**Our picture of the universe**

Aristotle thought the earth was stationery and that the sun, the moon, the planets, and the stars moved in circular orbits about the earth. This idea was elaborated by Ptolemy into a complete cosmological model. His model was accepted by the Christina church.

Copernicus proposed simpler model in 1514. His idea was that sun was stationery and the earth and the planets moved around it.

Kepler and Galileo started publicly to support the Copernican theory. Kepler introduced ellipses as moving trajectory. Explanation was provided by Newton in his Philosophiae Naturalis Principia Mathematica in 1687.

Even people that realized that Newton’s theory of gravity showed that the universe could not be static did not think to suggest that it might be expanding.

The questions of whether the universe had a beginning in time and whether it is limited in space were later extensively examined by the philosopher Immanuel Kant in his Critique of Pure Reason.

The concept of time has no meaning before the beginning of the universe. This was first pointed out by St. Augustine.

In 1929 Edwin Hubble made the landmark observation that wherever you look, distant galaxies are moving rapidly away from us. The universe is expanding. Hubble’s observation suggested that there was a time, called the big bang, when the universe was infinitesimally small and infinitely dense.

One can say that time had a beginning at the big bang.

A theory is a good theory if it satisfies two requirements. It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations.

Any physical theory is always provisional, in the sense that it is only a hypothesis; you can never prove it.

The eventual goal of science is to provide a single theory that describes the whole universe. The approach most scientists actually follow is to separate the problem into two parts. First, there are the laws that tell us how the universe changes with time. Second, there is the question of the initial state of the universe.

Today scientists describe the universe in terms of two basic partial theories – the general theory of relativity and quantum mechanics.

**Space and time**

Our present ideas about the motion of bodies date back to Galileo and Newton.

Galileo’s measurement indicated that each body increased its speed at the same rate, no matter what its weight. Newton used his measurement for his laws of motion.

The nonexistence of absolute rest therefore meant that one could not give an event an absolute position in space.

Both Aristotle and Newton believed in absolute time. Time was completely separate from and independent of space.

The fact that light travels at a finite, but very high, speed was first discovered in 1676 by the Danish astronomer Ole Christensen Roemer.

James Clerk Maxwell in 1805 provided a proper theory of the propagation of light. His theories about forces of electricity and magnetism. He fought that waves are traveling around with fixed speed.

Einstein started conversation about abandonment of the idea of absolute time. The theory of relativity put an end to the idea of absolute time.

In the theory of relativity, we now define distance in terms of time and the speed of light. Time is no longer separated from space; they now form space-time dimension.

The event is something that happens at a particular point in space and at a particular time.

The light spreading out from an event forms a (three-dimensional) cone in (the four dimensional) space-time. This cone is called the future light cone of the event. In the same way we can draw another cone, called the past light cone, which is the set of events from which a pulse of light is able to reach the given event. The events that do not lie in the future or past of P are said to lie in the elsewhere of P.

When we look at the universe, we are seeing it as it was in the past.

If one neglects gravitational effects, as Einstein and Poincare did in 1905, one has what is called the special theory of relativity. Einstein made a number of unsuccessful attempts between 1908 and 1914 to find a theory of gravity that was consistent with special relativity. Finally, in 1915, he proposed what we now call the general theory of relativity.

In general relativity, bodies always follow straight lines in four-dimensional space-time, but they nevertheless appear to us to move along curved paths in our three-dimensional space.

New understanding of space and time revolutionize also our view on universe. We can now think about dynamic and expanding universe that seemed to have begun a finite time ago, and that might end at a finite time in the future.

**The expanding universe**

The nearest star, called Proxima Centauri, is found to be about four light-years away.

Hubble found out that ours was not the only galaxy.

The apparent brightness of a star depends on two factors: how much light it radiates (its luminosity), and how far it is from us.

We can tell a star’s temperature from the spectrum of its light.

We can use the Doppler effect and the relationship between the wavelength and speed to estimate stars characteristic and their movement. Visible light consists of fluctuations, or waves, in the electromagnetic field.

The discovery that the universe is expanding was one of the great intellectual revolutions of the twentieth century. Even Einstein was sure that universe is static in the earlier age, he even introduced cosmological constant into his equation – as antigravity force.

The Russian physicist and mathematician Alexander Friedmann made two very simple assumptions about the universe: the universe looks identical in whichever direction we look, and that this would also be true if we were observing the universe from anywhere else. Friedman predicted in 1922, several years before Hubble’s discovery, that universe is not static.

In 1965 Arno Penzias and Robert Wilson from Bell Laboratories found that their detector was picking up a noise from universe and this noise was the same from whichever direction it came.

Bob Dickie and Jim Peebles were working on microwaves based on Gamow idea of dense and white-hot early universe. Penzias and Wilson realized that this was their noise and they won Nobel in 1978.

In Friedmann’s model, all the galaxies are moving directly away from each other. In Friedmann’s model the speed at which any two galaxies are moving apart is proportional to the distance between them.

A remarkable feature of the first kind of Friedmann model is that in it the universe is not infinite in space, but neither does space have any boundary. Gravity is so strong that space is bent round onto itself, making it rather like the surface of the earth.

We shall see later that when one combines general relativity with the uncertainty principle of quantum mechanics, it is possible for both space and time to be finite without any edges or boundaries.

Many people do not like the idea that time has a beginning, probably because it smacks of divine intervention. Some theories that want to avoid big bang moment. One was steady state theory from Hermann Bondi and Thomas Gold and Fred Hoyle.

Roger Penrose in 1965 introduced singularity or big bang moment through collapsing of star into black hole, due to gravity.

Penrose’s theorem had shown that any collapsing star must end in a singularity; the time-reversed argument showed that any Friedmann-like expanding universe must have begun with a singularity.

General relativity is only a partial theory, but so is the quantum mechanics. The effort to combine those two partial theories into a single quantum theory of gravity is the challenge for 21^{st} Century.

**The uncertainty principle**

Marquis de Laplace suggested that there should be a set of scientific laws that would allow us to predict everything that would happen in the universe, if only we knew the complete state of the universe at one time.

The doctrine of scientific determinism was strongly resisted by many people, who felt that it infringed God’s freedom to intervene in the world.

Max Plank suggested in 1900 that light, X rays, and other waves could not be emitted at an arbitrary rate, but only in certain packets that he called quants. Each quantum had a certain amount of energy, that was greater the higher the frequency of the waves, so at a high enough frequency the emission of a single quantum would require more energy than was available. Thus, the radiation at high frequencies would be reduced, and so the rate at which the body lost energy would be finite.

Werner Heisenberg introduced his uncertainty principle in 1926. In order to predict the future position and velocity of a particle, one has to be able to measure its present position and velocity accurately. By Planck’s quantum hypothesis, one cannot use and arbitrarily small amount of light; one has to use at least one quantum. This quantum will disturb the particle and change its velocity in a way that cannot be predicted. The more accurately you try to measure the position of the particle, the less accurately you can measure its speed, and vice versa. Heisenberg showed that the uncertainty in the position of the particle times the uncertainty in its velocity times the mass of the particle can never be smaller than a certain quantity, which is known as Planck’s constant.

Heisenberg’s uncertainty principle is a fundamental, inescapable property of the world.

The uncertainty principle signaled an end to Laplace’s dream of a theory of science, a model of the universe that would be completely deterministic.

Erwin Schrodinger, Heisenberg and Paul Dirac in the 1920’s reformulate mechanics into a new theory called quantum mechanics, based on the uncertainty principle. In this theory particles no longer had separate, well-defined positions and velocities that could not be observed. Instead, they had a quantum state, which was a combination of position and velocity.

Einstein never accepted that the universe was governed by chance. God does not play dice.

The phenomenon of interference between particles has been crucial to our understanding of the structure of atoms.

Niels Bohr in 1913 suggested that maybe the electrons were not able to orbit at just any distance from the central nucleus but only at a certain specified distance.

A nice way of visualizing the wave/particle duality is the so-called sum over histories introduced by Richard Feynman.

**Elementary particles and the forces of nature**

Universe is divided into matter and forces.

John Dalton pointed out in 1803 that it could be atoms that form units called molecules. J.J. Thomson demonstrated the existence of electrons. In 1911 Ernest Rutherford showed that atoms have internal structure – nucleus and electrons.

Up to thirty years ago, it was thought that proton and neutrons were ‘elementary’ particles, but some experiments showed new particles. These particles were named quarks by the Cal Tech physicist Murray Gell-Mann.

There are a number of different varieties of quarks: there are six flavors, which we call up, down, strange, charmed, bottom, and top. Flavor comes in three colors: red, green and blue.

A proton or neutron is made up of three quarks, one of each color.

Particle energies are usually measured in units called electron volts. The energy that electron gains from an electric field of one volt is what is known as an electron volt.

Using the wave-particle duality everything in the universe, including light and gravity, can be described in terms of particles. These particles have a property called spin.

Spins are 0,1,2, and ½. Particles of spin 1/2 make up the matter in the universe, the rest give rise to forces between the matter particles.

The matter particles obey what is called Pauli’s exclusion principle after Wolfgang Pauli. Pauli’s exclusion principle says that two similar particles cannot exist in the same state, that is, they cannot have both the same position and the same velocity, within the limits given by the uncertainty principle. The exclusion principle is crucial because it explains why matter particles do not collapse to a state of very high density under the influence of the forces produced by particles of spin 0,1, and 2.

Dirac theory gave us proper understanding of electron and other spins ½ particles.

Every particle has its antiparticle, with which it can annihilate.

Force-carrying particles can be grouped into four categories according to the strength of the force that they carry and the particles with which they interact.

The first category is the gravitational force. Graviton is particle of spin 2.

The next category is the electromagnetic force. Which interact with electrically charged particles like electrons or quarks. The electromagnetic attraction is pictured as being caused by the exchange of large numbers of virtual massless particles of spin 1, called photons.

The third category is called the week nuclear force. It acts on all particles with spin ½. Abdus Salam and Steven Weinberg both proposed theories that unified this interaction with the electromagnetic force.

The fourth category is the strong nuclear force, which holds the quarks together in proton and neutron. It is believed that this force is carried by another spin 1 particle, called the gluon.

The basic idea of GUT’s (grand unified theory) is that strong nuclear force at high energies gets weaker, the weak nuclear force and electromagnetism get stronger at high energies. Essentially, they all become different aspect of a single force.

GUTs allow quarks to change into antielectrons at high energy and antiquarks into electrons. There was a time in the very early universe when it was so hot that the particle energies would have been high enough for these transformations to take place.

Until 1956 it was believed that the laws of physics follow three symmetries called C, P, and T. C means that the laws are the same for particles and antiparticles. They symmetry P means that the laws are the same for any situation and its mirror image. The symmetry T means that if you reverse the direction of motion of all particles and antiparticles, the system should go back to what it was at earlier times; in other words, are the same in the forward and backward directions of time.

Weak force doesn’t obey P and C symmetry. And the early universe didn’t obey the T symmetry.

**Black holes**

John Weller created the term Black hole in 1969.

In 1783 John Michell pointed out that a star with enough mass could have such a strong gravitational force that light will not escape it.

Subrahmanyan Chandrasekhar calculated that a cold star of more than about one and a half times the mass of the sun would not be able to support itself against its own gravity – Chandrasekhar limit. If star’s mass is less than a limit, it could become ‘white dwarf’. Stars with bigger mass than limit will either explode or as Oppenheimer found out in 1939, could create a region called black hole. Its boundary is called the event horizon and it coincides with the paths of lights rays that just fail to escape from the black hole.

The work that Roger Penrose and I did between 1965 and 1970 showed that, according to general relativity, there must be a singularity of infinite density and space-time curvature within a black hole.

Penrose’s hypothesis of the cosmic censorship states that in a realistic solution, the singularities would always lie either entirely in the future (like singularities of gravitational collapse) or entirely in the past (like the big bang).

How could we hope to detect a black hole, as by its very definition it does not emit any light? As John Mitchell pointed out in 1783, a black hole still exerts a gravitational force on nearby objects.

Black holes are not really black after all; they glow like a hot body, and the smaller they are, the more they glow.

**Black holes ain’t so black**

In 1970 the definition of black hole from Penrose and Hawking was – a set of events from which it was not possible to escape to a large distance.

The second law of thermodynamics has a rather different status than that of other laws of science, because it does not hold always, just in the vast majority of cases.

In 1973 conversation with Yakov Zeldovich and Alexander Starobinsky they proposed that according to the quantum uncertainty principle rotating black holes should create and emit particles.

Black hole ought to emit particles. It was connected with virtual particles.

Planck’s quantum principle tells us that each gamma ray quantum has a very high energy, because gamma rays have a very high frequency.

The idea of radiation from black holes was the first example of a prediction that depend in an essential way on both the great theories of this century (20^{th}), general relativity and quantum mechanics.

The existence of radiation from black holes seems to imply that gravitational collapse is not as final and irreversible as we once thought.

**The origin and fate of the universe**

Einstein’s general theory of relativity, on its own, predicted that space-time began at the big bang singularity and would come to an end either at the big crunch singularity, or at singularity inside a black hole.

Hot big bang model assumes that the universe is described by a Friedmann model. In such models one finds that as the universe expands, any matter or radiation in it gets cooler.

At the big bang itself the universe is thought to have had zero size, and so to have been infinitely hot.

The picture of a hot early stage of the universe was first put forward by the scientist George Gamow in a famous paper written in 1948 with a student of his, Ralph Alpher. They add nuclear scientist Hans Bethe – Alpher, Bethe, Gamow.

Under chaotic boundary conditions, the probability of finding any particular region of space in any given configuration just after the big bang is the same, as the probability of finding it in any other configuration.

In the anthropic principle, we see the universe the way it is because we exist. There are two versions of the anthropic principle. The weak and the strong. Weak – universe is large and infinite, and the conditions for the development of intelligent life will be met only in certain regions that are limited in space and time. Strong – many different universes or many different regions of a single universe.

In quantum theory, particles can be created out of energy in the form of particle/antiparticle pairs.

Andrei Linde, Paul Steinhardt and Andreas Albrecht created the new inflationary mode of universe expansion based on the idea of a slow breaking of symmetry. Now this theory is a dead scientific theory.

When we apply Feynman’s sum over histories to Einstein’s view on gravity, the analogue of the history of a particle is now a complete curved space-time that represents the history of whole universe.

The boundary condition of the universe is that it has no boundary. Maybe time and space together formed a surface that was finite in size but did not have any boundary or edge.

Using sum over histories, our universe is not just one of the possible histories but one of the most probable ones.

The real importance of the singularity theorems was that they showed that the gravitational field must become so strong that quantum gravitational effects could not be ignored.

**The arrow of time**

Theory of relativity introduced personal aspect of time. Before it was more absolute concept. The laws of science do not distinguish between the past and the future.

Three arrows of time: thermodynamic, psychological and cosmological.

Our subjective sense of the direction of time, the psychological arrow of time, is determined within our brain by the thermodynamic arrow of time.

**Wormholes and time travel**

The first indication that the laws of physics might really allow people to travel in time came in 1949 when Kurt Godel discovered a new space-time allowed by general relativity. He was famous for proving that it is impossible to prove all true statements. Godel’s incompleteness theorem may be a fundamental limitation on our ability to understand and predict the universe.

A wormhole is a thin tube of space-time which can connect two nearly flat regions far apart. In 1935, Einstein and Nathan Rosen wrote a paper in which they showed that general relativity allowed what they called ‘bridges’ but which are now known as wormholes.

The reason we say that humans have fee will is because we can’t predict what they will do.

The radiation by black holes shows that quantum theory allows travel back in time on a microscopic scale and that such time travel can produce observable effects.

**The unification of physics**

It would be very difficult to construct a complete unified theory of everything in the universe all at one go. We have made progress by finding partial theories that describe a limited range of happening and by neglecting other effects or approximating them by certain numbers.

The main difficulty in finding a theory that unifies gravity with the other forces is that general relativity is a ‘classical’ theory; that is, it does not incorporate the uncertainty principle of quantum mechanics.

In attempting to incorporate the uncertainty principle into general relativity, one has only two quantities that can be adjusted: the strength of gravity and the value of the cosmological constant. But adjusting these is not sufficient to remove all infinities.

String theory, the basic objects are not particles, which occupy a single point of space, but things that have a length but no other dimension, like and infinitely thin piece of string.

String theories have bigger problem: they seem to be consistent only if space-time has either ten or twenty-six dimensions, instead of the usual four. The other dimensions are curved into a space of very small size.

**Conclusion**

In the nineteenth and twentieth centuries, science became too technical and mathematical for the philosophers, or anyone else expect a few specialists. Philosophers reduced the scope of their inquiries so much that Wittgenstein, the most famous philosopher of this century, said ‘The sole remaining task for philosophy is the analysis of language.’ What a comedown from the great tradition of philosophy from Aristotle to Kant.