The Theory of Everything summary
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The Theory of Everything Summary | Stephen Hawking

The Origin and Fate of the Universe

The Theory of Everything summary

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Stephen Hawking’s Perspective

Stephen Hawking was considered one of the most brilliant theoretical physicists in history. From the Big Bang to black holes, his work on the universe’s origins and structure revolutionized the field. Hawking was born in Oxford into a family of doctors. He began his university education at University College, Oxford, in 1959. He received a first-class BA degree in physics. Hawking began his graduate work at Trinity Hall, Cambridge, in 1962. He obtained his Ph.D. degree in applied mathematics and theoretical physics, specializing in general relativity and cosmology, in March 1966. Like Isaac Newton, he was the Lucasian Professor of Mathematics at the University of Cambridge between 1979 and 2009. At age 21, while studying cosmology at the University of Cambridge, he was diagnosed with amyotrophic lateral sclerosis (ALS). Part of his life story was depicted in the 2014 film The Theory of Everything.

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Introduction

The Theory of Everything is a series of lectures given by Stephen Hawking. The goal of these lectures is to outline what scientists believe is the history of the universe. As a result, he offers a history of science’s understanding of the universe. Additionally, he clearly explains the events that unfolded immediately after the Big Bang. Hawking also covers the cosmological field he is most famous for: the study of black holes.

StoryShot #1: The Original Four Ideas About the Universe

Aristotle

Aristotle considered the idea of a round Earth as early as 340 BC. In his book, On the Heavens, he wrote about two theories that suggested Earth was spherical. First off, he had observed that the Earth being between the Sun and the Moon caused the moon eclipses. As the Earth’s shadow on the Moon was always round, this suggested the Earth was round. Aristotle learned from his travels that the Pole Star is lower in the sky when viewed in the South. Again, this would propose that the Earth is spherical rather than disc-shaped. Although Aristotle’s conclusions were correct, his theories were still flawed. For example, he believed the Earth was stationary and that the Sun, Moon, planets, and stars had circular orbits around the Earth. 

Ptolemy

Ptolemy built upon these ideas in the first century AD. He created a complete cosmological model with Earth at the center. Eight spheres carrying the Moon, Sun, stars, and five planets surrounded the Earth. The five known planets were Mercury, Venus, Mars, Jupiter, and Saturn. Again, Ptolemy made apparent mistakes in his theory. However, he developed Aristotle’s ideas and provided a reasonably accurate system for predicting the positions of the structures visible at night. The Christian Church generally accepted this theory, partly because it placed the Earth at the center of the universe. 

Copernicus

In 1514, Nicholas Copernicus suggested a much simpler model of the universe. Copernicus was a Polish priest. He then published his model anonymously for fear of being accused of heresy. Copernicus argued that the Sun was stationary at the center of the universe. The Earth and planets moved in circular orbits around the Sun. No one took this idea seriously until approximately 100 years later. At this point, Johannes Kepler and Galileo Galilei started publicly supporting this theory. The recently invented telescope supported Copernicus’ view that the Earth was not the center of the universe. Galileo observed that several moons orbit Jupiter. This implied there was no need for all celestial bodies to orbit the Earth. Some still denied that the Earth wasn’t the center of the universe, though. They stated that Jupiter’s moons moved on extremely complicated paths around the Earth, suggesting that they orbit Jupiter. 

Newton

In 1687, Newton published his Mathematical Principles of Natural Philosophy. Hawking describes this as arguably the most crucial work ever published in the physical sciences. In this book, Newton proposed a theory of how bodies moved in space and time. This theory also explained a new idea of universal gravitation. Newton suggested that every celestial body in the universe was attracted to every other body. The larger the body, the stronger the gravitational pull. Newton went on to show that gravity causes the Moon to move in an elliptical orbit around the Earth. Likewise, gravity also causes the Earth and the planets to follow elliptical paths around the Sun.

There was still no hint of an expanding or contracting universe despite these advances before the twentieth century. It was generally accepted that either the universe existed forever in a stable state or was created at a finite time in the past. However, several academics questioned the possibility of an infinite, static universe. For example, Heinrich Olbers argued that nearly every line or side would end on the surface of a star in an infinite, static universe. As a result, one would expect the whole sky to be as bright as the Sun, even at night. The only way to avoid this conclusion would be if the stars were not shining forever. For example, they could have turned on at some finite time in the past.

StoryShot #2: The Expanding Universe

Multiple Galaxies

Our Sun and the nearby stars are all part of the Milky Way. For a long time, there was a consensus that the Milky Way was the entire universe. However, in 1925, Edwin Hubble demonstrated that the Milky Way was not the only galaxy. He found many other galaxies with vast amounts of space between them. To prove the legitimacy of his theory, he had to identify how extensive these empty spaces were. 

One way to directly identify a star’s distance from Earth is based on brightness. The brightness of a star is based on the star’s luminosity and its distance away. Therefore, if we can identify a star’s luminosity, we can use the apparent brightness to calculate the distances away. Hubble argued certain stars always had the same luminosity when they were near enough for us to measure. If we found such stars in another galaxy, we could assume they had the same luminosity. Thus, we could calculate the distance to that galaxy. We could be reasonably sure that our estimate is accurate if many stars in the same galaxy gave the same distance. Hubble calculated the distances to nine galaxies this way. We now know that our galaxy is only one of a hundred thousand million that modern telescopes can observe. There are some hundred thousand million stars within each galaxy. 

Expanding Universe

Hubble identified that the galaxies he observed all appeared red-shifted. Redshift is a key concept for astronomers. We can understand it literally: The wavelength of the light is stretched, so the light is seen as shifted towards the red part of the spectrum. This means each of these galaxies is moving away from us. Additionally, the speed at which each galaxy moved away from us depended on its distance. The farther away a galaxy was, the faster it moved away from us. Hawking describes this finding as one of the tremendous intellectual revelations of the twentieth century. 

Building on General Relativity and The Friedmann Equations

Alexander Friedmann, a Soviet physicist and mathematician, developed models of general relativity to account for the expanding universe hypothesis.

Friedmann showed that the universe is expanding so slowly that the gravitational attraction between the different galaxies is slowing the universe’s expansion. As a result, the expansion might be stopping. Then, the galaxies will start moving towards each other as the universe contracts. 

Friedmann also suggested the universe could be expanding so rapidly that the gravitational attraction won’t stop this expansion. It might slow down a bit, but the galaxies will eventually reach a state where they are moving apart at a steady speed. 

Finally, Friedmann offered a solution whereby the universe is expanding just fast enough to avoid contraction. With this solution, the speed at which the galaxies move apart will get smaller. It will never reach zero but will reach a stage where the movement is virtually zero.

We currently know about the galaxies’ expansion because the universe is expanding between five percent and ten percent every thousand million years. However, we are unsure which of Friedmann’s solutions are correct, as we are unsure of the galaxies’ mass. It is challenging to identify the mass of galaxies, as dark matter is present across galaxies. Dark matter is composed of particles that do not absorb, reflect, or emit light, so they cannot be detected by observing electromagnetic radiation. We cannot see dark matter directly. We know that dark matter exists because of its effect on objects we can observe directly. Likewise, we cannot easily identify the mass of dark matter.

The Big Bang 

The Friedmann solutions state that the distance between neighboring galaxies must have been zero between ten and twenty thousand million years ago. At that time, which we call the big bang, the universe’s density and space-time curvature would have been infinite. This means the general theory of relativity predicts a singular point in the universe.

The issue with a singular point in the universe is that this supports a biblical perspective. Therefore, the Church adopted the Big Bang as being a divine intervention. Thus, there were several attempts to avoid the Big Bang conclusion. The alternative was a steady-state theory. The Steady State theory was suggested in 1948 and argued that galaxies move away from each other. However, new galaxies were continually forming in the gaps in between. These new galaxies are formed from new matter that is being constantly created. Hence, the universe looks roughly the same at all times and at all points in space.

Wheeler, but it is at least two hundred years old as a concept. Two centuries ago, there were two theories of light. One argued that light is composed of particles. The other theory argued that light is composed of waves. In reality, both of these theories are correct. Those who believed in particle theory argued that this could impact our understanding of stars. They thought that stars were both massive and compact enough for their gravity to drag back any light emitted from the star’s surface. The star might not emit light far enough for us to observe it, but we would still feel its gravitational pull. Today, we know these stars as black holes. 

The Life Cycle of a Star

To understand black hole formation, we must understand the life cycle of a star. Stars form when large amounts of hydrogen collapse in on themselves due to gravity. The contraction leads to the gas colliding more frequently. As the gas moves at higher speeds, it heats up. When stars reach a critical temperature, the hydrogen atoms stop bouncing against each other. Instead, they merge, forming helium atoms. The heat of a star is what makes it shine, and it will continue to burn until it runs out of fuel (i.e., hydrogen). 

The more fuel a star starts with, the sooner it runs out. This is due to the size of the star, requiring more heat to balance its gravitational attraction. Higher heats need more hydrogen. Our Sun has probably got enough power for another five thousand million years or so.

The Chandrasekhar Limit

Subrahmanyan Chandrasekhar, an Indian-American astrophysicist, used the theory of relativity to show how the speed differences of star particles are limited. The particles cannot move faster than the speed of light.

A stable white dwarf star has a maximum mass. When it reaches this mass, the attraction of gravity is so strong that it causes it to collapse in on itself. The Chandrasekhar limit is about 1.4 times the mass of our Sun. 

Another potential state of stars is the neutron star state. These stars are much smaller than a white dwarf. They are supported by the exclusion repulsion between neutrons and protons, in contrast to the usual relationship between electrons. These neutron stars only have a radius of roughly ten miles. 

Finally, any stars that fall above the limit may explode when their fuel runs out. Many scientists, including Einstein, wrote papers explaining how this was impossible. Despite these objections, Chandrasekhar received the Nobel Prize in 1983 for his early work on the limiting mass of cold stars. 

Outline of Black Hole Formation

  1. The star’s gravitational field changes the paths of light rays in space-time.
  2. Light cones show the paths followed in space and time by flashes of light. They bend inwards near the star’s surface.
  3. As the star contracts, the gravitational field gets stronger at its surface. The light cones bend more.
  4. This bending makes it more difficult for light from the star to escape. As a result, the light appears dimmer and redder to observers. 
  5. When enough shrinkage has occurred, the gravitational field at the surface is so strong that light can no longer escape. 
  6. Nothing can travel faster than light, so nothing else can escape this gravitational field.

This boundary of black holes forms the event horizon. It coincides with the paths of the light rays that fail to escape from the black hole.

Hawking’s Discoveries

“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 within the black hole. This is rather like the big bang at the beginning of time, only it would be an end of time for the collapsing body and the astronaut. At the singularity, the laws of science and our ability to predict the future would break down. However, any observer who remained outside the black hole would not be affected by this failure of predictability, because neither light nor any other signal can reach them from the singularity.”

— Stephen Hawking, The Theory of Everything

This quote suggests there are solutions to general relativity. An astronaut may see a singularity, allowing them to avoid hitting it. They could fall through the wormhole, transporting them to another region in the universe in the form of space and time travel. Yet, Hawking admits that these solutions to the general relativity equation are unstable. The presence of an astronaut may cause a disturbance that would change the outcome. Also, they may not see the singularity until they hit it, and then they would die. The singularity always lies in their future and never in their past.

Black holes are examples of scientific theories developed as mathematical models before any observational evidence. 

Other Notable Terms

Quasar: A quasar is an extremely luminous active galactic nucleus (AGN). A supermassive black hole with mass ranging from millions to billions of times the mass of the Sun. A gaseous accretion disk surrounds it.

Pulsars: A pulsar is a rotating neutron star. It emits pulses of radio waves because of the indirection between its magnetic fields and surrounding matter. 

StoryShot #4: The Origin and Fate of the Universe

In the 1980s, the Vatican invited Hawking to a conference on cosmology. The Catholic Church had learned from its silencing of Galileo that they should not prevent scientific discovery. Hence, they decided a better approach would be to invite many experts to advise them on cosmology. The Pope told Stephen Hawking that he should not study the big bang despite this. The Pope viewed the big bang as the moment of creation. Hawking would not listen to this request. 

The Hot Big Bang Model

  • This model assumes that Friedmann’s model describes the universe.
  • The universe is expanding, reducing the temperature of matter and radiation. Temperature is a measure of the average energy of the particles. Hence, at high temperatures, the particles move so fast they are not attracted to each other. Yet, as they cool, the particles start clumping.
  • The big bang was when the universe had no size, meaning it must have been infinitely hot. As the universe expanded, the temperature of the radiation would have decreased.
  • Despite this, the big bang would have occurred at about ten thousand million degrees. This is the temperature of H-bomb explosions.
  • The world consisted of photons, electrons, neutrinos, and some protons and neutrons.
  • The universe continued to expand, and the temperature dropped. The production rate of electron pairs would have fallen below the rate at which annihilation was destroying them.
  • After one hundred seconds, the temperature would have fallen to one thousand million degrees. This is the temperature of the hottest stars. At this temperature, protons and neutrons would not have the energy to escape the strong attraction of nuclear forces.
  • These protons and neutrons combined. They produced the nuclei of heavy hydrogen and helium atoms and small amounts of elements like lithium and beryllium. 
  • Within a few hours of the big bang, the production of helium and other elements would have stopped. For the next million years or so, the universe continued expanding.
  • Eventually, the temperature dropped to a few thousand degrees. The electrons and nuclei were no longer able to overcome their electromagnetic attraction. They would have started combining to form atoms.
  • The universe continued expanding and cooling. Slightly denser areas were slowed by extra gravitational attraction. This attraction stopped the expansion and led to a recollapse. The gravitational pull of matter outside these regions caused the atoms to rotate as they collapsed.
  • As the collapsing areas became even smaller, they started spinning faster. Eventually, they span fast enough to balance the attraction of gravity. This is a possible explanation of the start of the disk-like rotating galaxies we see today.

StoryShot #5: What is the Theory of Everything?

“If we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all be able to take part in the discussion of why the universe exists. If we find the answer to that, it would be the ultimate triumph of human reason. For then we would know the mind of God.”

— Stephen Hawking, The Theory of Everything

Physics has been able to describe the beginnings of our universe with some partial theories. These theories describe a limited range of observations. They neglect other effects that are not yet understood. The goal of cosmology and physics is to find a complete, consistent, unified theory of the world. Stephen Hawking describes this as the unification of physics.

Einstein spent most of his later years searching for this unified theory. We are now in a much stronger position than Einstein to develop a unified view. 

Stephen Hawking is cautiously optimistic that we will discover the ultimate laws of nature. He is confident that we will find a complete unified theory one day if we are smart enough. This unified theory is not an ultimate theory. Instead, we have an infinite sequence of theories that each describe the universe with more accuracy.

Our current views on quantum physics have set us up to uncover the full secrets of the universe. Steven Hawking’s book is a great starting point for understanding how the universe works and the importance of stars within it.

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Editor’s Note: First published on 24/1/2022. Updated on 26/2/2022

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