The challenge of quantum gravity.
The challenge of resolving the foundations of quantum theory.
The challenge of unification of the particles and forces.
The challenge of the constants in the standard model.
The challenge of explaining dark matter, and dark energy.
Summary.
Physics has undergone many revolutionary periods.
The last one was the Copernican revolution, in the 16th century.
Aristotelian theories of space, time, motion and cosmology was over thrown.
It culminated with Newton's theory.
This revolution changed the nature, in which we perceived the universe.
The current revolution, began in 1900, with Max Planck theory of energy distribution,
in the spectrum of heat radiation.
The theory demonstrated that energy, is not continuous, but quantised.
This is a revolution in progress.
Many challenges have to be overcome to complete this revolution.
One of the greatest scientist who contributed to the current revolution, was Einstein.
He formulated the theory of general relativity.
This is the best theory we have, as of now, of space, time, motion, and gravitation.
He gave us the profound insight,
that gravity and motion, are intimately related to each other,
and to the geometry, of space and time.
Till this time, space and time, had been viewed as fixed and absolute.
They provide the background, which was used to define concepts like position and energy.
In Einstein's theory of relativity, space and time no longer provided a fixed absolute background.
Space is as dynamic as matter.
The whole universe can expand or shrink.
Time can begin like in the big bang.
Time can end like in the black hole.
Einstein also understood the need for a new theory of matter and radiation.
His theory of relativity pointed to this direction.
Eventually quantum theory was invented.
The discovery of relativity and quantum theory,
required as to break away from Newtonian physics.
These theories still remain incomplete.
One of the main reasons that each is incomplete,
is the existence of the other.
Nature in an obvious sense is unified.
The universe is interconnected, and everything interacts with everything else.
The new theory that we need, should be a complete theory.
It must encompass, everything that we know.
Currently the atomic realm, is governed by quantum theory.
We ignore gravity.
We can treat space and time as fixed, as an unchanging background.
In the cosmic scale, gravitation is very real.
Quantum phenomena is ignored at this scale.
This dichotomy is only a temporary, provisional solution.
This provides the first great challenge, to theoretical physics.
It is to combine general relativity and quantum theory, into a unified theory.
We can call this the challenge of quantum gravity.
There are other problems specific to each theory.
Each has a problem of infinities.
In nature we do not encounter something measurable,
which has a infinite value.
In both quantum theory and general relativity,
we encounter predictions of physical quantities, becoming infinite.
In general relativity, inside a black hole the density of matter,
and the strength of the gravitational field become infinite.
This appears to be the case, in the early history of the universe.
At the point at which density becomes infinite,
the equations of general relativity break down.
Some scientists speculate, that this inadequacy is because quantum theory is neglected.
Quantum theory, has its own problems with infinities.
This appears whenever we attempt to use quantum theory,
to describe fields like the electromagnetic field.
In quantum theory there are uncontrollable fluctuations,
in the values of each quantum variable.
There is a hope that these fluctuations, will be tamed, if gravity is taken into account.
Quantum theory, has been successful in describing, a wide variety of phenomena.
Its domain extends from radiation, to the properties of transistors,
and from elementary particle physics, to the action of enzymes, and other large molecules,
that are building blocks of life.
Quantum theory gives only probabilistic predictions, of subatomic behaviour.
It is limited by the uncertainty principle.
This principle states that, we cannot measure a particle's position and momentum at the same time.
For example, an electron can be anywhere, until we measure it.
Our observation in some way determines its state.
This is a little unsettling, because reality cannot depend on our existence.
Quantum theory divides nature into two parts.
The observer and the system to be observed.
Some scientists like, Bohr, Heisenberg, etc, embraced this new way, of doing science.
Some scientists like, Einstein, Schrodinger, de Broglie, did not like this approach.
They belong to the realist school of taught.
They felt quantum theory is incomplete, and needs to be further developed.
One of great challenges of physics, is to resolve its foundational problems, of quantum theory.
There are several approaches by which we can try to resolve,
the problems in the foundation of quantum theory.
Provide a sensible language for the theory,
which incorporates the division of system and observer,
as an essential feature of the theory.
Find a new interpretation of the theory, that is realist.
In this measurement and observation, play no role,
in the description of fundamental theory.
Invent a new theory that gives a deeper understanding of nature,
than quantum mechanics does.
Scientists are working, on these approaches.
One large question is, "how important is realism?".
Will realism as a philosophy die off?.
Some scientist believe that quantum mechanics,
is an incomplete description of reality.
They believe that the discovery of a new theory,
will make it amenable to a realist interpretation.
The solution of the problem, will probably emerge from unification.
The idea that physics should be unified, has motivated significant effort from scientist.
There are several ways to approach unification.
One is to find a single law.
There are also other ways.
There are theories of principle.
There are constructive theories.
A theory of principle sets up the framework, that makes the description of nature possible.
A theory of principle must be universal.
It must apply to all domains.
The world is a unity.
Everything interacts with everything else.
There can be only language, used to describe these interactions.
Quantum theory and general relativity are both theories of principle.
There is a strong need for their unification.
Constructive theories describe some particular phenomenon in terms of specific models.
The theory of electro magnetic field, and the theory of electron,
are constructive theories.
Such a theory cannot stand alone.
It must be set within the context of a theory of principle.
As long as the theory of principle allows, there can be phenomena that obey different laws.
For example, the electro magnetic field obeys laws,
different from those governing cosmological dark matter.
Dark matter does not give off any light.
It is likely that it doesn't interact with the electromagnetic field.
This means that two different theories coexists side by side.
The laws of electromagnetism, do not dictate what exists in the world.
For example, Quarks, neutrinos and dark matter.
The laws that describe the strong and weak nuclear force, within the atomic nucleus,
do not necessarily require that there be an electromagnetic force.
Is it possible that all forces, we observe in nature,
be manifestation of a single force?
This need not be true.
This might be true.
Maxwell unified electricity and magnetism, into one electromagnetic theory, in 1867.
A century later, scientist discovered that the electromagnetic field and the weak nuclear force,
could be unified.
This became the electroweak theory.
There are two fundamental forces in nature, that remain outside the electroweak theory.
These are gravity and the strong nuclear force.
The strong nuclear force is the force responsible, for binding quarks together,
to form protons and neutrons.
This is the next great challenge.
This challenge is to determine whether or not the various particles and forces,
can be unified.
This theory should explain all of them as manifestation of a single fundamental entity.
Unification of particles and forces, would involve in defining a single fundamental entity.
This is different from unification of laws.
If we leave out quantum mechanics, unified theories are easy to invent.
If we include quantum theory, the problem gets much much harder.
Since gravity is one of the four fundamental forces,
we must solve the problem of quantum gravity, along with the problem of unification.
With the discovery and refinement of the standard model,
the physical description of the world has become simpler.
There are only two types of particles.
Quarks and leptons.
Quarks are the constituents of protons, neutrons and some other similar particles.
Leptons include electrons, neutrinos, and similar particles.
The world is explained with six kinds of quarks,
and six kinds of leptons,
which interact with each other, through the four forces.
The four forces are gravity, electromagnetism, the strong nuclear force,
and the weak nuclear force.
There are twelve basic particles, and four basic forces.
The standard model explains all of these, except for gravity.
The standard model is consistent, with all experiments, conducted so far.
The standard model has some problems.
It has many adjustable constants.
The constants specify the property of the particles.
Some constants tell us the masses of quarks.
Some constants tell us the strength of forces.
There are about 20 such constants.
We do not know why these constants, have their values.
Each constant represents some basic fact, of which we are ignorant.
The challenge is to explain, how the values of the free constants,
in the standard model, are determined.
It is hoped that unified theory of particles and forces,
will answer the question,
how the value of the free constant, in the standard model is determined.
Even as we celebrate the success of the standard model,
there are two dark clouds which obstruct our knowledge of nature.
These clouds are dark matter, and dark energy.
We understand gravity quite well.
But we do not understand its relationship with quantum theory.
The predictions of general relativity, is in full agreement,
with observations and experiments.
The observations include falling bodies, light on Earth,
motion of planets and moons,
and the motion of galaxies and galaxy clusters.
Gravitational lensing, is in effect of the curvature of space by matter.
This is well understood.
It is used to measure the distribution of mass, in the galactic clusters.
When velocities are low, compared to the speed of light,
and masses are not too dense,
Newton's laws of gravity provide an excellent approximation,
to the predictions of general relativity.
Newton's law of gravity says that the acceleration of any object,
as it orbits another, is proportional to the mass of the body,
it is orbiting.
The heavier the star the faster is the orbital motion of the planet.
The planet orbiting a heavier star, will be faster,
than a planet at the same distance, orbiting a lighter star.
If we know the speed of a body in orbit around a star,
and the distance from the star, we can measure the mass of the star.
Stars orbit around the centre of their galaxy.
By measuring the orbital speed of the stars,
we can measure the distribution of mass in the galaxy.
Astronomers measure the distribution of mars in a galaxy,
in two different ways, and compare the results.
They measure the mass by observing the orbital speed of the stars.
They also make a direct measure by counting,
all the stars, gas and dust, in the galaxy.
We would expect that both the results would agree.
Surprisingly they don't.
Even more surprisingly the results don't differ, by a small amount.
The difference is by a factor of up to 10.
Interestingly there is always more mass, needed to explain,
the observed motion of the stars.
Counting the stars etc., does not provide for the mass,
that is required.
All forms of matter, give off light, either directly like stars,
or indirectly like planets, which reflect light.
If there is mass that we cannot see, it must be some unknown form of mass,
which neither emits or reflects light.
The observations indicate that most of the mass in the universe should be of such nature.
This mysterious missing matter, is referred to as dark matter.
Recent discoveries have made things even more mysterious.
When observations are made at large scales,
corresponding to billions of light years,
the equations of general relativity are not satisfied,
even accounting for dark matter.
The universe has been expanding, since the big bang, 13.7 billion years ago.
Given the observed amount of matter,
plus the calculated amount of dark matter,
the universe should be doing the opposite.
It should be decelerating.
One explanation is that there is a new form of energy.
Energy and mass are equivalent as given by the formula, E=mc squared.
This new form of energy, affects only the expansion of the universe.
This postulated strange new form of energy, is called dark energy.
Most kinds of matter are under pressure.
Dark energy is under tension.
It pulls things together.
Tension is sometimes called negative pressure.
In spite of the fact that dark energy is under negative tension,
it causes the universe to expand faster.
In general relativity, if negative pressure is negative enough,
it has the opposite effect.
It causes the expansion of the universe, to accelerate.
About 70% of the matter density in the universe, is dark energy.
26% is dark matter.
Only 4% is ordinary matter.
The standard model applies to 4% of the universe.
We are in the dark, about 96% of the universe.
We now have a standard model of cosmology.
This model has about 15 constants.
They denote, among other things,
the density of different kinds of matter and energy,
and the expansion rate.
These constants are derived from observation.
We do not know why they have these values.
There is no theory which explains this.
This presents the next great challenge.
The challenge is to explain dark matter and dark energy.
These five challenges represents the boundary of current knowledge.
Together they drive most of the current work,
in the frontiers of theoretical physics.
Any fundamental theory of nature, needs to address these challenges.