Complex problems usually have simple
Therefore it is not the solution that matters,
but the journey through unknown territory that leads to it.
All textual links in this page, except
those with the prompt (this link is integral to the text),
are best ignored at first.
Stages of Physics
Theory of Balance
Stages of Physics
is, perhaps, as old as the humanity itself, and it too has gone through
a number of recognisable evolutionary stages. The first of these, which
distinguished physics from other human arts and crafts, may have occurred
around 3000 BC in astronomical observations carried out in Egypt, Mesopotamia,
India and China. These observations also appear to be the first recognisable
scientific activity of the human awareness of nature. From those fragments
of ancient history available to us, it is possible to guess what really
led to it. Firstly, there were good practical reasons that were helpful
to the human survival and prosperity; time keeping for activities such
as farming and making astrological predictions appear to have ranked
foremost among these. Secondly, faced with the harsh reality of nature,
the ancients may have found solace in the thought that astronomical
observations enabled them to commune with the heavenly activities and
thereby remain just that much closer to the home of the gods that sparkled
in the sky night after night.
astronomy had an unsuspecting earthly companion which was geometry,
the art of measuring the earth. Practical geometry began in ancient
Egypt as rope-stretchers annually re-established the boundaries of the
farmlands that were flooded by the river Nile and it gradually became
a refined tool in the construction of the Egyptian pyramids. However,
geometry remained a mere practical tool until the Greek civilisation,
which appeared around 800 BC, distilled it into an abstract form. The
process of deductive reasoning, which promotes a healthy curiosity of
the knowable in place of a morbid fear of the unknowable, is the principal
character of the next stage of physics.
600 BC it appears that the human perception of the universe began to
change radically, profoundly and decisively. The epicentres of this
change were in India, China and Greece. Around this period, these countries
produced men who saw the universe not as a chaotic playground of numerous
capricious gods, but as an orderly cosmos which functioned harmoniously
with all living things. In India and China, the vision was sudden and
metaphysical, but in Greece, the new vision of the universe developed
much more gradually, involved generations of thinkers, and had the strong
undertones of a study aimed at a detailed exploration of the material
aspect of the universe. In laying the foundation of this study, all
they had was their imagination, and they unleashed it in a torrent of
magnificent ideas, some of which continue to hold their ground to this
gradual process of philosophic change in Greece began with the revolutionary
thoughts of a Milesian intellectual giant called Thales
(c. 624 - 546 BC). Thales primary aim was to replace the supernatural
with the natural through observation and experiment, but his lasting
contribution was converting geometry from an art of measurement into
an abstract science of deduction based on general propositions; those
given below are attributed to him.
An isosceles triangle
has two similar angles at its base. (The word similar suggests that
Thales may not have been able to assign a magnitude to angle).
The opposite angles at the intersection of two straight lines are similar.
The base and the two
angles at its ends determine a unique triangle.
A circle is divided
into two equal parts by a diameter.
A diameter of a circle
subtends a right angle at any point on the circumference.
Although such knowledge of geometry
is rudimentary and obvious to us now, it must have been an enormous
feat of imagination at that time.
next Greek thinker who made a substantial contribution to physics was
(c.570-500 BC), from Ionia. He and his followers made a truly fundamental
discovery in geometry which has become known as the
'Theorem of Pythagoras'. It says that 'the square on the hypotenuse
of a right-angled triangle is equal to the sum of the squares on the
other two sides'. Pythagoreans were said to be the first to have imagined
that the earth and all other heavenly bodies had spherical shapes. They
also believed that the earth, the sun and the other planets all moved
round a 'central fire' and that these movements were accompanied by
an inaudible music which they called the 'harmony of the spheres'. They
taught that light consisted of particles which travelled from an object
to the eye.
At the end of about one and half centuries of existence the Pythagorean
school started to dwindle, and around 380 BC a new Athenian school,
called the 'Academy' arose. The founder of this school was the Athenian
(429-347 BC) in whose fertile mind mathematics, and in particular geometry,
soared to the heights of divine knowledge. To Plato and his followers,
abstract geometrical forms became the true substance of the universe,
and the 'Academy', which lasted for nearly a thousand years, boasted
above its entrance door the motto 'Let none but mathematicians enter
here'. Naturally, geometers fashioned the heavens using abstract geometrical
forms, and astronomy and geometry finally shook hands.
the middle of the fourth century BC, science in Greece had begun to
decline, and, in about 300 BC, the centre of scientific excellence moved
from the Academy, in Athens, to the Temple of the Muses, the equivalent
of a modern university, in the city of Alexandria, Egypt. It was here
(c.330-275 BC) produced his 'Elements of Geometry' which consisted of
a coherent treatise of thirteen books on geometrical 'truths' which
may be regarded as the real foundation of the physical sciences. It
was also here that the great mathematician, Archimedes
(287-212 BC), had his education before returning to his native Sicily.
Then there were the four great astronomers;
Aristarchus of Samos (c.310-230 BC), who proposed a heliocentric
solar system; Eratosthenes
(c. 276-195 BC), the chief curator of the library of Alexandria, who
was the first to measure the distance between the sun and the earth
to a reasonable accuracy and was also said to have measured the 'obliquity
of the ecliptic' or the tilting of the earth's axis of rotation which
causes the seasons;
Hipparchus (c. 190-120 BC) of Nicaea who discovered and estimated
'the precession of the equinoxes', or the minute wobbling of the earth's
axis of rotation; and finally Claudius
Ptolemy who produced an extensive treatise on mathematics and astronomy.
This treatise, which became known as Almagest consists of a collection
of thirteen books and describes a geocentric universe which, although
completely erroneous, remained in authority until the sixteenth century
AD. Science continued to flourish in Alexandria until the Dark ages
began about 400 AD, when it became virtually dormant for a full thousand
1400 AD, concurrent with the literary renaissance in Europe, science
awoke from its slumber and the third stage of evolution in physics began.
Many regard Leonardo
da Vinci born near Empoli (1452 -1519), who was talented in virtually
every field of human endeavour, as the first renaissance scientist;
it appears that he studied nature in the same spirit as we do now. He
had been an advocate of the view propounded by the Greek thinkers
Democritus of Abdera (c.470-400 BC) and
Anaximander of Miletus (c. 611-545 BC) that the universe is governed
by mechanical laws. According to Leonardo, we should base science on
observation, discuss using mathematics and verify using experiment.
He was of the opinion that scientific certainty can only come from mathematical
we discussed above physics may have stirred to life through cosmic curiosity,
but it certainly found its feet through cosmic order. The first detailed
and systematic study of cosmic order was the geocentric system of the
universe produced by Ptolemy. The Polish astronomer Nicolaus
Copernicus, (1473-1543) sought to reduce the complexity of this
Ptolemaic system, which consisted of about eighty circles of deferents
and epicycles, by placing the sun at the centre of the system, rather
than the earth. He worked very hard at his heliocentric model but it
never occurred to him to question the prevailing belief in the 'naturalness'
and 'inevitability' of the circular motion of planets. Because of this,
his model too remained complex; but he managed to reduce the number
of circles to thirty-four.
hindsight we now know that all Copernicus had to do was to abandon circles
in favour of ellipses; a minor adjustment which would have reduced the
number of trajectories to seven and increased the accuracy of the model
beyond all expectations. However, no amount of speculation could have
bridged the gap which existed between the circle and the ellipse in
astronomy at that time. Masses of accurate astronomical data, a matching
mathematical acumen and a monumental perseverance were necessary for
this purpose. The man who had the means and the inclination to produce
such masses of data and satisfy the first of these three requirements
was the Danish astronomer Tycho
Brahe (1546-1601). He was weak in mathematics and great in astronomical
observations. To obtain better accuracy he used better equipment, repeated
a measurement many times over, and obtained their average. Thus, he
introduced a new standard of accuracy into astronomical measurements,
and to this accuracy he charted the positions of stars and planets for
a period of over twenty years. But the analysis of this data was beyond
his ken and destiny placed it in the hands of Johannes
Kepler (1571-1630), the brilliant German mathematician from Weil
near Stuttgart. Only Kepler had the qualities which satisfied our remaining
In a tireless attempt to fit Tycho Brahe’s observations on Mars
to an analytic curve, Kepler shattered the groundless belief that heavenly
bodies should, of necessity, move in circles merely because these display
an elegant symmetry not found in other ‘ lesser’ figures.
He found that all the observations fitted perfectly not to a circle
but to an ellipse, a curve which was believed to be imperfect. In 1609
he published his findings in a book called Astronomia Nova in the form
of the following two laws, which applied to the orbit of Mars.
The planet moves in an ellipse with
the sun at one of its foci.
he line joining the sun to the planet
sweeps out equal areas in equal times.
In 1618, in a second book called Epitome Astronomiae
Copernicae, Kepler next extended these laws to all the remaining planets,
the moon, and the four satellites of Jupiter; in other words to all
the planets and the satellites of the solar system known at that time.
Again in 1619 he published a third book, Harmonices Mundi, in which
he announced the following third law which too applied to all the planets.
The square of the time that any planet
takes to describe its orbit completely is proportional to the cube of
its average distance from the sun.
replacing the circular orbits with elliptical orbits, Kepler answered
the age-old question of ‘how’ the planets moved round the
sun. But in so doing, he naturally raised the question ‘why’
the orbits had to be elliptical and not any other geometrical curve.
Of course, the circular orbits, owing to their naturalness, escaped
this question completely. The best that Kepler could do was to imagine
that whilst the sun provided the motive force for the planets to move
round in circles, a force akin to magnetism pushed and pulled the circular
orbits into elliptical shapes. More than half a century was to elapse
before these qualitative conjectures were to become unnecessary in the
face of a superlative theory put forward by
Isaac Newton (1642-1727).
Kepler was discovering the architecture of the solar system, an Italian
physicist and astronomer, Galileo
Galilei (1564-1642), was investigating motion of bodies by conducting
rudimentary terrestrial experiments and, where such experimentation
was not possible, by resorting to ingenious thought experiments. Prior
to Galileo’s investigations it was believed that the natural state
of a body was that of rest and that a force was necessary to keep it
in motion. Galileo came to the firm conclusion that rest and uniform
motion were indistinguishable from each other if an external reference
was unavailable. He also concluded that a force just had the effect
of changing these states by producing acceleration. Thus, it was Galileo
who first concluded correctly, and demonstrated experimentally, the
principle of relativity and the principle of inertia which became corner
stones of the early classical physics.
being unable to shake off the influence of a prevalent belief that certain
motions, such as the fall of heavy bodies, result from a natural tendency
that is a factor present in addition to inertia and force, Galileo was
never able to state the principle of inertia with clarity. Nonetheless,
Galileo was able to shatter the belief that gravity causes heavier objects
to fall faster than lighter objects and to state quite clearly that
all objects fell at the same rate. Until the
time of Galileo, the analysis of the motion of a projectile, which formed
an important part of the curriculum of mechanics, remained a daunting
and an inconclusive task. Using his insight on inertia and the fall
of objects under gravity Galileo was able to analyse this motion correctly.
Galileo pioneered the telescopic astronomy, using telescopes he made
for himself. It is very likely that his were the first mortal eyes that
were able to examine closely the surface irregularities of the moon,
the stars which forms the Milky Way, the four satellites of Jupiter,
the phases of Venus, and the rings of Saturn. However, he wrongly interpreted
the rings of Saturn as two small spherical bodies touching Saturn at
the opposite ends of a diameter.
Kepler and Galileo provided the key features of an emerging system of
mechanics, of universal applicability, within which all primary physical
distinctions between the heaven and the earth were to disappear. The
formulation of this system of mechanics needed the insight of a genius
of extraordinary talent. This genius was the physicist and mathematician
Isaac Newton (1642-1727), from Lincolnshire, England. He reduced Kepler’s
three laws into a single universal law, set in a background of three
completely general laws of motion, two of which embodied Galileo’s
principal discoveries. Newton described this universal system of mechanics
in a book published in 1687 under the title ‘Philosophiae
Naturalis Principia Mathematica’; of this it can be justly
said that, with the possible exception of Euclid’s ‘Elements’
and the English naturalist Charles
Origin of Species’, no greater scientific work has been produced
by the human intellect, before or since. Newton's first law of motion
was a succinct statement of the principle of inertia that Galileo almost
had within his grasp. It was as follows.
Everybody continues in its state of
rest or of uniform motion in a straight line, unless it is compelled
to change that state by impressed forces.
Now a body may be at rest or be moving
uniformly with respect to some location on the earth, but since the
earth itself is moving non-uniformly with respect to the sun, the body
has a completely different motion with respect to the sun. As this state
of affair could continue, it is clear that motion is not an easy concept
to define. Newton was fully aware of this difficulty; as a way out,
he defined an absolute inertial frame in terms of the following two
Absolute space, in its own nature, without
relation to anything external, remains always similar and immovable.
Absolute, true, and mathematical time,
of itself, and from its own nature, flows equably without relation to
Newton attributed absolute space to the presence of huge, immovable
masses which delimited the universe; a kind of immovable framework within
which all movable bodies are to be found. Even Newton himself was ill
at ease with this framework and with the absolute clock that ticked
away regardless within it but, as there were no alternatives, they became
established concepts and held their ground for a period of nearly two
hundred years. Having made provisions for substantiating motion, Newton
next went on to give a quantitative definition of force in the form
of a second law of motion, as follows.
The rate of change of momentum of a
body is proportional to the impressed force and is in the same direction
as this force.
This law also introduced a new concept called momentum
and Newton defined it as velocity multiplied by an invariant property
of the body that he called mass. Thus it was Newton who introduced the
fundamental property of mass to physics. Next, Newton introduced the
following third law of motion which completed the general description
To every action there is always an equal
and opposite reaction.
Unlike the first two laws that were
in the making even before Newton appeared on the scene, this third law
was of Newton's own making. This law is a statement of a precise balance
that transcends time as the forces therein act instantaneously. As we
shall discuss below in due course, what Newton really saw was a transcendental
principle of balance that operates timelessly in the physical world.
Forces just happened to be the only medium of expression that was available
to him in his time.
system of mechanics and the absolute reference frame, which he defined
in terms of rigid measures of space and time, are still in use today
as they had been for hundreds of years in the past. However, our present
knowledge of the nature of space and time leaves us in no doubt that
Newtonian mechanics is only valid for speeds that are very much smaller
than the speed of light. At speeds that are significant in comparison
with the speed of light, relativity theories take over. According to
these theories, which were first formulated by Albert Einstein (1879-1955)
in a special form in 1905 and then in a generalised form in 1916, motion
is a relativistic concept which did not require the support of an absolute
space and time: they, after all, are mere hypothetical concepts. However,
a small trace of a similar hypothesis remains in relation to the rotary
motion of bodies; this remnant is Newton's belief that the cause of
the absolute nature of spin motion lies in distant masses of the universe.
We shall see later that the real reason for this difference between
linear and rotary motions is that their origins lie in fundamentally
different structures of spacetime.
single universal law to which Newton reduced the three laws of Kepler,
describes with a high degree of accuracy the universal phenomenon of
gravitation; this is the only physical phenomenon which affects and
is affected by all material bodies. Starting with cosmic systems of
planetary size, the force of gravitation is, perhaps, the only key factor
which determines the large-scale structure of the universe. Yet, Newton's
law for this force is simplicity itself, and it is as follows.
Everybody in the universe attracts
every other body with a force proportional to the product of their masses
and inversely proportional to the square of their distance of separation.
physics, which explained all the cosmic and terrestrial phenomena that
were significant in his time, reveals four basic parameters which can
remain unaffected by varying physical conditions. These invariant elements
of Newton's physical world are the mass, energy, momentum, and angular
momentum of a particle of matter. The appearance of these four conservable
physical parameters and the associated four laws of conservation marks
the beginning of a scientific analysis of the intuitive notion of permanence
which we habitually associate with the physical world.
In addition to gravity, there were two other basic phenomena, electricity
and magnetism, which had, since about 1600, drawn the attention of physicists.
With the availability of Newton's framework of mechanics, and aided
by his theory on gravity, electricity and magnetism began to develop
as two separate sciences called electrostatics and magnetostatics. From
1821 the English experimental physicist
Michael Faraday (1791-1867) began to conduct what we now call electromagnetic
experiments, and after a period of about ten years discovered the link
between electric and magnetic fields. In the fertile imagination of
Faraday the concept of physical field turned from fiction to fact. In
1856, the Scottish physicist and mathematician
James Clerk Maxwell (1831-1879) successfully arranged all the available
knowledge on electromagnetic phenomena, together with a small but vital
contribution of his own, into an elegant mathematical theory on electromagnetism,
Meanwhile Newton's physics had been evolving and by 1834 it had developed
mechanics. Many eminent people contributed to its growth, notably
Leonard Euler (1707-1783), Joseph
Louis Lagrange (1736-1813),William
Rowan Hamilton (1805-1865) and Jacobi
(1804-1851). A fundamental feature of analytical mechanics is that position
and momentum replace position and velocity (in Newton's physics) as
two independent base states. Thus analytical mechanics gives momentum
an identity of its own. Absence of any explicit forces is another important
feature which distinguishes analytical mechanics from Newton's physics.
A third difference is that analytical mechanics is totally independent
of coordinate systems. This feature enables a mechanical system to have
coordinates of its own. These coordinates, which are the positions and
momenta of the components of the mechanical system, define an abstract
space called phase space in which the entire mechanical system appears
as a single point. Finally, analytical mechanics is ideally suited for
the analysis of complex mechanical systems whereas Newton's physics
For a while it looked as if, within the theoretical framework provided
by Newton's gravitation, Maxwell's electromagnetism, and analytical
mechanics the physical world was about to unfold itself completely in
terms of just two independent basic properties of matter: mass and charge.
But that was not to be.
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In 1887, Albert
Michelson and Edward Morley established experimentally that the
behaviour of Maxwell's electromagnetic waves was incompatible with Newton's
absolute separation of space and time. In 1905, Albert
Einstein (1879-1955) who may not have been aware of the Michelson-Morley
experiment formulated a new theory of space-time that resolved this
incompatibility and showed that Newton's view of separate space and
time is flawed. Two others were individually active in this respect
and they were the Dutch physicist Hendrick
Antoon Lorentz (1853-1928) and the French mathematician Henri
Poincaré (1854-1912). In 1908 the Russo-German mathematician
Minkowski (1864-1909) found the correct interpretation of Einstein’s
theory and unlocked its full potential. According to Minkowski’s
interpretation, space and time are not separate entities as Newton had
imagined, but conditional partitioning of one continuum which we now
refer to as spacetime. With respect to this new continuum, the concept
of position, which used to consist of just three space-coordinates,
becomes broadened and includes the time coordinate on an equal footing.
This wider concept of position is termed 4-position or, simply, event.
Similarly, velocity and momentum, each of which used to consist of three
components, acquire a fourth component and become 4-velocity and 4-momentum,
respectively. A technically more correct name for the latter is momentum
1-form. The fourth component of 4-velocity prima facie carries no special
significance, but that of momentum 1-form represents the energy of matter.
Thus, the energy and momentum of a particle of matter, which are conserved
as two separate entities in Newton's physics, become a single conserved
entity in Einstein's theory which became known as special
relativity. Furthermore, the magnitude of this single entity becomes
the energy equivalent of the rest mass of the particle of matter. Thus,
in special relativity three of the four conserved entities in Newton's
physics unify, but the fourth entity of angular momentum remains separate.
fundamental changes that position, velocity, and momentum undergo in
special relativity are concomitant with the speed of light becoming
an absolute entity and occupying a special position in physics as required
by Maxwell's theory. More precisely, special relativity is an exposition
of the spacetime structure that Maxwell's theory demands and they fit
like hand and glove. For, in principle, Maxwell's theory is equivalent
to special relativity supplemented by just the Coulomb potential of
1916 Einstein's thoughts on the nature of gravity led him to a generalisation
of special relativity, called general
relativity. This generalisation clearly showed that the rigid, flat
space-time of special relativity is just the limiting form of a small,
local region of a flexible, globally curved space-time. Einstein with
his general relativity brought to an end physicists' belief in the supremacy
of Euclidean geometry and the uniqueness of the Euclidean straight line,
just as Kepler with his 'humble' ellipse brought to an end astronomers'
belief in the supremacy of the circle and the perfection of the circular
shape. A body, which freewheels along a 'straight' line in the curved
spacetime of general relativity, would produce the apparent impression
that it is under the influence of an invisible force. Thus, just as
Newton's force of gravity explained Kepler's elliptical orbits of planets,
Einstein's curved space-time explained Newton's concept of force. With
this immense achievement, Einstein showed that the entity that we call
the physical field consists of a component that we cannot construct
accurately using Newton's concept of force.
relativity established that the structure of this field component, which
forms at least the major part of the large-scale structure of spacetime,
originates in an entity called a metric
tensor which is present as a continuous distribution (or a field)
throughout spacetime. A metric tensor, in general, consists of a set
of sixteen numbers. However, a certain property of symmetry that the
metric tensor possesses effectively reduces this set to ten numbers.
Thus, in relativity theory, an event, which carries a label of four
arbitrary coordinates, receives ten more numbers which represent what
may be called its metric infrastructure. In a curved spacetime the metric
tensor varies from event to event no matter what coordinates are used;
in special relativity, it remains effectively constant throughout spacetime.
spacetime endowed with a metric tensor field is termed a metric manifold.
The term 'metric' signifies that this manifold is able to produce an
objective measure for length that we can transport unchanged from one
event to another. Also, in a metric manifold a unique line of optimal
length, called a geodesic, exists locally between two arbitrary events.
A geodesic is the curvilinear equivalent of the familiar straight line
in Euclidean geometry. Since in Euclidean space free motion describes
straight lines, it follows that in a metric manifold it describes geodesics.
The motion along a geodesic is expressible using either the velocity
or the momentum, since we can change these from one to the other using
the metric tensor without which the geodesic has no real existence.
Thus, in general relativity there is no substantial distinction between
momentum and velocity.
present, general relativity is not fundamentally equipped to assimilaie
matter into spacetime, at least not in the way Einstein wanted it, according
to his book, 'Out of My Later Years'. Only a conjectural equation that
Einstein himself proposed determines the metric tensor field, but only
in empty spacetime. Consequently, general relativity is still incomplete
and Einstein unreservedly maintained to the very end of his life, that
its completion entails just uniting gravitation and electromagnetism
in a single structure. Einstein believed that this structure would be
the Theory of Everything that happens in the physical world. This website
presents a theory called 'Balance' that completely vindicates Einstein's
belief. It preserves General Relativity as it applies to empty spacetime
intact, but only as far as the metric tensor field is concerned. Speeds
at which test particles move in this field are always higher than those
that general relativity predicts. However, the discrepancy becomes significant
only at distance scales of galactic magnitudes and over.
website presents a theory called 'Balance' according to which the physical
universe is the embodiment of a 'unique' state of balance between its
global and local, or field and particle, aspects. The theoretical representations
of these aspects in this theory are in terms of two respective tensor
fields and these are the symmetric metric tensor field in general relativity
and an antisymmetric tensor field which is a generalised form of the
Maxwellean electromagnetic field.
contemporary physics, strictly speaking, the global and local aspects
of the physical universe are separate. Their structures lie in the symmetric
metric tensor field and the Maxwellean electromagnetic field, respectively.
These structures form two separate rival schools of thought known as
General Relativity and Quantum Mechanics. At present Quantum Mechanics
is in vogue and its adherents advocate subsumption of General Relativity
into its body; the result would be a particle centred physical world
which would multiply abnormal complexities such as those involved in
entanglement. There are simple, but compelling, mathematical reasoning,
Space, which suggest that continuation and quantisation which are
the substrata of field and particle do, indeed, exist as a syzygy, or
an archetypal pairing, and that this syzygy is best reached from its
continuity side rather than from its quantum side.
are two crucial differences between quantum mechanics and the two theories
of Newton and Einstein. Firstly, quantum mechanics leaves us with a
feeling utter confusion, at best emptiness, whereas the two theories
possess an intuitive appeal and a sense of uniqueness in that they rise
or fall by their core structures within their areas of applicability.
Tinkering with the core structures is not an option. Secondly, whilst
quantum mechanics has always been a collective endeavour, each of the
two theories has been effectively a personal vision. Perhaps this may
mean that in any epoch Truth reveals itself only to one for the benefit
of many. That said, we should leave alone the chaotic and vibrant world
of Quantum Mechanics, and access its vast superlative knowledge base
only strategically and at opportune moments.
Theory of Balance
began with astronomical observations and the ancient astronomers used
these to build a model of the solar system based on circular symmetry,
which they thought symbolised 'divine' perfection. These astronomers
had been the pioneers who explored an uncharted terrain using only knowledge
and instruments to match and for that reason, they had no access to
the depths beneath its surface imagery. So, they unwittingly left the
future of what they had begun in the capable hands of their predecessors,
to name a few. Finally, it was Newton with his three laws of motion
and the law of gravitation who brought the ancient dream to life as
an order that operates throughout the physical world with clockwork
precision. However, laws of electromagnetism were outside Newton's framework
as electromagnetic observational data were then virtually non-existent
compared to the vast catalogue of accurate gravitational data that was
available due to millennia of dedicated labour in astronomy. Inclusion
of electromagnetism in the curriculum of physics meant that Newton's
physics had to give way to Einstein's
Relativity, which first appeared in a
special form in 1905 and then in a general
form about ten years after. General relativity has yet to realise Einstein's
vision of a complete theory of physics wherein gravitation and a generalised
form of the Maxwellean electromagnetism meet on equal grounds. This
website presents a theory called Balance that finally vindicates Einstein
with the emergence of General Relativity (GR) on a foundation of symmetry,
a rival emergence, which we now call Quantum
Mechanics (QM), took place on a foundation of antisymmetry. The
incidence of these two emergences borders on Jungian
Synchronicity and is a remarkable demonstration of the validity
of Bohr's dictum on opposites, stated at the beginning of the 'About'
page. With passing time, GR confined itself to the orderly cosmic domain
of the physical world where chaos is secondary, and QM, to the chaotic
atomic domain where order is secondary. They have remained just as far
apart as their two respective domains, to this day. According to Balance,
the reason for this persistent chasm is the failure to establish the
'timeless' symmetry-antisymmetry balance that holds the two domains
together in a cast-iron grip at core whence forces originate, but in
a feather-soft grip at periphery where motions take place.
We have yet to come across a natural state of symmetry existing at the
expense of antisymmetry, or vice versa, that is capable of leading to
a truly fundamental theoretical abstraction that can be the ultimate
foundation of physics. However, with time such naked symmetries, referred
to here as just symmetry for short, found their way into the
heart of physics, like in the case of GR and QM, and now symmetry
has become the foundation of physics, just as it had been in ancient
astronomy. Also the practice of building ‘epicycle’ upon
‘epicycle’ to adjust for the limitations of symmetry is
continuing still, just as it had been then, but at an even faster and
more furious rate. Such action goes against the grain of our intuition
and experience and this website shows that replacing symmetry with balance
as the foundation of physics all that we have to do to reverse this
trend. Because balance also includes symmetry-antisymmetry together
on an equal footing, this action does not abandon symmetry, but apportions
it a due place in an improved scheme of things to come so that it would
become stronger still, but within its own limits set by the concept
Physical world bears clear evidence that symmetry and antisymmetry in
their natural form exist inseparably on an equal footing. The long-range
force fields of Gravitation and Electromagnetism, which divide the physical
world between them into cosmic and atomic regions, are symmetric and
antisymmetric tensor fields, respectively. Of the two short-range force
fields, Weak force merges with Electromagnetic force at high energies,
and according to Balance, so should Strong with Gravity. Motion of a
fundamental particle of matter consists of linear and angular components
and these are characteristically symmetric and antisymmetric, respectively.
In other words, it is symmetry and antisymmetry operating on an equal
footing that hold the physical world together. Fundamental
entities of the same type in theoretical physics always have infrastructural
components of symmetry and antisymmetry. In the analytical
mechanics of Euler,
which is an elegant alternative representation of Newton's physics,
the kinetic and potential energies (T and V)
of a physical system that replace Newton's force are two such fundamental
entities. The 'difference' ± (T - V)
called the Lagrangian
is the antisymmetric component of these two energies, and the sum
(T + V) called the Hamiltonian
is their symmetric component. These two formulations lead to the same
dynamics of the physical system. However, while the differential equations
of Lagrangian dynamics are of the second order with respect to time,
those of Hamiltonian dynamics are of first order; hence the latter is
discussed above that GR and QM are representations of a physical world
torn asunder as regards its symmetry and antisymmetry. Yet the spell
of balance between these opposites is so overwhelming that GR and QM
each achieve a semblance of its own symmetry-antisymmetry balance within
the framework of analytical mechanics, in a startling fashion. For,
while the formal structure of GR is Lagrangian-based, that of QM is
Hamiltonian-based. Numerous attempts are being made at present to give
GR a Hamiltonian-based formal structure in an attempt to acquire gravity
quantisation; these clearly work against balance and hence likely to
be counterproductive. Also, if quantisation is a great truth, so is
continuation, at least according to Bohr, and to express all fundamental
physical phenomena in terms of quanta alone would be wrong.
as outlined in the 'About' page, is the first of the three pair-formations
that make up the foundation of the physical world. They are special
cases of a universal phenomenon of Isotypic Pairing that however has
not yet drawn the proper attention of physics; a surprising stance given
its pivotal role at every major turning point in the history of modern
physics and in its rapid rise to stardom. Modern physics began with
the works of Kepler and Galileo; Kepler's was sky-bound and it transformed
astronomy by establishing that planets move round the sun along elliptic
paths with the sun occupying one of the pair of foci of each ellipse.
Galileo's was earth-bound and his brilliant account of Salviati's
experiment established that unless a pair-formation exists between
the inner and the outer worlds of an observer, a rational judgment of
the observer's state of motion remains impossible. This pair formation
was the basis of the 1905 paper that established special relativity.
Pair formation continued to dominate the progress of physics beyond
relativity, as even at the heart of quantum mechanics are pairings,
called conjugate variables. Today Quantum
entanglement, more than any other phenomenon, beckons our attention
to pair formation with its near supernatural character symbolic of the
state of unbalance that exists in physics.
Stable structures, be they physical, biological, mathematical,
or otherwise, all have their foundations steeped in isotypic pair-formations.
Consider first the field structure of the physical world. In Balance
it consists of the pair of fields that are respectively symmetric and
antisymmetric in character. Infrastructure of these fields are a pair
of symmetric and antisymmetric tensor fields of the same type. The Figure
1 shows how they relate to the existing four forces.
The link between 'Symmetry' and 'Strong',
shown in red in the above figure, is yet to establish itself in contemporary
physics. In Balance, particles of matter, which are the physical manifestations
of the force fields, also pair-form thus.
Motion of these particles
of matter also pair-form as in the Figure 3.
Moving from physical to biological plane, we come across
the basic structural units of life, and yet again these DNA (deoxyribonucleic
acid), RNA (ribonucleic acid) and Ribosome each exist as pairs of some
sort. DNA consists of two helical suger-phosphate back bones joined
together by the base pairs, Adenine -Thymine and Cytosine - Guanine.
RNA and Ribosome which work as a team to manufacture proteins according
to information provided by the DNA, do so by pair-forming as in Figure
Pair formation does not stop with the
concrete but extends to the abstract world of mathematics also. The
simplest example in this case is the complex number, a pair formation
between two real numbers, which to a real number is, so to speak, as
human being to ape. An abstract example of a different kind
is the pair formation between an
event and a set of coordinates.
physical world has an irrefutable objective character in spite of what
quantum mechanics would have us believe, if by objectivity is meant
material existence unaffected by the subjectivity of life that probably
is related to the 'selfish
gene'. In the absence of such objectivity, how could we explain
the pre-biological period of the universe in which matter had been present
in a very 'stable' form just as not only matter but also as interrelated
assemblages in states of dynamic activity ranging from the infinitesimally
small to the infinitely large. However, there is evidence that the gene
scene is an integral part of the physical world and the present physical
form of this evidence is an extreme fine-tuning of the latter just so
that the former would eventually appear (strong
However, even millennia after the appearance of life (on earth), there
is this macrocosm of staggering proportions in comparison to which that
life is still virtually nonexistent and would continue to be so for
the foreseeable future. Also here is this microcosm which appears to
carryon in blissful ignorance of interference from the subjectivity
of life, as evinced by the objective stability of chemical elements
and compounds that exists side by side with the subjective element of
life. I, of course, can move matter around wilfully but that does not
count as a fundamental interaction that disturbs the objective character
of matter, as by my action I cannot wilfully change the basic structure
of fundamental particles of matter, whatever that may be. My will to
change things is a dimension that I possess in addition to those that
the physical world possesses. I can only change the field in which particles
sit and therefore I conclude that while my physical body is obviously
particle-based, my mind is field-based. The archetypal physical field
is gravity, and gravitational structure possesses a fundamental feature
of arbitrariness that may act as the niche for a feature that is integral
with the physical world and yet has a 'mind' of its own.
of us who believe that mind is simply a product of the physical world
may think that the contents of the preceding paragraph support their
belief. That, of course, would be the case for a self-contained physical
world. Although the concept of 'self-containment' as in the case of
axiomatic systems appears prima facie self-explanatory, Kurt
Gödel in his seminal paper titled 'On Formally Undecidable Propositions
of Principia Mathematica and Related Systems' showed that reality is
quite different, indeed. Gödel proved that any non-contradictory
system of mathematics, broad enough to contain at least arithmetic,
is not self-contained as it can produce results that are not contained
within its framework of axioms and procedural rules. In short, their
validity is ‘undecidable’ within the system itself. The
most curious of these ‘undecidables’ is the system consistency
of the axioms themselves. Therefore, even if the physical world is expressible
as an axiomatic mathematical system, for example special
relativity, it will still not be self-contained, or even self-consistent.
In other words, there is a great deal more to reality than what a physical
world by itself can provide, even if one were to exist by some chance.
consider the behaviour of light; in relation to the physical world,
it is ’immovable’, in that its motion is unaffected by the
motion of matter. In addition, it only makes a point contact with the
physical world, as the 4-dimensional distance that it travels in the
physical world is always zero. Also its composition is quite different
from that of matter; bosons vs. fermions. These are the characteristic
features of the fulcrum in an old-fashioned balance, indicating that
light can act as the fulcrum should there be a state of balance that
rules the physical world. There indeed is such a state with light as
the fulcrum, and this role of light is established and described in
mathematical details in the ‘Theory’ pages. It also becomes
clear therein that the entities which are being balanced are field and
particle, or simply spacetime and matter.
role of light as a fulcrum opens up a world of reality that is distinctly
different from the physical world and there are indications, albeit
intuitive, that it does so together with the stuff that we call mind.
This world then functions as the fulcrum for the field-particle physical
balance, with light taking up its position as pivot and mind-stuff as
base. All these unmistakably point to an almost esoteric objective character
of the physical world, and it appears that modern physics has attempted
to capture it rationally using the concept of 'symmetry', or more precisely
, as the nucleus of rationalisation.
mentioned at the outset, symmetry has an equal companion which is antisymmetry.
For example, symmetry and antisymmetry are respectively the basic characters
of the long range force fields of Gravitation and Electromagnetism which
divide the physical world between them as cosmic and atomic regions
respectively. On an abstract note, a general vector field which is the
most basic concept in classical physics is determined by the 'Div' and
the 'Curl' where the
former represents symmetry and the latter, antisymmetry. In both
these examples it may be said that symmetry and antisymmetry are on
an equal footing. However Symmetry Group disturbs this equality in the
sense that symmetry is made to become a function of a contrived antisymmetry.
For, a Symmetry Group operation is always associated with its reverse
operation thus making Symmetry Group operations antisymmetric and it
is this antisymmetric group of operations which captures symmetry. The
proper antisymmetry which complements symmetry is now completely decoupled
from it and is relegated to the background. In the case of the long
range forces, proper physical antisymmetry which characterises the atomic
region of the physical universe now operates remotely from symmetry
which characterises the cosmos; hence the past and present failures
to join together quantum mechanics and general relativity in spite of
sustained and strenuous efforts. So, Symmetry Group has considerable
limitations, however, it is also indispensable where it matters as its
persistence in physics indicates.