On the definition, design and implementation of an Integrated, Global,
Intelligent Capacity Agent for telecommunications a...
Abstract:

In this treatise, many interesting and revolutionary and evolutionary ideas have been
launched.

The research b...
PROCESS MODEL

This process model describes a basic application of the information definition later
delineated. It attempt...
T1 is Proportional to I1 is Proportional to P(ENGINEERING WORKS REQUEST),
where P(ENGINEERING WORKS REQUEST) = Time for pr...
delta Inf3,
                                           delta T3
  delta Inf5,
   delta T5
                                ...
Dynamic update of information content of the two systems depicted in the diagrams
above: "Delta I", is proposed.

If TD is...
The information based matrix switch utilizing the Infoton generation/
        transmission/detection mechanism (The switch...
8
ASSUMPTIONS OF THE INFORMATION MODEL.

-INFORMATION SUB-PARTICLES: "INFOTONS"---AT A QUANTUM LEVEL
-1 INFOTON HAS A CERTAI...
EQUIPMENT DATA FROM LIVE SYSTEMS —CIRCUIT DATA
THIS WILL FORM TWO MODULES : EQUIPMENT DATA MODULE AND C IRCUIT D ATA
MODUL...
APPENDIX 1:

Speculated relationship between information, events and time:
It can be predicted that Particle nature of inf...
APPENDIX 2:
INFOTONS? HIGGS BOSSONS?
INFORMATION? HIGGS FIELD?
IS THE INFOTON AND HIGGS PARTICLE MANIFESTATION OF THE SAME...
1. Most of the theoretical difficulties result from the existence of nonzero rest
       masses of the various particles. ...
proper Yang-Mills theory can be developed for the symmetry group U(1)xSU(2) that
incorporates both the electromagnetic and...
“Supersymmetry
It should be pretty clear by now that Higgs physics is very much tied in to the standard
model. Indeed, it'...
predictable by supersymmetry which further constrain the mass of the lightest Higgs
boson beyond what we might guess from ...
Eventually it was realized that there was a way to combine the two inadequate answers
mathematically in order to concoct a...
What all these examples have in common is that a piece of matter exhibits a higher
amount of symmetry at higher temperatur...
Even if a more complicated supersymmetric model is required to describe the real world
(because there are additional inter...
mass is an important issue, the concerns about the mechanism of symmetry breaking and
renormalizability might seem to be m...
28
As the universe cooled through the critical temperature (about 10 ° K) at first nothing
happened. But the universe was ...
Gravity
If "empty" space is actually filled with Higgs fields, and hence with rather massive Higgs
particles, how is it th...
symmetry. (One is inherent in the equations of the theory, and the other follows from the
fact quarks have mass, which is ...
In this scheme there would be a new set of spin 1/2 particles called (of course)
technifermions. A bound state of one of t...
Where are the Higgs particles?
This is the biggest concern at the moment. There should exist at least one Higgs boson
with...
Although the Higgs mechanism handles a number of puzzles fairly well it creates a rather
nasty problem of its own in grand...
How does the Higgs boson affect string theory?
      Question and answer (by Gordon Kane) from Scientific American's Ask t...
We can't be said to understand the constituents of matter if we don't have a satisfactory
answer to this question.
Peter H...
cluster round her. As she moves she attracts the people she comes close to, while the ones
she has left return to their ev...
Maxwell unified electricity, magnetism and light. Each synthesis extends our
understanding and leads eventually to new app...
Last updated on 30th August 1995, by Dr S.L.Lloyd “

“Ripples at the Heart of Physics
By Simon Hands Theory Division, CERN...
hints and speculations and its discovery is the most exciting prospect in contemporary
particle physics.

Last updated on ...
These are the convergence trends in information technology and telecommunications, where
there is no data or voice subscri...
With Voice over IP standards evolving and convergence in the computer-telephony worlds,
the desktop is not going to die. R...
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Invention

  1. 1. On the definition, design and implementation of an Integrated, Global, Intelligent Capacity Agent for telecommunications and unified networks based on quantification and qualification of information by an elementary, transaction based model (convergence and unification of Economics and Physics through an elementary definition of information: applications to a process definition) By Abdul-Basit Khan October 22nd, 2002 Additions and revisions, February 13th, 2005 Unification of Economics with Quantum Physics Telecommunications and Information Technology convergence Speculated relationship of Infoton* with Higgs Boson Info-phone, information-based-billing system, infotonic switch Impacts on telecommunications and IT industries A new dimension in Information Economics or “Econo-Physics” 1
  2. 2. Abstract: In this treatise, many interesting and revolutionary and evolutionary ideas have been launched. The research begins by showing a process model for the customer operations and provisioning group of an Incumbent Local Exchange Carrier. This is a system being modeled in terms of information flows, based on the quantum definition of information presented later. In this process the correlation between time (and incremental changes in time) with information (in terms of incremental changes in information) are described. In system terms the effects of quantum values of information on entropy (disorder in the system) and changes in entropy with time (as information flows) are modeled. This model is the foundation of the product space for the new products introduced in the second part of this paper. It can be seen that this entire process of provisioning and information flows can be optimized, if a quantum definition of information, defining quality and quantity of information, and defining information as an elementary force and field, possibly equivalent to the hypothetical Higgs field, where the Higgs Bosons are, in fact, the particle proposed in this paper: Infoton. A detailed description of Higgs particles and Higgs force is presented in Appendix 2. A strong correlation to the Infoton is described by the following link: http://www.coimbra.lip.pt/atlas/higgsmec.htm Process optimization, re-definition of information at a quantum level, relationship described between entropy, time and information, all lead to three new products for converging communication networks: (I) an intelligent unified capacity agent, which is an artificial intelligence based expert system (consisting of several knowledge modules, specified below) (ii) an information based/content based billing system (iii) an Infoton switch based on a principle similar to the Heisenberg Uncertainty principle, and quantum symmetry and pairing of elementary particles actually applicable to information retention and loss. These products lead to another theoretical arena and a hypothetical proposition (Appendix 1): Particle nature of information and wave nature of time. This proposition, taking into account information symmetry and completeness and correlation with time, directly provides a new evolutionary perspective for Economics impacting: Price theory. Game theory, arbitrage and negotiation economics (Nash/Cournot equilibriums), bargaining under uncertainty and dynamic games. 2
  3. 3. PROCESS MODEL This process model describes a basic application of the information definition later delineated. It attempts to model the provisioning process in a CLEC/ILEC environment and how capacity constraints come into play in the provisioning process. An intelligent system is defined and depicted to meet such capacity constraints in network and services planning in a CLEC or ILEC similar to AT&T, Verizon or Sprint. Later, a simple realization of the Intelligent Capacity Agent based on the currently available Information Warehouse (IW) is described. The information definition described below can be used for designing Next Generation wireless networks, optical systems and quantum databases. Mathematical proofs are currently being sought for such an elementary definition of information. This definition of information can be utilized in designing organizational decision support systems and network management and control systems. MODEL & PARAMETER DEFINITION: The various parameters used in the models described below are defined as following for the reader to get a better understanding of the optimization criteria and solutions being sought. The relationships between time, information, entropy and quantum uncertainty in event perception are applied in this model. Time and information are quantified and qualified as physically realizable entities. It is assumed that the reader has the general idea of the TELCO provisioning and order entry processes, for which these time/information relationship is demonstrated, from a Systems perspective. Order (Telco customer orders): 1. delta Inf4, delta T4: I4,T4 2. delta Inf1, delta T1: I1,T1 3. delta Inf2, delta T2: I2,T2 Critical I2,T2 4. delta Inf3, delta T3: I3,T3 5. delta Inf5, delta T5: I5,T5 delta Inf: I , Critical Information Qualified and Quantified. TD = Delivery of Service to Customer (Total Time of Delivery, from sales initiation to service delivery) TD = F(T1,T2,T3,T4,T5) = F(ALFA) TD = F(I1,I2,I3,I4,I5) = F(BETA) QI = F(I1, I2, I3, I4, I5) = F (Gamma) QI = Quality of Information Higher the delta I, superior the quality of information Process Optimization boils down to: Minimize TD = Min F(ALFA) & Max F (GAMMA) 3
  4. 4. T1 is Proportional to I1 is Proportional to P(ENGINEERING WORKS REQUEST), where P(ENGINEERING WORKS REQUEST) = Time for processing of ENGINEERING WORKS REQUEST (requests for equipment build/augmentation/removal) F(GAMMA) = Subjective to Personnel in each division, the information processing and the hierarchy Oc (T2) = Orders completed per designer is Proportional to F(T1,T2,T3,T4,T5) + F(I1,I2,I3,I4,I5) TD is Proportional to delta T3 + delta T2 + nxdelta T1 + mxdelta T5 + pxdelta T4 n, m, p is the number of times information is exchanged EVALUATION OF PARAMETERS AND CORRELATIONS TRACKING AVERAGE PROCESSING TIME FOR ENGINEERING WORKS REQUEST TRACKING FEEDBACK TIME FROM TECHS/INSTALLERS SALES: REDESIGN REQUESTS, VARIATIONS ON THE ORIGINAL DESIGN SPECIFICATIONS Tracking time delay *, ** 4
  5. 5. delta Inf3, delta T3 delta Inf5, delta T5 Order Managers After Completion of design * delta T1' (Reactive Capacity Growth) > delta T1" (Futuristic Capacity Growth) Capacity delta Inf2, Network delta T2 Engineering Sales delta Inf4, delta T4 delta Inf1, deltaT1 After completion of design ** Design 5
  6. 6. Dynamic update of information content of the two systems depicted in the diagrams above: "Delta I", is proposed. If TD is irrelevant to design, then first design (not re-design): I2,T2 = f((I4,T4),(I1,T1),(I5,T5)) I5 can come before I2 (if pre-design information is sought) I, Tools ----IBIS, FARS/NEAD, INM----different stages Intelligent Capacity Agent Ca---dynamically updated Intelligent Order Agent Oa---dynamically updated Ca Availability to designer minimizes T1, maximizes I1 Oa Availability to designer minimizes T4, maximizes I4 Ca-----Engineering Work Requests, Updated capacity information from actual Physical Status of Equipment, Predictive Capacity Growth depending on traffic forecast, node utilization (equipment utilization) Oa-----Intelligent update of order/requirement information Ca: INTELLIGENT CAPACITY AGENT (EXPERT SYSTEM) Expert System/DP System with dynamic information inputs Design specifications of an Intelligent Capacity Agent are described below, after a brief description of the two possible products: “Infophone” and “Information based billing system”, realizable in this product space. The Info-Phone Abstract: This is a quantum device based on the generation, symmetry, detection and inherent particle nature of information, which can be attributed to elementary “Infotons”, in fields parallel to the Higgs field (possibly the Higgs field itself). Spontaneous generation, symmetry and pairing of these particles, with ongoing elementary transactions, defines the generation, transmission and detection methodology for these elementary (possibly Higgs particles). The general idea behind the proposed development of an info-phone, a next generation personal communications device is described below in bullets: Based on the "infoton" transfer mechanism. Development of Information Sensors that detect "Infotons" and attribute values/energies to them. Development of a new device: Infophone Info-Phone would utilize a separate billing system based on "infotons" transferred. "Infoton" transfer mechanism would not require the normal telecom transmission media. Info-Phone would be based on elementary "infotons", which would be transferred by selective “ Information Windows”. Protocol independence, going beyond ATM, MPLS and cell switching. 6
  7. 7. The information based matrix switch utilizing the Infoton generation/ transmission/detection mechanism (The switch could be housed on a sub- atomic quantum chip (quantum processor) within the Info-Phone, where elementary particle generation and pairing (in probability windows of time) would activate the particular parts of the matrix Id = Ic Id Ic Ib Ia Ib = Ia Switching Matrix of Infoton/Higgs Boson the info-Phone: Even Symmetry (Even generator /transmitter/ Infoton generated/ number of point-masses/ detectors generators/detectors ) in the detected—Status: switch (on either side of the Lost/Retained partition), so events are symmetrical on each corresponding point-mass on Basit’s Uncertainty Principle: Either the sub-atomic switch fabric. the time of occurrence of an event or Information is either lost or retained (Infoton exists or complete and symmetrical decays)-PHYSICS information about an event can be Generation of information known produces competition, effects price level etc- Economics 7
  8. 8. 8
  9. 9. ASSUMPTIONS OF THE INFORMATION MODEL. -INFORMATION SUB-PARTICLES: "INFOTONS"---AT A QUANTUM LEVEL -1 INFOTON HAS A CERTAIN UNIT PRICE ASSOCIATED WITH IT -DELTA I= N  UMBER OF “INFOTONS” N -OPTIMAL BILLING S YSTEM IS ABLE TO EVALUATE DELTA I -THE PRICE/BILL TO THE SUBSCRIBER IS A FUNCTION OF NUMBERS OF I NFOTONS AND THE PRICE ASSOCIATED WITH EACH “ INFOTON ”. PROBLEMS ASSOCIATED WITH THE MODEL : CALCULATION OF THE “ INFOTONS” TRANSFERRED IN A GIVEN TRANSACTION OPTIMAL BILLING SYSTEM SHOULD BE ABLE TO CALCULATE THE NUMBER OF INFOTONS TRANSFERRED A PRICING FORMULA FOR THE “INFOTONS ” MUST BE ESTABLISHED VOICE, VIDEO , DATA CAN ALL BE BROKEN DOWN INTO THE NUMBER OF INFOTONS TRANSFERRED WORK TO BE DONE IN BUILDING THE THEORY. -QUANTIFICATION OF INFORMATION AS ELEMENTARY PARTICLES -ANALYZING VOICE /VIDEO /DATA TRAFFIC IN TERMS OF THE ELEMENTARY INFORMATION P ARTICLES -CAPABILITY OF THE OPTIMAL BILLING S YSTEM TO EVALUATE THE NUMBER OF ELEMENTARY PARTICLES TRANSFERRED IN A GIVEN INTERACTION THAT COULD BE A VOICE CALL , DATA TRANSFER, VIDEO TRANSFER ETC . TRANSACTION BASED SYSTEMS AT THE QUANTUM LEVEL, WHERE INFORMATION TRANSFER IS ACCURATELY QUANTIFIED AND QUALIFIED BASED ON THE CONTENT AND ATTRIBUTES OF INFORMATION. A MAJOR APPLICATION OF SUCH A TRANSACTION BASED SYSTEM IS TO CAPACITY PROBLEMS FACED BY TELCOS. ONE APPLICATION IS THE P REDICTIVE C A: INTELLIGENT CAPACITY AGENT (IDEA PRESENTED EARLIER). IT IS A TRANSACTION BASED DATA PROCESSING INTELLIGENT SYSTEM, WHERE INFORMATION INPUTS HAVE TO BE QUANTIFIED AND QUALIFIED FOR TRANSACTIONS BETWEEN THE DIFFERENT KNOWLEDGE MODULES . VARIOUS MATHEMATICAL TECHNIQUES OF QUANTIFYING INFORMATION BUT NOT FOR QUALIFYING INFORMATION ARE AVAILABLE. INFORMATION QUALIFICATION IS SUBJECTIVE AT PRESENT , PHYSICAL MODELS TO QUALIFY INFORMATION ARE REQUIRED, WHICH CAN BE INCORPORATED INTO DEVICES LIKE THE INFO -PHONE ( ABOVE). CAPACITY FORECAST: F ORECASTING K NOWLEDGE MODULES WITH A STATISTICAL INFERENCE ENGINE BASED ON: REGIONAL DATA: NPA NXX TYPES OF BUSINESSES—NEW SET-UPS—CONSTRUCTION OF NEW OFFICES/BUILDINGS. THIS DATA FOR EACH NPA-NXX WILL GO INTO A KNOWLEDGE MODULE: MARKET D ATA MODULE. EQUIPMENT UTILIZATION OVER TIME AND CIRCUIT DATA—NEW INSTALLATIONS, CANCELLATIONS ---USE DATA TO FORECAST CAPACITY GROWTH /CONTRACTION 9
  10. 10. EQUIPMENT DATA FROM LIVE SYSTEMS —CIRCUIT DATA THIS WILL FORM TWO MODULES : EQUIPMENT DATA MODULE AND C IRCUIT D ATA MODULE. TO BE DYNAMICALLY UPDATED, FOR THE INFERENCE RULES BASED INFERENCE ENGINE. TRAFFIC GROWTH OVER THE NETWORK OVER TIME OVER AN NPA-NXX. TRAFFIC FORECAST FOR A FUTURE PERIOD OF TIME. THIS PREDICTIVE MODULE WOULD BE THE TRAFFIC ANALYSIS DATA MODULE . USER INTERFACE OF THE INTELLIGENT CAPACITY AGENT: DATA INPUT/UPDATE INTERFACES FOR DIFFERENT MODULES, PROVIDING INPUTS TO THE LEARNING/INFERENCE ENGINES. CAPACILTY ANALYSIS INTERFACE: USER SPECIFIES DH TYPE AND END- POINTS OF THE SERVICE REQUESTED----OUTPUT IS LOW SPEED AND HIGH SPEED BANDWIDTH COMPONENTS AVAILABLE ON THE SYSTEMS, IN TERMS OF PORTS, BETWEEN THE TWO END- POINTS. ONLY END -POINTS AND DH -TYPE HAS TO BE SPECIFIED BY THE USER. F OR THE INTELLIGENT CAPACITY AGENT, CODE OPTIMIZATION IS ENTROPIC , MINIMIZING POSITIVE CHANGES IN ENTROPY. AN EARLY PRACTICAL REALIZATION OF THE INTELLIGENT CAPACITY AGENT CAN BE THROUGH THE INFORMATION WAREHOUSE. THE I NFORMATION WAREHOUSE (IW) CAN BE USED AS A PRELIMINARY CAPACITY ANALYSIS SYSTEM PROVIDING REALTIME AVAILABILITY STATUS OF THE PORTS OF THE NETWORK COMPONENTS REQUIRED FOR DELIVERING THE SERVICE, AS WELL AS OPTIMAL PATH , BASED ON RULES INCORPORATED AS QUALIFIERS, CAN BE DETERMINED THROUGH THE NETWORK DATA MODEL: THE VARIOUS NETWORK MANAGEMENT TOOLS WHICH GIVE THE LIVE STATUS OF PORTS IN THE ALLSTREAM NETWORK (LUCENT PORTS , F UJITSU PORTS, NORTEL PORTS, TITAN PORTS ) CAN BE INTERFACED IN REAL-TIME WITH THE IW. DATA CAN BE DUMPED TO THE IW FROM THESE NETWROK MANAGEMNT SYSTEMS IN REAL- TIME OR REAL-TIME INTERFACES CAN BE DEVELOPED . ALL THE PORT DATA CAN BE CONVERTED AND UPDATED INTO DATA OBJECTS /TABLES, WHERE NUMBER OF PORTS IS A KEY IN THESE DATA OBJECTS. THE RELATIONSHIPS BETWEEN THESE DATA OBJECTS, WHICH MODEL THE POINT TO POINT NETWORK , WOULD BE THE TYPE OF SERVICE (DS-1/DS-3/OC- 3/OC-12/ATM). T HE QUALIFIERS WOULD BE PROTECTION STATUS, DIVERSITY AND OTHER PARAMETERS DEFINING THE PATH THROUGH THE NETWORK. 10
  11. 11. APPENDIX 1: Speculated relationship between information, events and time: It can be predicted that Particle nature of information is related to wave nature of time. When an Event occurs in time, information is generated before, at the time of, and after the event. There is an uncertainty principle which comes into play at the time of occurrence of event. Either the time of occurrence or symmetrical information about the event can be known. Both quantities cannot be known at the same time. Information has two qualities: Symmetrical or Complete information. Asymmetric or incomplete information. Information has two states: either it is retained or released in the case of an event. At the time of occurrence of an event, symmetrical information is generated, but transmission and reception techniques render it asymmetric. Any event generates infotons*, which increases the entropy in the universe around the event. 11
  12. 12. APPENDIX 2: INFOTONS? HIGGS BOSSONS? INFORMATION? HIGGS FIELD? IS THE INFOTON AND HIGGS PARTICLE MANIFESTATION OF THE SAME PHENOMENA, TWO FACES OF THE SAME COIN? http://pdg.lbl.gov/atlas/etours_physics/etours_physics10.html Does Economics lead to the same results as theoretical physics? Information below is being quoted from: “http://www.openquestions.com/oq-ph008.htm” “We say "fortunately", because Higgs theory makes certain predictions which are still not verified experimentally -- the primary example of which is the existence of (at least) one massive spin 0 boson (i. e. a "scalar" boson) that has not yet been observed, despite intensive experimental searches -- the Higgs particle.” “The Higgs mechanism Let's review where we stand so far.  We have a nice, well-behaved (i. e., mathematically consistent, renormalizable) Yang-Mills gauge theory of the electromagnetic force, based on U(1) gauge symmetry.  We would like to have an equally nice Yang-Mills gauge theory of the weak force, and it should be based on a SU(2) symmetry.  Experimentally, it is known that the particles which mediate the weak force are massive, instead of massless as required in a Yang-Mills theory.  The electromagnetic and weak forces are intertwined, because the weak SU(2) symmetry exchanges particles that have different amounts of electric charge.  Yet any potential symmetry between electromagnetic and weak forces can't be exact, since the forces have different strengths. A series of profound insights by Sheldon Glashow, Steven Weinberg, and Abdus Salam, mostly as independent contributions, led to the unified theory of the electroweak force. This was accomplished by taking the above givens, making a few inspired assumptions, and synthesizing everything in a new -- and quite effective -- way. The insights were as follows: 12
  13. 13. 1. Most of the theoretical difficulties result from the existence of nonzero rest masses of the various particles. The masses break the symmetry between electrons and neutrinos (and other particle pairs), they are incompatible with a straightforward Yang-Mills gauge theory, and they are the root of the problems with renormalizability. 2. At very high energies, the energy contributed by a particle's rest mass becomes insignificant compared to the total energy. So at sufficiently high energy, assuming a particle rest mass of zero is a very good approximation. 3. A consistent, unified Yang-Mills theory of electromagnetism and the weak force can be formulated for the very high energy situation where particle rest masses are effectively zero. 4. At "low" energies (including almost all levels of energy which are actually accessible to experiment), the symmetries of the high energy theory are broken, and at the same time most particles acquire a nonzero rest mass. These two "problems" appear simultaneously when symmetry is lost at low energy, much as symmetry is lost when matter changes state from a gas to a liquid to a solid at low temperature. The "Higgs mechanism" is basically nothing more than a means of making all of this mathematically precise. The key ingredient not yet specified is to assume there is a new quantum field -- the Higgs field -- and a corresponding quantum of the field -- the Higgs particle. (Actually, there could be more than one field/particle combination, but for the purposes of exposition, one will suffice.) The Higgs particle must have spin 0, so that its interaction with other particles does not depend on direction. (If the Higgs particle had a non-zero spin, its field would be a vector field which has a particular direction at each point. Since the Higgs particle generates the mass of all other particles that couple to it, their mass would depend on their orientation with respect to the Higgs field.) Hence the Higgs particle is a boson, a "scalar" boson, since having spin 0 means that it behaves like a scalar under Lorentz transformations. The Higgs field must have a rather unusual (but not impossible) property. Namely, the lowest energy state of the field does not occur when the field itself has a value of zero, but when the field has some nonzero value. Think of the graph of energy vs. field strength has having the shape of a "W". There is an energy peak when the strength is 0, while the actual minimum energy (the y-coordinate) occurs at some nonzero point on the x-axis. The value of the field at which the minimum occurs is said to be its "vacuum" value, because the physical vacuum is defined as the state of lowest energy. This trick wasn't created out of thin air just for particle theory. It was actually suggested by similar circumstances in the theory of superconductivity. In that case, spinless particles that form a "Bose condensate" also figure prominently. The next step is to add the Higgs field to the equations describing the electromagnetic and weak fields. At this point, all particles involved are assumed to have zero rest mass, so a 13
  14. 14. proper Yang-Mills theory can be developed for the symmetry group U(1)xSU(2) that incorporates both the electromagnetic and weak symmetries. The equations are invariant under the symmetry group, so all is well. Right at this point, you redefine the Higgs field so that it does attain its vacuum value (i. e., its minimum energy) when the (redefined) field is 0. This redefinition, at one fell swoop, has the following results: the gauge symmetry is broken, the Higgs particle acquires a nonzero mass, and most of the other particles covered by the theory do too. And all this is precisely what is required for consistency with what is actually observed. In fact, the tricky part is to ensure that the photon, the quantum of the electromagnetic force, remains massless, since that is what is in fact observed. It turns out that this can be arranged. In fact, the photon turns out to be a mixture of a weak force boson and a massive electromagnetic boson that falls out of the theory. The exact proportion of these two bosons that have to be mixed to yield a photon is given by a mysterious parameter called the "electroweak mixing angle". It's mysterious, since the theory doesn't specify what it needs to be, but it can be measured experimentally. So, the Higgs mechanism is a clever mathematical trick applied to a theory which starts by assuming all particles have zero rest mass. This is especially an issue for the bosons which mediate the electroweak force, since a Yang-Mills theory wants such bosons to be massless. While the photon is massless, the W and Z particles definitely aren't. Where, then does their mass come from? Recall that we observed that spin-1 bosons have 3 "degrees of freedom" if they are massive, while only 2 otherwise. It turns out that this extra degree of freedom comes from combining the massless boson with a massive spin-0 Higgs boson. That Higgs boson provides both the mass for the W and Z, as well as the extra degree of freedom. In fact, the mechanism furnishes mass to all particles which have a nonzero rest mass. This occurs because all the fermions -- quarks as well as leptons -- feel the weak force and are permuted by the SU(2) symmetry. And since quarks acquire mass this way, so too do hadrons composed of quarks, such as protons and neutrons, which compose ordinary matter as we know it. But this mechanism is more than just a trick. If the whole theory is valid, then the Higgs boson (or possibly more than one), must be a real, observable particle with a nonzero mass of its own. This is why the search for the Higgs boson has become the top priority in experimental particle physics. What about renormalizability? Has this been achieved in spite of all the machinations? It seemed plausible that the answer was "yes", which was of course the intention, since the high-energy form of the theory has the proper gauge symmetry. But it took several years until a proper proof could be supplied, in 1971, by Gerard 't Hooft. “ 14
  15. 15. “Supersymmetry It should be pretty clear by now that Higgs physics is very much tied in to the standard model. Indeed, it's necessary in some form to make sense of many features of the standard model -- such as electroweak symmetry breaking and particle masses. In fact, it -- or something very like it -- seems to be necessary just to make the theory consistent. And yet it's not quite a part of the standard model either. It has a bit of an ad hoc feel to it. If, in fact, the Higgs mechanism exists in more or less the form outlined here, then the standard model certainly has no explanation for why it's there, for what makes it happen. We shall want more than that. We want to know the source of the Higgs physics itself. There may be a number of ways to do that (which might be related among themselves). But there is one body of theory which can provide exactly the explanation of Higgs physics we're looking for, and which has been in gestation since the early 1970s (i. e., since the time the standard model assumed its present form). It's called supersymmetry. We'll discuss it in much more detail elsewhere. All we need to say about it here can be put very simply. The essential idea is to postulate one more symmetry, but of a radical sort. This new symmetry relates bosons (particles with integral spin) to fermions (particles with half-integral spin). The symmetry associates to each fermion and boson a particle of the opposite type, known as its "superpartner". The equations of the theory are set up so that they remain true when a symmetry operation exchanges any fermion or boson with its superpartner. This is a radical step, because none of the postulated superpartners can be identfied with any known particle, so the theory immediately doubles the number of particles which must exist. Even the Higgs boson has a supersymmetric parther, the higgsino fermion. One justification for taking such a radical step is this: When the mathematics of supersymmetry is worked through, it turns out that the whole Higgs physics -- the Higgs field, the Higgs boson(s), and the Higgs mechanism -- falls out as a necessary consequence. This is great for Higgs physics, if in fact supersymmetry is a correct theory. But the other side of the coin is that if the Higgs physics can't be verified experimentally, then supersymmetry can't be correct. This is yet another reason why Higgs physics is of such urgent concern to particle physicists. The fact alone that the Higgs physics is a mathematical consequence of supersymmetry is quite striking. It doesn't seem likely to be just a concidence. Further, the discovery of any supersymmetric particles would validate the theory of supersymmetry, and thereby validate the Higgs physics also. On the other hand, the Higgs mechanism could still exist even if supersymmetry doesn't exist in nature. But it would have serious problems, such as the "hierarchy problem", and the lack of any obvious source or cause of the Higgs field. If supersymmetry is correct, then, so is the Higgs mechanism. And in fact, there are more detailed predictions. Most notably, there will be not one Higgs boson, but several, each with a different mass. All of the "extra" Higgs bosons could be quite a bit heavier than the lightest one which is needed by the standard model. In particular, they might be so heavy that they would not be detected soon, if at all. There are additional details 15
  16. 16. predictable by supersymmetry which further constrain the mass of the lightest Higgs boson beyond what we might guess from the standard model alone. If supersymmetric particles are detected before the Higgs boson, than will be confirmation of supersymmetry, so the Higgs particle must show up eventually as well. But what about the converse? Suppose the Higgs boson is detected first. Will that be evidence for supersymmetry? Yes, probably. The reason lies in what we have alluded to, namely that the Higgs physics by itself leaves something to be desired, as long as it is an ad hoc addition to the standard model. We really want to have a good explanation for the physics itself. Supersymmetry provides this. It automatically contains fields which behave as a Higgs field should, and hence entails the existence of Higgs bosons. It also says something about how standard model particles interact with these fields, which elucidates the mechanism. A Higgs mechanism without supersymmetry would also introduce what is known as the hierarchy problem. This problem arises if (as seems likely) the strong and electroweak forces are unified just as the electromagnetic and weak forces are -- but at a much higher 16 energy scale -- around 10 GeV. The problem is to explain how this can be so much higher than the electroweak unification scale of 100 GeV, or, alternatively, how the latter scale, and the masses of the W and Z bosons, can be so small. In short, if Higgs bosons are observed, we will have evidence for supersymmetry, as that is the only theory we know of that makes good sense of Higgs physics. More detail on supersymmetry Where does the Higgs field come from? OK. It's all well and good to say that mass comes from the Higgs field. But where does that come from? What is it exactly? Why is it there? The Higgs field, in some sense, answers the question of where mass comes from. But that merely shifts the question of explaining mass to that of explaining the Higgs field. This is still an open question, but there are some plausible answers, of different sorts. There is, first of all, purely a mathematical and theoretical answer. It so happens that there is a theorem, called Goldstone's theorem, after Jeffrey Goldstone, who came up with it around 1960. The theorem says that when a continuous global symmetry is spontaneously broken, there must exist a massless spin-0 boson. The particle is called (generically) a Goldstone boson. Unfortunately, such a particle has never been detected. Something's fishy. Oddly enough, there is also this puzzle regarding a massless spin-1 boson which Yang- Mills theory requires in order to carry a gauge force. Physicists were going crazy because that could not be found either, for the weak force. They spent a lot of time trying to get around the apparent requirement for both of these non-existent particles in the theory of the weak force. 16
  17. 17. Eventually it was realized that there was a way to combine the two inadequate answers mathematically in order to concoct an answer that worked. This is basically what Weinberg and Salam did in coming up with the theory of the electroweak force. They found that by adding yet another particle -- the Higgs -- they could make the Goldstone boson disappear and make the electroweak bosons massive. The electroweak bosons are said to "eat" the Goldstone boson and thereby put on weight. In the presence of the Higgs field, the Goldstone boson, in effect, becomes the third polarization state of a gauge boson. (Recall that massless spin-1 bosons have only two polarization states or degrees of freedom.) There is a second type of theoretical way to explain the Higgs mechanism. Recall that a basic postulate about the Higgs field was that when the energy of the field is plotted against the strength of the field, the resulting graph has a W shape. The simplest mathematical curve with such a shape is a fourth degree polynomial of the form E = x4 + Bx2, where E is energy and x is field strength. (E is plotted on the y-axis.) If B is negative, then for values of x close to 0 (but not exactly 0), E will be negative. Hence for such values, you actually get a lower energy with a non-zero field. Now, in the standard model, all this just needs to be taken as a given. But it turns out that in theories with supersymmetry, it is actually possible to compute how the coefficient B in this equation behaves as a function of temperature. It is found that at high temperatures (say, corresponding to an energy of 1000 GeV), B is positive. The polynomial expression for E in that case has just a single minimum value (of 0) when the field strength is 0. On the other hand, at lower temperatures (such as what we have in the universe at present), B is negative. In that case, there are two minima of the polynomial for E, at nonzero value of the field strength, which is just what we need. This mathematical behavior reflects exactly what is required to have a nonzero Higgs field appear "from nowhere" at relatively low temperatures. That is, the field doesn't exist at high temperatures, because minimizing energy requires it to not exist. Yet at lower temperatures it does exist, because in the changed circumstances, that is what yields a minimum energy. This puzzling behavior becomes much more plausible by analogy with a number of other physical phenomena. All of these involve a change of state, a "phase transition", in matter when the temperature of the system changes. Among the many examples are:  A magnetized piece of iron retains its magnetism up to a temperature of about 768° C but loses it above that point. Upon cooling below that point, the magnetic field reappears.  A number of materials have the property of superconductivity at very low temperatures, but lose this property at a few tens of degrees above absolute zero.  A crystal has a small number of distinct symmetry axes at low temperature, but loses these axes, and becomes more symmetrical, when the temperature is high enough to melt the crystal. Water, in the form of an ice crystal or snowflake is a perfect example. 17
  18. 18. What all these examples have in common is that a piece of matter exhibits a higher amount of symmetry at higher temperatures. In addition, this phase transition occurs at a definite point. Finally, the higher symmetry is lost if the matter is cooled below the critical point. This phenomenon is so familar we have various names for it (in different contexts), such as "precipitation" (e. g. rain), condensation, crystallization, etc. This is precisely what happens with the Higgs field. It is "really" there all along. However, at high temperatures the equations governing the field are such that it does not affect matter. As the temperature decreases, at some critical point the equations change and the field condenses into a new state where it does affect matter. It suddenly causes matter to have mass, because under the new equations the overall system has lower energy when matter has mass than when it does not. This new state at lower temperature also corresponds to the breaking of previous symmetry -- which is exactly what the Higgs mechanism is supposed to do. In fact, the mechanism was, originally, consciously invented to account for the breaking of symmetry which explains the phenomenon of superconductivity, as we mentioned earlier. Searching for Higgs bosons Why has it been so difficult to find the Higgs particle experimentally? The answer is that it must be fairly massive, so that very high energy particle accelerators are required for the search. Well, then, how massive is it? The answer is: the expected mass isn't very well constrained by the theory, which makes the search even harder. It becomes necessary to search systematically at every possible energy level, which becomes all the more tedious since the searches must be done at the limits of current accelerator capability. Fortunately, there are upper limits on the possible mass, given reasonable assumptions. The standard model itself and existing experimental results imply that the upper limit on a Higgs particle mass is about 8 times that of the Z boson. Since that is about 91.2 GeV, the upper limit on the Higgs is around 700 GeV. Under some plausible further assumptions, the limit can be lowered to around 3 times the mass of a Z, or about 270 GeV. Experimental results already obtained place further limits on the expected mass of a Higgs boson. The way this works is to assume some particular value for this mass and derive various experimental consequences from that. Then consider experimental results actually obtained. If you look at what the mass needs to be in order to agree with all the results simultaneously, you find that the mass of the Higgs can't be more than about 2 times the mass of a Z, or about 180 GeV. In the best case, if the simplest form of supersymmetry is correct, the limit must be even lower, perhaps about 1.5 times the mass of the Z, or 135 GeV. Although there may be more than one Higgs boson in a supersymmetric theory, this limit can be derived for the lightest Higgs boson. (There aren't similar constraints on the heavier Higgs bosons.) 18
  19. 19. Even if a more complicated supersymmetric model is required to describe the real world (because there are additional interactions and particles and forces), it appears the mass limit on the lightest Higgs is still no more than 2 times the Z mass. The very latest experimental results rule out any Higgs particles up to a mass of about 115 GeV, so there is actually rather little range left to search. Perhaps only to 135 GeV, or 180 GeV at most. We should expect some answers pretty soon. What sort of evidence is being sought in order to detect Higgs bosons? Explaining this gives a good illustration of how experimental particle physics works. To begin with, theory says the Higgs particles must decay into particle-antiparticle fermion pairs. Any supersymmetric particles, as well as the top quark (at about 155 GeV) would be too heavy. Further, since the Higgs generates the mass of other particles by its interaction with them, theory says its probability of interaction is proportional to the mass. Thus the probability of decaying into any particular (allowable) particle-antiparticle pair is in proportion to the particle mass. The next three heaviest standard model fermions are the bottom (or b) quark, the tau lepton, and the charm quark. All other fermions are much lighter. The bottom quark is the heaviest, so most of the time a Higgs will decay into b and anti-b pairs. Therefore, experiments seeking to detect the Higgs will look for events that generate mostly b, tau, and charm pairs in the appropriate ratios. There are only three accelerators in the world which could in principle detect a Higgs boson. Two are at CERN in Geneva. The first of these is the Large Electron Positron Collider (LEP), which has already been decommissioned to make room for the second, the Large Hadron Collider (LHC), which won't be ready to work before 2005 (or later). Just before the LEP was shut down late in 2000 there were hints that Higgs particles might have been detected. Subsequent analysis of the data indicated that this was a false alarm. That leaves only the Tevatron at Fermilab in Illinois. A good deal of time at that facility is now devoted to searching for the Higgs boson. If it is a real particle, it ought to be detected very soon -- given that experiments are quickly reaching the upper limit of the plausible mass range. By 2006 a large number of Higgs events should have been observed (again supposing the particle exists). This will permit even low probability decay modes to be studied and should produce enough information to discriminate among possible theoretical alternatives. Related issues Higgs physics may seem like an esoteric issue. Except for fairly superficial references to the search for Higgs particles and occasionally an allusion to the role that the Higgs field plays in explaining the source of particle mass, the subject is rarely discussed in publications intended for a general audience. While it's hard to disagree that the origin of 19
  20. 20. mass is an important issue, the concerns about the mechanism of symmetry breaking and renormalizability might seem to be merely technical details only physicists worry about. And yet it turns out that Higgs physics is involved in an astonishing -- almost an alarming -- number of aspects of frontier questions of physics and (especially) cosmology. In addition to the various topics touched on already, here are a goodly number of others. Grand unified theories and the hierarchy problem Following the succesful unification of the electomagnetic and weak forces in the electoweak theory around 1970, there was much enthusiasm to seek a similar unification of the electroweak and strong forces in a similar sort of Yang-Mills theory, called a "grand unified theory" (GUT), We discuss this in more detail elsewhere, but a central part of any such effort is the introduction of additional Higgs fields to account for the spontaneous breaking of the symmetry of this (hypothetical) unified theory. Suffice it to say that, for a variety of reasons, the search for a GUT has not yet proven successful. One of the problems is related to the vast difference in the energy levels that would be involved. If there were such a unification of the electroweak and strong forces, 15 it would be manifest only at extremely high energies -- at least 10 GeV. In contrast, the breaking of the electoweak symmetry occurs around 100 GeV. This is a difference of a factor of at least 10 13. There would have to exist many new bosons analogous to the photon, W, Z, and gluons. These bosons are collectively called X bosons, and they would have masses at least 1015 GeV. The Higgs particles to account for such massive bosons would need to be of a similar mass. It is theoretically difficult to understand how there could be such a huge mass difference between the lightest Higgs particle(s) which occur in the electroweak theory and these other hypothetical particles. This is an aspect of what is known as the "hierarchy problem". It is especially acute for Higgs particles, because they are scalar bosons, which reflect relationships between different energy scales. In particular, the masses of such bosons are related by equations whose parameters would require extreme "fine tuning" to account for particles of such vastly different masses. This problem can be handled if the theory of supersymmetry is correct. Inflationary cosmology As we noted above, systems of matter and energy tend to undergo what are called phase transitions as the temperature of the system varies. At a very early time in the existence of the universe (when it was about 10-36 seconds old, to be more precise), it is suspected that an extremely important phase transition took place. The temperature at that time corresponded to an energy of about 10 15 GeV. According to GUT models, somewhere around there is the critical point where the electromagnetic, weak, and nuclear forces have the same strength. Above that energy (and earlier in time), there was just one unified force. Below that energy, the electroweak force and the strong force become distinct. It is hypothesized that several Higgs fields exist which account for this symmetry breaking. (They are different from the Higgs field that breaks the electroweak symmetry at a much lower energy.) 20
  21. 21. 28 As the universe cooled through the critical temperature (about 10 ° K) at first nothing happened. But the universe was not energetically stable. It was in a state resembling a supersaturated solution or water cooled below the freezing point. This state has been called the "false vacuum". Then a phase transition took place and -- in technical terms -- all hell broke loose. So much energy was released by the phase transition (just as occurs when water freezes, but a lot more dramatically) that the universe quickly inflated in size by a factor of 1050. This is the event known as "cosmic inflation". Of course, it's still just a hypothesis. Yet it accounts for a number of features which can be observed in the universe today, which we discuss elsewhere. Indeed, the evidence for the correctness of this inflationary cosmology is good, and getting better all the time. The evidence for inflation, in fact, is much better than that for the Higgs mechanism. It seems pretty clear that inflation really did occur. It's less clear what the exact mechanism was. But the best guess is that various Higgs fields which account for the breaking of GUT symmetry were involved. If so, this is indirect evidence for the Higgs mechanism. Magnetic monopoles There is another complication related to the use of a Higgs field in grand unified theories. In some of those theories, such as the one based on SU(5) symmetry, if the Higgs field does exist, magnetic monopoles should have been created during the first 10-35 second after the big bang -- during the phase transition responsible for cosmic inflation. Magnetic monopoles would basically be constructed out of Higgs fields. Suppose there are three such fields. At each point in space, each field is described by a single number, since it's a scalar field. But with three fields, you need three numbers, so we have, essentially, a three-component vector at each point. During the chaos of the phase transition these vectors will tend to line up with each other at nearby points. But at a few points, conditions may be so chaotic that no consistent direction can be established. A magnetic monopole would develop at that point, with the magnetic field arising from the interaction of the various Higgs fields. A magnetic monopole is a type of 0-dimensional singularity. 1-dimensional and 2- dimensional singularities could also develop under these conditions. Such singularities are called "cosmic strings" and "domain walls", respectively. Objects of this sort are also called, collectively, "topological defects". Just as when a liquid cools very rapidly to a crystalline solid, different regions may crystallize in different orientations, resulting in a discontinuous boundary between the regions. This boundary would become a domain wall. The intersection of two walls would be a cosmic string. Such objects, if they exist, would be exceedingly massive, and could have acted to "seed" the clumping of matter when inflation ended. Despite numerous experimental searches, magnetic monopoles have never been conclusively observed. Cosmic strings and domain walls haven't either. However, this is not necessarily a fatal problem, since inflation itself handily disposes of it. If inflation occurred, all the monopoles that were created in the first instant would have been dispersed so thoroughly in the subsequent inflation that they would be very sparsely distributed in the present universe, and hence observation of them would be most unlikely. 21
  22. 22. Gravity If "empty" space is actually filled with Higgs fields, and hence with rather massive Higgs particles, how is it that they apparently have no gravitational effect at all? Yes, there is some sort of "dark matter" out there, apparently quite a bit of it. But physicists have ruled out any contribution in the form of Higgs particles to this dark matter. What's really going on here is concealed from us because we lack a viable quantum theory of gravity. Indeed, it certainly makes sense that if Higgs particles really do explain why particles of matter have mass, they there should be a very close connection with gravity -- which is a theory all about the reciprocal effects of mass and space on each other. The cosmological constant, vacuum energy density Although we do not yet possess a consistent quantum theory of gravity, some essential properties of such a theory are known. If there is a quantum theory of gravity at all, it must be mediated by a spin 2 boson, the graviton. The graviton must couple to anything which has mass or (by the equivalence of mass and energy) anything which carries energy, including the Higgs field. Computations of this hypothetical coupling indicate that the cosmological constant -- which occurs in Einstein's fundamental equation of general relativity -- should have a huge value far in excess of what is observed. In fact, the constant should be so large that the entire universe would curl up to have a diameter less than a meter. It's hard to see how this could be. Theoretical explanations are forced to assume that if there were no Higgs field in the vacuum, then spacetime would have a huge negative curvature precisely sized to cancel out almost exactly the positive curvature caused by the Higgs field. This does not feel like an aesthetically satisfying solution to the problem of the cosmological constant. We must, presumably, wait for a satisfactory quantum theory of gravity to really understand what goes on here. Axions A Higgs mechanism has been used to address a symmetry breaking problem quite different from that of the electroweak theory. The symmetry involved is called CP, which is a combination of two discrete symmetries: charge conjugation (C) and parity (P). There are various interesting issues associated with these symmetries and a third -- time reversal (T). We discuss these issues elsewhere, but the basic situation is that there's a basic theorem which states the combination of all three symmetries (CPT) is always preserved in nature. That is, if you take any particle interaction and simultaneously apply all three symmetry operations, the result will be another interaction that is exactly as likely to occur as the original one. This is not necessarily the case if you take only two symmetries at a time, however. CP symmetry, for instance, is often violated in weak interactions. But with interactions involving the strong force, the probability of CP violation is extremely small, possibly zero. There are two ways the strong force could violate CP 22
  23. 23. symmetry. (One is inherent in the equations of the theory, and the other follows from the fact quarks have mass, which is a consequence of the electroweak force.) If the actual violation is very small or zero, the two effects would cancel each other almost exactly, which is curious. This situation is known as the "strong CP problem". It turns out that the probability of CP violation in a strong force interaction can be interpreted as the average value of a spinless quantum field, and the quantum of this field is a particle called the "axion". The mathematics behind this result is basically the same as that of the Higgs mechanism employed in the electroweak theory. It involves the spontaneous breaking of a global symmetry called the Peccei-Quinn symmetry. The Higgs field which causes this symmetry breaking may have been one that contributed to the formation of domain walls. Like Higgs particles, axions have not yet been observed. Unlike the Higgs particles, however, they are expected to be extremely light -- less than 1/100 the mass of an electron. In spite of their light weight, some theorists think axions could be so numerous in the universe that they might be a prime candidate to constitute "dark matter". Alternatives to the Higgs mechanism In light of all that's been said about the importance of the Higgs field and the Higgs boson to particle physics, would it be a disaster if (as appears possible) no Higgs particle is actually found? No. There are alternatives to the Higgs mechanism for explaining electroweak symmetry breaking and particle mass, even though each has problems of its own. What we do know is that if no Higgs boson exists, then there must be some other particles or forces -- of an unknown type -- which play the same role. The symmetry breaking isn't simply an "accident". The typical form of such alternatives involves new particles and forces that bind together in such a way as to produce a composite particle which behaves in essential ways like the Higgs boson. Thus, although such a particle is not elementary, it still interacts with known particles to slow them down and give them mass. In any case, there would be no reason, based on current experimental evidence, to give up the present standard model. It is not in conflict with experiment. There are certainly many things which still require explanation. If something like the Higgs mechanism isn't true of the real world, then there will be other causes. It just may take a little longer to find them. Technicolor One of the more noteworthy alternatives developed in the late 1970s was an entirely new type of force called a "technicolor" force. The basic idea was to construct Higgs bosons as composite particles -- like mesons and hadrons -- rather than assume they are elementary particles like leptons and quarks. Essentially, this idea would hypothesize a new force rather like the color force, but at a scale about a thosand times smaller. The force was called technicolor because of the analogy with the color force. 23
  24. 24. In this scheme there would be a new set of spin 1/2 particles called (of course) technifermions. A bound state of one of these with its antiparticle would be a spin 0 particle (a boson) analogous to a pion (which consists of a quark and an anti-quark, bound by the color force). Naturally, this would be called a technipion. One such particle would play the role of the Higgs boson in lending mass to the gauge bosons of the weak force. There are a variety of problems with technicolor theory in its various forms. Just to begin with, while it explains the mass of the weak gauge bosons, it does not explain how fermions acquire mass. Although the theory predicts a large number of additional particles should exist, no evidence has been found for any of them, or any other effects of the hypothetical technicolor force. There are many other problems of a techni-cal nature, such as problems reproducing known phenomena of weak interactions. Efforts to extend the theory to deal with such problems have only made it even more baroque and artificial than it was to begin with. In short, theories of this kind are still pursued by some who dislike the Higgs mechanism for one reason or another. But deficiences and inelegance of such theories makes them unpopular with most physicists. Open questions To sum it all up, physicists have pursued an understanding of the Higgs mechanism for three related purposes:  To make the Yang-Mills theory of the electroweak force renormalizable and mathematically consistent  To provide an explanation for the fact most known particles (except for photons and gluons) have mass  To explain why spontaneous symmetry breaking occurs in the theory of the electroweak force (and the asymmetry of the electroweak and the strong force in a grand unified theory) Theoretically, this effort has been successful on all counts. Experimentally, however, until Higgs particles are actually observed, there remains substantial room for doubt. Some of the causes for concern, aside from the lack of direct evidence for Higgs particles, are as follows:  Introduction of new fields and particles to solve theoretical problems, without independent evidence, seems a little ad hoc and contrived.  There is little explanation of what causes or generates the Higgs field itself. (Perhaps another way of saying it is ad hoc.) This can be remedied with the help of more ambitions theories, such as supersymmetry, but such theories are themselves unverified.  Computations of the cosmological constant, assuming the existence of Higgs fields, produce a result that is absurdly large. 24
  25. 25. Where are the Higgs particles? This is the biggest concern at the moment. There should exist at least one Higgs boson with a mass less than about 135 GeV under reasonable assumptions. Actual experiments have already ruled out any Higgs bosons with masses close to this limit. What are the theoretical implications if Higgs bosons can't be found? The standard model would survive. The Higgs mechanism solves various problems for the standard model, but it is not actually predicted by the model. That is, the mechanism provides a sufficient, but not necessary, means of resolving the problems. The nonexistence of Higgs bosons would not lead to any conflict between theory and experimental results. The standard model is essentially a theory of massless particles. The Higgs mechanism provides a means of explaining the masses of particles, through their coupling with the Higgs field, without sacrificing mathematical consistency of the standard model. If Higgs particles do not actually exist, it may still be possible that there is a Higgs field which provides for mass. If there is no Higgs field at all (which would greatly mitigate the cosmological constant puzzle), then the explanation for particle mass would be a major mystery, yet the standard model itself wouldn't fall. What is the origin of mass? Assuming that the theory of the Higgs mechanism is essentially correct, and that Higgs particles are eventually observed, then all particles that "couple" with the Higgs field will acquire a certain amount of mass. Here then is an explanation of where mass comes from. In fact, none of the particles which occur in the standard model could have any mass that does not come from coupling with the Higgs field if the theory is to be mathematically consistent. But even if all this is correct, there are still puzzles. Where do the masses of the Higgs particles themselves come from? For any other particle, their observed mass is proportional to the strength with which they couple to the Higgs particle. But what is it that determines the strength of this coupling, and hence the specific mass of each particle? Most mysteriously of all, since gravity is preeminently the theory of the interaction of mass with spacetime, how is gravity related to the Higgs mechanism? What is the origin of the Higgs field itself? We have noted above various ways in which this question can partially be answered. But even if these answers are correct as far as they go, they don't seem like a "final" answer. The situation is somewhat similar to that of questions like "where does space come from?" or "where does time come from?" Physics may at some point be able to provide answers to questions like this. Or at least, to questions of where the hypothetical single unified force and the Higgs fields come from. (Ironically, though, the number of necessary Higgs fields seems to increase even as the number of independent forces decreases.) If there is a Higgs mechanism, what solves the hierarchy problem? 25
  26. 26. Although the Higgs mechanism handles a number of puzzles fairly well it creates a rather nasty problem of its own in grand unified theories, which unify three of the four fundamental forces (excepting only gravity). This hierarchy problem, though rather technical, doesn't seem capable of being dismissed as a mere aesthetic blemish. That would entail a fantastically improbable circumstance. Supersymmetry offers a solution, but supersymmetry itself currently lacks critical experimental evidence. If supersymmetry is real, many puzzles are solved. In particular, we have a way to explain the origins of the Higgs mechanism and to handle the hierarchy problem. But without supersymmetry, we must find alternative solutions to both problems. If there is a Higgs mechanism, what keeps the cosmological constant small? The problem is, in short, that the Higgs mechanism is a bit too efficient. If the vacuum is actually as full of nonzero Higgs fields as it seemingly must be to account for particle mass and spontaneous symmetry breaking, then the cosmological constant (i. e., vacuum energy density) must be enormous -- 120 orders of magnitude larger than what observation seems to allow. Somehow, the effects of all the Higgs fields need to cancel each other out almost (but not quite) entirely. It's a "fine tuning" situation that could hardly happen by chance. Even supersymmetry does not appear to help out.” “Surveys, overviews, tutorials Higgs boson Article from Wikipedia. See also Technicolor (physics). Physics with ATLAS: The Higgs Particle Overview of the role of the Higgs field in accounting for the mass of Standard Model particles. The Higgs Mechanism An elementary explanation in cartoon form, based on ideas by David J. Miller. The original brief article is here. The Waldegrave Higgs Challenge The best 5 one-page particle essays on Higgs physics, written in response to a challenge by UK Science Minister, William Waldegrave. My Life as a Boson: The Story of 'the Higgs' A slide presentation by Peter Higgs, given at the 2001: A Spacetime Odyssey conference. The search for a standard model Higgs at the LHC PhD thesis by Ulrik Egede. Detailed technical treatment of theoretical and experimental Higgs physics. Look in particular at Higgs physics at the LHC. The Linear Collider Opportunity An essay by Gordon Kane on the need for construction of a new linear collider. The essence of the matter is that an understanding of electroweak symmetry breaking and the Higgs mechanism is a top priority in theoretical particle physics and that a NLC will provide experimental data not obtainable any other way. What exactly is the Higgs boson? Question and answers from Scientific American's Ask the Experts section. 26
  27. 27. How does the Higgs boson affect string theory? Question and answer (by Gordon Kane) from Scientific American's Ask the Experts section. What is a Goldstone Boson? Goldstone bosons play a technical role in symmetry breaking via the Higgs mechanism. The question is answered by Jeffrey Goldstone. The Higgs Boson Brief introductory information. Higgs Boson: One Page Explanation Five articles that explain the Higgs boson in a page or less. Recommended references: Magazine/journal articles Jiggling the Cosmic Ooze Peter Weiss Science News, March 10, 2001, pp. 152-154 The Higgs particle is thought to be responsible for the existence of mass in the standard model. Detection of the Higgs particle is the highest priority objective in current high-energy physics. The Higgs Boson Martinus J. G. Veltman Scientific American, November 1986, pp. 76-84 Historically, physicists have developed the theory of Higgs fields for two different reasons: to account for masses of elementary particles, and to give consistency to the mathematics of elementary particle theory. Actual existence of Higgs fields and bosons would solve some problems, but pose others. Recommended references: Books Abdus Salam -- Unification of Fundamental Forces Cambridge University Press, 1990 An introductory lecture by one of the co-recipients of a Nobel prize for work on the unification of the weak and electromagnetic forces. “ “How Particles Acquire Mass By Mary and Ian Butterworth, Imperial College London, and Doris and Vigdor Teplitz, Southern Methodist University, Dallas, Texas, USA. The Higgs boson is a hypothesised particle which, if it exists, would give the mechanism by which particles acquire mass. Matter is made of molecules; molecules of atoms; atoms of a cloud of electrons about one-hundred-millionth of a centimetre and a nucleus about one-hundred-thousandth the size of the electron cloud. The nucleus is made of protons and neutrons. Each proton (or neutron) has about two thousand times the mass of an electron. We know a good deal about why the nucleus is so small. We do not know, however, how the particles get their masses. Why are the masses what they are? Why are the ratios of masses what they are? 27
  28. 28. We can't be said to understand the constituents of matter if we don't have a satisfactory answer to this question. Peter Higgs has a model in which particle masses arise in a beautiful, but complex, progression. He starts with a particle that has only mass, and no other characteristics, such as charge, that distinguish particles from empty space. We can call his particle H. H interacts with other particles; for example if H is near an electron, there is a force between the two. H is of a class of particles called "bosons". We first attempt a more precise, but non-mathematical statement of the point of the model; then we give explanatory pictures. In the mathematics of quantum mechanics describing creation and annihilation of elementary particles, as observed at accelerators, particles at particular points arise from "fields" spread over space and time. Higgs found that parameters in the equations for the field associated with the particle H can be chosen in such a way that the lowest energy state of that field (empty space) is one with the field not zero. It is surprising that the field is not zero in empty space, but the result, not an obvious one, is: all particles that can interact with H gain mass from the interaction. Thus mathematics links the existence of H to a contribution to the mass of all particles with which H interacts. A picture that corresponds to the mathematics is of the lowest energy state, "empty" space, having a crown of H particles with no energy of their own. Other particles get their masses by interacting with this collection of zero-energy H particles. The mass (or inertia or resistance to change in motion) of a particle comes from its being "grabbed at" by Higgs particles when we try and move it. If particles do get their masses from interacting with the empty space Higgs field, then the Higgs particle must exist; but we can't be certain without finding the Higgs. We have other hints about the Higgs; for example, if it exists, it plays a role in "unifying" different forces. However, we believe that nature could contrive to get the results that would flow from the Higgs in other ways. In fact, proving the Higgs particle does not exist would be scientifically every bit as valuable as proving it does. These questions, the mechanisms by which particles get their masses, and the relationship amongs different forces of nature, are major ones and so basic to having an understanding of the constituents of matter and the forces among them, that it is hard to see how we can make significant progress in our understanding of the stuff of which the earth is made without answering them. Last updated on 21st September 1998, by Dr S.L.Lloyd “ “Politics, Solid State and the Higgs By David Miller Department of Physics and Astronomy, University College, London, UK. 1. The Higgs Mechanism Imagine a cocktail party of political party workers who are uniformly distributed across the floor, all talking to their nearest neighbours. The ex-Prime Minister enters and crosses the room. All of the workers in her neighbourhood are strongly attracted to her and 28
  29. 29. cluster round her. As she moves she attracts the people she comes close to, while the ones she has left return to their even spacing. Because of the knot of people always clustered around her she acquires a greater mass than normal, that is she has more momentum for the same speed of movement across the room. Once moving she is hard to stop, and once stopped she is harder to get moving again because the clustering process has to be restarted. In three dimensions, and with the complications of relativity, this is the Higgs mechanism. In order to give particles mass, a background field is invented which becomes locally distorted whenever a particle moves through it. The distortion - the clustering of the field around the particle - generates the particle's mass. The idea comes directly from the physics of solids. instead of a field spread throughout all space a solid contains a lattice of positively charged crystal atoms. When an electron moves through the lattice the atoms are attracted to it, causing the electron's effective mass to be as much as 40 times bigger than the mass of a free electron. The postulated Higgs field in the vacuum is a sort of hypothetical lattice which fills our Universe. We need it because otherwise we cannot explain why the Z and W particles which carry the weak interactions are so heavy while the photon which carries electromagnetic forces is massless. 2. The Higgs Boson Now consider a rumour passing through our room full of uniformly spread political workers. Those near the door hear of it first and cluster together to get the details, then they turn and move closer to their next neighbours who want to know about it too. A wave of clustering passes through the room. It may spread to all the corners or it may form a compact bunch which carries the news along a line of workers from the door to some dignitary at the other side of the room. Since the information is carried by clusters of people, and since it was clustering that gave extra mass to the ex-Prime Minister, then the rumour-carrying clusters also have mass. The Higgs boson is predicted to be just such a clustering in the Higgs field. We will find it much easier to believe that the field exists, and that the mechanism for giving other particles is true, if we actually see the Higgs particle itself. Again, there are analogies in the physics of solids. A crystal lattice can carry waves of clustering without needing an electron to move and attract the atoms. These waves can behave as if they are particles. They are called phonons and they too are bosons. There could be a Higgs mechanism, and a Higgs field throughout our Universe, without there being a Higgs boson. The next generation of colliders will sort this out. Last updated on 30th August 1995, by Dr S.L.Lloyd “ “Of Particles, Pencils and Unification By Tom Kibble Department of Physics, Imperial College, London, UK. Theoretical physicists always aim for unification. Newton recognised that the fall of an apple, the tides and the orbits of the planets as aspects of a single phenomenon, gravity. 29
  30. 30. Maxwell unified electricity, magnetism and light. Each synthesis extends our understanding and leads eventually to new applications. In the 1960s the time was ripe for a further step. We had a marvellously accurate theory of electromagnetic forces, quantum electrodynamics, or QED, a quantum version of Maxwell's theory. In it, electromagnetic forces are seen as due to the exchange between electrically charged particles of photons, packets (or quanta) of electromagnetic waves. (The distinction between particle and wave has disappeared in quantum theory.) The "weak" forces, involved in radioactivity and in the Sun's power generation, are in many ways very similar, save for being much weaker and restricted in range. A beautiful unified theory of weak and electromagnetic forces was proposed in 1967 by Steven Weinberg and Abdus Salam (independently). The weak forces are due to the exchange of W and Z particles. Their short range, and apparent weakness at ordinary ranges, is because, unlike the photon, the W and Z are, by our standards, very massive particles, 100 times heavier than a hydrogen atom. The "electro-weak" theory has been convincingly verified, in particular by the discovery of the W and Z at CERN in 1983, and by many tests of the properties. However, the origin of their masses remains mysterious. Our best guess is the "Higgs mechanism" - but that aspect of the theory remains untested. The fundamental theory exhibits a beautiful symmetry between W, Z and photon. But this is a spontaneously broken symmetry. Spontaneous symmetry breaking is a ubiquitous phenomenon. For example, a pencil balanced on its tip shows complete rotational symmetry - it looks the same from every side. - but when it falls it must do in some particular direction, breaking the symmetry. We think the masses of the W and Z (and of the electron) arise through a similar mechanism. It is thought there are "pencils" throughout space, even in vacuum. (of course, these are not real physical pencils - they represent the "Higgs field" - nor is their direction a direction in real physical space, but the analogy is fairly close.) The pencils are all coupled together, so that they all tend to fall in the same direction. Their presence in the vacuum influences waves travelling through it. The waves have of course a direction in space, but they also have a "direction" in this conceptual space. In some "directions", waves have to move the pencils too, so they are more sluggish; those waves are the W and Z quanta. The theory can be tested, because it suggests that there should be another kind of wave, a wave in the pencils alone, where they are bouncing up and down. That wave is the Higgs particle. Finding it would confirm that we really do understand the origin of mass, and allow us to put the capstone on the electro-weak theory, filling in the few remaining gaps. Once the theory is complete, we can hope to build further on it: a longer-term goal is a unified theory involving also the "strong" interactions that bind protons and neutrons together in atomic nuclei - and if we are really optimistic, even gravity, seemingly the hardest force to bring into the unified scheme. There are strong hints that a "grand unified" synthesis is possible, but the details are still very vague. Finding the Higgs would give us very significant clues to the nature of that greater synthesis. 30
  31. 31. Last updated on 30th August 1995, by Dr S.L.Lloyd “ “Ripples at the Heart of Physics By Simon Hands Theory Division, CERN, Geneva, Switzerland. The Higgs boson is an undiscovered elementary particle, thought to be a vital piece of the closely fitting jigsaw of particle physics. Like all particles, it has wave properties akin to those ripples on the surface of a pond which has been disturbed; indeed, only when the ripples travel as a well defined group is it sensible to speak of a particle at all. In quantum language the analogue of the water surface which carries the waves is called a field. Each type of particle has its own corresponding field. The Higgs field is a particularly simple one - it has the same properties viewed from every direction, and in important respects is indistinguishable from empty space. Thus physicists conceive of the Higgs field being "switched on", pervading all of space and endowing it with "grain" like that of a plank of wood. The direction of the grain in undetectable, and only becomes important once the Higgs' interactions with other particles are taken into account. for instance, particles called vector bosons can travel with the grain, in which case they move easily for large distances and may be observed as photons - that is, particles of light that we can see or record using a camera; or against, in which case their effective range is much shorter, and we call them W or Z particles. These play a central role in the physics of nuclear reactions, such as those occurring in the core of the sun. The Higgs field enables us to view these apparently unrelated phenomenon as two sides of the same coin; both may be described in terms of the properties of the same vector bosons. When particles of matter such as electrons or quarks (elementary constituents of protons and neutrons, which in turn constitute the atomic nucleus) travel through the grain, they are constantly flipped "head-over-heels". this forces them to move more slowly than their natural speed, that of light, by making them heavy. We believe the Higgs field responsible for endowing virtually all the matter we know about with mass. Like most analogies, the wood-grain one is persuasive but flawed: we should think of the grain as not defining a direction in everyday three-dimensional space, but rather in some abstract internal space populated by various kinds of vector boson, electron and quark. The Higgs' ability to fill space with its mysterious presence makes it a vital component in more ambitious theories of how the Universe burst into existence out of some initial quantum fluctuation, and why the Universe prefers to be filled with matter rather than anti-matter; that is, why there is something rather than nothing. To constrain these ideas more rigorously, and indeed flesh out the whole picture, it is important to find evidence for the Higgs field at first hand - in other words, find the boson. There are unanswered questions: the Higgs' very simplicity and versatility, beloved of theorists, makes it hard to pin down. How many Higgs particles are there? Might it/they be made from still more elementary components? Most crucial, how heavy is it? Our current knowledge can only put its mass roughly between that of an iron atom and three times that of a uranium atom. This is a completely new form of matter about whose nature we still have only vague 31
  32. 32. hints and speculations and its discovery is the most exciting prospect in contemporary particle physics. Last updated on 21st September 1998, by Dr S.L.Lloyd “ APPENDIX 3 Some research and notes on convergence preliminaries by Abdul-Basit- Khan: 1. “Nowhere to Hide” Question: How would you define “convergence” as it relates to information technology? Give an example. Telecommunications and information technologies are converging in more than one way. The very definition of information is changing. Telecommunications networks carried data in bits per second (bit: our quantum of data) and computers were processing data as bytes, according to older definitions. The new perspective is that both computational and telecommunications systems are processing information, a fundamental of this universe, an entity that has a quantity as well as a quality parameter. Information, however it may be quantified (and qualified) is being processed and transferred between systems around the world. Cellular networks were separate from the world-wide-web, now they are supporting Internet enabled devices as well. With the introduction of General Packet Radio Service Standards, and the overlay on GSM networks of GPRS by cellular providers, and the interconnectivity of fixed data networks to mobile networks by Gateway nodes, the very definition of Customer Premises Equipment is changing. A hand held or a cell phone, is not only a communication device but it is also a small computer, an information processing and transferring system. With new Fixed Wireless Applications in the local loop, with a convergent IP Phone/ Computer (internet device), consumer would find no difference between telephony and computation. An example of this is ever increasing enhancements in browsing /surfing capabilities of cell-phones. With standards evolving such as ENUM standards, a unique phone number for every subscriber in the world would identify him/her on any of his communication devices/media, which ever one he sets his /her preference parameters to. Whether the subscriber is logged into MSN Messenger on the desk-top, on the cell phone, on the land-line or has the preferences set to any other personal communication device, such as a blackberry, his/her unique telephone number will identify him on this grand unified voice/data network of tomorrow. All networks will converge, where not data alone, or voice alone, but “INFORMATION” is transmitted. 32
  33. 33. These are the convergence trends in information technology and telecommunications, where there is no data or voice subscriber, but it’s a unified network with a unique identifier, which is more than an IP address, more than a telephone number, to locate the end-user on any communications medium of choice. 2. Question: Do you agree or disagree that the desktop is dead? Why? Desktop is not completely dead, but it is mutating, changing and evolving. With Voice over IP as the new mode of unified communication, and ENUM standards evolving, the nature of Customer Premises Equipment is evolving. The desktop with a hard-drive and large, permanent memory has traditionally been used as the repository of personal information for individual consumers and users of information. As illustrated in the “Mirror Worlds”, Internet as the world’s largest distributed information system is taking over many of the functions of the desktop. Distributed databases, information storage and retrieval systems and transaction-based systems, do not require large storage memories on the desktop any more. The constraint is now the speed of the communications channel, and the efficiency of the queries. Many of us, use contact management software such as PLAXO to store contact information on a central server, to be retrieved in an instance on the desktop. Often, we use hot-mail to store important e-mails and to refer to them on a later date. For this course all the information exchange, submissions and grades, lie on a server at Humber. The desktop’s functionality has totally changed. We use the desktop to view information saved on remote servers accessible by the Internet. In the current telecommunications world, an example of this kind of phone-desktop hybrid is the Bell’s Vista 350 telephone. Stock quotes, weather reports, all accessible by the touch of a finger, on buttons configured based on preferences. With Voice over IP and convergent technologies evolving, the speed and bandwidth of communications channels will be much enhanced. Voice over IP will lead to new web devices, which would not require a large hard-drive or memory. The functionality of these devices will be only to retrieve and display information. There will be enhanced bookmarks and new desktop software (i.e. Scope ware) to manage trends and mimic usage patterns and behaviour of individual consumers. The emphasis will be on faster and more organized information retrieval and display. The management of distributed information, retrieved on the desktop and the pointers to this information would be dictated by the usage patterns. An interesting device currently available the web-racer mouse, which on the click of buttons, surfs the preferred Internet sites. 33
  34. 34. With Voice over IP standards evolving and convergence in the computer-telephony worlds, the desktop is not going to die. Rather it is going to mutate into a specialized and customized user interface for globally distributed storage media. 34

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