Last year I read Black Holes and Baby Universes and other essays by Stephen Hawking. It literally exploded my mind. In the book he has wondered in many places how many people have ACTUALLY read A Brief History of Time, his all time bestselling book first published in the year 1988. He has this idea that a lot of people buy the book no doubt but then just use it as home decoration.
It was like he knew me personally and talking about me! It is really embarrassing how long I have been meaning to read the book. After reading him rebuking me personally (almost) I promised myself to read A Brief History of Time: From Big Bang to Black Hole this year no matter what.
This piece is not a review but summing up of the information given in the book. So it is more like a companion to the book.
The introduction of the book is written by Carl Sagan. Sagan states this book is for non-specialists. This book covers the fields of physics, astronomy, cosmology, courage and God. Einstein had famously asked if God had any choice in creating the universe. According to Sagan in this book Hawking has tried to understand the mind of God vis-à-vis universe. And also is there a God or an absence of God?
It is better to read the chapters in the book in sequence because there is certain continuity.
Chapter 1: Our Picture of the Universe
(i) It gives an empirical study of the history of scientific thoughts in western world on the position of earth vis-à-vis universe.
Aristotle-Ptolemy theory states earth is sphere in shape and stays stationary. Sun, moon and 5 planets (known at that time) revolve around earth in 8 spherical paths. But for this Ptolemy had to assume moon follows a path, which brings moon halfway closer to earth some time. So on some night moon’s size should be doubled. Ptolemy himself accepted this fallacy in his theory. Yet Christian church accepted this theory because outside the 8 spheres this theory leaves a lot of space for heaven and hell.
Nicholas Copernicus first came up with the theory of a stationary sun and planets revolving around it in circular paths. Later Johannes Kepler and Galileo Galilei supported this theory publicly. Kepler also theorised the shape of revolving paths of planets to be elliptical. He had this idea that planets are made to revolve around sun due to magnetic forces. But he could not develop the idea.
Then Sir Isaac Newton published Philosophiae Naturalis Principia Mathematica in 1687. According to Hawking this probably is the most important work in physical sciences because it gives logically the nature of planets’ revolving around Sun. Newton mathematically explained the elliptical shapes of orbits (revolving paths). He postulated a law of universal gravitation to explain the reason behind orbiting.
(ii) Nature of universe
If universe is finite then following universal gravitation law all bodies will collapse into the midpoint of the universe. This does not happen so this may imply universe is infinite and there’s no definite midpoint. But is this infinite universe stationary or expanding? Using a couple of simple logics Hawking says universe is expanding.
(iii) Origin of universe
According to Abrahamic religions the universe begins in 5000 BC (given by St. Augustine). This is in a way logical because civilization as we know it today, really begins in 5000 BC. Although universe is much older. Greek philosophers assume universe has no beginning but to explain the limited development achieved by human they give a cyclical great flood or other natural disasters. This theory is based on the idea that time is eternal, but is it? Science till now favours big bang. At big bang universe was infinitesimally small and infinitely dense. The universe has been expanding as the aftermath of the big bang explosion.
(iv) Time
There was no concept of time before big bang nor there is physics. Interestingly enough this idea was first propagated by St. Augustine, who had said there was no time before God created the universe.
(iv) Mechanisms used to study universe
A good theory must describe a large class of observations and it must be able to predict correctly. Any theory can be scrapped if even one experiment does not agree to it. In real life old theory is not always scrapped. Some time the new theory is only an extension of old theory. Newton’s theory of gravity is still used as it is easy to use and its prediction is only slightly off from Einstein’s general theory of relativity, the most accurate theory.
Today scientists use two partial theories to explain universe.
~ General theory of relativity – large structures of universe
~ Theory of quantum mechanics – phenomena of extremely small scale
Unfortunately both theories are inconsistent with each other. There have been efforts to combine these two theories.
There should be a unified theory explaining the universe.
Paradox of the unified theory: If it explain all phenomena maybe it will predict our failure to have a unified theory.
Using Darwin’s principle of natural selection Hawking predicts the nature will help us in finding a unified theory. Because natural selection gives us the capacity to find whatever is required for our survival or at least it will not lead us to wrong conclusion regarding unified theory.
(v) God
An expanding universe does not preclude a God but it puts a limit of God’s function. One may say God is managing the world in anyway he wants. That’s true he can run the world in any arbitrary way but he is running it following the strict laws of physics, that is limitation on his functioning. Since there is definite laws regarding functioning it is natural to assume that there should physics laws about origin too.
This is not a very difficult chapter to understand for average readers.
Chapter 2: Space and Time
(i) Motion
Aristotle was of the view is the natural state of an object is being at rest. Motion happens because of force or impulse. Also Aristotelian tradition is of the view that any scientific theory can be imagined in one’s mind. There is no use of experimentation or observation.
Galileo first observed two objects of different weight fall on ground from some height at the some velocity and acceleration (rate of increase in velocity). Unless one is taking a iron ball and a feather. For very light object like feather the speed slows down because of air resistance.
Newton uses Galileo’s observations as basis for his laws of motion.
1st law: Natural state of an object is to move at a uniform speed on a straight line (going against Aristotle). When force is applied the object may come to rest, change direction, or change speed.
2nd law: The change of speed (acceleration) is directly proportional to applied force (as force is increased the speed increases). Acceleration is smaller the greater is the mass of the object.
Newton also discovered a universal law of gravity, according to which every body attracts every other body with a force proportional to its mass and inversely proportional to the distance between the bodies.
This is why all bodies fall at the same rate. The heavier body will have more gravitational pull (universal law of gravity) but more mass will reduce the speed (2nd law of motion). So both affects cancel each other out.
The gravity law predicts the shapes of orbits with great accuracy.
If the gravitational attraction increases at a faster rate when the gap between bodies reduces then the planets will spirally fall into sun.
If the gravitational attraction goes down slower as the gap between bodies increased then gravitational forces from distant stars could dominate earth.
Galileo and Newton are against Aristotle regarding preferred state as there is no unique standard of rest. For instance someone travelling in a train going at 100 kilometres per hour is sitting inside the train. According to him he is at rest while for someone watching him from outside the train he is travelling at 100 kilometres per hour.
The non-existence of absolute rest means there can’t be an absolute position in space. Newton worried by these conclusions as it clashed with his believe in an absolute God. He ended up rejecting his own theories.
Both Aristotle and Newton believed in absolute time, independent from space.
(ii) Light
Light travels at a very high but finite speed was discovered in 1676 by Christensen Roemer.
James Clark Maxwell’s equation on 1865 predicted in a combined electromagnetic field there can be a ripple or wave like disturbances. Wavelength is the distance between one wave crest and the next.
Wave length equal to or great then a metre à radio waves
Wave length equal of few centimetres à micro waves or infrared
Even shorter wavelengths are known as ultraviolet, X rays, and gamma rays
Visible light has wavelength between 40 to 80 millionths of a centimeter
Since Newton’s theory got rid of fixed state the light has to travel with respect to something. So if light travels at a fixed speed the speed should be calculated with respect to something. This “something” is taken to be ether.
So speed of light measured in the direction of earth’s motion around sun (when we are moving towards the source of light) should be higher than the speed of light measured at the right angles to the motion (when we are not moving towards the source of light). But Michelson-Morley measured the speeds in these positions and found the speeds to be equal in both positions.
So Einstein came up with the theory to chuck out the ether. Speed of light is uniform compared to everything if one is willing to abandon the concept of absolute time.
(iii) Theory of relativity
The basic postulate of the theory is the laws of physics should be the same for all freely moving observers, no matter what the observers’ speed be.
This postulate has many remarkable consequences such as the equivalence of mass and energy summed up in equation E =MC^2 and nothing may travel faster than light.
Because of equivalence of mass and energy, when an object is in motion the energy gained through motion is added to the mass.
Hence, increase in speed of object A à increase in energy of A à increase in mass of A à reduction of speed (because of Newton’s second law)
So as the speed increases, speed also has to come down. This self destructing phenomenon can’t allow A to move at a very high speed (or at a speed of light)
Only light, or other waves that have no intrinsic mass, can move at the speed of light.
This theory puts an end to the concept of absolute time. Suppose A, B, and C are travelling separately in space holding individual clocks. An event happens at a single point. A, B, and C will record the time of the event looking at their individual clocks. They will assign measurements of times and positions to the event depending on their own positions.
The measurements are different but in no way, one is more correct than others. But the measurements are related. A can calculate the measurements given by other two if relative velocities of B and C compared to A’s velocity is known to A.
(iv) Space
Each space is defined in terms of 3 coordinates. But the coordinates are not fixed.
For instance we can say “my house is on the left side of Tabassum salon”. This is meaningless for someone not living in my area. If they are in a different area but same city I will describe the space of my house in a different way. For someone out of the city it will be another way and so on.
Similarly we can say earth is near Mars with reference to our solar system. But for a hypothetical person living outside Milkyway “near Mars” is meaningless.
One may describe the whole universe in terms of a collection of overlapping patches. In each patch, we can use a different set of 3 coordinates to specify the position of a point.
(v) Time
An even happens at a particular point in space and time. We can add time to 3 coordinates and make it 4 coordinates or 4 dimensional space called space-time.
In relativity there is no real difference between coordinates. Because one can show Delhi in comparison to Mumbai or New York, it does not matter.
(vi) Light funnels
When a pulse of light is emitted it creates 2 cones on both side. One is future light cone and other one is past light cone.
Past light cone describes all events leading to point 0, which is the emission of light. Future cone depicts where the light will travel in the future as compared to the point of emission. For every event in the universe a light cone can be created.
(vii) General theory of relativity
The special theory of relativity is inconsistent with the Newtonian theory of gravity. Einstein tried to make both compatible without success. Finally in 1915 he suggested this general theory.
He said gravity is not a force but a consequence of the fact that space-time is not flat but curved/warped.
Bodies like earth don’t revolve in orbit because of gravity but they always move in a straight line on 4 dimensional space, which appears to be curved to our eyes used to 3 dimensions.
Since space is curved light does not travel in a straight line.
Light should bent by gravitational field according to this theory. Hence light slightly bents inward when comes near to sun because of its mass which creates the gravitational field. So when we observe far away star we may see their position wrong as the light from them bent near sun. On the days of eclipse (in absence of sunlight) the positions of faraway star can be observed more correctly.
Another prediction of this theory is that time appears to move slowly near heavy body like earth. This is because there is a relation between the energy of light and its frequency (number of waves of light emitted per second). The greater the energy, the higher the frequency. As light travels upward and away from earth’s gravitational field, it loses energy so frequency becomes lower hence less waves would be emitted per second or length of time from one wave crest to another goes up. To someone high up it would appear things are happening slowly on earth.
Various experiments and observations have confirmed this general theory of relativity. Like observing stars during full eclipse, or comparing time in watches kept on ground and on a high tower etc.
This is not exactly a difficult chapter but in many places there are ambiguities mostly owing to language. A better editing would have made a big difference.
Chapter 3: The Expanding Universe
Till very recently (1920s) the scientist community strongly believed the universe is static.
The whole universe is in motion but when we see the night sky we can detect the changing position of the bodies nearer to Earth, the other bodies seem to be static in position. To the naked eyes the stars in the night sky may look to be spread over the whole sky. But actually stars are concentrated around arms of an imaginary spiral called milky way, our galaxy (group of stars in comparatively close proximity).
First pictures of universe are taken by Edward Hubble in 1924. He found ours is not the only galaxy. There are others.
Edward Hubble worked out distances to 9 galaxies using the following method.
The apparent brightness of a star depends on two factors: its luminosity and distance from earth
For nearby stars apparent brightness and distance are known so luminosity can be worked out.
If we know luminosity of the faraway stars, by measuring their apparent brightness the distance can be worked out.
With modern telescopes we can see some hundred thousand million galaxies.
Our galaxy is about one hundred thousand light-years across and slowly rotating.
Newton discovered when light passes through triangle-shaped piece of glass (prism) it breaks down into its component colours (its spectrum). On focusing telescope on a star or galaxy the spectrum of their light can be observed.
We can tell the temperature of a star by observing its spectrum of light.
We can tell the elements present in a star by the colour missing from spectrum of its light. A specific element absorbs a characteristic set of very specific colours. Hence missing colours connects us to the elements present in the star.
Doppler effect:
We know light travels in waves with high frequencies ranging from 4 to 7 hundred million million waves per second. In this range, lights of different frequencies appears of different colours to human eyes. Lowest frequencies appear at the red end of the spectrum and highest frequencies appear at the blue end of the spectrum.
If a star is stationary the frequency of its emitted light would be constant. If it is coming nearer, the frequency will be higher than stationary position and the opposite if the star is moving away from us.
More galaxies are found to be red-shifted à lower frequency à stars moving away from us
In 1929 Hubble found the size of a galaxy’s red shift is proportional to its distance from us.
This proved the universe is expanding. Hawking calls it “one of the great intellectual revolutions of 20th century.
Hawking felt Newton and Einstein could easily have inferred this long back based on their theories.
Newton: Universe has to expand at a rate above a critical rate. If universe is not expanding or expanding slowly then gravitational force would finally contract the universe.
Einstein: His general theory of relativity predicted the universe is expanding but he was so hung up on static universe that he introduced a term, cosmological constant, just to balance the effect of expansion.
Alexander Friedmann was willing to take the general theory of relativity without cosmological constant.
He took 2 assumptions:
The universe looks identical in whichever direction we look.
This would be true if we observe from any point of universe.
These two assumptions are not accurate if one focuses on small scale but for the bigger picture it is not wrong.
In 1965 Arno Penzias and Robert Wilson observed this while testing very sensitive microwave detector. The detector picked up noises in whichever direction it was directed at any time.
Bob Dicke and Jim Peebles said the glow of the dawn of the universe can still be seen as that glow from farthest part of universe reaching us now. Those would be too red shifted and appear as microwave radiation to us.
There can be 3 models based on Alexander Friedmann’s assumptions.
Universe is expanding slowly so gravitational attraction finally put a stop to expansion. Universe is not infinite in space but space has no boundary. Gravity is so strong that space is bent round onto itself like earth but in 3 dimension.
Universe is expanding so rapidly that gravitational attraction can never stop the expansion. Space is infinite and bent like a saddle.
Universe is expanding only fast enough to avoid collapse. Space is infinite and flat.
To know the specific model describing our universe we must know the rate of expansion of universe and present average density.
Present rate of expansion can be calculated by using Doppler effect to measure the velocities at which galaxies are moving away from us. It is estimated that universe is expanding y between 5% and 10% every thousand million years.
There is great uncertainty over present average density of the universe. If this density is less than a certain critical value the gravitational attraction will be too weak to stop the expansion.
If we add up densities of all stars we know the total is one hundredth of the critical value.
Galaxies contain dark matter, which can’t be observed directly. We know their existence because of their gravitational effect on other stars and galaxies. If we add up dark matter with stars we get only one tenth of the critical value.
Hence probably universe will expand forever. At least it will not collapse before ten thousand million years, same as the period it has been already expanding.
In all three scenarios universe starts at 0 and expands. That 0 is big bang. At that time density of the universe and space-time curvature would be infinite. Since mathematical theories don’t work for infinite numbers. All physics theories are based on the assumptions that space-time curvature is almost flat. Hence the theories of physics can’t be applied to the time at and before big bang. One has to assume time starts after big bang and events before that is irrelevant.
Many people in the beginning did not like the idea of there’s a beginning of time, especially the religious people. So scientists try to develop other theories on universe, which does not involve a big bang.
The steady state theory is one such theory, suggested in 1948. According to this theory due to continuous creation of new matter the universe is in the same state forever. The general theory of relativity can adapt to this idea with a minute change. The prediction of the theory that the number of galaxies or similar objects in any given volume of space should remain constant wherever and whenever we look.
But the observed non-uniform radio waves and microwave radiation indicating much denser universe in the past debunked the steady state theory.
Theory of Ebgenii Lifshitz and Isaac Khalatnikov:
In Friedmann’s model since the galaxies are moving away from each other, it can be inferred once they were together. But in real world the galaxies are moving away from each other but also they have small sideways velocities so it is not necessary they were together in the past. They might have been at a close distance from each other in past. So one can think the beginning was not a singularity like big bang but a contracting phase.
They initially felt there are infinitely more Friedmann like models without a big bang singularity. But later they realised there are much more general class of Friedmann like models with singularities in which the galaxies don’t have to move away in a certain way.
They withdrew their theory.
Penrose’s theorem:
Any body undergoing gravitational collapse must eventually form a singularity.
Roger Penrose showed that a star collapsing under its own gravity is trapped in a region whose surface eventually shrink to zero size hence volume will also be zero. Since all matter in it would shrink to volume zero, its density will be infinite. The curvature of space-time will also be infinite.
It is a singularity contained within a region of space-time known as black hole.
Hawking decided to work on this theorem for his PhD thesis. He reveres the sequence so singularity becomes matter. He wrote a joint paper with Penrose to combine the two with required mathematics.
This established big bang beyond doubt. But this made few people unhappy. Ironically, later Hawking changed his mind about the singularity in the beginning.
Since general theory of relativity can’t predict how the universe started, it is a partial theory.
According to big bang the singularity is very very small. For that small-scale another theory works, it is the quantum mechanics.
Chapter 4: The Uncertainty Principle
Because of success of many scientific theories, in the beginning of the 19th century, scientist Laplace argued the universe including human behavior, is completely deterministic. A set of scientific laws should be able to predict and govern everything. However Laplace’s dream is shattered by the uncertainty principle.
It started with Rayleigh and Jeans suggesting that a hot object, or body, such as a star, must radiate energy at an infinite rate. This is because the number of waves a hot body radiates in a second is unlimited and hot body radiates energy in waves.
Planck rectified this result. He said waves couldn’t be emitted at an arbitrary rate. They emit in packets called quanta. Each quantum has a certain amount of energy, which is directly proportional to the frequency of the waves. As frequency becomes higher the emission of wave will require more and more energy. So at one point frequency will become so high that the required energy won’t be available. So the rate which body radiates energy will be definite.
WERNER HEISENBERG’S UNCERTAINTY PRINCIPAL
The more accurately one wants to measure the position of a particle the less accurately they can measure the velocity of it and vice versa.
To know the position of the particle light shined on it. After this the exact position is not known but a range is known. This range is same as the distance between the wave crests of the wave of the light shined on it. So to get more accurate result, it should be preferable to reduce the distance between the wave crests of the wave. So light with shorter wavelengths is preferred to know the position better.
We already know we have to use at least one quantum of light wave not less than that. As wavelength gets shorter the energy of single quantum becomes higher. Higher energy of light wave will disturb the velocity of particle more. So it will become more difficult to determine the velocity.
Heisenberg showed
(Uncertainty in position * uncertainty in velocity*mass of the particle) can never be smaller than Planck’s constant
Since we can’t even measure the particle’s position and velocity accurately at present how can we predict the future. This brings an end to the deterministic idea.
QUANTUM MECHANICS: Mechanics reformulated by incorporating uncertainty principle. According to this, particles no longer have well defined positions, velocities etc. They are in a quantum state, a combination of position and velocities. There is no definite result but a group of possible outcomes with probabilities.
Instead of playing a big role in development of this theory, Einstein opposed the theory because according to him “God does not play dice” or universe is not left to randomness.
In all fields of science quantum mechanics has been incorporated successfully, except in gravity and large scale structure of the universe.
DUALITY BETWEEN WAVES AND PARTICLES: Planck’s quantum hypothesis given the idea that waves in some ways behave like particles. While Heisenberg’s uncertainty principle implies particles in some respects behave like waves.
This duality helps in taking waves as particles some time and vice versa some other time in quantum mechanics.
An important consequence of this duality is interference between two sets of waves or particles. The crests of one set of waves may coincide with the troughs of another set of waves. The two sets cancel each other out instead of adding up together to make a stranger wave.
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STRUCTURE OF ATOM: As we know in an atom electron revolves around the nucleus. Without quantum mechanics the available theories predicted electrons would lose energy over time and its orbit will spiral down and finally electron will collapse into the nucleus.
This implies matters will rapidly collapse into a state of very high density.
Niels Bohr suggested this actually will probably not happen because maybe electron may revolve around nucleus only at a specified distance. So the electron can’t change its orbit or can’t spiral down. But this model could not explain any atom more complex than hydrogen.
Quantum mechanics resolved this problem. Revolving electron can be taken as wave, with a wavelength depending on its velocity. In the orbits where wavelengths are whole number, wave crests would be at the same position each time round so waves would add up. But if wavelengths are fractions, the crest will be cancelled out by troughs.
Full number
/\/\/\/\
/\/\/\/\
Fraction
/\/\/\/
\/\/\/\
Hence only those wavelengths are possible which don’t cancel each other out, these are the probable orbits as stated by Bohr.
SUM OVER HISTORIES: In this concept introduced by Feynman there is not a single history or path in space-time, in quantum theory. A particle can take all paths from A to B. Each path has two numbers: size of a wave and position in cycle. The probability of going from A to B can be found by adding up all waves. The paths for which the waves don’t cancel each other correspond to Bohr’s allowed orbits.
GENERAL THEORY OF RELATIVITY: General theory of relativity does not account for quantum theory and generally this does not create any issue. However, this will be an issue when gravitational field is very strong like in case of black hole and big bang.
There has not been successful incorporation of these two theories but we do know the features the unified theory must possess.
Chapter 5: Elementary Particles and Forces of Nature
Aristotle believed everything in universe is made up of 4 basic elements – earth, fire, air, and water. Two forces work on elements – gravity (sinking of earth and water), levity (rising of fire and air). This division of contents into matter and force is still used today.
HISTORY
Aristotle believed matters are continuous. It can be divided into smaller pieces without limit. Democritus believed there is a small particle called atom. Every matter is made up of different kinds of atoms.
Einstein in 1905 gave his verdict in favour of Democritus. But it was suspected, atom is not the smallest part of a matter.
In 1911 Rutherford showed atom has a tiny positive charged nucleus around which negatively charged electron revolve. In 1932 Chadwick discovered nucleus has a part called neutron, which does not have any charge.
Later it was found out electron, proton, and neutron are not basic particles. They are made of smaller particles called quarks.
KINDS OF QUARKS
There are quarks of at least 6 flavours – up, down, strange, charmed, bottom, and top.
Each flavour comes in 3 colours – red, green, and blue.
It should be noted here colour and flavour are not used in their traditional senses. These are just labels. Quarks are much smaller than wavelength of visible light so they don’t have any colour in the normal sense.
A proton contains 2 up and 1 down quark. A neutron contains 2 down and 1 up quark. Any other combination will be unstable and finally would reduce to the above-mentioned combo.
Wavelength of light is larger than size of atom. Hence it can’t observe atom. We need something with wavelength less than size of atom to observe it. We know higher the particle energy lower the wavelength of corresponding wave.
With development in science we are being able to generate more and more particle energy hence smaller wavelength possible, which can observe smaller atom particle over time. This way we have gone discovering from atom to electron, neutron, proton to quarks.
SPIN
Particles have a property called spin. But uncertainty principle tells us particles don’t have well defined axis so this spin does not mean spinning around an axis like a top. This spin tells us how a particle will look from different directions. Particles of spin ½ makes all the matter in the universe. Particles of spin 0, 1, and 2 give rise to forces between particles.
Spin 0 – a dot and will look the same from all directions
Spin 1 – an arrow with one head, particle will look same only with a 360 degree revolution
Spin 2 – A double headed arrow, particle will look same with a 180 degree revolution
Spin ½ – They look same after two complete revolutions
PAULI’S EXCLUSION PRINCIPLE
Two similar particles can’t exist in same state, that is, having the identical position and velocity. This has helped atom particles create separate and well defined atoms. In the absence of this principle all would have collapsed into a soup.
INTERACTIONS BETWEEN PARTICLES
In quantum mechanics all interactions between matter particles are supposed to be carried away by particles of integer spins 0,1, and 2. This interaction happens thus – A matter particle emits a force carrying particle then matter particle recoils hence there’s change in its velocity. The force-carrying particle collides with a second matter particle and gets absorbed. The collision changes the velocity of the second matter particle.
FORCE-CARRYING PARTICLE
Force-carrying particles don’t follow Pauli’s exclusion principle. There is no limit to how many force-carrying particles will be exchanged. But with the combination of force-carrying particles as the mass increases the range they cover becomes shorter. The force-carrying particles are sometime can be detected by a particle detector and sometime not. When they are not detected they are called virtual particles but their effect can be measured.
Force-carrying particles can be divided into 4 man made categories. Although the long term of goal of physicists is to find a unified theory for all kinds of force-carrying particles so that forces can be explained as different aspects of the same force.
CATEGORIES OF FORCE-CARRYING PARTICLE
1. Gravitational force
This is the weakest of all 4. This force is universal, works over large distances, and always attractive. This force-carrying particle called the graviton has spin of 2 and no mass. For instance, the attraction between Sun and Earth is due to exchange of graviton between the matter particles, which make up these two bodies.
2. Electromagnetic force
This is a strong force but it interacts only with electrically charged particles, not with uncharged particles such as graviton. Hence the positive and negative charged particles cancel each other and there is little net electro magnetic force in the universe. The revolution of electron around nucleus happens because of this force.
The electronic magnetic attraction happens because of exchange of spin 1 massless particles named photons.
3. Weak nuclear force
This is responsible for radioactivity and works only on particles with spin ½.
4. Strong nuclear force
This force holds quarks together in proton and neutron and also holds proton and neutron together in nucleus. This force is carried by a spin 1 particle called gluon. It interacts only with itself and with quarks.
It has an interesting property called confinement. It always binds particles together into a combination that has no colour.
Because of this property we can’t have a single quark because it will have a colour. If there is a combination of quark and antiquark make a particle called mesons. This is unstable as quark and antiquark annihilate each other.
Similarly it is not possible to find a single gluon, which will have a colour. Instead we will have collection of gluons forming an unstable particle called a glueball.
There is another property called asymptotic freedom. At very high energies strong force becomes weak and quarks and gluons behave almost like free particles.
GRAND UNIFIED THEORY
At very high energy strong nuclear force becomes weak whereas weak nuclear force and electro magnetic force become strong. Because weak nuclear force and electro magnetic force are not asymptotically free. So at a strong energy all 3 forces should have same strength. At this high energy quarks, electrons, anti-electrons would all be essentially same.
But it is not feasible. For that kind of energy generation a machine as big as our solar system is required.
At the high energy level the 3 quarks inside proton turn into antielectron and thus resulting into spontaneous proton decay. We can’t generate such high energy but the reverse has been the reason behind our existence. In the beginning the high leftover energy after big bang created protons from antielectron.
C, P, T SYMMETRIES
Till 1956 it was believed laws of physics obeyed these three separate symmetries.
Symmetry C – Laws are same for particles and anti-particles
Symmetry P – Laws are same for any situation and its mirror image
Symmetry T – Laws are same in the forward and backward directions of time
After 1956 it was proved that the weak force does not obey C and P but obeys combined CP. That is, the universe will develop in the same way as its mirror image if in the mirror image all the particles are swapped by anti-particle.
Does this remind you of Lewis Carroll’s Through The Looking Glass?
Cronin and Forth showed laws of physics must change if one reverses the direction of time or they don’t obey symmetry T.
Early universe did not obey symmetry T. As time passes the universe expands. There are forces that don’t obey T. These forces ensure that more antielectron turns into quarks than electron turning into antiquarks. Finally quark and antiquark cancel each other with leftover quarks created everything including us. So our existence is the qualitative proof of grand unified theories.
In this unified theories gravitational force is not included. Its size is insignificant so it does not matter at atom level. But since the force works in long range and always attractive, at large level it can dominate over all forces. Gravity determines the evolution of the universe.
Chapter 6: Black Holes
Black hole is a comparatively new term coined in 1969 by John Wheeler as a graphic description of a two hundred year old idea.
John Michell in 1783:
A massive and compact star can have such strong gravitational field that light can’t be emitted from its surface. It is dragged back.
These are black holes. We can’t see them as light does not emit from these bodies. We can only feel their gravitational attraction.
Few years later Laplace also came up with this idea, independently supposedly.
Light is particle or wave:
Initially light is thought to be made up of particles then it will be affected by gravitational force. Then light is thought to be made up of waves. Waves are not affected by gravitational force. But the particle-light duality in theory of relativity confirms affect of gravitational force on light hence the phenomenon mentioned by John Michell.
A star is born:
When large amount of gas (mostly hydrogen) starts to collapse in on itself due to the gravitational attraction. As it contracts the atoms of the gas collide with each other more frequently at greater speed. This makes the gas to heat up. Eventually the gas will be so hot that the atoms colliding with each other will not bounce away from each other but they will fuse together to form helium atoms.
The heat released from this chemical reaction balances the gravitational force among the atoms. So the star will stop contracting. Thus star will stay stable as long as hydrogen atoms are made into helium atoms while releasing heat.
Death of a star:
Eventually star will run out of hydrogen. With absence of a heat to balance gravitational force, the pull among atoms will contract.
The bigger a star, the more fuel it needs, hence sooner the hydrogen runs out and hence sooner it will start to contact.
Our Sun has got fuel for perhaps another five thousand million years.
Subramanyan Chandrasekhar:
He researched on how big stars can sustain after they exhaust all their fuel. According to Pauli’s exclusion principle atoms can’t have same velocity and position. So when atoms come very near to each other, their velocity must differ and thus taking them away from each other. This will protect the stars from contracting.
But there is a limit Pauli’s exclusion principle can help in protecting stars. Chandrasekhar defined a limit to know about life cycle of stars.
He calculated that a cold star of more than about one and half times the mass of the Sun would not be able to support itself against its own gravity. This came to be known as Chandrasekhar Limit.
If a star’s mass is less than this limit, then it contracts and settle down to be a white dwarf star.
Stars with masses above the limit may explode.
Chandrasekhar faced lots of hostility from scientist community regarding his theory hence he had to abandon this study. However, his study shows the world Pauli’s exclusion principle can’t avert collapse of stars. Thus clearing the path for research on black hole.
Black hole and event horizon:
The gravitational field of a star changes the path of light rays in space-time from what would have been their path in absence of star. When the star shrinks to a certain critical radius, the gravitational field of the star becomes so strong that light bends inward and can’t escape. This shrunken star is called black hole. Its boundary is called event horizon, which coincides with the path of the light ray that fail to escape. It acts as an one way membrane around the black hole.
According to theory of relativity, there must be a singularity of infinite density and space-time curvature within a black hole. This is end of time, just like singularity at big bang is beginning of time.
Roger Penrose’s cosmic censorship hypothesis:
Weak hypothesis states it protects observers who remain outside the black hole from the consequences of the breakdown of predictability that occurs at the singularity, but it does nothing at all for the poor unfortunate astronaut who falls into the hole.
Strong hypothesis states that in a realistic solution, the singularities would always lie either in the future or entirely in the past.
Shape of black hole:
Any nonrotating star of any kind of shape and internal structure, after gravitational collapse it becomes a perfectly spherical black hole. The size of the black hole depends only on the mass of the star.
In case of rotating star, after gravitational collapse black hole bulges outwards near its equator (like Earth’s shape). The faster it rotates bigger the bulge.
Hawking proved that any stationary black hole would indeed have an axis of symmetry.
After gravitational collapse a black hole must settle down into a state in which it could be rotating but not pulsating.
Proof of black hole:
Initially there was no observational evidence of black hole, only mathematical calculations.
First evidence came in in 1963 in form of anomaly in observed red shift. It was too large to be caused by a gravitational field.
In 1967 Jocelyn Bell found positive evidence that neutron stars existed. A neutron star is only few times larger than black hole. So if stars can contracts to size of neutron stars they can further contracts and become black holes.
How to detect black holes:
Astronomers have observed many systems in which two stars orbit around each other, attracted toward each other by gravity. They also observe systems in which there is only one visible star that is orbiting around some unseen companion.
One such system is named as Cygnus X-1.
From the observed orbit of the visible star, one can determine the lowest possible mass of the unseen object. In case of Cygnus X-1, this is about 6 times the mass of Sun, which according to Chandrasekhar’s result, is too great for the unseen object to be a white dwarf or a neutron star. It must be a black hole.
The number of black holes in universe maybe greater than visible stars. The extra gravitational attraction of such a large number of black holes could explain why our galaxy rotates at the rate it does, the mass of the visible stars is insufficient to account for this.
We have some evidence that there is a huge black hole, of hundred thousand times mass of Sun, at the centre of our galaxy.
As the matter spirals into black hole, it would make black hole rotate in the same direction, causing it to develop a magnetic field.
Primordial black hole:
Low-mass black holes could form only if matter was compressed to enormous densities by very large external pressures. Such large pressure is not feasible by man. A more practical possibility is that such low-mass black holes might have been formed in the high temperature and pressures of the very early universe. Primordial black hole depends on the conditions of the early universe.
Black holes are not black but they glow like hot bodies. The smaller the size the brighter they glow hence easier to detect.
Chapter 7: Black Holes ain’t so Black
It is a bittersweet experience to see Hawking’s partner in the research on black hole in the context of general relativity, Roger Penrose getting 2020 Nobel prize in physics for the same research. Hawking is being badly missed.
Before 1970 Hawking’s research on general relativity was in the area of big bang singularity. But after 1970 his focus shifted to black hole.
THE CONVENTIONAL DEFINITION OF BLACK HOLE USED TODAY IS GIVEN BY HAWKING-PENROSE:
The set of events from which it was not possible to escape to a large distance.
The boundary of the black hole known as event horizon, is formed by the paths in space-time of rays of light that just fail to get away from the black hole, hovering forever just on the edge.
These rays of light must move away from or be parallel to each other. They should never approach each other. What is the problem if they approach each other?
Hawking’s explanation is at best fuzzy in the book. From Internet I found out if they approach each other they annihilate each other and thus reducing the area of event horizon.
The area of the event horizon might stay the same or increase with time but it could never decrease.
THE NON-DECREASING PROPERTY:
If two black holes collide and merge together to form a single black hole, the area of event horizon of the final black hole will be greater than or equal to the areas of the event horizons of the initial two black holes.
This property is similar to the behavior of a physical quantity called entropy.
Entropy: Degree of disorder of a system
SECOND LAW OF THERMODYNAMICS:
When two systems are joined together, the entropy of the combined system is greater than the sum of the entropies of the individual systems.
This law has a different status than other laws of science because it does not hold always, only in vast majority of cases.
From his discussions with scientists from all over the world Hawking came to know black hole appears to be emitting particles and radiation.
Jacob Bekenstein suggested that the area of the event horizon is a measure of the entropy of the black hole. So if a box carrying entropy falls on black hole. Some entropy went inside black hole and some fell outside. The total entropy (after falling) is calculated by summing over area of event horizon and the entropy outside the black hole. After entropy falls the area of event horizon goes up so the sum will be never less than the entropy we had before falling.
This satisfies second law of thermodynamics.
But if the black hole has entropy à it has temperature à it must emit radiation
But inference about black hole emitting anything seems to be a basic flaw hence Jacob Bekenstein’s theory of considering the event horizon as a measure of the entropy of the black hole can’t be true. Or can it be?
Hawking co-authored a paper showing this flaw. Although he could not deny that there are similarities between entropy and area of the event horizon. Because available evidences support this theory.
Two Soviet scientists showed him how according to quantum mechanical uncertainty principle, rotating black holes should create and emit particles.
He did not like their maths though, so he made his own mathematical model to prove this idea. Through his own model Hawking found out, not only rotating but non-rotating black holes too should create and emit particles and radiation at a steady rate. Others later confirmed Hawking’s theory with their calculations.
Higher the mass of a black hole à lower the temperature of the black hole à lower the radiation
HOW CAN BLACK HOLE EMIT ANYTHING?
Quantum theory tells us these emissions don’t come from within the black hole but from the empty space just outside black hole’s event horizon.
If this space is absolutely empty à gravitational and electromagnetic fields are zero à value of fields are like position of the space, which is zero
Rate of change with time, which is the velocity of this empty space would be zero too
But according to uncertainty principle we can’t predict both position and velocity.
Hence there has to be certain uncertainty or quantum fluctuations in this space.
One can think of these fluctuations as pairs of particles of light or gravity. These particles are virtual particles, like the ones that carry the gravitational force of the sun. They can’t be observed directly, their indirect effect can be measured.
The uncertainty principle predicts there will be similar virtual pairs of matter particles – one particle and other antiparticle. One partner will have positive energy and other will have negative energy.
It is possible the virtual particle with negative energy falls inside the black hole and becomes a real particle/antiparticle. Whereas its partner virtual particle with positive energy may either follow the partner and fall inside the black hole or having positive energy it might also escape from the vicinity of the black hole as a real particle/antiparticle. To an observer from distance this seems emission from black hole.
The smaller the black hole, the shorter the distance the particle with negative energy will have to go before it becomes a real particle, and thus the greater the rate of emission and greater will be the apparent temperature of the black hole.
E = MC^2
Hence energy is proportional to mass. As negative energy falls inside black hole, it loses mass proportionately. Lower the mass becomes à greater the emission/temperature à loses mass more quickly
WHAT HAPPENS WHEN A BLACK HOLE LOSES ALL ITS MASS?
What happens when mass of a black hole becomes extremely small is not clear. Hawking guesses black hole will evaporate eventually with a final burst of emission. But it will take a long long time.
PRIMORDIAL BLACK HOLES
Primordial black holes with initial mass less than a thousand million tons would have evaporated by now. The ones with slightly more initial mass must be still radiating X rays and Gamma rays. These rays have much shorter wavelength than light waves.
It is difficult to observe rays from individual primordial black hole but total may be detectable. But the background gamma ray may include other activities than black hole emission. It doesn’t say anything but the total figure can tell the maximum possible number of primordial black hole, which is quite low.
Our earth’s atmosphere is one great gamma ray detector. As the ray enters our atmosphere, because of friction with out atmosphere, it creates a pair of electron-antielectron. They create other such pair by hitting other atoms. Finally an electron shower is created which results in Cerenkov radiation.
It looks like flashes of light shower in night sky. But these flashes can happen for different reasons. To be more sure, multiple scientists must observe it at separate locations. Even then one can’t be 100% sure.
The scarcity of observable primordial black holes tells us the early universe must have been very smooth and uniform with a high pressure. These conditions create less of primordial black holes. A chaotic, irregular, and low pressure early universe would have created a lot of primordial black holes.
THE IDEA OF RADIATION FROM BLACK HOLE
This idea is the first example in science, which depends essentially on both quantum theory and theory of relativity.
The idea also tells us gravitational collapse is not final and irreversible. Anything falling inside a black hole will be returned from their in form of energy radiation.
Chapter 8: The Origin and Fate of the Universe
In the introduction as mentioned above Carl Sagan wrote this book is about God. I feel in the book, this chapter is more about God than any other chapter.
If the universe is a beginning, the singularity where all laws of science, then there is a scope for God. Because the initial condition is unknown and unexplainable by anyone.
HOT BIG BANG MODEL
At big bang universe supposed to have
– zero size
– infinite density
– infinite temperature
Then universe cools down, expands and matters are created within it. The theory agrees with observations but it leaves out many UNANSWERED QUESTIONS
– Why was early universe so hot?
– Why is universe so uniform on large scale?
– Why the universe has been expanding at the critical rate? A little less than the rate the universe would collapse.
– Even if on large scale universe is uniform there are local irregularities in terms of density. What is the reason behind the density fluctuations?
The general theory of relativity on its own can’t explain these questions.
One answer maybe that God started the universe for reasons and the ways we can’t understand. But if God kept the beginning incomprehensible why did he made universe evolve in the way we can comprehend?
If universe is running with an underlying order then that order should have been maintained everywhere including its boundary, which is the singularity.
There can be multiple initial stages possible which all follow this order. There should be a principle, which can choose one initial stage and one model. Basically the principle should choose our universe among the possibilities.
Many theories have been put forward to study why and how the universe is the way it is. We will in brief touch on the theories
CHAOTIC BOUNDARY CONDITIONS
These implicitly assume either universe is spatially infinite or there are many universes.
In the initial stage universe was chaotic.
It may have been sheer coincidence that we are living in that part of the universe which is smooth and uniform. This can be explained by anthropic principle, which has two versions.
WEAK ANTHROPIC PRINCIPLE
In a universe that is large or infinite in space and/or time, the conditions necessary for the development of intelligent life will be met only in certain regions that are limited in space and time. Informally speaking it means – what it is, what it is.
STRONG ANTHROPIC PRINCIPLE
There are either many different universes or many different regions of a single universe, each with its own initial configuration or perhaps with own set of rules.
But there are many objections against this principle. If there are many different universes then what happen in other universes is of no consequence to us. The rules of science can’t be different for different regions of the same universe. Their initial configurations might be different and out of those one region is chosen for life so it becomes weak anthropic principle.
Strong anthropic principle also goes against the history of science. According to the principle whole construction exists for our sake. Then what is the point of all those galaxies and everything out of the solar system!
ALAN GUTH’S INFLATIONARY PRINCIPLE
Universe started as chaotic, very hot and with high energy. Then it expanded at an increasing rate as opposed to today’s decreasing rate. With proper care water’s temperature can be reduced below freezing point without formation of ice. Universe had the same situation. Its temperature reduced below critical value without the symmetry between the forces being broken. This way much more energy is produced compared to a scenario where symmetry is broken with reduction in temperature.
This extra energy has anti-gravitational effect and it acts as the cosmological constant Einstein had introduced in theory of relativity.
The gravitational pull is offset by cosmological constant hence the inflationary expansion. This will give enough time for flow of light from one region to another and thus making the universe uniform.
This ensures critical rate of expansion.
The total energy of the universe is zero. Matters are created from positive energy. Negative gravitational energy exactly cancels out the positive energy represented by matters. Matters can be doubled with doubled gravitational energy. The total energy would still be zero. In inflationary growth model universe expands by a large extent thus making lots of energy available to turn into matter. This explains why there are so many matters in the universe.
In case of normal expansion model this can’t happen as matter energy density decreases as universe expands. While in inflationary expansion matter energy density remains constant.
But why today universe is not expanding in inflationary way? Guth successfully could not take care of the problem. He proposed of bubbles of broken symmetry would have formed in the non-broken symmetry inflationary phase. They would expand and join together to take the universe rapidly to a new phase from the inflationary phase. But Hawking argued against this saying while universe expands so rapidly the bubbles would travel away from each other.
THE NEW INFLATIONARY MODEL
What if the bubble is so big that our region of the universe is inside it? In this case the change from symmetry to non-symmetry happens slowly inside the bubble.
This model was rejected very soon as predicted variation in temperature was much higher than observed one. There were doubts regarding phase transition in the early stage of universe.
CHAOTIC INFLATIONARY MODEL
There is no supercooling or phase transition. There is a spin 0 field. Because of quantum fluctuations there will be large values in some regions in the beginning of the universe. The energy in those regions would work like cosmological constant. It will lead to inflationary expansion. As they expands the energy in these field would decrease and then expansion would become same as hot big bang model. One of such regions becomes our observable universe. This model does not depends on phase transition and its predictions is fairly close to observations.
….
Inflationary models show the present universe could have been resulted from quite a large number of different initial configurations. Initial state could not have to be chosen carefully by some one (read God). But every initial configuration would not lead to our present state.
Inflationary models too can’t tell us why the initial configuration was not something else, which would have resulted in something else.
A unified theory combining quantum mechanics and gravity should incorporate:
– Feynman’s proposal to formulate quantum theory in terms of a sum over histories. A particle does not have a single history but many histories corresponding to every path it can take in space-time.
– Einstein’s idea that gravitational field is represented by curved space-time.
Whole history
When we apply Feynman’s sum of histories to Einstein’s view of gravity, it represents the whole history of the universe
In classical theory of general relativity, there are many curved space-times corresponding to initial configuration of the universe. If we know the initial configuration we can know the whole history.
In quantum theory of gravity there are many possible quantum states of the universe. We would know the quantum state of the universe if we know curved space-times in the sum over histories behaved in the early times.
Classical theory of gravity – two possibilities – universe has existed for infinite time or finite time (with a singularity at the beginning)
Quantum theory of gravity – Apart from the above mentioned two, there is a third possibility – Finite space time with no boundary (sort of like Earth, its area is finite but it has no boundary)
In that case the universe would be completely self-contained and not affected by anything outside itself (read by God). It would neither be created nor destroyed. It would just BE.
Interestingly, Hawking put forward this theory first time in Vatican and also this theory goes completely against all his earlier works supporting singularity.
In real time, the universe has a beginning and an end at singularities which form a boundary to space-time and where laws of science break down. But in imaginary time there is no boundary. So maybe imaginary time is more basic and real time we have invented to comprehend the universe.
No boundary condition has interpretations for universe’s evolution
The uncertainty principle implies the early universe could not be completely uniform. Using no boundary condition we find the universe must have started off with just the minimum possible non-uniformity allowed by uncertainty principle. In expanding phase, when density differs from region to region, the denser regions have slower expansion, which turns into contraction. It results in formation of galaxies, stars, and eventually us.
Chapter 9: The Arrow of Time
Till beginning of 20th century people believed in absolute time.
Then the idea changed to time as a personal concept because of theory of relativity. According to this theory each observer has his own measure of time according to the clock he or she is carrying. Mind it, here observers should have a clock showing accurate time. A watch running 10 minutes fast does not count as their personal time.
When one tries to unify gravity with quantum mechanics then imaginary time has to be introduced.
One can go backward or forward in imaginary time. The laws of science do not distinguish between past and future.
But there is a big difference between the forward and backward directions of real time in ordinary life.
There are at least 3 arrows of time. Arrow of time is something that distinguishes the past from the future, thus giving direction to time.
(i) Thermodynamics arrow of time
Imagine a cup of water falling off a table and breaking into pieces while the water spill all over the floor. If we film this and run it backward we will see spilled water and broken pieces of glasses gather together and become a cup of water on a table.
In real life we can’t see backward like this because of the second law of thermodynamics. This law states with time entropy or disorder can only increase.
(ii) Psychological arrow of time
We don’t know how human brain works but we know how computer’s brain work. We can take computer’s brain as an approximation of human brain. Suppose a disorganised data is transferred into computer’s memory in an orderly fashion. So one would expect disorder has reduced over time. But while storing the data, the heat produced by the computer and the energy consumed by it create lots of disorder. It can be shown the disorder attained thus is always more than the achieved order in the data. So the disorder increases over time.
So psychological arrow of time is determined by the thermodynamics arrow of time.
(iii) Cosmological arrow of time
With time universe expands and disorder increases.
What happens when universe collapses? Will the disorder decrease then?
This idea is attractive as it would mean nice symmetry between expanding and contracting phases.
But the idea of a finite universe without boundary implies the disorder would continue to expand even in contracting phase. So the thermodynamics and psychological arrows of time would not reverse when universe starts contracting. Because the working of expansion of universe is totally different from the way contraction or collapse of universe works.
So cosmological arrow of time also point to the same direction as the thermodynamics arrow of time.
The reason of this can be explained by weak anthropic principle. If they don’t point to same direction we would not be existing to discuss about it.
In order to survive human beings have to eat food (ordered form of energy) and convert it into heat (disordered form of energy).
Our universe is expanding at a critical rate to avoid collapse for a long long time. When finally universe will collapse there will be lots of disorder everywhere leaving out very little scope for increase in disorder. But till then universe expands and it is essential for existence of intelligent life.
Chapter 10: The Unification of Physics
The quest for a complete unified theory of everything in the universe is called The Unification of Physics.
Such a theory has been elusive till now. Scientists use partial theories to explain various phenomena of the universe. For a certain phenomenon the partial theory would make assumptions that the elements not coming under the theory to remain constant or something to that effect.
The main difficulty in finding a theory that unifies gravity with the other forces is that general relativity does not incorporate the uncertainty principle of quantum mechanics. On the other hands the partial theories depend on quantum mechanics in an essential way.
The consequences if general relativity is combined with quantum mechanics:
1. Black hole would not be so black (implying black hole does not suck up everything forever)
2. The universe would not have any singularity. It would be self-contained and without a boundary.
3. Uncertainty principle states even empty spaces are filled with pairs of virtual particles and antiparticles. These pairs would have infinite energy hence by E = mc^2 infinite mass. Their gravitational attraction would turn the universe into infinitely small size. It is obvious this consequence is problematic.
In partial theories when such absurd infinities come up then they are cancelled out by introducing other infinities. This process is called renormalisation.
Renormalisation has its own issues. Instead of predicting values of variables, the values of variables have to be chosen to fit the observations.
To combine theory of relativity with uncertainty principle a concept called supergravity was introduced.
The idea is to combine 4 new particles with particle graviton and all of them are considered different aspects of the same super particle. Out of these 5 particles 2 are matter particles with negative energy and 3 (including graviton) are force particles with positive energy. They should cancel out each other.
But
It is suspected some infinities might still remain. The calculations required to confirm this suspicion was long (like 4 years long) and complex. No one was keen to take it up.
Secondly, The observed particles did not seem to match the particles in the supergravity theories.
Despite these some scientists feel supergravity is an efficient method of unifying gravity with other forces.
String Theory
String theory was invented in 1960s in an attempt to find a theory to describe the strong force. In 1974 it was theorised this theory can describe gravitational force under special circumstances. But the theory really got the centre stage in 1984. This happened because of two reasons.
Research on supergravity was not going anywhere.
It was shown that string theory might be able to explain the existence of particles that have a built-in left-handedness.
Lots of physicists started working on it and a new version of the theory named heterotic string was developed.
In this theory basic objects are not particles which occupy a single point in space. The basic objects are things with length and no other dimension, like an infinitely thin piece of string.
Open strings – strings with ends
Closed strings – strings in closed loop
Two strings could be joined to form another single string. Two open strings join at the ends. Two closed strings they become something like two legs joining in a pair of trousers.
One string can be divided into two strings.
A particle occupies at each instant of time one point of space so its history in space-time is a line called the world-line.
On the other hand, a string occupies at each instant of time a line in space so its history in space-time is a two dimensional surface called the world-sheet.
The world-sheet of an open string is a strip and its edges represent the paths through space-time of the ends of the string.
The world-sheet of a closed string is a cylinder or tube. A slice through the tube is a circle which gives the position of the string at one particular time.
Sun’s gravitational force on the earth:
In particle theory sun’s one particle emits graviton which is absorbed by a particle of the earth.
In string theory, which Hawking thinks is like plumbing, the attraction happens in shape of an H shaped pipe. The vertical lines of H are the strings of sun and earth. Graviton travels through the horizontal bar.
Problems in string theory:
1. There might be some infinities but they all should be cancelled out in heterotic string theory. But this has never been tested.
2. String theory can be consistent only if space-time has 10 or 26 dimensions instead of the usual 4.
Why don’t we notice these extra dimensions?
It is suggested that they are curved up into a space of very small size, say about million million million million millionth of an inch. So we don’t notice them.
In very early universe all the dimensions should have been curved. But why did only one time and three dimensions flattened out while the others stayed tightly curled up?
Again here too weak anthropic principle comes to rescue. We can exist only in 3 dimensions.
Suppose there were only 2 dimensions then we could not have existed. For instance in a 2 dimensional universe food can’t get inside our body and also the blood circulation system can’t work.
The gravitational force between two bodies would decrease more rapidly with distance as the number of dimensions increase.
As the distance is doubled
In 3 dimension gravitational force drops to ¼th
In 4 dimension gravitational force drops to 1/8th
In 3 dimension gravitational force drops to 1/16th
So on.
This will result in instability in earth’s orbit around sun. A little attraction from another body and earth will spiral away from sun.
On smaller scale it will make the atoms unstable. Electron might spiral away from the atom.
Can there really be a unified theory? There are three possibilities.
(i) There is such a theory and we will some day discover it if we are smart enough.
(ii) There is no ultimate theory but infinite sequence of theories that describe the universe more and more accurately.
This is in agreement to our experience. The world is witnessing more and more refined theories. Further refinement in theories depends a lot on finding new layer of structure beyond quarks, which is considered to be most basic particle now. But there is a limit to finding basic particle or in Hawking’s words box inside box.
Early universe had enough energy to cut this limit. So Hawking is hopeful about a theory if we ever be able to study early universe in details.
(iii) There is no such theory. Events can’t be predicted as they happen in random and arbitrary manner.
If one likes then they can ascribe this randomness to God but then by definition it would not be random.
What would it mean if we ever discover the unified theory?
First of all we can’t be certain it is THE theory as theories can’t be proved. But we can be sure if it is mathematically consistent and its predictions agree with observations. It would also mean an end to a long glorious struggle of humankind to understand the universe.
Even if we get the theory we can’t predict everything accurately because of two reasons:
– The uncertainty principle
– The equations can be solved only in very simple cases
So the next challenge would be to develop better approximation method so that useful predictions can be made in realistic situations.
Chapter 11: Conclusion
He sums of the whole book while stressing on the fact that a unified theory of universe should be accessible to people from all disciplines and all walks of life.
Supplement
The supplement of the book has a glossary of the scientific words used in the book and short essays on 3 scientists: Albert Einstein, Galileo Galilei, and Isaac Newton.
The chapter on Einstein narrates volatilities in his life. He was not religious and denounced God through his theories. But the rising anti-Semitism in Europe, especially in his own country Germany made him a lifelong advocate of Zionism. He was a pacifist yet he proposed the nuclear bomb building to American government to destroy anti-Jewish Hitler. After the war again he continued his anti-war activities.
Hawking considers Galileo Galilei is responsible for the advent of modern science more than anyone else. The chapter on Galileo narrates his life long struggle with catholic church and briefly about the two important books written by him: “Dialogue Concerning the Two Chief World Systems”, “Two New Sciences”. Galileo remained lifelong devout catholic in spite of everything but he believed it was not Bible’s job to explain scientific matter and sometime the writing in it has to be taken allegorically.
Newton’s “Principia Mathematica” is the most influential physics book ever written according to Hawking. And that is the only positive thing he has to say about Isaac Newton in the chapter. The rest of the chapter is about Newton’s notorious career and conflict with fellow scientists such as John Flamsteed and Gottfried Leibniz.
When and how did I read the book
The book is not an easy read. Each chapter I read at least twice. Once I read it then again I read it to sum it up for this piece. This gave me more clarity about concepts. Some difficult portions I read more than twice. Anyone planning to read the book, I would suggest them to make notes of the chapters for better comprehension.
I read the book with other books, especially novels. I took a long time to finish the book as I tackled one chapter at one go. Reading other books on the side gave me much needed break from a complex book.
Some part of the book I read when I was in one of the toughest phases of my life. To my surprise the complexities of the book kept me off the emotional turmoil and thus provided much needed respite.
My Two Pennies
According to Hawking every time an equation is used in a book, the readership would be slashed in half. Hence he has used only one equation in this book, which is E = MC^2.
I personally feel the book could have been more accessible for layman by use of bullet points and some changes in formatting, like using different kinds and sizes of fonts. For instance after a big description the gist could have been given in simpler language and in bold letters. Suppose if to someone even the minimum logical exclamation is cumbersome to read they can stick to the bullet points and gist.
This book could have been more comprehensive had Hawking included the traditional oriental ideas on the universe along with the traditional Christian and occidental thoughts. The philosophies and sciences of ancient cultural leaders like China and India are completely missing from the book.
There are some overlappings or repetitions in the book, which could have been easily edited out.
However, overall the book is written in the simplest language possible and has a very approachable style. One must try not to get overwhelmed just by looking at the cover. Once one gives the book a chance they would explore the universe. Personally, I feel we must know at least some minimum things about the universe we are living in.
Last but not the least, the book gives lots of positive vibes.
What can be more positive than a man talking through machine and sitting on wheel chair is exploring the universe with immense hope and a dry sense of humour!
It gives such hope in these difficult times to know science is constantly progressing with contributions from scientists belonging to the whole world. They are working in unison, sometimes without even planning on it. If one is stuck at one point then a small discovery at the other end of the world gives them a big push.
Musings 
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