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Ann. Henri Poincaré 4, Suppl. 1 (2003) S15 – S30 c Birkhäuser Verlag, Basel, 2003 1424-0637/03/01S15-16 DOI 10.1007/s00023-003-0903-4 Annales Henri Poincaré Probing Physics at the Planck Scale G.G. Ross Abstract. We review the ideas for extending the theory of the strong, electromagnetic and weak interactions to the Planck Scale and a unification with the gravitational interaction. 1 Introduction One of the triumphs of modern physics has been the construction of the “Standard Model”, the theory of the strong, electromagnetic and weak interactions [1]. The Standard Model is a quantum field theory based on the principle of local gauge invariance. It describes essentially all the observed phenomena of the fundamental interactions as proceeding through the exchange of the elementary quanta of the force carriers; the photon for the electromagnetic interaction, the gluons for the strong interaction and the W ± and Z bosons for the weak interactions. However many physicists think that the Standard Model is incomplete and are pursuing the elusive “Theory of Everything” which they think represents the ultimate unification of the fundamental forces, including gravity. In this talk I will discuss how such searches have led to a discussion of Physics at the Planck Scale where the unification of the fundamental forces, including gravity, is thought to occur. 2 The Standard Model 2.1 The states of matter The Standard Model describes all the matter we observe in the universe in terms of a small number of elementary particles with interactions described by simple laws. The protons and neutrons which make up the atomic nucleus are made from elementary constituents, the (charge 23 ) up and the (charge - 13 ) down type quarks and the “gluons”, the carriers of the strong force which holds them together. In addition the Standard Model includes the electron (charge -1) as an elementary state and its neutral partner, the neutrino. These “leptons”, like the quarks, feel the electromagnetic and weak forces but, unlike the quarks, do not feel the strong force. To complete the Standard Model, three families or copies of the quarks and leptons are needed to describe the states currently observed c.f. Figure 1. S16 G.G. Ross Ann. Henri Poincaré Figure 1: The matter states of the Standard Model 2.2 The interactions The laws that govern the strong and weak interactions follow from the same local gauge principle applied to a relativistic field theory that led to Quantum Electrodynamics (QED), the quantum version of Maxwell’s theory of electromagnetism. The underlying ingredient is the recognition of a symmetry relating the states of the theory. Such a symmetry is based on patterns and the patterns of the Standard Model are illustrated in Figure 1. The experimental observation of the weak interactions of the left-handed electron and its neutrino suggest that these states are intimately related and have similar properties. In the Standard Model these states are assigned to doublets of the group SU (2) as is shown in Figure 1. The weak force is due to the exchange forces generated by with the gauge bosons of SU (2), the W ± and Z bosons. The charged weak interaction arises through the exchange of a W boson which changes a left-handed electron into a left-handed electron neutrino. The neutral weak interaction arises through the exchange of a Z boson which couples an electron. The representation is “chiral” in the sense that the transformation properties of the left- and right- handed states differ. The right-handed components of the electron, muon and tau are singlets under SU (2), hence do not change under an SU (2) rotation. In turn this means they carry no weak charge and do not couple to the weak gauge bosons and do not participate in the weak nuclear force. Note that we have not observed right-handed components of neutrinos and they are not included in the Standard Model particle content. As may be seen from Figure 1 the same pattern is repeated for the quarks with the Vol. 4, 2003 Probing Physics at the Planck Scale S17 left-handed components assigned to doublets and the right handed states singlets under SU (2). The strong interactions result from the gauge bosons of an SU (3) local gauge symmetry, with each quark coming in three “colours” and belonging to a triplet of states related by SU (3) rotations as shown in Figure 1. There are eight gauge bosons, “gluons”, associated with SU (3) corresponding to the different ways they can couple to the three colours of quarks. In order to include electromagnetism in the Standard Model, it is necessary to add a “U (1)” gauge symmetry corresponding to the local conservation of electric charge. This gives rise to a single gauge boson B (since there is only one type of electric charge). The photon is made up of a mixture of B and the W 3 gauge boson of Figure 3a. The orthogonal combination of the B and W 3 gauge bosons is the neutral weak boson, the Z. This completes the gauge symmetry structure of the Standard Model. The full gauge symmetry is SU (3) ⊗ SU (2) ⊗ U (1). The Standard Model has been found to be amazingly successful in describing all phenomena associated with the strong and electroweak interactions, the success culminating with the discovery of the W and Z bosons in 1983 at CERN [3] and the gluons at DESY [4]. 2.3 Partial Unification The exchange forces associated with these gauge bosons provides us with a partially unified quantum description of the strong, the weak and the electromagnetic interactions and, to date, essentially all observed phenomena are consistent with the predictions of the Standard Model. A very important property of these interactions is that the strength of the interactions depends on the length scale being probed, a property due to the screening effects of the virtual states necessarily present. This is illustrated in Figure 2 [5]. It may be seen that the strength of the strong force reduces as the momentum scale increases (or the distance scale decreases) the effect being dominated by the antiscreening effect of the virtual gluons. As a result at high momentum scales the strength of the strong force approaches that of the electromagnetic force which is also shown. Finally it may be seen that the strength of the weak force also approaches that of the other forces at high scales. In addition to a small screening effect there is a significant change in the effective weak coupling due to the weak propagator. The dimensionless coupling characterizing the underlying strength of the weak interactions is given by GF (Q)Q2 where GF (Q) is the Fermi coupling. In the Standard Model this cou2 2 pling is due = g 2 /8.Q2 /(Q2 + MW ) √ to the exchange of a W boson so GF (Q)Q 2 2 where g/2 2 is the gauge coupling constant and 1/(Q + MW ) is the gauge boson 2 and is weak due to the large propagator. At low scales GF (Q)Q2 g 2 /8.Q2 /MW 2 W mass MW 80GeV. At high scales GF (Q)Q g 2 /8 and, as may be seen from Figure 2, is intermediate in strength between the strong and weak interactions. S18 G.G. Ross Ann. Henri Poincaré Figure 2: The experimental measurement of the running of the strong force with the momentum scale Q at which it is measured. Also shown are the electromagnetic and weak interactions as a function of the momentum scale. However the approach of the coupling strengths, while suggestive, represents only a partial unification in as much as the couplings are not equal and there is no explanation in the Standard Model why they should even approach each other because the gauge group, SU (3) ⊗ SU (2) ⊗ U (1), involves three unrelated factors. Moreover, as may be seen from Figure 1, there is a complicated (chiral) multiplet structure needed which has been input by hand to generate the observed structure. Perhaps most importantly, the unification is of only three of the four fundamental interactions and there is no connection with the gravitational force. The gravitational coupling is proportional to Newton’s constant with inverse mass di19 2 mensions, GN ∝ MP−2 lanck . MP lanck is the Planck mass, approximately 10 GeV /c 2 (the unit of mass used in particle physics is 1 GeV /c , approximately the mass of the proton). The weak coupling is given at low energies by the Fermi constant, −2 , where the W boson mass MW is approximately 102 GeV /c2 some 17 GF ∝ MW orders of magnitude smaller than the Planck mass. The quark and charged lepton masses range from 12 10−3 GeV /c2 for the electron to approximately 175GeV /c2 for the top quark while the neutrinos in the Standard Model are massless. For many the origin of this hierarchy is the most pressing of all the questions raised by the Standard Model. Vol. 4, 2003 Probing Physics at the Planck Scale S19 3 Grand Unification Apart from the inclusion of gravity, an answer to the questions raised by the partial unification of the Standard Model is provided by Grand Unification. Grand Unified theories (GUTs) seek to embed the Standard Model in a unified structure which can relate its multiplet structure and interactions by extending the patterns that led to the Standard Model. The archetypical GUT is based on the symmetry group SU (5), chosen because it is the smallest group which can accommodate the SU (3) ⊗ SU (2) ⊗ U (1) gauge group of the Standard Model [6, 7, 2]. In this the strong, the weak and the electromagnetic forces are just different facets of the one underlying (SU (5)) local gauge interaction. The quarks and leptons are also related in SU (5) because they belong to the common multiplets as shown in eq.(1). dr dy db e+ −ν c R 0 −ucb ucy −ur −dr ucb 0 −ucr −uy −dy −ucy ucr 0 −ub −db ur uy ub 0 −e+ dr dy db e+ 0 (1) L Of course there must be an explanation for the non-observation of the additional gauge bosons implied by SU (5). Provided the mass of these bosons, MX , is larger than the current energy of particle accelerators we will not have been able to find the X bosons directly. However a much stronger bound is available through the virtual effects of the X bosons since they mediate new processes which have not, so far, been observed. In particular the new interactions of SU (5) mediate proton decay. The current experimental limit on the decay lifetime of the proton is an impressive 1032 years giving a limit on the X boson mass of MX > 1016 GeV /c2 ! Note also that in SU (5) there is no room for a right-handed neutrino component. This offers an explanation for the different properties of the neutrino for the absence of this state is what forces the neutrino to be massless in the Standard Model. In extensions of SU (5) to more unified GUTs such as SO(10) the missing righthanded neutrino appears. However it is expected to acquire a mass at the stage of spontaneous symmetry breaking of SO(10) to SU (5) which we expect to be very large and greater than MX . As a result the left-handed neutrino states remain 2 /MX ) with the result that the left-handed neutrino very light with mass ≈ O(MW states can only acquire a very small mass, in agreement with recent measurement. In fact SO(10) is a very attractive extension of SU (5) because a single 16 dimensional representation contains all the states of a single family plus the right handed neutrino. Thus it enormously simplifies the multiplet structure of Figure 1, leaving only the family replication to be explained, perhaps by extending the symmetry to include a family symmetry. There remains, of course, the question of determining the couplings and masses in the Standard Model. In a GUT, such as SU (5), with a single group factor, there is a single gauge coupling constant describing the strong, weak and S20 G.G. Ross Ann. Henri Poincaré Figure 3: Plot of the (inverse) couplings of the Standard Model gauge group factors up to the Grand Unified mass scale electromagnetic couplings. Thus it offers an explanation of the partial unification of couplings observed in Figure 2. However the unification of couplings should apply at a scale at which the differences between the gauge bosons of SU (5) can be neglected. This means we should continue the couplings above the mass of the X bosons. This is shown in Figure 3 where it may be seen that the couplings continue to approach each other, suggesting a true unification [9]. Moreover the scale at which they come together is very high, in agreement with the scale needed to inhibit proton decay. However, in detail, the couplings never meet, the discrepancy being 8 or 9 standard deviations. 4 Supersymmetry Grand Unification, while very attractive, introduces a fundamental problem. This occurs because in a field theory with pointlike couplings, radiative corrections probe all virtual momentum scales. As a result they can generate large corrections to particle masses unless the mass is protected by a symmetry. Most of the states of the Standard Model are protected. The gauge bosons cannot acquire a mass while the gauge symmetry is unbroken and thus the gluons and the photon remain massless even after radiative corrections are included. The fermions belong to chiral representations and similarly cannot acquire mass while the Standard Model gauge group is unbroken. The problem occurs in the sector needed to spontaneously break the SU (2) gauge symmetry. In this spontaneous breaking Vol. 4, 2003 Probing Physics at the Planck Scale S21 the order parameter is supplied by the vacuum expectation value of a scalar field, the Higgs boson. However its mass is not protected by a symmetry and so receives large radiative corrections which drive it up to the Grand Unified scale. This would mean that the SU (2) symmetry is broken at the scale MX , giving mass of O(MX ) to the W and Z bosons and to the quarks and lepton. To avoid this unacceptable conclusion requires that the symmetry of the Standard Model be extended to include a new symmetry capable of protecting the Higgs scalar mass from large radiative corrections. The only possible symmetry capable of keeping a Higgs boson light is supersymmetry (plus a chiral symmetry) . Supersymmetry [8, 2] assigns scalars to supermultiplets with fermion partners and thus their properties are related : φ (J = 0) SUSY −→ ψ (J = 1 ) requires mψ = mφ 2 Thus if the fermion mass mψ is forbidden by a chiral symmetry as discussed above the scalar mass will also vanish. In this case there must be supersymmetric partners to the Standard Model states. In order to prevent radiative corrections reintroducing the hierarchy problem, the states must be quite light, less than or of order 1 TeV. The extension of the Standard Model to include supersymmetry requires the addition of many new states. These include the “squarks” and “sleptons”, spin zero partners of the spin-one-half quarks and leptons respectively. Also needed are the “gluinos”, the “Wino”, the “Zino” and the “photino”, spin-one-half partners of the Standard Model gauge bosons, the gluon, the W, the Z and the photon respectively. Although these new states are thought to be considerably heavier than their partners, and hence should not yet have been found directly in laboratory experiments, they will contribute as virtual states to the radiative corrections discussed above. The exciting observation that solves the hierarchy problem is that the new SUSY radiative corrections have the same magnitude as the Standard Model contributions but opposite sign. Thus, when SUSY is exact, there is no correction to the Higgs mass. When SUSY is broken at a scale MSUSY the new supersymmetric states acquire mass of O(MSUSY ) and this cancellation is spoilt. However the resultant contribution is of O(MSUSY ) and provided this is not too large (i.e. ≤ O(1T eV )) it is consistent with the observed electroweak breaking. In summary the supersymmetric solution to the hierarchy problem requires new physics beyond the Standard Model in the form of the spectrum of new SUSY states at a scale accessible to the next generation of accelerators. 5 Unification of couplings Although there is no direct evidence for a new supersymmetric state, the is strong indirect evidence for the existence of such states coming from the unification of gauge couplings. This follows because the new supersymmetric states must be light S22 G.G. Ross Ann. Henri Poincaré Figure 4: Evolution of the gauge couplings in the supersymmetric extension of the Standard Model to protect the Higgs from receiving large radiative corrections to its mass. These light states also contribute to the screening of the gauge couplings and thus affect the gauge unification prediction. In Figure 4 I show the evolution of the couplings in the Supersymmetric Standard Model. One may see that that the supersymmetric prediction is quantitatively better than the non-supersymmetric case shown in Figure 3. This only works if the new supersymmetric states are “light” on the Grand Unified scale with masses less than 1T eV /c2 just as is required if one is to keep the Higgs boson light. A better way to illustrate this may be obtained by using the assumed unification to predict the value of the strong coupling in terms of the weak and electromagnetic couplings[11]. This is shown in Figure 5 where one may see that the predicted region in the sin θ W − αs plane occupies only a very small part of the a priori allowed region. This is quite impressive already as it appears to be better than one part in one hundred. If one adds the constraint that MX must be large to avoid rapid proton decay this region shrinks even further. Using the measured value of the strong coupling one may use this plot to determine the prediction for sin2 θW . One finds sin2 θW = 0.2314 ± 0.002 − 0.25(αs − 0.119)) to be compared with the experimental value sin2 θW = 0.2312 ± 0.0002. Vol. 4, 2003 Probing Physics at the Planck Scale S23 Figure 5: Graph (bottom left) illustrating the precision of the test of gauge unification. The area between the two curves is the predicted region allowing for the uncertainties in the supersymmetric particle masses with no constraint on the unification scale. The graph (upper right) indicates the prediction for the unification scale that results from the requirement that the gravitational strength should also unify. 5.1 Unification with gravity Given the success of the unification prediction one may ask whether the unification can extend to include gravity as well. Following our discussion of the weak force where the relevant dimensionless coupling was GF (Q)Q2 . In this case the relevant coupling is GN (Q)Q2 where GN (Q) is Newtons constant. In Figure 5 I show that this coupling also comes close to unification with the other couplings provided the unification scale is vey high, close to the Planck scale, In my opinion this is a very strong hint that the four fundamental interactions do unify and motivates the search for the underlying theory capable of doing so. The only candidate is the (super) string. 6 String Unification Since others at this meeting will talk about string theories themselves, I will concentrate on the question how is unification changed in superstring theories? String theory is the only candidate we have for a unification of all the fundamental in- S24 G.G. Ross Ann. Henri Poincaré teractions including gravity [12]. Of course at low energies one is looking at the four dimensional effective field theory which results from string theory defined at the Plack scale. Often this involves a stage of compactification of some of the space-time dimensions and in the low energy theory these act as internal degrees of freedom. The resulting 4D theory has several promising properties : • The symmetries are specified by the underlying string. For consistency the string theory should be supersymmetric and this symmetry may survive in the low energy effective theory offering an explanation for the hierarchical structure of masses observed. In the heterotic string case there is an E8 ⊗ E8 gauge symmetry before compactification leading to an E8 ⊗ E6 on compactification on a Calabi Yau manifold. The resulting gauge group can easily accommodate the Standard Model but also can be larger. For example it can incorporate the Grand Unified groups SU(5), SO(10) or E6 . The only symmetries that are known to descend from the string are gauge symmetries, either continuous or discrete. Unfortunately there are many possible vacua in the compactified 4 dimensional theory and we do not know how to select between them. • The multiplet structure is specified in a given string vacua. Usually this includes some number ng of chiral families + some number nV of vector like states which come in complex conjugate pairs. The latter are expected to acquire mass at a high scale through a stage of symmetry breaking below the compactification scale. Many 3 generation examples are known. Moreover, if the string theory is built from level-1 Kac Moody level theories the representation content of the theory is restricted offering an explanation to the question why only low lying representations of quark and leptons are observed. • String theory has only one fundamental parameter, the string scale which can be related to the Planck scale. All other parameters are determined in terms of the vacuum expectation values (vevs) of moduli fields, ΦM . For example the string coupling constant is determined by 1/2 gi (Mstring ) = ki 2 gstring (2) where ki is a parameter associated with the particular string construction and 1 2 . (3) = gstring <S> Here S is a moduli field known as the dilaton. In the absence of supersymmetry breaking the moduli fields have no potential and any value for their vacuum expectation value gives a viable string theory. Once supersymmetry is broken, the moduli’s vev will be fixed and the coupling will be determined Vol. 4, 2003 Probing Physics at the Planck Scale S25 as in eq 3. Similarly the Yukawa couplings which determine the quark and lepton masses are determined as functions of additional moduli known as complex structure moduli. (Unfortunately we are still far from an understanding of the string vacuum structure and hence from a prediction of the string coupling.) 6.1 M-theory determination of the gauge unification scale The prediction for the gauge unification scale in the weakly coupled heterotic string follows from the general form of the 4D Lagrangian [15] 4 1 √ 2 Lef f = − d10 x gα−1 10 ( 4 R + 3 T rF + · · ·) α α √ 4 1 2 = − d4 xV gα−1 (4) 10 ( 4 R + 3 T rF + · · ·) α α In this we may see that Newton’s constant, GN , and the value of running gauge couplings at the unification scale, αGUT , are given in terms of the 10D string 1 coupling α10 , the string tension α ∼ Mstring and the volume of the 6D compactified space V by α10 α4 α10 α3 , αGUT = (5) GN = 64πV 16πV −6 For the case that α10 is small the volume V is approximately Mstring and one obtains eq(6) eliminating V between the two equations. Mstring ≈ gstring × (5.2 × 1017 GeV ) ≈ 3.6 × 1017 GeV (6) which, c.f. Figure 3, is only a factor of 20 above the “observed” gauge unification scale [16]. It is difficult to overemphasize the potential importance of this result. Our belief that there is a stage of Grand Unification of the strong, weak and electromagnetic interactions rests largely on the quantitative success of the unification of the associated couplings. The prediction of the unification scale would be the first indication of unification with gravity. While the prediction within a factor of 20 is encouraging, the residual discrepancy raises some doubts. One promising explanation comes from the string itself. If one uses the “measured” value for V = O((1 − 3).1016 GeV −6 ) one may obtain the value of α10 instead. This gives an enormous value, quite inconsistent with the assumption of weak coupling that went into the derivation of eq(5). Thus the failure of the prediction of eq(6) is not surprising - it was the wrong calculation. Instead one should go to the strongly coupled case. That it is now possible to discuss strong coupling relies on an understanding on relations between strong coupling and weak coupling regimes known as dualities. It has long been known that there are five distinct classes of string theory, a S26 G.G. Ross Ann. Henri Poincaré fact that has caused concern because one might hope that the “Theory of Everything” is unique. However developments in string theory have shown that there is a rich class of duality symmetries relating various string theories [13, 14] so now the expectation is that all string theories are related to each other and to an underlying theory known as “M-theory”. This theory lives in eleven dimensions and the various string theories may be viewed as different limits of this underlying theory. In addition it is now realised that eleven dimensional supergravity also belongs to this web of inter-related theories. A feature of the dualities relating different theories is that they often relate one theory in the weak coupling (perturbative) limit to another theory in the strong (nonperturbative) limit or one theory in the small compactification radius limit to another in the large compactification limit. By making use of these dualities one may gain insight into non-perturbative physics by performing calculations in the dual theory in which the perturbation series makes sense. In the strongly coupled heterotic string case Horava and Witten [15] showed that the theory is equivalent to M-theory. Although it is not possible to construct M-theory explicitly it is possible to write down the long-distance effective field theory coming from M-theory. It is just 11 dimensional supergravity compactified on a six-dimensional Calabi-Yau space times a line interval, CY3 ⊗ S1 /Z2 . The effective Lagrangian in this case is given by [15] Lef f 1 =− 2πκ211 √ d x gR − 11 1 8π(4πκ211 )2/3 √ d10 x gT rF 2 + · · ·) (7) giving GN = κ211 (4πκ211 )2/3 , αGUT = 2 16π V R11 2V (8) The reason this form changes is that the gravitational fields now propagate in the bulk of the 11th dimension while the gauge fields live on the end points of the line integral (one E8 on each fixed point) and propagate only in 10D. One may see that this changes the relation between Newton’s constant and αGUT through the appearance of the radius of the 11th dimension, R11 . Given the appearance of a new parameter it is clear one may adjust it to eliminate the discrepancy between scales found in the weakly coupled case. This gives [16] πR11 = (5.1015 GeV )−1 (9) While it is encouraging that the discrepancy between scales has been eliminated, apparently the predictive power has been lost. In order to determine the size of the compactified dimensions it is necessary to understand the vacuum structure of the theory which determines the magnitude of the moduli field setting this scale. At present this is beyond our ability so the unification with gravity, while suggestive, remains unproven. Vol. 4, 2003 Probing Physics at the Planck Scale S27 7 Probing the Planck scale In this talk I have described some very promising ideas for the complete unification of the fundamental forces, including gravity. Will these ideas be tested in the foreseeable future? As we have discussed there is already evidence for unification coming from the unification of the gauge couplings of the theory. Additional predictions of relations between the masses of the fundamental matter fields, the quarks and leptons are also in good agreement with measurement. In addition there is a good explanation for why the SU (2) symmetry is broken to give masses to the W and Z bosons leaving the gluons and photon massless. These indirect tests of the underlying theory are encouraging. What about more direct tests of unification? One of the central ingredients is the need for supersymmetry with its associated states with a mass in the T eV range. Such states will be accessible to the next generation of accelerators, the LHC at CERN and the Tevatron at Fermilab in Chicago. It may be that the new supersymmetric states provide a source of the missing dark matter in the universe and searches for supersymmetric dark matter are being actively pursued. 7.1 Epilogue In this talk I have concentrated on the “classic” unification prediction which applies close to the Planck scale some fifteen orders of magnitude above the energy scale accessible to present accelerators. In this case it is impossible to produce the string states which would directly verify an underlying string unification. The best we can hope for is that these states may leave an imprint on the development of the universe after the Big Bang which is visible today in the structure of the universe and the microwave background. However recent developments in the study of string theory have raised another interesting possibility that may make the string states more accessible to experimental test. As discussed in the previous Section it is possible that the relation between the string scale and the Planck scale gets modified through the appearance of a new space dimension with radius R11 much larger than the Compton wavelength of the string states. As a result the underlying unification scale can be reduced. This has raised the question how large can such new dimensions be and how low can the string scale be? Surprisingly it is possible to have new space dimensions as large as 0.1mm [17]! The first indication of such a new space dimension would be new massive “Kaluza Klein” excitations of the graviton, perhaps as light as fractions of an electron volt! However these states couple with gravitational strength and so would not yet have been observed. Associated with a large new dimension is the reduction in the string scale and the extreme possibility is that the string scale should be as low as a T eV. In this case the Planck scale reflects the existence of a very small coupling and not the existence of very heavy states. In this extreme case one might even do without supersymmetry because the virtual momenta involved in radiative corrections are S28 G.G. Ross Ann. Henri Poincaré cut-off at the T eV scale. In such schemes the next generation of accelerators would even be able to directly produce string excitations. While an interesting possibility, I consider such low scale unification schemes to be much less likely than the “classic” picture. If the gauge couplings are to unify at a low scale there must be additional light states which change the running of the couplings. As a result the remarkably precise prediction for the unification of gauge couplings discussed above would then have to be considered to be a complete accident. 8 Conclusion The 20th century has seen the construction of a relativistic quantum field theory of the strong, electromagnetic and weak interactions. This theory is remarkably successful and its predictions are consistent with all observed phenomena. However the theory leaves unanswered several important questions, perhaps the most important being what is the origin of the mass of the fundamental states and how does the unification extend to the fourth fundamental force, gravity? Remarkably there is already indication that there is an underlying “Theory of Everything” capable of providing answers to these questions. Provided there is a new symmetry, supersymmetry, the observed strengths of the interactions become equal at a scale close to the Planck scale. In string theories the unification scale is related to the string or Planck scale offering a simple explanation for high scale unification. The small mass of the neutrinos is a natural outcome of the large scale of unification. The parameters determining the quark, charged lepton and neutrino masses fit well with an underlying GUT combined with a spontaneously broken family symmetry. If these ideas are correct we should be on the threshold of observing completely new phenomena associated with the new supersymmetric states. The very real hope is that the 21st century will see our understanding of the origin of mass and the construction of a fully unified theory of all the fundamental interactions. Vol. 4, 2003 Probing Physics at the Planck Scale S29 References [1] For introductory reviews of the Standard Model see : M. Veltman, “Gauge Theories,” In Fraser, G. (ed.): The particle century, Bristol, UK: IOP (1998) 46–56; G. Altarelli, “How The Standard Model Works,” In Fraser, G. (ed.): The particle century, Bristol, UK: IOP (1998) 127–141. [2] G. Ross, ”The Standard Model and Beyond,” In Fraser, G. (ed.): The particle century, Bristol, UK: IOP (1998) 155–168. [3] C. Rubbia, “Hunting the carriers of the weak force,” In Fraser, G. (ed.): The particle century, Bristol, UK: IOP (1998) 196–104. [4] S.L. Wu, “Quark Glue,” In Fraser, G. (ed.): The particle century, Bristol, UK: IOP (1998) 116–126. [5] G. Altarelli, Ann. Rev. Nuc. Part. Sci. 39 (1989); S. Bethke, J. Phys. G 26 (2000). [6] H. Georgi and S.L. Glashow,Phys. Rev. Lett. 32, 438 (1974); Nucl. Phys. B 193, 150 (1981). [7] For general reviews of GUTs see: P. Langacker, Physics Reports 72, 185 (1981); G.G. Ross, Grand Unified Theories, Benjamin/Cummings (1984); R.N. Mohapatra, Unification and Supersymmetry, Springer-Verlag, (1992). [8] For reviews see: J. Wess and J. Bagger, Supersymmetry and Supergravity (Princeton University Press, 1993); H.-P. Nilles, Phys. Rep. 110, 1 (1984); H.E. Haber and G.L. Kane,Phys. Rep. 117, 75 (1985). [9] H. Georgi, H.R. Quinn, S. Weinberg, Phys. Rev. Lett. 33, 451 (1974). [10] S. Dimopoulos, S. Raby and F. Wilczek, Phys. Rev. D 24, 1681 (1981); L.E. Ibanez and G.G. Ross, Phys. Lett. 105B, 439 (1982); M. Einhorn and D.R.T. JonesNucl. Phys. B, 196, 475 (1982). [11] D. Ghilencea and G. G. Ross, Phys. Lett. B 442, 165 (1998) [arXiv:hepph/9809217]. [12] For a general review of string theories see M.B. Green, J.H. Schwarz, and E. Witten, “Superstring Theory”, Cambridge University Press, 1988; J. Polchinski, “String Theory”, Cambridge, UK: Univ. Pr. (1998). [13] C. M. Hull and P. K. Townsend, Nucl. Phys. B 438, 109 (1995) [hepth/9410167]. [14] E. Witten, Nucl. Phys. B443, 85 (1995) [hep-th/9503124]. S30 G.G. Ross Ann. Henri Poincaré [15] P. Horava and E. Witten, Nucl. Phys. B 475, 94 (1995) ; P. Horava, Phys. Rev. D 54, 7561 (1996). [16] E. Witten, Nucl. Phys. B 471, 135 (1996). [17] N. Arkani-Hamed, S. Dimopoulos and G. Dvali, Phys. Lett. B 429, 263 (1998); Phys. Rev. D 59, 086004 (1999).; I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. Dvali, Phys. Lett B 426, 257 (1998). G.G. Ross Department of Physics Theoretical Physics University of Oxford 1 Keble Road Oxford OX1 3NP U.K. and Theory Group CERN 1211 Geneva 23 Switzerland