Physicists naturally try to see phenomena in simple terms.
You might say that the primary justification for doing elementary particle physics
with all its expense and difficulty is the opportunity it gives us of seeing all of nature in somewhat simpler terms.
Great progress had been made a few years ago, say from the late 1960’s to the mid 1970’s,
in clarifying the nature of the elementary particles and their interactions.
Then starting about the mid 1970’s, we began to confront a series of problems of much greater difficulty.
And I would have to say that very little progress has been made.
I would like first of all today to remind you of what the present understanding of elementary particle physics is,
as it was already formulated by the mid 1970’s.
And then for the larger part of my talk discuss the attempts that have been made since the mid 1970’s
to go beyond this to the next level of simplicity.
The present understanding of elementary particle physics, I would say, is based on three chief elements.
First of all, there is a picture of the interactions of the elementary particles
as being all extremely similar to the one interaction that was earlier well understood, the electromagnetic interaction.
You know that the electromagnetic interaction is carried by a massless particle of spin-1, the photon,
which for example is exchanged between the electron and the proton in the hydrogen atom.
In the present understanding of elementary particle physics there are 12 photons.
And I should do this, meaning that the word is put in quotation marks.
There are 12 photons which carry all the forces that we know of between the elementary particles.
These 12 photons comprise first of all the familiar old photon which is emitted say by an electron or by any charged particle,
and then by three siblings, three family members called intermediate vector bosons, a W-, a W+ and a Z0,
which are emitted for example when leptons change their charge.
When electrons turn into neutrinos or neutrinos turn into electrons.
And the neutral one, the Z0 is emitted by electrons and neutrinos when they don’t change their charge.
Similarly the W and the Z are also emitted by quarks when they do or do not change their charge respectively.
In addition to the four “photons” of the electro weak interactions, there are eight similar particles known as gluons,
that Sam Ting has already mentioned, which are emitted when quarks change, not their charge,
but a different property which has been humorously named their “colour”,
so that a green quark may turn into a red quark emitting a red-green gluon.
There are three colours and hence there are eight gluons.
You may ask why not nine gluons and I will tell you if you ask me privately later.
Now, in electromagnetism we have not only the general idea of a photon
but a very clear picture of a symmetry principle of nature which determines the properties of the photon
and determines in particular all of its interactions.
The principle known as gauge invariance.
In a sense, from the point of view of the theoretical physicist,
the photon is the way it is because gauge invariance requires it to be that way.
The 12 photons of the elementary particle interactions as we know them are also governed by a principle of gauge invariance,
but the group of gauge transformations is larger and it is known mathematically as SU(3)x SU(2)x U(1).
The SU(2)x U(1) is a 4-dimensional group which governs the four particles of the electroweak interactions,
the W and the Z transmit the weak nuclear force, which gives rise to radioactive beta decay.
So this whole set of interactions are called the electroweak interactions.
And the SU(3) governs the eight gluons which give rise to the strong nuclear forces.
This is sometimes called the 321 theory.
The theory of the eight gluons by itself is what is known as quantum chromo dynamics.
The electric charge of the electron say is in fact just a peculiar weighted average of coupling constants,
G and G prime associated with these two groups, SU(2) and U(1),
G and G prime play the same role for these groups of gauged transformations
that the electric charge played in the older theory of quantum electrodynamics,
and the electro charge in fact is given by a simple formula in terms of them.
And similarly there is another coupling constant.
A coupling constant is just a number that tells you the strength with which these particles are emitted and absorbed.
There’s another coupling constant that tells us how strongly gluons are emitted,
say when quarks change their colour, known as G sub S for the group SU(3).
Now, this is a very pretty picture, especially since, based as it is on familiar old ideas of gauge invariance,
it requires us really to learn very little new.
Always to be preferred.
But there’s an obvious difficulty with it, that is that gauge invariance requires,
that the vector particles, the spin-1 particles that transmit the force, have zero mass.
Just as for example electromagnetic gauge invariance requires the photon to have zero mass.
But of course the W and the Z do not have zero mass.
They have masses which are so large that no one so far has been able to produce them,
although we have strong reasons to think we know where they are.
The explanation for this is now universally believed to be, that the gauge symmetry, although precise and exact,
in no sense approximate, is subject to a phenomenon known as spontaneous symmetry breaking.
That is these are symmetries of the underlying equations but they are not realised in the physical phenomena.
This is a lesson that elementary particle physicists learn from solid state physicists who understood it much earlier than we did.
That symmetries can be present at the deepest level and yet not apparent in the phenomena.
The symmetries are just as fundamental as if they were not broken but they’re much harder to see.
Because the electroweak symmetry of SU(2)x U(1) is spontaneously broken, the W and the Z have masses,
the W mass is greater than 40 GeV, the Z mass is greater than 80 GeV
and the precise values are determined by an angle which just basically tells you the ratio of these two coupling constant.
The angle is measured in a great variety of experiments
and on the basis of that we believe the W will be at a mass of about 80 GeV and the Z will be at a mass of about 90 GeV.
Of course we anxiously await confirmation of that.
The second of the three ingredients,or the three elements on which our present understanding is based,
is the menu of elementary particles.
I won’t dwell on this, there are six different varieties of quarks,
of which five have been discovered and the sixth is anxiously awaited.
Each one of these varieties, sometimes called flavours of quarks,
according to quantum chromo dynamics comes in three colours, so that altogether there are 18 quarks.
And then in parallel to the quarks there are doublets of leptons, neutrino-electron
and then the muon behaving like a heavier electron has its own associated neutrino and the tau lepton has its associated neutrino.
Physical processes are most simply seen in terms of these quarks and leptons.
So for example, when a neutron decays,
a state which was originally an up quark and two down quarks of three different colours,
turns into two up quarks and a down quark of three different colours,
a W- being emitted, which then turns into an electron and an antineutrino.
This menu of elementary particles is in no sense forced on us by theory,
except for the structure of doublets of quarks and leptons and colour triplets of quarks.
The fact that there are 6 flavours is just taken from experiment.
And it has to be regarded as just an independent empirical foundation of our present understanding.
The third of the foundations of the present understanding of physics is more mathematical but I think equally important.
The idea of renormalisability, renormalisability is very simply the requirement
that the physical laws must have the property that whenever you get, calculate a physically relevant quantity,
you don’t get nonsense, you don’t get divergent integrals, you get an integral which converges, that is a finite number.
I think we’ll all agree that that is a desirable quality of a physical theory.
The physical theories that satisfy that requirement are actually very easy to distinguish.
If an interaction of some sort has a coupling constant G,
like the coupling constants G and G prime and GS that I discussed earlier.
And if that coupling constant has the dimensions of mass to some power minus D, let’s say a negative power, D is positive.
And when I talk about dimensions, I will always be adopting the physicists system of units
in which Planck’s constant and the speed of light are one.
Then, because the coupling constant has the dimensions of a negative power of mass,
the more powers of coupling constant you have in the matrix element for any physical process,
the more powers of momentum which have the dimensions of a positive power of mass, mass to the first power,
the more powers of momentum you will have to have in the integrals.
So that as you go to higher and higher order in the coupling constant,
you get more and more powers of momentum in the integrals and the integrals will therefore diverge worse and worse.
That’s a bad thing, that’s not a renormalisable theory.
The allowed interactions, the renormalisable theories are those with coupling constants therefore,
which are not negative powers of mass,
but which are either dimensionless like the electric charge of the electron or positive power of mass like for example any mass.
A physically satisfactory theory ought to be one which contains only such coupling constants.
Now, that is enormously predictive because the energy densities
or the Lagrangians that determine physical laws always have a fixed dimensionality, mass to the 4th power.
And I remind you that I am using units in which Planck’s constant and the speed of light are one.
So energy has the unit of mass and length has the unit of inverse mass.
So therefore, if a coupling constant appears in an energy density and it multiplies an operator,
a function F with a dimensionality mass to some power D,
then the dimensionality of the coupling constant must be just the dimensionality of the Lagrangian 4 minus D.
So therefore, in order to keep the dimensionality of the coupling constant positive or zero,
we must have the dimensionality of the operators 4 or less.
But almost everything has positive dimensionality, fields have dimensionality 1 for boson fields or 3 half for spino fields.
Derivatives, space-time derivatives have dimensionality 1, and therefore,
as you make an interaction more and more complicated, its dimensionality inevitably increases.
But the allowed interactions have dimensionality only 4 or less.
And therefore the principle of renormalisability limits the complexity of interactions that are allowed in physics.
This is just what physicists need, they need something to tell them
“do not think about all conceivable theories, think about a limited set of simple theories.”
The limited set of simple theories that we allow ourselves to think about
are those with interactions whose dimensionalities are 4 or less
and therefore are sharply limited in the number of fields and derivatives that they can have.
In fact so powerful are these limitations that principles A, B and C determine a physical theory uniquely,
except for a few free parameters.
The free parameters are things like the electric charge of the electron, the Fermi coupling constant of beta decay,
the mixing angle between the Z and the photon, a scale parameter of quantum chromo dynamics
which tells us where the strong coupling constant begins to become very large.
And of course all the quark and lepton masses and masses for other particles called Higgs bosons, that I haven’t mentioned.
But aside from this fairly limited set of free parameters,
not as limited as we would like but still not enormous number of free parameters,
the physical theory of elementary particles in their observed interactions is completely determined.
And not only determined but agrees as far as we know with experiment.
One of the features of this understanding, which I think is perhaps not as widely emphasised as I would like,
to me it seems one of themost satisfactory aspects of what we know about physics, is that the conservation laws of physics,
that were painfully deduced from experiment in the 1930’s, 1940’s and 1950’s and 1960’s
are now understood as often approximate consequences of these deeper principles.
The theory, as constrained by gauge invariance and by renormalisability and other fundamental principles,
cannot be complicated enough to violate this symmetry principle.
So for example, as long as you assume that certain quark masses are small,
the strong interactions must obey the symmetries of isotopic spin invariants chirality
in the "eightfold way" of Gell-Mann and Ne'eman, which were previously deduced on the basis of data.
Whatever the values of the quark masses,
the strong and the electromagnetic interactions must conserve the quantities known as strangeness,
charge conjugation invariance and with certain qualifications, parity and time reversal invariance.
And independently of the values of the quark masses, and without any qualifications at all,
the strong, weak and electromagnetic interactions must conserve baryon and lepton number,
there is no way of writing down a theory complicated enough to violate these conservation laws,
a theory that would be consistent with the principles that I’ve described.
This understanding of the physical origin of the symmetry principles leads us to a further reflection.
We now understand why, let us say, strangeness is conserved.
Strangeness, the property that distinguishes a K meson from a Pi meson or a hyperon from a nucleon
is not conserved because the laws of nature contain on some fundamental level a principle of strangeness.
Strangeness is conserved as a more or less accidental consequence of the theory of strong interactions
known as quantum chromo dynamics.
The theory simply cannot be complicated enough to violate the principle of strangeness conservation.
Because strangeness conservation can be understood without invoking strangeness as a fundamental physical conservation law,
we are led to reflect that perhaps it is not a fundamental symmetry and perhaps when you widen your scope
beyond the strong interactions you will see that strangeness is not conserved.
That’s in fact of course true and it’s been known to be true
since the first days that people started talking about strangeness conservation.
The weak interactions don’t conserve strangeness,
for example a hyperon is able to decay into an ordinary proton or neutron
violating the conservation of the strangeness quantum number that distinguishes the two.
In exactly the same way, because we now understand that baryon and lepton number.
By the way, baryon number is just a number which counts the number of quarks, it´s 1/3 for each quark,
and lepton number is a number which counts the number of leptons, it´s 1 for each lepton.
The conservation of baryon and lepton number for example prohibits processes
like the proton decaying into a positron and a Pi 0, which would otherwise be allowed.
Because the conservation of baryon and lepton number is understood
as a dynamical consequence of the present theory of electroweak and strong interactions and the principle renormalisability,
there is no reason to doubt that, when we go to a wider context, that this conservation law will be found to be violated.
Because it is not needed as a fundamental conservation law.
It is understood without it´s being needed on a fundamental level.
A great deal of attention has been given to this possibility, that baryon and lepton number are not conserved.
Suppose for example that there are exotic particles with masses much greater than the W or the Z.
Let me take the mass capital N as just some characteristic mass scale for a new world of exotic particles
that have not yet been discovered, and by exotic I mean rather precisely particles
with different quantum numbers for the gauge symmetries, SU(3)x SU(2)x U(1) than the known quarks and leptons and gauge bosons.
The world that we know of is just the world of those particles that have much smaller masses than this new scale capital N.
And that world is described, since we’re not looking at all at physics, we’re only looking at part of physics,
not by a fundamental field theory but what's called an effective field theory.
We should describe our present physics in terms of an effective Lagrangian.
That effective Lagrangian, since it’s not the ultimate theory of physics,
might be expected to contain non-renormalisable as well as renormalisable terms.
In the same way that when Euler and Heisenberg in the mid 1930’s wrote down an effective Lagrangian
for the scattering of light by light at energies much lower than the mass of the electron,
they wrote down a non-renormalisable theory because they weren’t working at a fundamental level
but only with an effective theory that was valid as a low energy approximation.
The effective theory should contain non-renormalisable terms, and as I indicated before,
these are terms whose coupling constant has the dimensionalities of a negative power of mass.
That is we have operators O with dimensionality D and coupling constants with dimensionality 1 over mass to the D minus 4.
And what mass would this be?
Well, it would have to be the mass of the fundamental scale of the particles
that have been eliminated from the theory the same way the electron is eliminated from electrodynamics
in the Euler-Heisenberg theory of the scattering of light by light.
This tells us then that the reason, that physics appears to us to be dominated by renormalisable interactions at low energies,
is not because the non-renormalisable interactions aren’t there,
but because they’re greatly suppressed by negative powers of some enormous mass.
And we should expect in the physics of low energies
to find not only the renormalisable interactions of the known electroweak and strong interactions but much weaker,
subtler effects due to non-renormalisable interactions suppressed by very large masses
in the denominator of the coupling constant.
There has been work by myself and Wilczek and Zee
to catalogue all possible interactions of this sort up to dimension-6 or -7 operators.
The lowest dimensional operators that can produce baryon violation turns out are dimension-6operators
and hence according to the general rules I’ve given you, are suppressed by two powers of a super large mass.
A catalogue has been made, of - these dimension-6 operators of the form quark, quark, quark, lepton.
A catalogue has been made of all of these interactions and it turns out that they all satisfy the principle that,
although they violate baryon and lepton conservation, they violate them equally,
so that for example the proton can decay into an antilepton.The neutron can also decay into an antilepton,
neutron can decay into e+ Pi-, but the neutron cannot decay into a lepton, neutron cannot decay into e- Pi+.
And there are other consequences of the simple structure of these operators, something like aDelta I =1/2 rule.
The decay rate of the proton into a positron is 1/2 the decay rate of the neutron into a positron.
We can say all these things with great confidence without being at all sure that protons and neutrons actually decay.
The decay rate of the proton and the neutron, that is decay at an observable rate, the decay rate of the proton,
let us say, will be suppressed in the matrix element by two powers of a super large mass,
and there’s sure to be a coupling constant factor like the fine structure constant.
You square the matrix element and multiply by a phase space factor, the proton mass to the 5th power to get a decay rate.
The big unknown in this formula for the proton decay rate is of course the super heavy mass scale.
We know the proton is more stable than, well its lifetime is longer than 10 to the 30th years
and therefore this mass must be very large indeed, it must be larger than about 10 to the 14thGeV.
There are other effects that violate known symmetries.
Lepton number is violated by an operator that has dimensionality, not 6 but only 5.
And this produces neutrino masses of the order of 300 GeV2 divided by the super heavy mass scale,
that’s a very low neutrino mass, that’s less than 1 volt if the mass scale is greater than 10 to the 14thGeV.
Now, there is other debris, which might be expected to be found in the low energy world
and I simply won’t have time to discuss this.
In a sense gravity itself can be regarded as the debris in our low energy effective field theory
of a more fundamental theory that describes physics at a mass scale above 10 to the 14thGeV.
Why in the world should there be a mass scale so much larger,
twelve orders of magnitude larger than the highest masses that we’re used to considering?
A possible answer comes from the general idea of grand unification.
Grand unification is very simply the idea that the strong and electroweak gauge groups
are all parts of a larger gauge group, which is here simply denoted G.
Just as the electroweak gauge group is spontaneously broken, giving masses to the W into the electromagnetic gauge group,
and that’s why the W and the Z are so heavy and have not yet been discovered,
the grand gauge group G is assumed to be broken at a very high energy scale, M, into its ingredients SU(3)x SU(2)x U(1).
And one coupling constant will turn out hopefully to generate the strong and the electroweak coupling constants
in the same way that the two electroweak coupling constants combine together to give the electric charge.
Another hope here, equally important, is that the quarks and leptons would be unified into a single family
so that we wouldn’t have red, white, blue and lepton colours but we would have one quartet for each flavour of quarks and leptons.
Models which realise some of these ideas were proposed, beginning in 1973, starting with the work of Pati and Salam,
and then Georgi and Glashow, and then Fritsch and Minkowski, and then many other people.
But an obvious difficulty with any model of this sort is the fact that the strong coupling constant,
as its name implies, is much stronger than the electroweak couplings.
Sam Ting told us that the fine structure constant for the strong interactions is about .2
and we all know the fine structure constant for the electromagnetic interactions is 1 over 137.
How can two such different strengths of force arise from the same underlying coupling constant G sub G.
The answer which is now I think the most popular was proposed in 1974 by Georgi, Quinn and myself,
our answer was that these coupling constants are indeed related to a fundamental coupling constant,
but they’re related only at a super large mass scale M.
The strong and electroweak couplings, which are indicated here as these three curves, are not really constants,
they’re functions of the energy at which they’re measured.
This is well known in quantum electrodynamics, the property of asymptotic freedom
means that the coupling constant shrinks with energy.
The coupling constants of the electroweak force, one of them shrinks, one of them increases.
One imagines there might be a point at which they all come together, at some very high energy.
Indeed there is such a point but since this variation with energy is very slow, it´s only logarithmic,
the energy at which the coupling constants come together is exponentially large.
It’s given by the formula that the logarithm of the ratio of this fundamental mass scale to the W mass
is something like 4 Pi square over 11 e square, where e is the electric charge,
with this correction due to the strong interactions.
And that comes out to be about 4 to 8 times 10 to the 14thGeV.
So we see now why there has to be a scale of energies greater than 10 to the 14thGeV.
It’s to give the strong interactions time to get as weak as the electroweak interactions.
These three curves are coming together at one point, it’s not easy to get three curves to intersect at a single point,
and in fact the way it’s done is by carefully adjusting the data at the low energy end
to make them aimed in the right direction so that they’ll all hit at the same point.
That careful adjustment of the data I can put in a slightly more complementary way, as saying that we predict
and this was done by Georgi, Quinn and me, we predict certain ratios of these coupling constants
which can be expressed as a prediction of the value of the mixing angle between the Z and the photon.
That prediction was in conflict with experiment in 1974,
in agreement with experiment now and it’s the experiment that changed, not the theory.
There are a great many problems, I would say in fact that this prediction of this mixing angle
is the only tangible success, quantitative success so far of grand unification.
There are a number of problems with further progress.
One problem is that we have had no convincing explanation of the pattern of quark and lepton masses.
By convincing explanation I mean more than a theory
in which you’ll have enough free parameters to rearrange things the way you want.
But something that really gives you a feeling you understand it.
There’s been no convincing explanation of the pattern of generations
that we have not only an up down electron generation and a charm strange muon generation but a third generation,
maybe a fourth generation, we don’t know why any of that is true.
Perhaps the most puzzling problem of all, we have no fundamental explanation of the hierarchy of forces,
that is that there is a ratio of 12 orders of magnitude between the symmetry breaking scale of the grand gauge group
and the electroweak gauge group.
We know that that’s true, we think we know it’s true because the strong force at low energy
is so much stronger than the electroweak force.
But where this number of 10 to the 12thcomes from is endlessly speculated about,
there are many, many ideas but there’s no one idea that really convinces people.
And finally there’s no one model that stands out as the obvious model.
There are many candidate models of grand unification but since all of them leave A, B and C un-understood,
we can’t really attach our allegiance to any one of these models.
There is a further development which started in 1974
which has occupied a large part of the attention of theoretical physicists in the succeeding years,
this is a symmetry called supersymmetry, invented, although there were precursors,
invented by Wess and Zumino and then carried on by Salam and Strathdee and many other people.
Supersymmetry is a symmetry which operates in a sense orthogonally to the symmetries that I’ve been discussing up till now.
The electroweak gauge symmetry for example connects the neutrino and the electron,
both particles of the same spin but different charge.
Supersymmetry connects particles of different spin but the same charge, flavour, colour etc.
For example supersymmetry would connect the electron which has spin ½ with another particle that might have spin-0 or spin-1.
It had been thought that such symmetries were impossible and in fact they’re almost impossible.
There is a theorem by Haag, Lopuszanski and Sohnius, terribly important theorem
that tells us that the kind of supersymmetry, which was invented out of whole cloth,
just out of the richness of their imagination by Wess and Zumino turns out to be unique.
It is the only mathematically allowed way of having a symmetry that connects particles of different spin.
And therefore, without too much arbitrariness,
we can fasten our attention on a particular kind of symmetry
which is simply called supersymmetry and explore the consequences of it.
And we know that, whether it’s right or wrong, there isn’t anything else that could unify particles of different spin.
Now, we don’t see any trace in nature of supermultiplets of this sort,
that is the electron does not seem to have a partner of spin-0 or spin-1.
Well, that in itself should not convince us the idea is wrong,
we’re used by now to the idea that symmetries can be true at a fundamental level and yet spontaneously broken.
Supersymmetry must be spontaneously broken.
In fact there is not a trace in nature of any supermultiplet that is visible to us.
Sometimes it’s said that supersymmetry is the symmetry that unifies every known particle with an unknown particle.
Supersymmetry is surely spontaneously broken, the big question is: Where is it broken?
And I’ve been giving a lot of attention to this question lately and I think I will close by just summarising my conclusions,
you might think perhaps that supersymmetry is broken at the same sort of energies
at which the electroweak gauge symmetry is broken, that is energies like MsubW or of the order of 100 GeV.
There are many reasons why that doesn’t work.
The partners of the quarks, which are scalar particles, spin-0 particles and hence are called squarks,
would give very fast proton decay.
This could be avoided by inventing new symmetries.
The squarks and the sleptons would be too light,
that is they would be light enough to have been observed and as I already told you they haven’t been observed.
This also can be avoided by inventing new symmetries, in particular Fayet has explored this possibility.
These unwanted new symmetries and other new symmetries that you can’t avoid in such theories
lead to light spin-0 particles called Goldstone bosons, which are apparently impossible to get rid of,
and Glennys Farrar and I have been exploring their properties.
And we have come to the conclusion, or I should say I have come to the conclusion,
I’m not sure if Glennys agrees, that supersymmetry broken at these low energies is really hopeless.
Another possibility is that supersymmetry is broken at medium high energy.
That is supersymmetry is broken at energies which are much larger than the W mass,
much smaller than the mass scale at which the grand unified symmetry is broken.
Now,supersymmetry is a gauge symmetry like the electroweak gauge symmetry,
it has an intermediate vector boson but because of the peculiarity of supersymmetryit’s not a vector particle spin-1,
it’s a spin-3 half particle called the gravitino.
The gravitino like the W particle has a mass and the mass is related to the scale at which the supersymmetry is broken.
And in fact the mass of the gravitino which is a super partner of the graviton, the quantum gravitational radiation,
the mass of the gravitino is the symmetry breaking scale square divided by 10 to the 19thGeV.
10 to the 10thGeV is the famous Planck mass.
If the symmetry breaking scale is in a very broad intermediate range, from 10 to the 6 GeV up to 10 to the 11th,
10 to the 16thGeV, then the gravitino would be far too heavy to be present in large numbers in the present universe,
it would wreck the universe, its mass density would reduce much too large a deceleration of the expansion of the universe.
And yet the gravitino’s would be much too light to have decayed by now, so that they would be present in very large numbers.
It would be a cosmological disaster.
So we can conclude therefore that this large range of intermediate scales of supersymmetry break down are forbidden
and therefore that supersymmetry, if valid at all, can only be broken at the very highest energies,
energies comparable to the energies at which the grand unified group is broken or perhaps even higher.
This means that supersymmetry is going to be primarily of importance,
not to the experimentalist but to the poor theorist who is struggling to produce a more satisfactory theory.
Nevertheless I feel that supersymmetry must survive as an ingredient in a final theory
because sooner or later we must ultimately have a unification,
not only of electromagnetism with the weak interactions and electrons with neutrinos,
but we must have a unification of all the particles of nature, the W boson with the electron, with the graviton.
And within a very broad mathematical context we now have a theorem that tells us
that the only way that that’s possible is through supersymmetry.
So in the end I’m very optimistic about supersymmetry but I’m afraid that the problems of supersymmetry
are going to be solved only when a larger class of problems having to do with grand unification are solved.
Theoretical physicists in the last few years have not been making rapid progress in solving these problems.
I would say that this has been one of the most frustrating periods that I have seen during my period in physics.
At the present moment the theorists, somewhat through exhaustion,
are waiting for the completion of a series of heroic experiments which we hope will break the logjam and get us started again.
There are a number of key experiments that deal with the problems that I have been discussing here.
Well, first of all of course there are the experiments like the experiments that Sam Ting was discussing
and other experiments to find the W and the Z particle as isolated physical particles,
which are crucial in pinning down the parameters and in confirming the existing understanding.
But to go beyond the existing understanding,
I would say there are three chief classes of experiments which are being actively pursued.
There are experiments on proton decay, which test the conservation of baryon number,
there are experiments on the mass of the neutrino which test the conservation of lepton number.
And finally there is the question of whether the magnetic monopole,
which was discovered perhaps a few months ago at Stanford, is real.
And that will be tested by continuing those experiments at Stanford with a larger apparatus.
The grand unified theories,
as pointed out by Polyakov and ´t Hooft characteristically predict the existence of magnetic monopoles
with masses of the order of 137 times the grand unified mass scale.
So roughly speaking 10 to the 16thGeV.
The grand unified theories themselves of course don’t tell us how many of these particles there are in the universe,
they just tell us that they can exist.
At Stanford there is a possibility that such a particle has been discovered and we eagerly await confirmation of its existence.
These experiments have all so far in fact yielded positive results,
there are a few proton decay experiments in an experiment in the Kolar gold field in India.
There are preliminary indications of a neutrino mass in an experiment in Russia and in another one in California,
or rather in Georgia.
And then of course there is the magnetic monopole, for which we have exactly one candidate.
We are now in the position of sitting at the edge of our chairs,
waiting to see whether these preliminary indications of proton decay and neutrino masses and magnetic monopoles
will in fact be born out by further experiments.
And I will be happy to tell you my predictions for this after the experiments are completed.
(Applause).