Theory of Everything by Stephen Hawking

1. Early Cosmological Models

• Aristotle (340 BC): Argued that the Earth was a round sphere rather than a flat plate, based on observations like the shape of Earth's shadow during eclipses.

• Ptolemy (2nd Century AD): Developed a complete model with Earth at the center, surrounded by eight spheres carrying the heavenly bodies. It was adopted by the Christian church as it left room beyond the stars for heaven and hell.

• Nicholas Copernicus (1514): Proposed a much simpler model where the Sun was stationary at the center and the Earth and planets moved in circular orbits around it.

2. The Newtonian Era & Gravity

• Universal Gravitation (1687): Newton postulated that every body in the universe is attracted to every other body. This force is stronger the more massive the bodies are and the closer they are together.

• The Static Universe Problem: Newton realized that in a finite universe, stars should eventually fall together due to gravity. To avoid this, it was argued that the universe must be infinite and static, though we now know such an equilibrium would be unstable.

• Olbers’ Paradox (1823): Heinrich Olbers argued against an infinite static universe. He noted that if the universe were infinite and uniform, every line of sight would end on a star, making the entire night sky as bright as the Sun.

3. The Expanding Universe

• Edwin Hubble (1929): Made the landmark observation that distant galaxies are moving rapidly away from us. This proved the universe is expanding.

• The Big Bang: Hubble’s discovery implied that at an earlier time (10 to 20 billion years ago), all objects were at the exact same place—a state that was infinitely dense, known as the Big Bang. This marked the point where time itself had a beginning.

4. Predicting and Proving the Expansion

• Alexander Friedmann (1922): Using General Relativity, Friedmann predicted the expansion of the universe years before Hubble's discovery, based on the assumption that the universe looks the same in every direction.

• Penzias and Wilson (1965): While working at Bell Labs, they accidentally discovered Cosmic Microwave Background Radiation. This uniform "noise" coming from every direction in the sky provided the remarkably accurate evidence needed to validate Friedmann’s model.

5. Modern Spectroscopy

• Stellar Temperatures and Composition: By passing starlight through a prism, we can see its spectrum. Missing colors (absorption lines) act like a fingerprint, allowing us to determine both a star’s temperature and the chemical elements present in its atmosphere.

• The Doppler Effect & Red-shift: Just as a car’s engine sounds lower in pitch as it moves away, light from receding galaxies is shifted toward the red end of the spectrum. The fact that nearly all galaxies are "red-shifted" confirms they are moving away from us.

 

6. Predicting and Proving the Expansion 

• The Gamow Prediction: George Gamow (a student of Friedmann) suggested that the early universe was incredibly hot and dense, glowing "white hot."

• Red-shifted Microwaves: Dicke and Peebles argued that we should still be able to see this glow today. However, due to the universe's expansion, the light would be so greatly red-shifted that it would appear to us now as microwave radiation.

• Nobel Discovery: While Dicke and Peebles were searching for this radiation, Penzias and Wilson found it by accident at Bell Labs. Penzias and Wilson received the Nobel Prize in 1978 for this "smoking gun" evidence of the Big Bang.

7. The Nature of the Expansion

• The Balloon Analogy: Friedmann’s model suggests the universe looks the same in every direction from any galaxy, not just ours. This is like a balloon with spots painted on it being blown up; every spot moves away from every other spot, and no single spot is the "center."

• The Critical Density: Whether the universe expands forever or eventually recollapses (the "Big Crunch") depends on its current rate of expansion and its average density.

  • Low Density: Gravity is too weak to stop the expansion.

  • High Density (above critical value): Gravity will eventually stop the expansion and cause the universe to recollapse.

• The Dark Matter Mystery: When we add up the mass of all visible stars, it is less than one-hundredth of the amount needed to halt expansion. Even including "dark matter" (which we infer from its gravitational pull on star orbits), we only reach about one-tenth of the required mass.

8. The Singularity and the Big Bang

• Roger Penrose's Theorem: Penrose showed that any collapsing star must end in a singularity (a point of infinite density).

• Hawking's Contribution: Hawking realized that if you "reverse the direction of time," this theorem proves that any Friedmann-like expanding universe must have begun with a singularity. In 1970, a joint paper by Penrose and Hawking proved there must have been a Big Bang singularity, provided General Relativity is correct.

9. Black Holes and Stellar Death

• Early Concepts: The idea of "dark stars" (stars so massive light cannot escape) goes back to John Michell (1783) and Laplace. The term "Black Hole" was later coined by John Wheeler in 1969.

• The Chandrasekhar Limit: In 1928, Indian graduate student Subrahmanyan Chandrasekhar calculated that there is a maximum mass (1.4 times the mass of the Sun) that a cold star can support against its own gravity.

• Stellar Remnants:

  • White Dwarfs: Stars below the limit supported by the "exclusion principle" repulsion between electrons.

  • Neutron Stars: Smaller, denser stars supported by the exclusion principle repulsion between neutrons and protons.

• The Fate of Massive Stars: Stars above the Chandrasekhar limit have a "big problem." Once they run out of fuel, they may collapse to infinite density (a black hole).

10. The Physics of Black Holes

• Origins: John Michell (1783) first suggested "dark stars" where gravity is so strong light cannot escape. The term "Black Hole" was coined by John Wheeler in 1969.

• The Chandrasekhar Limit: Subrahmanyan Chandrasekhar (1928) calculated that a cold star more than 1.4 times the mass of the Sun cannot support itself against gravity and must collapse.

• Stellar Remnants: * White Dwarfs: Supported by electron exclusion.

  • Neutron Stars: Supported by neutron exclusion.

• The Kerr Solution (1963): Roy Kerr found a solution for rotating black holes. These are not perfectly round but "bulge" at the equator due to rotation.

• "No-Hair" Theorem: A black hole "has no hair," meaning it settles into a state where its only measurable properties are its mass and rate of rotation. All other information about the body that collapsed is lost.

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11. Hawking Radiation: "Black Holes Ain't So Black"

• The Discovery: In 1973, after discussions with Soviet experts (Zeldovich and Starobinsky), Hawking mathematically proved that black holes emit particles.

• Mechanism: Empty space is not empty; it's filled with "virtual particle" pairs that appear, move apart, and annihilate each other. Near a black hole's horizon, one particle can fall in while the other escapes. To an outside observer, the black hole appears to be emitting radiation like a hot body.

• Paradox: The smaller the black hole, the higher its temperature and the faster it glows. This prevents violations of the Second Law of Thermodynamics.

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12. The Arrows of Time

• The Thermodynamic Arrow: Driven by the Second Law of Thermodynamics, which states that disorder (entropy) always increases with time. A broken cup on the floor is more disordered than an intact one on the table.

• The Psychological Arrow: This is the direction in which we feel time pass and remember the past, not the future. It is identical to the thermodynamic arrow because our brains (or computers) require energy and create disorder to store memories.

• The Cosmological Arrow: The direction in which the universe is expanding rather than contracting.

• The "Mistake": Einstein once introduced a "Cosmological Constant" to keep his model of the universe static. He later called this the "biggest mistake of his life."

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13. Open Questions in Cosmology

• Uniformity: Why was the early universe so hot?

• Smoothness: Why does the universe look the same in all directions (isotropic) on a large scale?

• Boundary Conditions: Why did it start with such a precise rate of expansion to avoid immediate recollapse?

14. The Quest for Unification

• Partial Theories: Currently, physics relies on "partial theories" that describe limited ranges of effects (like General Relativity for gravity and Quantum Mechanics for the subatomic).

• Einstein’s Struggle: Einstein spent his later years unsuccessfully seeking a unified theory, largely because he refused to accept the Uncertainty Principle of quantum mechanics.

• The Conflict: General Relativity is a "classical" theory (it assumes smooth space-time), whereas the other three forces (strong, weak, and electromagnetic) depend on quantum mechanics. A "Theory of Everything" must reconcile these two.

• False Dawns: Physics has seen many "false dawns" where scientists thought the end of theoretical physics was near (e.g., Max Born in 1928), only for new discoveries like the neutron to reset the quest.

15. Extra Dimensions & String Theory

• Hidden Dimensions: To make unification work, some theories suggest the universe has many more than four dimensions (3 space + 1 time).

• The "Orange" Analogy: We don't notice these extra dimensions because they are "curled up" into a space of incredibly small size (10^(-30) inches). It is like looking at an orange from a distance; it looks smooth and 1D, but up close, it is a 3D surface with bumps and curvature.

• Anthropic Principle: One possible answer for why we only see three expanded space dimensions is that life could likely only exist in a universe where the other dimensions remained tightly curled.

16. The Philosophical Goal

• Democratizing Knowledge: In Newton's time, an educated person could grasp the whole of human knowledge. Today, specialization makes this impossible.

• The Ultimate Goal: If a complete unified theory is discovered, it would eventually be simplified and taught in schools. This would allow everyone, not just a few specialists, to have a "proper grasp of the laws that govern the universe and which are responsible for our existence."