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Particle-Wave Duality: from Time Confinement to Space Transcendence

by Mohamed Haj Yousef



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1.5 Western Philosophy and Physics


Following the Middle Ages, the Renaissance started in Italy in the 13th century after series of famines and plagues that reduced the population to around half of what it was before the calamities. Despite these crises, there was some noticeable progress as the interest in ancient philosophy resumed when many Byzantine scholars had to seek refuge in the West when Constantinople was conquered by the Ottomans in 1453. After appreciating the Greek and Arab learning systems, arts and sciences started to flourish, especially following the invention of printing in the 14th century, which allowed faster propagation of literature. Science and art were initially mingled, with artists such as Leonardo da Vinci (1452-1519 AD) making observational drawings of anatomy and nature.

By the 15th century, with the discovery of the New World by Christopher Columbus in 1492, the Aristotelean classical view of the world had been challenged, and people started to question the previously sacred theological truths, searching for more reasonable answers. This led Francis Bacon (1561-1626) to develop the philosophical basis of the modern scientific method, starting from his belief in the right of man to dominate nature: “to bind her to your service and make her your slave” Jardins (2012).

However, although this boosted the spirit of exploration, with Columbus arriving in America and Magellan sailing around the tip of South America, it was sadly accompanied by the tragic abolishment of much of the historical and cultural heritage of these countries that were invaded by the Europeans, who believed that non-Christian cultures were worthless. This resulted in the complete destruction of Central American civilizations and greatly affected many other countries in Asia and Africa.

Nevertheless, during the Renaissance period, Europeans started to invent their own learning system and philosophy, especially after Martin Luther dared to question the authority of the Catholic church on scriptural matters, which was followed by the Protestant Reformation in the 16th century.

By the efforts of St. Aquinas, the Catholic Church was convinced that Aristotelian philosophy is compatible with theology, and they decided to adopt Ptolemy’s geocentric model as a theological principle, and considered scientists who criticized this model as heretics.

Eventually, in his heliocentric model, published in 1543, Copernicus postulated that the Sun and the stars are stationary and the earth and the planets circulated around the sun in circular orbits. Therefore, after Galileo invented the telescope, the geocentric model was completely discarded by knowledgeable researchers. At around the same date (1609-1619), Johannes Kepler formulated three mathematical statements that accurately described the revolution of the planets around the Sun. This was followed, in 1687, by Newton’s famous theory of gravity, which supported the Copernican model and explained how bodies more generally move in space and time.

The Copernican model marked the beginning of modern astronomy and scientific revolution. It is certainty a remarkable departure from the Ptolemaic system that prevailed for many centuries. Copernicus may have been aware that Aristarchus had already proposed a heliocentric theory, and he cited him in an early manuscript of his book before it was published, but there is no evidence that he had knowledge of its specific details. Some scholars suggested recently the possible transmission of earlier Islamic heliocentric models to Europe, after they discovered some of them are mathematically identical to those of Copernicus. In particular, the Damascene astronomer Ibn al-Shatir (1304-1375 AD), working at the Umayyad Mosque, wrote a major book entitled Kitab Nihayat al-Sul fi Tashih al-Usul (A Final Inquiry Concerning the Rectification of Planetary Theory). The theory of Ibn al-Shatir was identical with that of Copernicus, except for trivial differences in parameters.

Some years after its publication, the heliocentric model caused a strong controversy, especially after Tycho Brahe (1546-1601 AD) published his similar variation, followed by the advent of the telescope. When the heliocentric model started to become popular, the church considered it formally heretical and the Pope banned all books and letters advocating it.

It was Galileo Galilei (1564-1642 AD) who took the challenge to defend this controversial model, but he was met with strong opposition from astronomers and theologians which later led to his misfortune. Galileo was a polymath interested in astronomy, physics, philosophy, and mathematics. He studied gravity and free fall, velocity and inertia, projectile motion and and pendulums, and the principle of relativity, in addition to many other related applications. He contributed in transforming Europe from natural philosophy to modern science.

One of Galileo’s greatest contributions was to recognize that the role of science was not to explain “why” things happened as they do in nature, but only to describe them, which greatly simplified the work of scientists, and liberated them from the influence of theologians. Subsequently, this led Galileo himself to describe natural phenomena using mathematical equations, supported with experimentation to verify their validity. This marked a major deviation from the qualitative science of Aristotelian philosophy and Christian theology.

Based on these ideas Galileo was able to develop the mechanics of falling bodies from the earlier ideas of the theory of impetus that tried to explain projectile motion against gravity. By dropping balls of the same material, but with different masses, from the Leaning Tower of Pisa, he showed that all compact bodies fell at the same rate. Galileo then proposed that a falling body would fall with a uniform acceleration, as long as the resistance of the medium through which it was falling remained negligible, which allowed him to derive the correct kinematic law that the distance traveled during a uniform acceleration is proportional to the square of the elapsed time.

However, as it was the case with Copernicus, Galileo’s discoveries had been also clearly stated by many Muslim scholars more than five centuries before, and they even quoted and developed older theories in this regard. For example, we find Hibatullah ibn Malaka al-Baghdadi (1080–1164), an Islamic philosopher and physician of Jewish descent from Baghdad, originally known by his Hebrew birth name Baruch ben Malka and was given the name of Nathanel by his pupil Isaac ben Ezra before his conversion from Judaism to Islam towards the end of his life. In one of his anti-Aristotelian philosophical works Kitab al-Mutabar (The Book of What Has Been Established by Personal Reflection), he proposed an explanation of the acceleration of falling bodies by the accumulation of successive increments of power with successive increments of velocity Crombie (1959). In this and other books and treatises, he described the same laws of motion that were later presented by Newton, except that they were not formulated in mathematical equations.

Nonetheless, by the 17th century, the Copernican and Galilean heliocentric models started to replace the classical ancient worldview, at least by knowledgeable researchers. Between the years 1609-1619, the scientist Johannes Kepler (1571-1630 AD) formulated his three mathematical statements that accurately described the revolution of the planets around the Sun. In 1687, in his major book Philosophiae Naturalis Principia Mathematica, Isaac Newton provided his famous theory of gravity, which supported the Copernican model and explained how bodies more generally move in space and time.

Isaac Newton (1642-1726 AD) is considered one of the most influential scientists in Western history. He laid the foundations of classical mechanics, in addition to his other contributions in optics. He is also credited, along with his contemporary philosopher Gottfried Leibniz (1646-1716 AD), for developing the mathematical basis of infinitesimal calculus.

In the Principia, Newton formulated the laws of motion and gravitation, which allowed mathematical derivation of Kepler’s laws of planetary motion, predicting the trajectories of comets, explaining tides and the precession of the equinoxes, in addition to other celestial and terrestrial motions. This theory removed all doubts about the validity of the heliocentric model. In return, this convinced most European scientists of the superiority of Newtonian mechanics over the earlier corpuscular mechanical philosophy.

As we noted above, the laws of motion were clearly stated by many Muslim scholars more than seven centuries before Newton, but they were not formulated in mathematical equations. Ibn Malaka al-Baghdadi distinguished between velocity and acceleration, and showed that force is proportional to acceleration rather than velocity Gutman (2003). He also suggested that motion is relative: “there is motion only if the relative positions of the bodies in question change.” , and he stated that “each type of body has a characteristic velocity that reaches its maximum when its motion encounters no resistance.” Langermann (1998).

On the other hand, there has been a long philosophical debate about the structure of matter and whether it is infinitely divisible. Atomists posited that matter consists of two fundamental principles: atom and void, but these philosophical atoms are not like the atoms we now known in science, whose internal structure is identified down to the levels of elementary particles and fields, whereas the philosophical atoms are absolutely indivisible. Conversely, the substance theory is based on a prime material continuum that remains qualitatively invariant under division.

This philosophical debate between the continuum and discretuum views of matter lead eventually to the development of calculus by both Isaac Newton and Gottfried Leibniz in the 17th century. Newton became most famous because his pioneering work on gravity and mechanics, that is essentially built on the concept of an absolute and continuous space and time, was exceptionally successful in explaining the various phenomena of motion, and was eventually developed by Einstein into the Theory of Relativity. On the other hand, Desecrate and Leibniz built their philosophies on the atomic theory, which was developed into the Corpuscular Mechanical Philosophy, but unlike Newton’s Mechanics which quickly found many industrial and practical applications, this line of thinking had not been given adequate consideration, otherwise it would have been developed faster into Quantum Mechanics that eventually came out with new terminology, although the Standard Model of Quantum Field Theory is essentially based on the same concepts because the elementary particles, that are the quanta of field excitations, are nothing but the monads advocated by Leibniz.

Monads can also be compared to the corpuscles of the Mechanical Philosophy, they are the ultimate elements of the universe. They are substantial forms of being, they are eternal, indecomposable, individual, subject to their own laws, un-interacting, and each reflecting the entire universe in a pre-established harmony. Monads are also centers of force, while space, matter, and motion are merely phenomenal. Therefore, for Leibniz space and time are systems of relations that exist between objects, unlike Newton’s space and time that are entities in their own right.

The word monad appears in the doctrines of Pythagoras, as the unity from which all number and multiplicity are derived. Plato used in the plural as a synonym for the Ideas, while Aristotle use it as the principle of number, itself being devoid of quantity, indivisible and unchangeable. For many Greek philosophers, including Pythagoras, Parmenides, Xenophanes, Plato, Aristotle, and Plotinus, Monad is the first being, the totality of all beings, the source or the One, as God. It also occurs as a synonym for atom, as incorporeal or spiritual entity.

For Leibniz, monads are simple unextended substances, that cannot begin or end except by creation or annihilation. He also considers them independent, although they are capable of internal activity, but cannot be influenced in a physical manner by anything outside themselves. Moreover, each monad is unique; that is, there are no two monads alike. He described in his Monadologie that monads must have qualities, otherwise they would not even be entities.

Unfortunately, Descartes and Leibniz theories of corpuscles and monads had not received adequate attention, unlike Newton’s Mechanics which quickly found many industrial and practical applications, and was eventually developed by Einstein into the Theory of Relativity. Although, in essence, had it been given similar consideration, Quantum Mechanics would have been a natural successor of Monadology. It is only because of this historical break that Quantum Mechanics came out late and with new terminology, and physicists had to wait many decades after the beginning of Quantum Mechanics until the Standard Model of Quantum Field Theory established the fact that elementary particles are the quanta of field excitations, which are nothing but the monads.

Islamic scholars were particularly fascinated with the theory of atoms or monads. Although the Mutazilites and Asharites disagreed about certain secondary issues, they generally posited that all matter is composed of identical and indivisible particles; that acquire quantitative or qualitative properties only when at least two of them unite to form physical bodies.

Leibniz tried to reconcile the doctrine of the Atomists with the scholastic theory of matter and form. He also wished to avoid both the extreme mechanism of Descartes, who taught that all matter is inert, and the monism of Spinoza, who taught that there is but one substance, God. Descartes defined substance in terms of independent existence, and Spinoza was merely inferring what was implicitly contained in Descartes’ definition when he concluded that therefore there is only one substance, the supremely independent Being, who is God.

Nevertheless, Newton’s mechanic was good enough to be applied to the solar system, but as a cosmological theory it was completely false insofar as it still considered, like Aristotle, the stars to be fixed and the Universe outside the solar system to be static. This belief in the Aristotelian static Universe was so deep and strong that it persisted for some three centuries after Newton. Stephen Hawking says:

Even Einstein, when he formulated the general theory of relativity in 1915, was so sure that the Universe had to be static that he modified his theory to make this possible, introducing a so-called cosmological constant into his equations.(Hawking 1998: 42)  This of course was soon proved to be wrong, and everybody now knows that the cosmos is in continuous motion. Einstein himself later considered this to be one of his greatest mistakes. As we noted in Volumes I and II, Ibn al-Arabi, however, declared plainly that the stars can’t be fixed at all, and he even gave numbers and units to the speed of their proper motion [II I.548.28, II.441.33], which are consistent with the latest accurate measurements.

After these developments, and with the advent of new technologies employed in making even more accurate observations, in addition to accelerated research in physics and astronomy, a whole new view of the cosmos finally replaced the ancient short-sighted ones. However, we cannot ever claim that all the questions have been answered and that we have drawn a fully correct picture of the cosmos. On the contrary, new sets of even more profound questions are still a riddle, such as dark matter and energy in addition to the weird quantum behavior.

Along with the vast amount of data collected by telescopes and space shuttles in recent decades, many new theories have arisen to try to explain those observations. The mere concepts of “time” and “space” were in focus especially after the strange and courageous ideas of Einstein about relative and curved space-time were proved by Eddington, through the observation of the total eclipse of the sun in 1918 in South Africa. Since then, other theories including Quantum Field Theory and the Superstrings, have tried to discover and describe the actual relation between material objects and energy, on one hand, and between space and time on the other hand. Yet no fully convincing view has ever been achieved.

Aristotle’s notion of circular time, based on an eternal (un-created) Universe, could not generally be accepted by most theologians of the three Abrahamic religions: Islam, Christianity and Judaism, insofar as they considered time to be linear, with a definite created beginning and end.

St. Augustine, and later Thomas Aquinas, objected to Aristotle’s belief that time is circular, insisting instead that human experience is a one-way journey from Genesis to Judgment, regardless of any recurring patterns or cycles in nature. This latter view was later adopted by Newton in 1687, when he represented time mathematically by using a line rather than a circle.

As we noted above, there was already an earlier debate in Greek philosophy as to whether time exists objectively, or is just constructed by our minds. Puzzled about time, St. Augustine concludes that time is nothing in reality, but it exists only in the mind’s apprehension of that reality.

On the other hand, Henry of Ghent and Giles of Rome both said that time exists in reality as a mind-independent continuum, but is distinguished into earlier and later parts only by the mind.

Isaac Newton considered time (and space) as an independent quantity that exists and flows regardless of matter or mind, a view which Leibniz strongly criticized. Leibniz argued that if space is distinct from everything in it, it would have to be completely uniform and homogeneous; thus he reached the conclusion that it is unreal and relative, in anticipation of Einstein’s Relativity, though he never put that insight into the form of mathematical equations (Ross 1984: 47).

Newton also rejected Aristotle’s linkage between time and motion, when he said that time is something which exists independently of motion and which existed even before God’s creation. He argued that time, and space, is an infinitely large ‘container’ for all events, and that the container exists with or without the events: this is called the ‘absolute’ theory of time. Leibniz, who adopted the relational view, objected to that and argued that time is not an entity existing independently of events.

In the eighteenth century, Kant said that our mind structures our perceptions so that space always has a Euclidean geometry, and that time has the structure of the infinite mathematical line (Kant 1998: 158-76). This view, however, lost its mathematical support with the discovery of non-Euclidean geometries in the 1820s.

In his Critique of Pure Reason, Kant presented, in the first antinomy, two equally plausible arguments that at the end lead to opposing conclusions: the first shows that the world had a beginning in time, while the other shows that the world had no beginning in time. For the second proposition, if we suppose that the world had no beginning in time, then this means that at any particular moment of time, an infinite number of events have passed—but infinity may never be completed. On the other hand, if the world had a beginning in time then all previous times before that beginning have been blank, and there is no any specific reason why the world should have begun at this time in particular.

On the other hand, there has also been a great debate as to whether time is continuous or a discrete quantity. Most western philosophers think of time as a continuous quantity, but after the advent of Quantum Mechanics the idea of quantum time was revived, although Quantum Theory itself doesn’t consider time to be quantized.



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  • ... Relative Position =>:

  • ... locity and acceleration, and showed that force is proportional to acceleration rather than velocity Gutman (2003). He also suggested that motion is relative : “there is motion only if the RELATIVE POSITION s of the bodies in question change.” , and he stated that “each type of body ha ...


  • ... Including Quantum =>:

  • ... ideas of Einstein about relative and curved space-time were proved by Eddington, through the observation of the total eclipse of the sun in 1918 in South Africa. Since then, other theories including Quantum Field Theory and the Superstrings, have tried to discover and describe the actual ...


  • ... Planetary Motion =>:

  • ... eloping the mathematical basis of infinitesimal calculus. In the Principia, Newton formulated the laws of motion and gravitation, which allowed mathematical derivation of Kepler’s laws of PLANETARY MOTION , predicting the trajectories of comets, explaining tides and the precession of the ...


  • ... Ptolemaic System =>:

  • ... ed how bodies more generally move in space and time. The Copernican model marked the beginning of modern astronomy and scientific revolution. It is certainty a remarkable departure from the Ptolemaic system that prevailed for many centuries. Copernicus may have been aware that Aristarchus ...


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  • ... ecific reason why the world should have begun at this time in particular. On the other hand, there has also been a great debate as to whether time is continuous or a discrete quantity. Most WESTERN PHILOSOPHERS think of time as a continuous quantity, but after the advent of Quantum Mechani ...


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  • ... Gave Numbers =>:

  • ... imself later considered this to be one of his greatest mistakes. As we noted in Volumes I and II, Ibn al-Arabi, however, declared plainly that the stars can’t be fixed at all, and he even GAVE NUMBERS and units to the speed of their proper motion [II I.548.28, II.441.33], which are consi ...


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I have no doubt that this is the most significant discovery in the history of mathematics, physics and philosophy, ever!

By revealing the mystery of the connection between discreteness and contintuity, this novel understanding of the complex (time-time) geometry, will cause a paradigm shift in our knowledge of the fundamental nature of the cosmos and its corporeal and incorporeal structures.

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Mohamed Haj Yousef


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