A Ball Pool Model to illustrate the Higgs physics to the public
AA Ball Pool Model to illustrate the Higgs physics tothe public
Giovanni Organtini ”Sapienza”, Universit`a di Roma & INFN-Sez. di Roma, Roma, P.le A. Moro 2I-00185E-mail: [email protected]
Abstract.
A simple model is presented to explain the Higgs boson physics to thegrand public. The model consists of a children ball pool representing a Universe filledwith a certain amount of the Higgs field. The model is suitable for usage as a hands-ontool in scientific exhibits and provides a clear explanation of almost all the aspects ofthe physics of the Higgs field interaction with other particles.PACS numbers: 01.20.+x, 01.50.My, 01.40.-d, 14.80.Bn
Submitted to:
Physics Education a r X i v : . [ phy s i c s . pop - ph ] J a n Ball Pool model for the Higgs
1. Introduction
The Higgs boson was discovered in 2012 by the ATLAS and CMS Collaborations atLHC [1] [2]. The physics of the Higgs boson interactions with other particles andwith itself has been elucidated by few qualitative models, suitable to illustrate it toundergraduate students and to the grand public. A very popular model is the oneformulated by David Miller of University College London (for which he won a champagnebottle awarded by the UK Science Minister William Waldegrave intended for those whowould be able to explain the Higgs mechanism to the people) [3].Since then a number of analogies were proposed to help people understand the Higgsmechanism, most of which relies on the analogy of the Higgs field with a viscous mediumin which particles move slower than in air. Such an analogy provides an effective wayto illustrate how the interaction of a field with a massless particle gives rise to the massof the latter: the mass appears as a reduction of the particle speed in vacuum , wherethe vacuum is a state with the minimum possible energy.These analogies do not face the problem of explaining the nature of the vacuumstate that does not correspond to an empty space, but to a space filled with a certainamount of Higgs field for which the Higgs auto-interaction potential attains its minimum.They also fail in explaining what it means to observe a Higgs boson.In our recent works we provided two alternative models addressing these problems.One is a video (in Italian) [4] illustrating the interaction of massless particles, representedby steel balls, with the Higgs field represented by magnets. In this video a masslessparticle interacts with the field that limits its ability to move in a given region of space,depending on the nature of the particle (i.e., on the coupling constant between the fieldand the particle). Another resource is a paper [5] illustrating the Higgs mechanism usinga completely classical formalism, suitable to be understood by most of teachers (eventhose who does not know about quantum mechanics) and at least part of the students.None of the models cited before is suitable for the realisation of a hands on installation, as it may be required by scientific museums or institutions. In this paperwe propose a model that is very attractive because it permits to realise an installationin which people can immerse themselves to directly experiment the interaction with aHiggs boson. In the following sections we illustrate the installation and its usage asa pedagogical tool to address all the aspects of the interaction of the Higgs field withmassless particles, namely:(i) contrary to familiar fields, when the Higgs potential V attains its minimum value V = V ( φ ) in a volume there is, in fact, a certain amount of field φ (cid:54) = 0 that,however, is unobservable;(ii) if the amount of the Higgs field φ = φ + η inside this volume is reduced or increased,the potential changes and the Higgs field becomes observable (this is an optionalfeature);(iii) a massless particle in such a field moves with a speed lower than the speed of light,just because it interacts with the Higgs field; Ball Pool model for the Higgs Figure 1.
A children ball pool is a good model of a Universe filled by a certain amountof Higgs field (image is a courtesy of Tutto Gonfiabili – Play Wily). (iv) the interaction of matter fields with the Higgs field may led to the observation of aHiggs boson.Section 2 describes the setup of the installation; Section 3 shows how to use theinstallation to illustrate the properties of the Higgs boson.
2. The setup
A very simple setup can be realised with a children ball pool, such as in Fig. 1. Thewalls of the pool must be opaque and the pool must be partially filled. It should stay ata height such that people looking from outside cannot see its content. Optionally, thepool must sit on a scale through which its weight can be measured. The sensitivity ofthe scale must be good enough to make it possible to appreciate a variation in weightdue to the removal of few balls and must indicate zero in normal conditions.The pool represents the Universe, while the balls represent the Higgs fieldpermeating the Universe. The balls have a nice feature in this context: while actingalmost as a fluid when treated as a whole, they are discrete objects. Such a featureprovides a very good support to explain the dual nature of quantum fields that behave,at the same time, as waves and particles.The setup is easy to be realised, cost effective and clean (no liquids required).
3. The illustration of the Higgs physics
In this section we illustrate the various aspects of the Higgs physics using our model ofthe Universe, represented by the pool, and of the Higgs field, represented by the balls.
The first feature of the Higgs field, listed in Section 1, namely the fact that the Higgsfield is unobservable when it attains its minimum energy, is shown looking at the pool
Ball Pool model for the Higgs scientist can only conclude that theUniverse, represented by the pool, is empty. However, we do know that such a Universeis not empty: there is, actually, some field inside. The only way to try to detect thisfield is to interact with it.
In the Higgs mechanism, the field φ interacts with itself with a potential reaching itsminimum for a value φ (cid:54) = 0. That means that the state of the lowest possible energyconsists in a state in which some Higgs field is present, contrary to what happens in thecase of the more familiar electromagnetic field, for which the minimum possible energyis attained when both the electric field E and the magnetic field B are zero.A consequence of this behaviour is the following. In classical physics, if a givenvolume is empty its energy attains its lowest possible value. Such a state is called the vacuum state meaning that, to increase its energy, something must be added to thevolume. In the case of the Higgs field, the lowest possible value of the energy in avolume is obtained when the volume contains a field φ = φ . Adding some Higgs fieldto such a volume increases its energy, as for the electromagnetic field. However, in thiscase, the energy inside the volume increases even when the Higgs field is removed fromthe volume. For this reason the vacuum state, considered as the state with the lowestpossible energy, no longer coincide with an empty state.In order to detect the presence of some field or particle in a volume we must interactwith that field or particle. As a result the energy of the field or particle changes. In thecase of the Higgs field, the only way to detect its presence consists in interacting with itcausing an increase of the energy in the volume in which is contained. For this reasonit is impossible to see the field φ : each time one tries to interact with it, the energy inthe volume increases and that implies an increase of the field φ > φ .Removing or adding some extra field to our setup means removing or adding ballsfrom it. This changes the weight of the pool and the effect can be read on the scale.When the scale is not at zero the system is not in equilibrium. Correspondingly one can see the removed balls or the added ones from outside, concluding that there is somethingelse in the region out of the vacuum. The only way to return the system to the stablecondition is to bring it back to the original condition of zero weight. Here, the weightof the system plays the role of the Higgs potential. When such a potential is null thesystem is at its equilibrium and this happens when there is a specific amount of fieldinside the volume, that cannot however be detected. The detection of some extra Higgsfield implies a non vanishing potential.This analogy is only partial, in fact. While the Higgs potential always increases,irrespective of the sign of η , the weight of the system either increases or decreases.However, the scale can be configured such that it only shows the absolute value of thedifference in weight and this recover the analogy.Moreover, the Higgs field would spontaneously recover the equilibrium, if the field Ball Pool model for the Higgs
The mass of the fermions in the Standard Model (SM) arise from the Yukawa interactionof otherwise massless particles with the Higgs field at its minimum value [6]. In otherwords, the mass of a particle ceases to be a property of that particle, like its electriccharge, but arises from dynamical effects consisting in the interaction of the Higgs fieldwith the particle itself that, in this model, would be massless if not interacting withsuch a field.Explaining how an interaction can lead to the appearance of a mass for a particlehas been the goal of most of the metaphors developed so far (see, e.g. [3]).In our analogy, a massless particle is represented by a person moving in the spacearound our Universe consisting of the pool. Those people can move at their own speedwithout limitations. If the same person walks inside the Universe filled with the Higgsfield, its speed is reduced, as if it acquires inertial mass. On the other hand, inertialmass is a measure of how difficult is to make a particle to accelerate. The reduction ofthe particle speed depends on the fact that now the particle interacts with the field .Different persons may interact differently with the balls, as different particles dowith the Higgs field, leading to particles with different mass. A muon differs from anelectron just because its interaction with the Higgs field is stronger than that of theelectron. A tall person may move faster than a short boy in the ball filled Universe,because the degree of interaction of the latter is higher.Experimenting the effect by themselves makes it extremely clear one of the mostdifficult concepts to understand in Higgs physics: how the interaction with a field canlead to a mass for an otherwise massless particle.In summary, people observing a person (representing a massless particle) walkinginside the pool can only measure the speed of it (the particle) to be lower than thatwould be outside the
Universe .The conclusion is that particles that move at the same speed in an empty Universe,move with different speeds in a Universe filled with some Higgs field at its lowest energystate, that however appears as empty since such a field is not observable. The speedof each particle depends on the coupling between the Higgs field and the particle: thestronger the coupling, the lower the speed, hence the higher the inertial mass.
When a person moves inside the pool, people can only see part of its body. They donot see the field : it is still not possible to observe any Higgs boson in these conditions.
Ball Pool model for the Higgs materialise into a particle that eventuallywill disappear decaying into a pair of other particles. As a matter of fact, Higgs bosonscan be produced at LHC because the energy of the collision between protons turns intothe mass of the Higgs boson plus other particles. In other words, one need to transferenough energy to the vacuum to produce real observable Higgs bosons.In order to provide enough energy to the vacuum field, one may run inside thepool at enough speed. In this way the kinetic energy of the particle interacting withthe Higgs field can be gained by such a field and few balls can scatter high enough tobecome visible out of the walls of the pool. Soon after the balls return to their originalposition, however the bottom line will be that people observing a certain region of theUniverse in which particles are injected with enough energy may lead to the productionof new particles, otherwise unobservable: these new particles can exist only for a verylimited amount of time and are what physicists call the Higgs bosons.
It is important that a public installation conveys the right messages and does not becomemerely a toy to play with. To this purpose, the shape and colour of the pool can beadjusted such that the attention of the visitors is maintained on the installation topic.For example, if the pool is narrow and long, such that visitors can only walk along itslength, part of the playful aspect vanishes or, at least, diminishes. A similar effect canbe obtained using monochromatic balls (and possibly of a neutral colour), in contrastwith those found in playgrounds and shown in Fig. 1.On the other hand, the requirements in terms of size and shape of the model arenot so stringent. Even if, as stated above, a narrow, long enough pool helps in conveyingthe right message, the proposed metaphor can be realised at almost any size. A tabletopsetup, for example, can be used almost in the same way: in this case one can use a cartmoved by hands to simulate the effects of a person walking in the pool. The perceptionwould be similar and understanding why the interaction lead to the appearance of amass would be equally convincing.
4. Summary
We described a possible installation that can be used in scientific exhibits as well asin classrooms to explain the physics of the Higgs boson to the grand public. Such aninstallation is easy to realise and cost effective and potentially addresses all the featuresof the Higgs field interaction with other particles. It is aimed at all ages and versatileenough to modulate the level of the analogy according to the audience background.
Ball Pool model for the Higgs Acknowledgments
I am indebted with the Director of Exhibits and Media Studio at the S. Francisco’sExploratorium Thomas Rockwell for his precious suggestions and his advices.
References [1] ATLAS Collaboration ”Observation of a new particle in the search for the Standard ModelHiggs boson with the ATLAS detector at the LHC”, Phys. Lett. B, 716, (2012) 1-29 doi:10.1016/j.physletb.2012.08.020.[2] CMS Collaboration ”Observation of a new boson at a mass of 125 GeV with the CMS experimentat the LHC”, Phys. Lett. B, 716, (2012) 30-61 doi: 10.1016/j.physletb.2012.08.021.[3] Miller, D.J. ”A quasi–political explanation of the Higgs boson”, published in [4] Organtini, G. ”Il meccanismo di Higgs”, on .[5] Organtini, G. ”Unveiling the Higgs mechanism to students”, Eur. J. Phys. 33 (2012) 1397-1406 doi: 10.1088/0143-0807/33/5/1397.. See also Organtini, G ”The Higgs mechanismfor undergraduate students”, Nucl. and Part. Phys. Proc., 273-275 (2016) 2572-2574, doi:10.1016/j.nuclphysbps.2015.09.463.[6] Olive, K.A. et al. (PDG), Chin. Phys. C38, 090001 (2014) ( http://pdg.lbl.govhttp://pdg.lbl.gov