The first day of the SEARCH workshop was focused on current and future measurements of the new Higgs particle discovered in 2012. A lot of the issues I’ve written about before (for instance here and here) and most of the updates were rather technical, so I won’t cover them today. But I thought it useful to take a look at what was said by Raman Sundrum and separately by Nima Arkani-Hamed, whom you’ve heard about many times (for instance, here and here), on the subject of the hierarchy problem and “naturalness”.

First, let me remind you of the issue. The hierarchy problem can be phrased in many ways. Here’s one. Here’s another: for a Standard Model Higgs (the simplest possible type of Higgs particle) to show up, without any other new particles or forces at the Large Hadron Collider, is … well, let’s say it’s completely shocking, with a caveat. Why?

- Because every spin-zero particle (or particle-like object) that has ever been observed, in particle physics and in similar contexts within solids and fluids, has been accompanied by new phenomena at an energy scale comparable to the scalar’s mass-energy (E=mc
^{2}energy). - And although we cannot calculate the mass of the Higgs particle using the Standard Model (the equations we use to predict the behavior of the known particles and forces) — the Higgs particle’s mass is something we put
**in**to the equations, which is why we didn’t know, before the LHC, what it would be — there are many speculative theories that go beyond the Standard Model where the Higgs particle’s mass*can*be computed, or at least estimated. And in all of these cases, the Higgs particle is accompanied by other particles and forces that show up at scales comparable to the Higgs particle’s mass-energy.

This fact — that spin-zero particles like the Higgs are accompanied by other particles and forces at a similar energy range — isn’t a mystery. Particle physicists (and others who use quantum field theory, the type of math used in the Standard Model) understand *why* this should be true, and have for several decades. The jargon is that it is “**natural**” (not meaning “from nature”, but rather meaning “generically true”) for spin-zero particles to have other particles and forces around at comparable energy scales. (I’ll explain the argument another time.)

So to discover the Higgs particle at a mass-energy of 125 GeV, and no other new particles or phenomena below, say, 1000-2000 GeV or so, would fly in the face of what we’ve seen again and again in physics, both in past data and in calculations within speculative theories. In this sense, *finding nothing except a Standard Model Higgs at the LHC would be shocking*. (I say “would be” rather than “is” because the LHC is still young, and no overarching conclusions can yet be drawn from its current data.)

But — here’s the caveat — how bad is this shock? After all, *somewhat* surprising things do happen in nature all the time. Only astonishingly, *spectacularly* surprising things are very rare. Yes, it would be a very big shock if new particles and forces associated with the Higgs have a mass-energy a trillion trillion times higher than that of the Higgs. But what if they’re just a *few* times higher than would be natural, let’s say at 10,000 GeV — which would be out of reach of the LHC? Maybe that is a small enough shock that we shouldn’t pay it much attention. Unfortunately, this is a judgment call; there’s no sharp answer to this question.

As Sundrum put it, there are (crudely) three logically distinct possibilities for what lies ahead:

- No shock: The hierarchy problem is resolved naturally; the associated new particles will soon be seen at the LHC.
- Mild shock: The hierarchy problem is resolved in a
*roughly*natural way; most of the associated new particles will be a bit beyond the reach of the LHC, but perhaps one or more will be lightweight enough to be discovered during the lifetime of the LHC. - Severe shock: The hierarchy problem is not resolved naturally; any associated particles may lie far out of reach, though of course other particles (associated, say, with dark matter) might still show up at the LHC.

Arkani-Hamed made a similar distinction, but addressed the third case in more detail, breaking it up into two sub-cases.

- The solution to the hierarchy problem is that it results from a
*bias (= selection effect = a form of the “anthropic principle”)*; the universe is huge, complex and diverse, with particles and forces that differ from place to place [sometimes called a “multiverse”], and most of that universe is inhospitable to life of any sort; the reason we live in an unusual part of that universe, with a lightweight unaccompanied scalar particle, is because this happens to be the only place (or one of very few places) that life could have evolved. A key test of this argument is to show that if the particles and forces of nature were much different from what we find them in our part of the universe, then our environment would become completely inhospitable — perhaps there would be no atoms, or no stars. It is controversial whether this test has been passed; good arguments can be made on both sides. - The solution to the hierarchy problem involves
*a completely novel mechanism*. Easy to say — but got any ideas? Arkani-Hamed gave us two examples of mechanisms which he had studied that he couldn’t make work — but perhaps someone else can do better. One is based on trying to apply notions related to self-organized criticality, but he was never able to make much progress. Another is based on an idea of Ed Witten’s that perhaps our world is best understood as one that- has two dimensions of space (not the obvious three)
- is supersymmetric (which seems impossible, but in three dimensions supersymmetry and gravity together imply that particles and their superpartner particles need not have equal masses)
- has extremely strong forces

All of this seems completely contradictory with what we observe in our world. But! One of the important conceptual lessons from string theory

*[this is yet another example of something important that would not have been learned if people hadn’t actually been studying string theory]*is that when forces become very strong, making the physics extremely complicated to describe, it is possible that a better description of that world becomes available — and that in some special cases, this better description has*one additional dimension of space*and*weaker forces*. In short, Witten’s idea is that our way of understanding our world, with three spatial dimensions, no apparent superymmetry and no extremely strong forces, might actually be simply an alternative and simpler description of a supersymmetric world with only two spatial dimensions with an extremely strong force. Arkani-Hamed, trying to apply this to the hierarchy problem, noticed this idea makes a prediction, but he showed that the prediction is false in the Standard Model, and it seems impossible to add any collection of particles that would make it true.

Two dimensions? Multiverse? Blinking heck Matt. That’s way out. That sort of stuff isn’t going to help HEP at all. Not a bit.

Thank you for your uninformed opinion.

The “multiverse” is not a new idea, and it is in fact a very reasonable one. Why shouldn’t the universe be a large and diverse place? What do we know for sure, other than the region of the universe that we can see with our telescopes is fairly uniform? There may be a “multiverse” even if its existence has nothing to do with the hierarchy problem.

Two spatial dimensions would be radical. But the statement that a theory in one set of dimensions may have an alternate description that uses a different set of dimensions is a

factin quantum theory, not a speculation. This fact may seem strange to you (it seemed strange to us when it was discovered, but the mathematics is very clear) but sometimes it pays, before you spout hot air, to actuallyreadwhat scientists have been doing in the last few decades. Now this fact may not be relevant in the real world — but it is worth thinking about it.The solution to the hierarchy problem involves a completely novel mechanism. Easy to say — but got any ideas?

Yes Prof it seems obvious that we only exist in 1 dimension, which has matter ‘currently’ in our universe which causes us to think we live in 3D thanks to Euclid. And forget Minkowski temporal time. 1 dimension + constant time but with 3 choices of orthogonal directions thanks to matter. Which are not dimensions just ‘directions’ in same dimension.

The mass of the smallest possible black hole defines what is known as the Planck Mass.

Plank mass is based on the V velocity of light ( in his equation if I am not mistaken )

Velocities occurring within a BH may be superior V – which impacts on predicted Plank mass above .

Also does energy have a mass? I suspect no particles exist in BH’s – just energy as everything is stripped down and unidentifiable in the conventional 2000 AD science.

Energy and mass are properties of things; energy is not a thing and it cannot “have” a property of things, like mass or momentum or charge or…

What happens to your plank mass it we change the value of C in his equations? C is a constant only because it is a popular number for its v which we cannot challenge. This does mean that higher velocities cannot exist – just we cannot demonstrate it. I think there is a relationship between C and Space. C can only achieve C when space is emerging at this background velocity. From the mind of Newton. Not that this specifically was in his head. The conditions in space determine the velocity of C. If it changes so does C and matter disappears. We are trying to understand the universe based upon the characteristics of matter. This is not the path to wisdom ( in my humble world ).

If we exist in 1 dimension with constant time

No time shall pass as we move from one location to another ( our entire lives )

If we are measuring our distance by means of matter then we shall see everything differently in the real world

Please don’t leave a long unbroken sequence of comments, especially ones that have no relevance to the post. It clutters up the comments and annoys other readers.

Once I asked you if you think there was any connection between Higgs energy (246 Gev) and cosmological constant (Dark energy Lambda). I think your answer was a firm no. Then recently I watched Sean Carroll’s talk at Fermi lab. On a graph showing the bottom of the potential energy valley in which Higgs is sitting, he had written dark energy. This does not look like typo, because in the same sentence he talked about accelerating universe. My question is: are there physicists who think there is a connection between dark energy and Higgs energy and is your answer still no? Thanks.

kashyap vasavada

I don’t remember your precise question or my precise answer, so I can’t compare what I’ll say now to what I said before.

First: when you ask “are there physicists who think X?”, the answer is almost always “yes”. If you ask “do most physicists think X?”, you may get a very different answer.

However:

There is no such thing as “Higgs energy”.

There is a Higgs particle mass. That is determined by the *shape* of the potential energy function, in particular the curvature at the minimum of the potential.

There is a Higgs field “value” (“expectation value”). This is ALSO determined by the *shape* of the potential energy function, in particular the *horizontal location* of the minimum of the potential.

There is dark energy, which depends on all sources of energy density in the universe, not just Higgs. This determines the *vertical location* of the potential energy function on Sean’s graph, shifting it up or down. I believe this is what Sean was showing.

There is no obvious connection between the shape of the potential energy functional and its overall vertical location. The calculation of these two things is very, very different.

Attempts — none of them widely considered successful — have been made to link the shape of the potential to its vertical location. So the answer to your question is: no one has made a link that is widely considered plausible between the dark energy and either the Higgs particle’s mass or the Higgs particle’s value. One of the best attempts was made by my Rutgers colleague Tom Banks, see for example http://arxiv.org/pdf/hep-th/0305206v1.pdf

Thanks for clarification. I was thinking that since he called the vertical displacement “dark energy” he may have a model in which vacuum expectation value of Higgs field or shape of the potential energy makes dominant contribution. I suppose the situation may be fluid now and there may be many models. Congratulations on your move to Harvard. Please keep us in mind when you move to Harvard!

I’m sure he doesn’t have such a model.

Thanks; I won’t be dropping the blog except when science requires it.

Prof how do you know the Higgs phenomena was not a 2+1 or 2+2 collision vs 1vs1 contact. And if so how would this affect the outcome of detection data?

Two dimensions? link/url to something explaining how the real world could have only two spatial dimensions? It really appears so far from reality. Thanks for your kind answer

Google “holographic principle”.

You answered my question.

Now this holographic principle can well be a better mathematical explanation of black holes and quantum gravity and maybe susy particles, ok, interesting model, but, ehm… you can fft a bread&butter’s image but can’t eat its holographic pixels 🙂

Sure you can eat it, if what you’re made from is also hologram.

I couldn’t find a very good link, (http://en.wikipedia.org/wiki/Uncertainty_principle#Signal_processing gives some explanation) but sound is an example of something we perceive as having three dimensions (time, frequency, amplitude) while it really only has two.

Naively, as position and momentum have an uncertainty principle for the same reasons time and frequency does (correct me if I’m wrong) it wouldn’t seem very far fetched if our 3-d space is really 2-d.

The incertainty principle is again a quantum mechanics principle: there is no such incertainty in classical physics, nor entanglements or nonlocality… Strings theory strives to reconcile this duality, with no experimental evidence as far as I know… ?

Are the slides from the conference available anywhere? I can find the SEARCH 2012 stuff, but not for this one.

They’re at http://scgp.stonybrook.edu/search

Thanks!

You say “[t]he hierarchy problem can be phrased in many ways”, but I cannot see the connection with the hierarchy problem you describe in your other article. Does it just mean we don’t know why the Higgs mass is of a certain magnitude/new phenomena do not occur at that magnitude, or is there more to it?

Also, »our way of understanding our world, with three spatial dimensions, no apparent superymmetry and no extremely strong forces, might actually be simply an alternative and simpler description of a supersymmetric world with only two spatial dimensions with an extremely strong force« sounds fascinating, but is there any chance of explaining how this would work? Witten kind of lost me with »supersymmetric bose-fermi degeneracy«.

And the final sentence:

»Arkani-Hamed, trying to apply this to the hierarchy problem, noticed this idea makes a prediction, but he showed that the prediction is false in the Standard Model […]«

This means the standard model makes different predictions?

»[…] and it seems impossible to add any collection of particles that would make it true.«

And this means you can modify the standard model in a restricted way (by adding new particles); but no such modification would yield the same prediction as Arkani-Hamed’s idea? Am I correct? Sorry, if I am obtuse.

Not obtuse at all.

1) the hierarchy problem is the question of why gravity is so weak compared to other forces; equivalently, why the Higgs particle’s mass and Higgs field’s value are so small compared to the Planck scale, where gravity becomes strong; equivalently, why the Higgs particle of the Standard Model can be so light compared to any particles that would have a hope of preventing quantum mechanics from making its mass much larger. This set of linkages requires a long set of articles that I have not attempted to write yet.

2) to explain how a world with a certain number of dimensions could be equivalent to a world with a different number of dimensions is not at all easy; quantum mechanics plays a role, and you have to think very, very carefully about what it means to observe the world around you. I have not attempted to write such an article as yet.

3) What Arkani-Hamed meant: Witten’s idea, at least as Arkani-Hamed tried to implement it, is not consistent with the known particles and forces, whose properties we calculate using the Standard Model. It appears to be impossible to imagine additional unknown particles and forces that would fix this idea. In short: by doing a calculation, Arkani-Hamed found that all versions of Witten’s idea that he could think of — an infinite set — appear to give an incorrect prediction.

Both Ed Witten and Arkani-Hamed might be making all kinds of sense on their saying to physicists. But, an old grandmother would like to ask two simple questions.

She has learned two concrete material facts about *this* universe.

a. There are 48 Standard Model matter particles, verified by tons of test data.

b. She herself is alive, and life needs a computing device to maintain an ordered envelop (the body) in the torrent of entropy (going to disorder).

The two questions are very simple.

1. Can these two find the theoretical *base* of the 48 SM particles of *this* universe from their zillion multiverse? Note: she is not interested in those other-verses which she is not lived in.

2. Is the computing device which supports her life embedded in the physics laws of *this* universe? Or, she picked it up from somewhere else?

These are indeed two very simple questions. Yet, they are still not fair questions if no one else can answer them. Did someone else answer them already?

“There are 48 Standard Model matter particles, verified by tons of test data.”

Where did you get this from? While there are some intricate subtleties regarding how the particles should be counted, and when two particles can be considered “different”, it is absolutely not true that there are 48 of them. The actual number is much more close to 100.

Let’s see… Quarks: left up, left down, right up, right down, each coming with either R,G or B color. That gives 12 quarks (in the first generation). Leptons: left electron, right electron, left neutrino (I am discussing the *old* Standard Model, so there are no assumptions about right neutrinos or such). Leptons are colorless, so there are 3 of them. This means that the full number of particles in the first generation is 12+3=15. Now, there are three generations, and there is an antiparticle for each of these particles. So we have 15x3x2 = 90 fermions in the Standard Model. Now let’s see the interactions. In the electroweak sector, we have four of them: photon and Z_0 (each being its own antiparticle), W^+ and W^- (each other’s antiparticles) — so 4 electroweak, corresponding to 4 generators of SU(2)xU(1). The strong sector — 8 gluons, corresponding to 8 generators of SU(3) (mutual antiparticles among themselves). Scalar sector — 1 Higgs so far observed (self-antiparticle). Gravitational sector — 1 graviton suspected (without observations, self-antiparticle). So the interactions total 4+8+1+(maybe 1) = 13+(maybe 1).

So the grand-total is 90 fermions plus 13+1 interactions: minimum 103 different elementary particles so far observed, with one more expected but beyond observation. When you look at it, it’s similar to the number of chemical elements in the Mendeleev periodic table. 🙂

And that doesn’t count dark matter, dark energy, inflatons, supersymmetry, quintessence, GUT particles, and all other stuff that physicists sometimes expect to observe in collider experiments, but don’t.

As a side remark — if one counts the number of independent degrees of freedom instead of the number of particles (i.e. the grand-total number of “fields” in that quantum field theory we call the Standard Model), the number goes roughly from 103 to somewhere around 400. This is mostly due to the fact that each of the fermions is described by a “four-component field”, while the interactions are not too far behind that.

So 48 is waaay off. 😉

HTH, 🙂

Marko

The grandmother will be their (Ed Witten and Arkani-Hamed) disciple if they can reproduce (derive) “48” (out of those zillions in your count) from their theories.

Counting both the particle and its antiparticle seems odd to me. And to Dirac, I would think.

Red quark has a different quantum field than a blue quark (of otherwise the same type)?

Of course it does, color is a charge like any other charge (say, electric charge). A particle cannot change its charges, nor can a field. Charges are called “good quantum numbers”, because there is a conservation law for each of them.

It is the same situation with antiparticles (regarding the question by Xezlec). The charge of a positron is opposite from electron, and they are experimentally distinguishable. They should certainly be counted as different particles, because their charge is conserved and cannot be changed.

HTH, 🙂

Marko

vmarko — you are correct that color is a good quantum number, but you are not correct that “red-ness” is conserved AT ANY ONE PARTICLE. A quark can change from red to blue if it is hit by a blue/anti-red gluon — and inside a proton this happens every 10^(-24) seconds or so.

One thing to note is that red quarks are continuously changing into blue and green quarks and back, because of the nature of the strong nuclear force. This makes it impossible to really ascribe a particular color to a particular quark. All we can do is count the number of colors — 3 — that we need to put into our equations. With 3, we match all known experiments; with any other number, we don’t even come close.

Couldn’t find the “reply” button to your previous comment, so I’ll have to reply here, sorry… 🙂

“you are not correct that “red-ness” is conserved AT ANY ONE PARTICLE. A quark can change from red to blue if it is hit by a blue/anti-red gluon”

Note that my reply was in context to Martin’s question, asking about a single Dirac field changing its color. So the word “particle” in my answer should be understood as a “free field excitation”-particle, rather than the “1/3 of a proton”-particle. So much for terminology.

A red quark cannot change its color to blue *by itself*, it needs to interact with a gluon. And in this interaction, one red quark gets annihilated, while one blue quark gets created. These two quarks are *different* particles, described by different Dirac fields. In that sense, the “red-ness” is indeed conserved for a given single field, or “at any one particle”.

By the logic of your argument above, you could also have said that the electron and a neutrino are the “same particle”, because an electron can “change” into a neutrino by absorbing a W^+ boson. But it does not make much sense to call them the same, and either way you need *two* Dirac fields to account for the interaction, one cannot be enough. Similarly, when you say

“One thing to note is that red quarks are continuously changing into blue and green quarks and back, because of the nature of the strong nuclear force.”

it can be interpreted in a misleading way. Red quarks do not “change” to blue and green — rather, red ones get annihilated, while blue and green ones get created. And vice-versa. But they must still be different particles, each being an excitation of its own Dirac field.

I hope this clears up my previous comment. 🙂

Best, 🙂

Marko

/2. Is the computing device which supports her life embedded in the physics laws of *this* universe? Or, she picked it up from somewhere else?/

It is non axiomatic, non semantic (ineffable) – but in “this” universe, not in other verses.

It may be the “space” in local symmetry filled with non axiomatic linguistic manifestation (effable). Standard model filled it with virtual particles or artifices – which artificially creates warped extra dimensions. ?

How it went? At the Frontier: Where New Physics May Lie Hidden (45 min) Matt Strassler… I hope you brought ToEbi on the table 😉 Here is my latest treat //toebi.com/documents/AtomModelAndRelativity

Kimmo — this site is not a freebie location for you to advertise your personal ideas. Please don’t use it as advertising space. I’ve considered charging for the privilege ($100 per usage), but right now, it’s simply forbidden.

So be it.

While I admire the creative effort involved in the idea that the gravitational force is so much weaker than the other forces because gravitons are closed strings that naturally escape our 4-d space-time flittering through higher dimensional spaces and thereby diluting the force between objects in our space-time – currently there is not the slightest bit of experimental evidence for such a conjecture.

I have taken a different approach and plan to publish it eventually…depending on upcoming experimental results. It truly unites the gravitational and electrical force and makes a number of very specific predictions. I’ll give you a couple of them and perhaps you can set me straight right off…

Among other things it is predicted that there is an interaction between electric charge and mass. For most distances (>>10^-16 m and <<10^22 m) the equation for the interaction reduces to: F = – (GK)^1/2 mqR/r^3 where G is the Gravitational constant , K is coulombs constant (1/4πε), m is the mass of one body, q is the charge on the other body, r is the distance between them and R is a new constant ~ 4.0×10^-16 m.

By coincidence it turns out this electrogravitational force between an electron and the Earth is repulsive but about equal in magnitude to the gravitational force between them (especially when the fact that the Earth is an extended and not a point mass is taken into account). Thus (depending on altitude) a free electron will not fall!

Also, because under the theory the true nature of gravity is electric and because the electric properties of antimatter are reversed (and I’m not talking about the charges of 10^-19 coulomb being reversed, I’m talking about charges on the order of 10^-39 coulomb also being reversed) it is predicted that antihydrogen will fall up. This outrageous prediction (a clear violation of General Relativity) will be tested, finally, in the next few years when the LHC beam comes back on line. See AEgIS experiment.

This is not free advertising space for commenters’ personal scientific ideas. It is for comments about the post.

Sorry about that Matt. You are of course right. I got carried away and violated one of my own principles.

Possible typo.

“has two dimensions of space (not the obvious three)

is supersymmetric (which seems impossible, but in three ”

did you mean two in the second line? Otherwise I have to think hard!

I did mean “two”. The problem is not just that you have to think hard; you have to know more, too. There’s a reason I haven’t covered this type of issue on this website; these “rewritings” (or “dualities”) between one theory and another generally involve a profound, technical, and sophisticated understanding of quantum mechanics, quantum field theory — and (often) gravity — and (sometimes) string theory.

Could you tell us about the prediction of the 3-d strong coupling theory which is in contradiction with SM (and why it seems hard to fix) that Nima was referring to?

As you make the 2-spatial dimensional force stronger and stronger, what is happening in the alternate description (the 3-spatial dimensional one) is that the third dimension, which is in the form of a circle, becomes larger and larger. Nima noted that the energy density of the theory should not depend on the radius of this circle, if Witten’s idea were right, would not depend on the radius. But you can calculate that energy density in the Standard Model if one of the dimensions were in the form of a circle, and it’s not true — and moreover, it seems impossible to alter the Standard Model so that it would become true.

You say that Arkani-Hamed’s prediction was false in the Standard Model — does this mean that it’s actually contrary to experiment, or just that the SM predicts something different, but it hasn’t been measured experimentally yet?

The SM predicts something different. See my answer above.

“Because every spin-zero particle (or particle-like object) that has ever been observed, in particle physics and in similar contexts within solids and fluids”

Could you give us some examples of such known spin-zero objects? I would like to learn more about them.

As for the main point what makes hierarchy problem so special? There are many more important problems with SM IMHO. From not being mathematically well defined ($1M prize) to having countless empirical parameters and a mysterious structure.

Why 3 families, why the masses we observe, why the particular set of forces, why the symmetries we see, why CP violation…

What makes the hierarchy problem extremely special — the only one that particle physicists and string theorists alike agree is central to our understanding of nature — is that there is no known way to argue it away easily without new particles accessible at the LHC.

Moreover, it’s a problem (within the Standard Model plus gravity) of 32 orders of magnitude. None of the other problems you mention are anywhere near so severe. The only worse problem is the cosmological constant (120 orders of magnitude).

“Not being mathematically well-defined”; you’re misinterpreting what the $1 million prize is for. The reason the Standard Model’s definition is subtle doesn’t have to do with that issue at all.

I agree all the other problems of the Standard Model are extremely important. But the hierarchy problem (i.e. the unnaturalness of the Standard Model) easily trumps them all.

Hi Matt,

You wrote ““Because every spin-zero particle (or particle-like object) that has ever been observed, in particle physics and in similar contexts within solids and fluids”. As an earlier poster wrote,could you give some examples of spin-0 states being associated with new physics at the roughly same mass scale ?

Regarding the whole business of fine tuning problems, it would be good to have examples showing that naturalness arguments can be used to successfully predict new physics. I recently read one of Giudice’s papers (arXiv:0801.2562). He describes how the values of electron and pion masses, and the Gim mechanism support using naturalness to predict new physics. Do you know of any other examples ?

I must confess to being somewhat agnostic as to whether naturalness is a useful condition for motivating searches. It would be useful for me (and I’m sure many posters) to see how this has worked in the past.

I hope this isn’t too much off-topic!

In particle physics, Guidice’s examples are the main ones I know of, except to note that the only scalars among QCD hadrons (there are dozens) that have low mass are the pions, whose masses are light due to an approximate but “spontaneously broken” (i.e., hidden but still recognizable) symmetry. If naturalness weren’t true, there could easily have been other QCD spin-zero hadrons that were light. There have also been computer simulations of other theories, e.g., theories with only gluons. And there are certain theories in two dimensions that can be solved exactly, or approximately. In no cases do we see exceptionally light spin-zero particles unless there is supersymmetry or the particle is pion-like.

Meanwhile there are dozens of examples in “condensed matter” (i.e. solids and fluids etc.). In literally ANY solid or fluid system near a 2nd-order phase transition, there is a Higgs-like excitation. Right at the phase transition — a highly non-generic situation — it’s massless. As you move away from the phase transition, it generally becomes as heavy as you’d expect. There are no examples where it stays extremely close to massless even though you’re at a generic point far from the phase transition.

What’s even more important is that we believe we have long understood *why* there should be no such things in nature. And that goes to the heart of how quantum field theory (the math behind all particle physics) works. And we have no evidence from data or from any simulations that have been done that our understanding of quantum field theory is fundamentally bad. The fact that a profound understanding of the mathematics accompanies the long list of anecdotal examples is very important in justifying the logic.

The hierarchy problem: Does this come down to the difference between the WNF and Gravity? where G is 4 quadrillion times smaller than the WNF? And the mystery is why is it so trivial in comparison. I have read your links several times. Then this causes a conflict with Planks distance? I am seeking a simple summary –

It’s not a “conflict” with the Planck distance. The ratio of the Planck distance to the distance scale of the Weak Nuclear Force is a restatement of the weakness of gravity — i.e., it’s the same issue, written in another language.

Curious how locality (and causality) translate between the 3-d view and the alternative 2-d view. Is it like the events on a light cone map to being local in the 2-d view ?

Would love to see a future post on the holographic principal.

Well, there’s a reason I haven’t posted on this. It’s hard enough for experts to understand properly and state simply, much less explain it to a non-expert audience. We’re still learning things.

1)”it is “natural” (=”generically true”?) for spin-zero particles to have other particles and forces around at comparable energy scales.”

2)”spin-zero particles like the Higgs are accompanied by other particles and forces at a similar energy range”

3)Because every spin-zero particle (or particle-like object) that has ever been observed, in particle physics and in similar contexts within solids and fluids, has been accompanied by new phenomena at an energy scale comparable to the scalar’s mass-energy (E=mc2 energy).

1,2,3 sound like the same thing.

Why is this true? And, what is the connection between “spin-zero” and “other particles/forces at a similar energy range”? “spin-zero particles” are “always?” accompanied by other particles and forces at a similar energy range? only spin-zero? what about non-zero spin particles? If so, why this must be so? What is the mechanism?

1,2,3 are all the same thing but from different points of view. 1 and 2 are statements about our undersatnding of quantum field theory as a mathematical tool. 3 is a statement about data.

The reason it is true requires a long discussion. It isn’t something I can fit into a comment. The best way to say it is that naively *all* particles should have large masses, because of quantum mechanics shifting all particles masses around by large amounts, comparable to the Planck scale, which is billions of billions of billions of times more than the mass of a proton. However, there are exceptions when there is a fundamental difference between a massless particle of some type and its massive version. For instance: a massless photon has 2 polarization states, while a one with a mass has 3. That means that the complexities of quantum mechanics CANNOT change a massless photon into a massive one; and it also means, more subtly, that they can’t directly change the mass of a Z particle (which is much like a photon, but with a mass) by a huge amount (as long as there’s a Higgs-like particle around). Similar arguments apply for electrons and neutrinos and quarks; massless ones and massive ones are completely different, so quantum mechanics cannot change the mass of an electron by a huge amount. But no such argument applies for spin-zero particles like the Higgs. To prevent a large change in the Higgs particle’s mass (and consequently the Higgs field’s value, and consequently and indirectly, the W particle’s and Z particle’s mass) there must be some cancellations between different quantum mechanical effects; and for that to happen requires additional particles and/or forces that assure that cancellation.

At least, that’s the situation in any generic Standard-Model-like theory. You can make the quantum mechanics effects cancel by hand, but if you do that, and then you change the top quark’s interaction with the Higgs by 0.000001% or even less, all the masses of all the Standard Model’s particles will change by enormous amounts, because the by-hand cancellation requires such extreme care.

“a massless photon has 2 polarization states, while a one with a mass has 3.”

Not only a photon but Any? massless non-spin zero particle such as a gluon has only 2 polarization states(=+ or – along its traveling/propagating direction) ->correct? If correct, why this must be always the case? I believe if a graviton (assuming it is massless and comes with non-zero spin) exists it also has 2 polarization states. correct? but why?

Why a massive particle has only 3 polarization states? It looks like the spin of a massive particle (with non-zero spin) can point to any direction. For example, an electron’s spin can point any direction: this means it has many more? polarization states than just 3 or not? Why did you say just 3 for massive one?

Do all massive particles have only 3 polarization states regardless of its spin?

A)massive particles with zero-spin ->no polarization states? or it is polarized into all directions and on average it appears to have no polarization states?

first of all, Higgs particles must be “massive” “zero-spin”? if so, why? If Higgs particles were:

1)massless and zero-spin ->what happens/what’s wrong?

2)massive and non-zero-spin ->what happens/what’s wrong?

3)massless and non-zero-spin ->what happens/what’s wrong?

“scalar fields” are always accompanied by zero-spin particles or not? If so why? and Higgs fields are really scalar fields? Or, Higgs fields are vector fields that only appear scalar fields because on average they(=vector fields) cancel each other and appear to have no direction?

First of all, are there true scalar fields in nature? or The fields in nature are all (variants of) vector fields even if they look scalar fields? It just looks that vector fields contain scalar fields but not the other way around. Is this the case or not? and why?

I’m afraid you have too many questions here for me to answer in a comment. Yes, what I said about the photon is true for all spin-one particles. You might start your learning process here. http://www.physicsforums.com/showthread.php?t=12373

The Higgs particle (which, as you can see in data, has a mass) must be spin-zero because if it is not, then when the Higgs field developed a non-zero value, it would ruin the rotational invariance of the equations of our world. For example, if it were spin-one, it would point in a particular direction, and that would mean equations for how things behave would differ depending on which direction they were moving. We can see that in our world that’s not true. (Furthermore, if you study the equations very carefully, you find a spin-zero Higgs field is the only one that can give the combination of masses and forces that we observe… but to understand this requires some expert knowledge.)

Fields and their particles always have the same spin. I don’t know your background but you might want to study http://profmattstrassler.com/articles-and-posts/particle-physics-basics/fields-and-their-particles-with-math/ and http://profmattstrassler.com/articles-and-posts/particle-physics-basics/how-the-higgs-field-works-with-math/ .

Why does the original Bardeen’s idea on conformal invariance seem in disgrace? This http://prl.aps.org/abstract/PRL/v110/i15/e151601, a rather recent paper, should show, once more, how this idea is indeed viable for the hierarchy problem.

I have thought about Bardeen’s suggestion quite a lot… it’s not in disgrace, but it has few adherents. I haven’t written any papers on it, because I (as is the case for most, but certainly not all, of my colleagues) think it cannot be made to work. This recent paper you quote doesn’t look very plausible, but I haven’t read it or thought about it carefully. Keep in mind there have been a lot of wrong papers written in the past year about the hierarchy problem… when you say this idea is “viable”, all you mean is that

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