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Conflicts and creativity — II
Scientists cannot verify string theories directly. They can study only their low energy consequences, which are not unique
Following the successful description of electromagnetic interaction through quantum electrodynamics, physicists sought to apply similar principles to other fundamental forces — the strong and weak nuclear forces and the gravity.
When the chirality principle invented by Prof Abdus Salam for the neutrino was extended to other spin ½ fermions by Marshak and Sudarshan, and independently by Feynman and Gell-Mann, it resulted in the V-A theory of weak interactions. This theory, involving an effective four-fermion interaction, had a remarkable success in the low-energy region, but was not renormalizable and as such required an infinite number of parameters to absorb the infinities.
A unified model of electromagnetic and weak interaction, proposed in 1967 by Weinberg and independently by Salam (known as the Glashow-Salam-Weinberg or the Standard Model), ultimately proved to be renormalizable. According to this theory, the weak nuclear force and the electromagnetic force are two different facets of the same basic force.
Thus, spin 1 photon, which is the carrier of the electromagnetic force, is joined by three other spin 1 partners W+, W- and Z0 mediating the weak interactions. The Z0 mediates a new weak interaction, called neutral weak interaction.
At very high energies, the four particles are predicted to behave in a similar manner. However, at lower energies this symmetry must be broken, without destroying the renormalizability of theory, to explain that photon has zero rest mass (electromagnetic forces are long range) while W+, W-, Z0 are all very massive (weak interaction is short range).
One of the intriguing ideas in modern physics is that the laws of Nature can have symmetries that are hidden from us because the vacuum or the ground state need not respect all the symmetries. The process by which the vacuum hides the symmetry is known as the Higgs mechanism, named after the physicist Peter Higgs, also known as spontaneous symmetry breaking. This is responsible for giving masses to W± and Z0, keeping the photon without mass. This also predicts a neutral spin zero particle, called Higgs particle, whose mass is not predicted by the theory. This has not yet been discovered experimentally.
A remarkable set of experiments confirmed the predictions of the Salam-Weinberg theory, including the discovery of W± and Z0 bosons at CERN with masses as predicted by the theory. “This indeed was a long shot and can rightly be described as one of the examples of the theoretical prophecy coming true that the last century has witnessed.” The only missing link is the Higgs boson, which hopefully would be discovered at the World’s largest accelerator, Large Hadron Collider (LHC), being constructed at CERN that should be ready by 2007.
Once again the success was an incentive to search for a renormalizable theory for strong interactions. Yukawa theory of strong nuclear force between two spin ½ nucleons (neutron or proton) mediated by spin of pi meson is not a fundamental theory, since the proton, neutron, pi meson or other hadrons (a name given to strongly interacting particles) are not elementary but are respectively bound states of a group of three quarks or quark-anti-quark pair. The quarks can move freely inside a hadron, but it is impossible to obtain just one quark on its own.
To explain this and to satisfy the Pauli principle, it was postulated that quarks are endowed with an attribute called colour. Each species of quark has three different colours — red, green and blue — but any isolated bound state forming a hadron is colourless.
Just as the electroweak interactions are mediated by spin 1 photon, W± and Z0 bosons, the strong interaction between quarks is mediated by eight spin 1 particles called gluons. Unlike the photon, which carries no charge, gluons carry colour charges and they and the quarks obey a renormalizable theory, called Quantum Chromodynamics, or QCD for short.
It is a consequence of the renormalization procedure that the effective coupling constant of the theory depends on the energy at which it is measured. It turns out that this coupling gradually decreases and tends towards zero at very high energies. This is known as asymptotic freedom.
As a result, the quarks inside a hadron behave almost like free particles so that in high-energy collisions their interactions can be treated by perturbations. The predictions of perturbation theory are in quantitative agreement with observations. The asymptotic freedom property of QCD has now been established experimentally, resulting in the award of the 2004 Nobel Prize to H. Politzer, David Gross and Frank Wilczek.
At low energies the effective coupling constant becomes large and the perturbation theory breaks down and as a result it is hoped that the quarks are permanently confined to a hadron, a colourless bound state. This has yet to be demonstrated in a convincing manner, however.
Having obtained renormalizable theories for electroweak and strong interactions, there was an incentive to extend further the ideas of unification, that is, to develop a unified theory (called Grand Unification or GUT for short), which embraces not only electroweak interactions but the strong interactions too. Here also, Abdus Salam, with Jogesh Pati, was among the first contributors.
As mentioned earlier, the effective coupling constant of QCD gradually decreases with energy and that of quantum electrodynamics, which is small at low energies (a = e^2/4p = 1/137), increases gradually with energy. This theory is not asymptotically free as the photon does not interact with itself in contrast to gluons which have self-interactions as they carry colour charges). Finally, the effective weak-coupling constant of the Salam-Weinberg theory, which is greater than alpha at low energies, also decreases gradually with energy but at a much slower rate than the QCD coupling constant.
If we extrapolate the low energy rate of increase and decrease of the coupling constants, it is found that they become equal at energy of about 10^16GeV. So the electroweak and strong interactions are unified at the above energy but at lower energies there is spontaneous breaking which make them distinct.
Energy of the order of 10^16GeV is well beyond the scope of laboratory experiments; the next generation of accelerators, for instance the LHC, can produce mass energies of 14TeV. However, low energy predictions may be tested.
One such prediction is that the proton is not completely stable but decays with a life-time of some 10^31 years. The present experimental limit is >10^31 years. But the idea that quarks and lepton can be treated on an equal footing, which Pati and Salam proposed in 1973, is now an integral part of GUT modes.
The mother of all conflicts
So far gravity has been neglected. One justification for this is that gravity is so weak compared to electroweak and strong interactions that quantum gravity effects could be neglected well beyond even the GUT scale. The second reason is that although we have an excellent theory of gravity —Albert Einstein’s general theory of relativity — it seems to be non-renormalizable and leads to irremovable infinities.
As we have seen, QFT is the framework for particle forces, except gravity. The big problem of contemporary physics is: How to combine these two highly successful theories? Einstein’s theory of gravity has singularities at very short distances. It also breaks down inside black holes. Thus, for very short distances, Einstein’s theory might need quantum mechanics to smear out the singularities.
One possible solution is to change classical theory, replacing general relativity by ‘supergravity’ or ‘superstring theory’. One of the key ideas here is supersymmetry, which relates fermions to bosons. Though there is no direct experimental evidence supporting supersymmetry, there are indirect hints and it is theoretically a most attractive hypothesis, which does much to tame the infinities.
Here also Salam and his collaborators played a leading role. Salam and Strathedee’s formulation of this symmetry in terms of ‘superspace’ and related concept of ‘superfield’ is not only the most elegant one, but it also provides a useful tool for carrying out this programme, ensuring manifest supersymmetry at each step of the calculation.
It turned out that to include gravity, one: needs a higher dimensional space time; needs supersymmetry to tame the divergences and avoid tachyons (the particles which move faster than the speed of light); and, needs to go beyond a point field theory, that is the most fundamental entities are not point-like but extended one dimensional string-like objects. This too helps tame the infinities.
The above three ingredients are incorporated in the superstring theory. It naturally contains a massless spin 2 particle, which could be identified by graviton, the mediator of the gravitational interaction. It may provide a consistent quantum field theory, containing gravity and other fundamental forces of nature. The dynamics of the superstring theory can be formulated in D = 10 space-time dimensions; four familiar space-time dimensions, while the extra six dimensions have to be so curled up so as to be unobservable.
There are many possible ways of doing this and, as a result, one loses predictivity and making contact with the experiment becomes difficult. The point here is that to probe string theories, one needs energies of 10^19GeV while the available energies are of the order of 14TeV. Thus, one cannot probe string theories directly. One can study only low energy consequences, which are not unique.
These are the problems, which would be occupying physicists and mathematicians in the present century. (Concluded)
The author is distinguished national professor and director-general of the National Centre for Physics, Quaid-i-Azam University, Islamabad
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