree mathematics is not "enough" for physics (up to a certain extend), some insight is required, but this insight is to help you simplify/make sense out of the mathematics. Sometimes, there are claims without much (or no) mathematical statements, most of those are unsatisfactory for physicists.

If you think about it, quantum mechanics itself begins more or less purely mathematical, it is rather counter intuitive. Funny enough, it gives some good prediction.

I still don't quite understand what is lacking of physical insight. I am trying to guess what you are suggesting the "problem" with non massless Higgs is, correct me if you are wrong. Are you saying the Higgs (or particles in general) shouldn't experience time dilation?

The Higgs mechanism is related to the Standard Model, which itself is a Quantum Field Theory (QFT). In QFT, it combines both quantum mechanics + special relativity. So, Higgs mechanism (if exists) won't contradict special relativity.

"Mathematics is simply a sequence of consistent equalities, of replacements of values (or names or expressions) with new ones; it can not resolve an inconsistency."

To most modern theorists, mathematics is more than this. (An extremely debatable point here)

"You know, a completely different, and physically tenable, way of postulating a massive Higgs boson is to say that the particle simply was something or other named after a great physicist, Higgs, and was unrelated to the postulated Higgs field . . .."

Not quite sure where you got this from. Some physicists might say Higgs is quite "dodgy" . To a lot of theorists, it would actaully be more exciting if the Higgs doesn't exist. Once again not the main point for this discussion.

One possible suggestion, if you are that strongly belief your theory is correct. Why not try and rewrite this blog into a more formal format (scientific paper) and try and submit it to couple of scientific (physics) journals and see if they would publish it. Also maybe e-mail Peter Higgs and couple other physicists that came up with the Higgs mechanism, show them this blog or your new rewritten paper and see what they have to say about it. Maybe they would agree with you and try and fix the problem.

**the Higgs field couples to it to give it its (always exactly the same!) mass. There may not be a causal sequence in what should be considered a typical point interaction. Perhaps one should consider equally valid that charge conservation occurs first, then apportionment of the net-zero charge, and momentum, among the particles created. If the creation interaction did not conserve charge, the electron could not be created; at least, that's what is observed.**

*then*Feynman diagrams are cartoons. They simplify the problem by representing perturbative solutions. If a perturbative term includes a negative term which may be used to negate a time coordinate, it doesn't mean that the actual interaction involves time-reversal (which violates the Second Law) -- even if it represents motion of a virtual particle. I don't think a Feynman diagram should be used to prove or disprove anything which might depend on ignored, nonperturbative terms. You might have to look into the work of Schwinger for insight.

*c*, as has been argued in a brief proof at http://www.siuc.edu/~pulfrich/Pulfrich_Pages/lit_nonp/phys_astro/2007_cS...

By arguing about axioms doesn't that make them no longer axioms?

http://en.wikipedia.org/wiki/Axioms

Quote “In the modern understanding, a set of axioms is any collection of formally stated assertions from which other formally stated assertions follow by the application of certain well-defined rules. In this view, logic becomes just another formal system. A set of axioms should be consistent; it should be impossible to derive a contradiction from the axiom. A set of axioms should also be non-redundant; an assertion that can be deduced from other axioms need not be regarded as an axiom.”<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

Typically, the

**number**of (nonredundant) axioms is more important than the particular set chosen for some purpose. A system becomes more complex, the more the axioms. An analogy here might be that axioms determine something similar to the dimension of a vector space: The bigger the basis set, the more the dimensions -- where the analogy fails, the difference here, is that in math the algebra is the same no matter how big the basis set. In logic, there is a QUALITATIVE change produced by adding axioms.

For example -- maybe a little off-topic -- the famous Goedel proof of the undecidability of certain propositions requires an axiomatic system with at least two independent operators (say,

*and*and

*or*; or

*nand*and

*nor*;

*etc*.) a system with just one operator can not contain undecidable propositions and therefore differs fundamentally from one with several.

Thanks

OK. Here is a slighr generalization and, I think, a conclusion for this blog:

A. Scalar particles do not break Lorentz symmetry.

B. Massive particles break Lorentz symmetry.

**Conclusion: No scalar particle can be massive.**

Corollary 1: Any logically correct derivation which implies a massive scalar particle is based on at least one unphysical assumption.

Corollary 2: Any assumption of a massive scalar particle is unphysical.

*Specifically, if the Higgs boson exists and is massive, it can not be a scalar particle.*

just like an atom of a refractive material, e.g., water, glass.

And just like the atom, the Higgs can be massive itself.

All the other particles in the Standard Model obtain

their mass dynamically when propagating in the Higgs medium,

similarly to how photons obtain an effective mass in water or glass.

One can think of a snake as a worm or an eel and thus assume that, just like worms, snakes are slimy -- which they are not.

If a Higgs boson existed and was massive, it would have to be at rest in some inertial frame. Therefore, the mass it gave to other particles would have to decrease as their velocity increased in that frame. This is not observed.

This is not necessarily true, depends on the precise form of interaction with the medium.

Getting rid of the Higgs boson means that the standard model will lack unitarity, so it now becomes an "effective theory". Everybody believes that it already is an effective theory. The problem really is: mass is a gravity parameter and to derive the values of mass must bring in gravity. The standard model has no gravity, so how could you imagine you can solve the origin of mass within the model?

Quote:

"OK. Here is a slighr generalization and, I think, a conclusion for this blog:

A. Scalar particles do not break Lorentz symmetry.

B. Massive particles break Lorentz symmetry.

Conclusion: No scalar particle can be massive." End Quote

Simple counter example: the neutral kaon (real observed particle) is scalar and massive

I can give you more detailed reasons of why your arguments are so wrong, but first you need to (seroiusly) study some basic physics, otherwise it's a waste of time

Because neutral kaons do not determine the mass of other particles, are not involved in anything but their own mass, they are irelevant to this discussion.

Special relativity works; therefore, there can not be a MASSIVE Higgs boson, whether scalar or not.

Calling you a crackpot is not silly name-calling, but an accurate description. I have to give it to you though, you belong to the new generation of crackpots who, finally, have moved on from relativity and are now focusing their FUBAR arguments on quantum/particle physics

Anyway, it was a funny game to pick on you crackpots but now is becoming boring, so here's a final assignment: study the Higgs sector Lagrangian of the SM, specially the mass term after symmetry breaking, or better yet, start with a simple non-interacting fundamental scalar field and check if a mass term exists that fulfills all the requirements of a relativistic quantum field theory

If a scalar boson exists which determines the mass of a particle, that boson can not be massive, or relativistic time dilation would cause the standard Lorentz transformations to fail for the latter particle. We know these transformations work, so putting a lot of (quantum) crystallography before actual facts belies the claim that such a boson might be massive. There might indeed be a boson which is massive and as yet undetected; if so, it won't have the properties usually ascribed to the Higgs.

You know almost nothing about me, or what I know, or which courses I have take to support my claims. Or who I have studied under. You don't agree with my assertions -- which of itself is fair -- but you jerk your knee instead of your brain and substitute name-calling and other ignorant tactics for reasonable disagreement. Shame on you! Who on Earth do you think cares whether you are "bored" or not? Spend some more time gazing at your image in the pool, and stop bothering people trying to hold a serious discussion. Why criticize me; I'm just the messenger . . .?

Morabito, D. L.; Fujita, S.; Godoy, S.

American Physical Society, APS/AAPT Joint April Meeting, April 18-21, 1998 Columbus, Ohio, abstract #N27.05

(For abstract, see http://adsabs.harvard.edu/abs/1998APS..APR.N2705M)

Unfortunately, the link to the "full text" of the article is broken.

Using the authors' quantum statistics arguments, Higgs bosons can exist (as massive particles) if they are not elementary, i.e., they are composites of some elementary fermions. The article postulated Lorentz-invariance for the centre-of-mass of such composite particles.

I see this discussion is in part revolving around the mass of the Higgs Boson. When I was studying physics 26 years ago, I learned that mass itself was a function of inertia. I wonder if that view still prevails? If so, are we in essence extrapolating that mass is, in essence, a fundamental interaction [inertia] between e.g. the Higgs field and those particles which we observe as massive [i.e. those which couple with Higgs bosons]?

From my position of vast ignorance my brain is trying to extrapolate outwards from existing knowledge, and is drawing parallels with the e.g. simplicity of Fleming's Left Hand Rule, and I find myself wondering if the CMS experiment at CERN is essentially observing an interaction with analogous characteristics but set in an entirely different context?

This position of ignorance being quite a cosy place, the above thought is not lonely. Side-stepping the question of whether or not the Higgs field is uniform or not [and accepting the fact that so far we have only "observed" the Higgs under outrageously extreme conditions], I am curious to understand where any postulated "Higgs Field" may exist in entropic terms. Does our understanding suggest that the Higgs field exists today [i.e. in a background state, the "ether"] but is not directly observable, or does it suggest that it may exist only within a defined range of energies or states? My idiotic and ignorant questions are asked to help me understand how entropy would feature in this scenario. We discuss the fundamental particles of the Standard Model, where they seem to exist for fleeting moments, or in curious pairings. Yet the observable universe, entropy notwithstanding, appears to be stable given the rate with which we observe the passage of time... So... if the Higgs field exists throughout the universe today, do we have Higgs particles imparting mass to observable "matter"? If so [and again, my ignorance suggests this must be the case], how come we can only observe them at CMS-level energies? [ Is this simply the level at which we can observe them as discrete entities - i.e. they're there all the time, but to observe discretely we need to excite some matter to a point where a Higgs detaches and becomes separately observable? ]

Attempting to return to my theme.... If there is a "Zero Point Energy" - i.e. a theoretic or otherwise entropic "nothing" at which all fundamental activity in the universe stops, then what we are able to conventionally observe would seem to exist in a relatively narrow "energy band". The CMS experiment shows that different particles and forces exist [discretely] at different energy levels. Is it possible that other [as yet un-named, un-observed, un-postulated] fields could co-exist in this space-time, but at much higher energy levels? In trying to wrap my feeble brain around recent news announcements, I formed this mental image of a three-dimensional space in which a multitude of different radio waves were propogated. Each signal existed at a different frequency and thus didn't interfere with the other signals. I wonder if what we have here is a complex universal system that exists with more than one "energy layer"... [ and I am sorry that I am making such a terrible job of trying to explain myself].

We know that when we connect a high electrical potential to an earth, an electrical current will flow. We think we understand how this happens, but I am less sure that we understand the *why* of it. But what about an analogous interaction in terms of energy states. My limited understanding of entropic flow suggests that matter existing at high energy levels will disseminate, distribute or share that energy until it gradually reduces it's own energy level. Steam condenses: water freezes. We have succeeded in using such thermodynamic principles to our advantage [i.e. heat pumps, refrigerators]. Does the possibility exist, therefore, that just as we learned how to harness electrical potential difference and exploit it as units of energy (watts) that we might be able to harness the potential differences between energy at these different states in a similar way?

I'll end as I began: please forgive my ignorance. I guess the important thing is to never stop asking, "Why?"

Thanks in advance to anyone who has the patience to respond.

I do hope someone here with the right credentials, will soon respond to your seemingly to me, very intelligent questions and observations regarding the Higg's boson and results and shed a bit of light for us all. Good luck.

Yes, I've read the report of CERN, that either the predicted, massive Higgs boson has been derived from respectable data, or that, maybe, some more or less equivalent massive particle has been derived.

I may modify my post to acknowledge that it is wrong, for some reason, but I am awaiting more information concerning what it is that CERN is studying.