The Holy Qur'an and Dirac's Theory of Pairs

Sultan Bashir Mahmood

2009-03-01 00:00:00

Paul Dirac (1902–1984), one of Newton’s successors to the Lucasian Chair of Mathematics at Cambridge, was one of the greatest physicists of the twentieth century and his work is one of the monuments of modern physical theory (See Abdus Salam 1966). This paper highlights his great work on the possible existence of all matter in pairs, and the revelation of the same theory in the Holy Qur’an, thirteen hundred years before Dirac’s research.

Dirac’s discovery

Dirac had the honor of being the first scientist in history to demonstrate the principle that all particles in the universe must exist in pairs, that for each particle there must exist a corresponding anti-particle of exactly the same mass but with an opposite electrical charge. For all matter in the universe, in other words, there must exist an equal amount of anti-matter. Thus the existence of a proton must imply the possible existence of an anti-proton; if a hydrogen atom exists, there must equally exist an atom of anti-hydrogen, perhaps in some distant corner of the universe.

Equal amounts of matter and anti-matter must have been produced in the first moments of the Big Bang. In our present universe, however, a particle will not be found co-existing peacefully side by side with its corresponding anti-particle. To understand this, we could recall the old European myth of the doppelganger, the perfect double of the unlucky hero. The message of the stories is always to avoid the doppelganger: if you meet your double you will be destroyed.

Just so, if matter and anti-matter meet they annihilate each other, their energy and momentum dissolving into heat and light. According to Dr. Abdus Salam of the International Centre for Theoretical Physics, “In Dirac’s language, anti-matter is ‘minus matter’; matter and anti-matter just cannot co-exist in the same part of the universe without the ever-impending catastrophe of annihilation; and indeed some astronomers do believe that just this type of annihilation of galaxies and anti-galaxies is taking place at the sites of powerful X-ray sources in the heavens” (See Abdus Salam 1966).

Dirac predicted the existence of anti-matter in 1934, and the discoveries of specific anti-particles in the following years confirmed his prediction.

The Fish Problem

According to an apocryphal story, the germ of Dirac’s breakthrough materialized from a mathematical brainteaser seemingly unrelated to theoretical physics. During a meeting of the Cambridge Undergraduate Mathematical Society, the Archimedians, the following problem was presented. Those who like a challenge can try working it out for themselves. The answer is provided below for those whose brains become tangled by figures.

After a long day, three fishermen have caught a good amount of fish. They are about to set sail for home when a storm suddenly builds up. Under raging skies, they decide to seek shelter on a nearby island. They unload their catch and set a fire before falling asleep. A few hours later, one fisherman wakes up to find that the weather has settled enough for a safe return to be possible. Not wanting to disturb his friends, he divides the haul into three equal parts. There is one fish remaining, and this the fisherman throws back into the sea. He then leaves with his share.

A little later, the second fisherman awakes, also with the desire to get back home. Unaware that one of his friends has already left, he too divides the catch into three equal parts. Again there is one fish remaining, and again this is thrown back into the sea. The fisherman rows off with his portion. Finally, the third fisherman arises and goes through the same process, dividing the remaining fish into three parts, finding one fish remaining, which he then throws back into the sea. He leaves the island with his portion.

And now for the problem: What is the minimum number of fish in the original catch? To put it another way, what is the smallest number which can be subdivided three times, leaving one fish outstanding each time?

Dirac’s answer

Dirac thought for a while before arriving at the answer: minus two. If you divide minus two fish three times, each third will contain minus one fish, with plus one fish outstanding. Each time a fisherman throws the plus one fish into the sea, and rows off with the minus one fish. Expressed in an equation, it looks like this: -2 = -1-1-1+1.

Minus one fish is obviously no use to anyone, and this is certainly a brainteaser. It is important only in that it gave birth to the notion of anti-particles in Dirac’s mind and can help us to understand the mathematical principle behind his discovery. It led him to the conclusion that all particles exist in opposing pairs and allowed him to see the symmetry of matter and anti-matter.

The Holy Qur’an and Dirac’s theory

As we have already noted, Dirac was the first man in the history of science to make this profound discovery. For this he must be congratulated, and so must the modern scientific methods which have brought us so much practical information about ourselves and the universe in which we live.

Many centuries before Dirac, however, a text was revealed to an unlettered man in the Arabian desert. Its primary message was of the existence of one Creator and of an Afterlife in which human beings would account for their conduct while on earth. But this was no ordinary religious book, for it continually exhorted its readers to examine the natural world around them for the signs of God, to develop logical and objective thinking, and to place a crucial emphasis on education. This Book broke down the artificial boundaries which divide material and spiritual study. In the Holy Qur’an, science and religion are entirely compatible. Indeed, they cannot be distinguished.

In the Qur’an, we find the following verses, which may be considered relevant to Dirac’s discoveries of the pairings and symmetries of the universe’s structure, and in fact much more:

Glory to God
Who created all things in pairs,
Those that the earth produces,
As well as their own (human) kind,
And things of which
They have no knowledge
(Ya Sin 36:36)

The line “Who created all things in pairs” clearly shows that the Qur’an is referring to a law of nature; all things on earth and in the heavens-animal, vegetable or mineral (and even sub-atomic)-have been created in pairs. (Modern science has evolved around the study of pairs, from the male/female pair which generates animal and plant life to the pairings of quarks and leptons which are the most basic building blocks of the universe.) The line “Things of which they have no knowledge” suggests that the theory of pairs is of universal scope. It applies equally at all points in time and space; even in worlds of which we have no knowledge.

Elsewhere in the Qur’an we find a statement which modern science has spent its history confirming:

Verily all things (without exception),
We have created,
In exact measures and proportions.
(Hadid 57:49)

The line “In exact measures and proportions” is most revealing from a scientific point of view. The Qur’an contains the unambiguous lesson that as well as having perfect symmetry, every force in the universe is definite, of exact measurement and proportion following precise laws:

And there is not a thing,
But its storehouse is with Us,
And We send them down,
But in definite ascertainable measures.
(Hijr 15:21)
God, the Absolute Singularity
The Holy Qur’an tells us of God:
He is the First,
And the Last,
He is the Outermost,
And the Innermost,
And He is the knower of all things.
(Hadid 57:3)

In this verse “the First” and “the Last” relate to the time domain, and “the Outermost” and “the Innermost” to the space domain. As such time and space are the first pair of nature. By extension all pairs are finally unified in the only Singularity in the universe-God. All pairs are aspects of the same reality, to which they all must return-the oneness of God.

But the Qur’an does not only give us information about the universe. It goes a step further, requiring us to use this information to develop our thinking. As always, the Qur’an demands the active participation of its reader:

And of everything,
We have created in pairs,
That you may reflect.
(Dhariyat 51:49)

The Qur’an asks us to think, offering both a mental challenge and a proof of God’s existence. If we reflect on the paired structure of the universe by using the methods of scientific reductionism, breaking a complex system down into its simplest units, we will finally come back to a single point of origin, an absolute singularity, the one source of time and space: God (See Mahmood 1987). As the Qur’an says,

And all that is in the heavens,
And all that is in the earth,
It is from God;
And (in the final analysis)
Everything will return to Him.
(Al Imran 3:109)

Guidance for the modern age

The Qur’an comments on many areas of interest to modern science, from medicine to geology. Many verses of the Qur’an have taken on added significance as new scientific discoveries have been made. In fact, it seems that science has been following the Qur’an’s lead for centuries.

Furthermore, in an age when progress in such fields as genetic engineering and chemical weaponry has raised complex ethical questions, the Qur’an teaches the salutary lesson that science should be the servant of humankind, not vice versa. It provides a model for all our endeavors in which symmetry is a prime value. Technological progress must be balanced by a symmetrical spiritual development. The new freedoms that we have won through our expanding knowledge must be balanced by an awareness of our new responsibilities. Otherwise our achievements will turn upon us, polluting our environment and increasing rather than diminishing our suffering. Without the guidance of Islam through the Qur’an, humankind with its scientific achievements will be like a child surrounded by dangerous toys.

This Book provided the light by which a great scientific culture once thrived. The Muslim world today, cursed as it is by illiteracy, intolerance and superstition, is a poor reflection of that former glory. This is the fault of human beings, not of the message of Islam, whose light continues to shine. Its light is every bit as available to a non-Muslim as it is to someone who has grown up in a Muslim environment. Once we move beyond our habitual beliefs and prejudices, all of us can profit from the message of the Qur’an. An independent and freethinking mind is all that is necessary to see its light. If we read, discuss and reflect upon the Qur’an, we can use that light to guide us now in our explorations of the universe and ourselves.

For this reason, we appeal to you to read the Qur’an. The example of the Qur’an’s truth presented in this paper is only one starting point. The Qur’an reveals further riches with each reading. The light of this Book, which spoke to seventh-century Arabs of things of which they had no knowledge, can teach modern humankind too.

Dr. Sultan Bashir Mahmood is the founder of the Holy Quran Research Foundation in Islamabad. Mr. Robin Yasin Qusab is a graduate of Cambridge University and a freelance journalist.


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  • Bashir-ud-Din Mahmood, “Symmetry of the Universe and the Qur’an,” Science and Technology in the Islamic World, Vol. 5, No. 1, Jan. 1987. National Science Council of Pakistan.
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  • Sultan Bashir Mahmood
  • Robin Yasin Qusab