History of strong interactions

Indian Lattice Gauge Theory Initiative,
Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India

Factoid

The universe was born 14 billion years ago in a big bang. After the big bang, the universe began to expand and cool. When it was 10 micro seconds old it was full of a state of matter called the quark gluon plasma. This is the state of matter we study on super computers.

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A brief history of strong interactions

Atoms

Atoms as an indivisible component of matter were hypothesized by many thinkers through history. Converting these philosophical speculations into today's science required almost 300 years of quantitative work; eventually achieving levels of precision which were undreamt of in previous history.

The modern notion of the atom follows from fundamental discoveries in chemistry. The foremost among these were the law of conservation of mass (1789) by Lavoisier, and the law of stoichiometry (1799) by Proust. By putting these together with the gas laws of Boyle (1622) and Charles (1788), Dalton reached the conclusion (1803) that the atom was the smallest unit of matter which retained the chemical properties of larger amounts of the same kind of matter.

This notion was sharpened through the following couple of centuries. When the differences between chemical elements and chemical compounds became clear, then the name atom began to be used only for the smallest unit of an element which retained the chemical properties of the larger amounts of that element. For compounds the smallest element is called a molecule. The experimental methods of the 18th and 19th centuries could never see individual atoms. While the quantitative usefulness of the notion of atoms was clear, the fact that they could not be seen led to philosophical discussions about whether atoms "really" existed. Eventually, in 1905, Einstein demonstrated the reality of atoms through his analysis of Brownian motion.

Meanwhile, with improvements in the sensitivity of measurements which began in the closing years of the 19th century, it became possible to make measurements at the atomic scale. Brownian motion was just the first of these observations. The most important was the count of the number of molecules in one gram mole of a chemical compound, a number which is now called Avogadro's Number. This is a 24 digit number, whose value is approximately 6.022 141×1023. From a knowledge of Avogadro's number one can find the typical weight of a molecule or atom. It is equal to

the atomic or molecular weight × 1/(6.022 141×1023) gms.

Soon experiments had measured the physical size of an atom; it turned out to be around 10-9 m (called a nano-meter).

In the early years of the 20th century it was found that atoms could be divided: they contained electrons. Since atoms are not electrically charged whereas electrons are negatively charged, it followed that the atom also contained positively charged particles. Rutherford performed a series of experiments which showed that the positive charge resided in an atomic nucleus that was a thousand times smaller than the atom, and contained about 99.9% of its mass. This is the modern picture of an atom: a massive positively charged nucleus surrounded by a cloud of almost massless electrons distributed over distances 1000 times the size of the nucleus. The atom is held together by electromagnetic forces. These electromagnetic forces are also the main forces in chemistry.

Strong interactions

The story of strong interactions is relatively brief: it covers only a hundred years; but it is full of many deeply mysterious phenomena, each of which had to be solved using methods which were developed specially for that problem. As a result, this is the one field which has gathered the maximum number of Nobel prizes: the most recent in 2008.

Since the atom is divisible, it is not elementary. Among the elementary particles one had to count the negatively charged electron. It became clear that the nucleus of hydrogen was another. This was called the proton. Electrical forces bound electrons and nuclei together into atoms, since they had opposite charges. How could the nucleus, made entirely of positive charges be bound together? Positive charges would repel. Since they are bound, there must be a new force involved: this is the strong nuclear force.

The new science of nuclear physics involved itself with the study of the strong force. The electrically neutral neutron was discovered to be another elementary particle which is found in the nucleus. Just as the photon is the particle involved in the transmission of the electromagnetic forces, a different particle was found to be involved in the transmission of the strong nuclear force; it was given the name "pion". By the 1940s the full theory of the nucleus seemed to be within reach.

In the 1950's there were a series of new discoveries which complicated everything again. Particle accelerators were constructed to smash together particles at high speeds. In the debris of these collisions many new particles were found. Most of these particles had strong charge. There seemed to be a large periodic table of strongly interacting particles: the hadrons. Was there a "periodic table" of hadrons? What principles would underlie such a table?

When a periodic table was constructed, and new particles were predicted and found, then the principles became clear. The hadrons were not elementary at all: for 50 years people had been looking in the wrong place for the elements of matter. The elementary particles were fewer in number and were given the name of quarks. Strong forces bound the quarks into hadrons and the strong nuclear forces were but a shadow of these forces. After twenty years of development it became clear that these quarks were real, and there were new particles which carried the strong force: called gluons. A theory of the strong interactions was developed and tested. This is called Quantum ChromoDynamics (QCD).

Quantum ChromoDynamics

QCD is a theory of quarks and gluons. It is the most mathematically intractable among all fundamental theories that we have. It has been tested in high energy collisions, where the calculations become relatively simple. However, all other aspects, including the existence of hadrons and the emergence of nuclear physics, have not yet been derived from the theory.

The main method for systematic and accurate calculation in a field theory is "perturbative": a power series expansion in the strength of the interaction. If the interaction strength is called α, then one can try to write any quantity as

(#) + (#) α + (#) α2 + (#) α3 + ...

where each of the numbers (#) can be calculated from the theory. When α is small, as it is for electromagnetic and weak interactions, the series of terms above is very well approximated by the first few terms. As a result, this method works well. Strong interactions are involve large α, as a result of which the method can fail.

For reasons which are intimately connected with the nature of quantum theories, the strong coupling strength becomes effectively weak for high energy processes. This is called asymptotic freedom. As a result, the series above can be approximated by a small number of terms, and predictions for high energy collisions can be made with accuracy. QCD has been tested and found to be correct in this domain.

The only other systematic quantitative method is one developed by Kenneth Wilson called lattice gauge theory. In this method one uses supercomputers to compute the predictions of a theory without resorting to a series expansion as above. For QCD this is the only method available for most calculations. Using this method it is predicted that matter above a temperature of about 1 trillion degrees or density of a few times larger than nuclear density undergo a transition to a new form called the quark gluon plasma.

This is not the only new phase of matter that is predicted by QCD. At small temperatures but extremely high densities there are superconducting phases. These are probably the highest temperatures at which matter is superconducting. These extreme phases of matter are currently being investigated on supercomputers, probed in experiments and searched for in the universe at large.

Our calculations in Mumbai have also predicted a temperature and a density at which there is no distinction between normal nuclear matter and the quark gluon plasma. This prediction is under experimental test at the nuclear accelerator called the RHIC in the Brookhaven National Laboratory in USA.