A Brief History Of Time

Stephen Hawking

🔬
Physics

Date

Aug 11, 2021

Read time

45 minutes

Rating

Hawking writes in non-technical terms about the structure, origin, development and eventual fate of the Universe. He talks about basic concepts like space and time, basic building blocks that make up the Universe (such as quarks) and the fundamental forces that govern it (such as gravity).

Our Picture of the Universe

Aristotle & Ptolemy already believed that the Earth was round but thought that it was the center of our Solar system.

Ptolemy's model or Geocentric model is a model of the solar system with the earth in the middle.

Copernicus, and later Galileo Galilei & Johannes Kepler came up with Heliocentrism.

In 1687, Isaac Newton's Principia Mathematica proved Heliocentrism.

Newton's model also meant that stars, like the Sun, were not fixed but, rather, faraway moving objects. Nevertheless, Newton believed that the Universe was made up of an infinite number of stars which were more or less static. Many of his contemporaries, including German philosopher Heinrich Olbers, disagreed.

In 1929, astronomer Edwin Hubble discovered that most galaxies are redshifting. They gave a red glow which means that the galaxies are moving away from eachother. Which could only be explained if the Universe itself was growing in size. Between ten and twenty billion years ago, they were all together in one singular extremely dense place.

Today, scientists use two theories, Albert Einstein's general theory of relativity and quantum mechanics, which partially describe the workings of the Universe.

Scientists are still looking for a complete Grand Unified Theory that would describe everything in the Universe.

Hawking believes that the discovery of a complete unified theory may not aid the survival of our species, and may not even affect our lifestyle, but that humanity's deepest desire for knowledge is justification enough for our continuing quest, and that our goal is nothing less than a complete description of the Universe we live in.

Space and Time

Aristotle's theory of absolute space came to an end following the introduction of Newtonian mechanics:

Whether an object is 'at rest' or 'in motion' depends on the inertial frame of reference of the observer; an object may be 'at rest' as viewed by an observer moving in the same direction at the same speed, or 'in motion' as viewed by an observer moving in a different direction and/or at a different speed. There is no absolute state of 'rest'.

Galileo Galilei also disproved Aristotle's theory that heavier bodies fall more quickly than lighter ones. He experimentally proved this by observing the motion of objects of different weights and concluded that all objects would fall at the same rate and would reach the bottom at the same time unless an external force acting on them.

Aristotle and Newton believed in absolute time: If an event is measured using two accurate clocks in different states of motion from each other, they would agree on the amount of time that has passed (today, this is known to be untrue).

The fact that the light travels with a finite speed was first explained by the Danish scientist Ole Rømer, by his observation of Jupiter and one of its moons Io. He observed that Io appears at different times when it revolves around Jupiter because the distance between Earth and Jupiter changes over time.

James Clerk Maxwell, who concluded that light travels in waves moving at a fixed speed, argued that light must travel through a hypothetical fluid called “aether”, which was disproved by the Michelson–Morley experiment. Einstein and Henri Poincaré later argued that there is no need for aether to explain the motion of light, assuming that there is no absolute time. The theory of special relativity is based on this, arguing that light travels with a finite speed no matter what the speed of the observer is. The speed of light is the fastest speed at which any information can travel.

Mass and energy are related by the equation E=mc2, which explains that an infinite amount of energy is needed for any object with mass to travel at the speed of light. "Events" can also be described by using light cones, a spacetime graphical representation that restricts what events are allowed and what are not, based on the past and the future light cones. A 4-dimensional spacetime is also described, in which 'space' and 'time' are in a way linked. The motion of an object through space inevitably impacts the way in which it experiences time.

Einstein's general theory of relativity explains how the path of a ray of light is affected by 'gravity’, which according to Einstein is an illusion caused by the warping of spacetime, in contrast to Newton's view which described gravity as a force which matter exerts on other matter. In spacetime curvature, light always travels in a straight path in the 4-dimensional "spacetime" but may appear to curve in 3-dimensional space due to gravitational effects. These straight-line paths are geodesics. In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime geometry where the source of curvature is the stress-energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting a star is the projection of a geodesic of the curved four-dimensional (4-D) spacetime geometry around the star onto three-dimensional (3-D) space.

The twin paradox, a thought experiment in special relativity involving identical twins, considers that twins can age differently if they move at different speeds relative to each other, or even if they lived in different locations with unequal spacetime curvature. Special relativity is based upon arenas of space and time where events take place, whereas general relativity is dynamic where force could change spacetime curvature and which gives rise to the expanding Universe. Hawking and Roger Penrose worked upon this and later proved using general relativity that if the Universe had a beginning then it also must have an end.

The Expanding Universe

In this chapter, Hawking first describes how physicists and astronomers calculated the relative distance of stars from the Earth.

In 1924, Edwin Hubble discovered a method to measure the distance using the brightness of Cepheid variable stars as viewed from Earth. The luminosity, brightness, and distance of these stars are related by a simple mathematical formula. Using all these, he calculated the distances of nine different galaxies. We live in a fairly typical spiral galaxy, containing vast numbers of stars.

The stars are very far away from us, so we can only observe their one characteristic feature, their light. When this light is passed through a prism, it gives rise to a spectrum. Every star has its own spectrum, and since each element has its own unique spectra, we can measure a star's light spectra to know its chemical composition. We use thermal spectra of the stars to know their temperature. In 1920, when scientists were examining spectra of different galaxies, they found that some of the characteristic lines of the star spectrum were shifted towards the red end of the spectrum. The implications of this phenomenon were given by the Doppler effect, and it was clear that many galaxies were moving away from us.

It was assumed that, since some galaxies are red shifted, some galaxies would also be blue shifted. However, redshifted galaxies far outnumbered blueshifted galaxies. Hubble found that the amount of redshift is directly proportional to relative distance. From this, he determined that the Universe is expanding and had had a beginning. Despite this, the concept of a static Universe persisted until the 20th century. Einstein was so sure of a static Universe that he developed the 'cosmological constant' and introduced 'anti-gravity'* forces to allow a universe of infinite age to exist. Moreover, many astronomers also tried to avoid the implications of general relativity and stuck with their static Universe, with one especially notable exception, the Russian physicist Alexander Friedmann.

Friedmann's model gave rise to three different types of models for the evolution of the Universe. First, the Universe would expand for a given amount of time, and if the expansion rate is less than the density of the Universe (leading to gravitational attraction), it would ultimately lead to the collapse of the Universe. Secondly, the Universe would expand, and at some time, if the expansion rate and the density of the Universe became equal, it would expand slowly and stop, leading to a somewhat static Universe. Thirdly, the Universe would continue to expand forever, if the density of the Universe is less than the critical amount required to balance the expansion rate of the Universe.

The first model depicts the space of the Universe to be curved inwards. In the second model, the space would lead to a flat structure, and the third model results in negative 'saddle shaped' curvature. Even if we calculate, the current expansion rate is more than the critical density of the Universe including the dark matter and all the stellar masses. The first model included the beginning of the Universe as a Big Bang from a space of infinite density and zero volume known as 'singularity', a point where the general theory of relativity (Friedmann's solutions are based on it) also breaks down.

This concept of the beginning of time (proposed by the Belgian Catholic priest Georges Lemaître) seemed originally to be motivated by religious beliefs, because of its support of the biblical claim of the universe having a beginning in time instead of being eternal. So a new theory was introduced, the "steady-state theory", to compete with the Big Bang theory. Its predictions also matched with the current Universe structure. But the fact that radio-wave sources near us are far fewer than from the distant Universe, and there were numerous more radio sources than at present, resulted in the failure of this theory and universal acceptance of the Big Bang Theory.

Roger Penrose used light cones and general relativity to prove that a collapsing star could result in a region of zero size and infinite density and curvature called a Black Hole. Hawking and Penrose proved together that the Universe should have arisen from a singularity, which Hawking himself disproved once quantum effects are taken into account.

The Uncertainty Principle

Werner Heisenberg's uncertainty principle says that the speed and the position of a particle cannot be precisely known. To find where a particle is, scientists shine light at the particle. If a high-frequency light is used, the light can find the position more accurately but the particle's speed will be less certain (because the light will change the speed of the particle). If a lower frequency is used, the light can find the speed more accurately but the particle's position will be less certain. The uncertainty principle disproved the idea of a theory that was deterministic or something that would predict everything in the future.

The wave-particle duality behavior of light is also discussed in this chapter. Light (and all other particles) exhibits both particle-like and wave-like properties.

Light waves have crests and troughs. The highest point of a wave is the crest, and the lowest part of the wave is a trough. Sometimes more than one of these waves can interfere with each other. When light waves interfere with each other, they behave like a single wave with properties different from those of the individual light waves.

Elementary Particles and Forces of Nature

Quarks and other elementary particles are the topic of this chapter. Quarks are elementary particles which comprise the majority of matter in the universe. There are six different "flavors" of quarks: up, down, strange, charm, bottom, and top. Quarks also have three "colors": red, green, and blue. There are also antiquarks*, which differ in some properties from quarks.

All particles (for example, the quarks) have a property called spin. The spin of a particle shows us what a particle looks like from different directions. For example, a particle of spin 0 looks the same from every direction. A particle of spin 1 looks different in every direction unless the particle is spun completely around (360 degrees). Hawking's example of a particle of spin 1 is an arrow. A particle of spin two needs to be turned around halfway (or 180 degrees) to look the same. The example given in the book is of a double-headed arrow.

There are two groups of particles in the Universe: particles with a spin of 1/2 (fermions), and particles with a spin of 0, 1, or 2 (bosons). Only fermions follow the Pauli exclusion principle. Pauli's exclusion principle (formulated by Austrian physicist Wolfgang Pauli in 1925) states that fermions cannot share the same quantum state (for example, two "spin up" protons cannot occupy the same location in space). If fermions did not follow this rule, then complex structures could not exist.

Bosons, with a spin of 0, 1, or 2, do not follow the exclusion principle. Some examples of these particles are virtual gravitons and virtual photons. Virtual gravitons have a spin of 2 and carry the force of gravity. This means that when gravity affects two things, virtual gravitons are exchanged between them. Virtual photons have a spin of 1 and carry the electromagnetic force, which holds atoms together.

Besides the force of gravity and the electromagnetic forces, there are weak and strong nuclear forces. The weak nuclear force is responsible for radioactivity. The weak nuclear force affects mainly fermions. The strong nuclear force binds quarks together into hadrons, usually neutrons and protons, and also binds neutrons and protons together into atomic nuclei(plural of nucleus). The particle that carries the strong nuclear force is the gluon. Due to a phenomenon called color confinement, quarks and gluons are never found on their own (except at extremely high temperature), and are always 'confined' within hadrons.

At extremely high temperature, the electromagnetic force and weak nuclear force behave as a single electroweak force. It is expected at even higher temperature, the electroweak force and strong nuclear force would also behave as a single force. Theories which attempt to describe the behavior of this "combined" force are called Grand Unified Theories, which may help us explain many of the mysteries of physics that scientists have yet to solve.

Black Holes

Black holes are regions of spacetime where gravity is so strong that nothing can escape from within it. Most black holes are formed when very massive stars collapse under their own gravity. Black holes then collapse at the end of their lives. A star must be at least 5-25 times heavier than the Sun to collapse into a black hole. The boundary around a black hole from which no particle can escape to the rest of spacetime is called the event horizon.

Black holes that do not rotate have spherical symmetry. Others that have rotational angular momentum have only axisymmetry.

Black holes are difficult for astronomers to find because they don't produce any light. One can be found when it consumes a star. When this happens, the infalling matter lets out powerful X-rays, which can be seen by telescopes.

In this chapter, Hawking talks about his famous bet with another scientist, Kip Thorne, that he made in 1974. Hawking argued that black holes did not exist, while Thorne argued that they did. Hawking lost the bet as new evidence proved that Cygnus X-1 was indeed a black hole.

Black holes aren’t that black

This chapter discusses an aspect of black hole behavior that Stephen Hawking discovered.

According to older theories, black holes can only become larger, and never smaller, because nothing which enters a black hole can come out. However, in 1974, Hawking published a new theory which argued that black holes can "leak" radiation. He imagined what might happen if a pair of virtual particles appeared near the edge of a black hole. Virtual particles briefly 'borrow' energy from spacetime itself, then annihilate with each other, returning the borrowed energy and ceasing to exist. However, at the edge of a black hole, one virtual particle might be trapped by the black hole while the other escapes. Because of the second law of thermodynamics, particles are 'forbidden' from taking energy from the vacuum. Thus, the particle takes energy from the black hole instead of from the vacuum, and escape from the black hole as Hawking radiation.

According to Hawking's theory, Black Holes must very slowly shrink over time because of this radiation, rather than continue living forever as scientists had previously believed. Though his theory was initially viewed with great skepticism, it would soon be recognized as a scientific breakthrough, earning Hawking significant recognition within the scientific community.

The Origin and Fate of the Universe

The beginning and the end of the universe are discussed in this chapter.

Most scientists agree that the Universe began in an expansion called the "Big Bang". At the start of the Big Bang, the Universe had an extremely high temperature, which prevented the formation of complex structures like stars, or even very simple ones like atoms. During the Big Bang, a phenomenon called "inflation" took place, in which the Universe briefly expanded ("inflated") to a much larger size. Inflation explains some characteristics of the Universe that had previously greatly confused researchers. After inflation, the universe continued to expand at a slower pace. It became much colder, eventually allowing for the formation of such structures.

Hawking also discusses how the Universe might have appeared differently if it grew in size slower or faster than it actually has. For example, if the Universe expanded too slowly, it would collapse, and there would not be enough time for life to form. If the Universe expanded too quickly, it would have become almost empty. Hawking argues in favor of the controversial "eternal inflation hypothesis", suggesting that our Universe is only one of countless universes with different laws of physics, most of which would be inhospitable to life.

The concept of quantum gravity is also discussed in this chapter.

Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics, and where quantum effects cannot be ignored, such as in the vicinity of black holes or similar compact astrophysical objects where the effects of gravity are strong, such as neutron stars (A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses).

Three of the four fundamental forces of physics (Electromagnetism, Weak force, Strong force & Gravity) are described within the framework of quantum mechanics and quantum field theory. The current understanding of the fourth force, gravity, is based on Albert Einstein's general theory of relativity, which is formulated within the entirely different framework of classical physics. However, that description is incomplete: describing the gravitational field of a black hole in the general theory of relativity, physical quantities such as the spacetime curvature diverge at the center of the black hole. This signals the breakdown of the general theory of relativity and the need for a theory that goes beyond general relativity into the quantum. At distances very close to the center of the black hole (closer than the Planck length, it is impossible, using the known laws of quantum mechanics and the known behavior of gravity, to determine a position to a precision smaller than the Planck length), quantum fluctuations of spacetime are expected to play an important role. To describe these quantum effects a theory of quantum gravity is needed. Such a theory should allow the description to be extended closer to the center and might even allow an understanding of physics at the center of a black hole. On more formal grounds, one can argue that a classical system cannot consistently be coupled to a quantum one.

The field of quantum gravity is actively developing, and theorists are exploring a variety of approaches to the problem of quantum gravity, the most popular being M-theory and loop quantum gravity. All of these approaches aim to describe the quantum behavior of the gravitational field. This does not necessarily include unifying all fundamental interactions into a single mathematical framework. However, many approaches to quantum gravity, such as string theory, try to develop a framework that describes all fundamental forces. Such theories are often referred to as a theory of everything. Others, such as loop quantum gravity, make no such attempt; instead, they make an effort to quantize the gravitational field while it is kept separate from the other forces.

One of the difficulties of formulating a quantum gravity theory is that quantum gravitational effects only appear at length scales near the Planck scale, around 10−35 meters, a scale far smaller, and hence only accessible with far higher energies, than those currently available in high energy particle accelerators. Therefore, physicists lack experimental data which could distinguish between the competing theories which have been proposed, and thus thought experiment approaches are suggested as a testing tool for these theories.

The Arrow of Time

In this chapter Hawking talks about why "real time", as Hawking calls time as humans observe and experience it (in contrast to "imaginary time", which Hawking claims is inherent to the laws of science) seems to have a certain direction, notably from the past towards the future. Hawking then discusses three "arrows of time" which, in his view, give time this property.

Hawking's first arrow of time is the thermodynamic arrow of time. This is given by the direction in which entropy (which Hawking calls disorder) increases. According to Hawking, this is why we never see the broken pieces of a cup gather themselves together to form a whole cup.

The second arrow is the psychological arrow of time. Our subjective sense of time seems to flow in one direction, which is why we remember the past and not the future. Hawking claims that our brain measures time in a way where disorder increases in the direction of time – we never observe it working in the opposite direction. In other words, Hawking claims that the psychological arrow of time is intertwined with the thermodynamic arrow of time.

Hawking's third and final arrow of time is the cosmological arrow of time. This is the direction of time in which the Universe is expanding rather than contracting. Note that, during a contraction phase of the universe, the thermodynamic and cosmological arrows of time would not agree.

Hawking claims that the "no-boundary proposal" for the universe implies that the universe will expand for some time before contracting back again. He goes on to argue that the no-boundary proposal is what drives entropy and that it predicts the existence of a well-defined thermodynamic arrow of time if and only if the universe is expanding, as it implies that the universe must have started in a smooth and ordered state that must grow toward disorder as time advances.

Hawking argues that, because of the no-boundary proposal, a contracting universe would not have a well-defined thermodynamic arrow and therefore only a Universe that is in an expansion phase can support intelligent life. Using the weak anthropic principle*, Hawking goes on to argue that the thermodynamic arrow must agree with the cosmological arrow in order for either to be observed by intelligent life. This, in Hawking's view, is why humans experience these three arrows of time going in the same direction.

Wormholes and Time Travel

Many physicists have attempted to devise possible methods by humans with advanced technology may be able to travel faster than the speed of light, or travel backwards in time, and these concepts have become mainstays of science fiction.

Einstein–Rosen bridges were proposed early in the history of general relativity research. These "wormholes" would appear identical to black holes from the outside, but matter which entered would be relocated to a different location in spacetime, potentially in a distant region of space, or even backward in time.

However, later research demonstrated that such a wormhole, even if it possible for it to form in the first place, would not allow any material to pass through before turning back into a regular black hole. The only way that a wormhole could theoretically remain open, and thus allow faster-than-light travel or time travel, would require the existence of exotic matter with negative energy density, which violates the energy conditions of general relativity. As such, almost all physicists agree that faster-than-light travel and travel backwards in time are not possible.

Hawking also describes his own "chronology protection conjecture", which provides a more formal explanation for why faster-than-light and backwards time travel are almost certainly impossible.

The chronology protection conjecture is a hypothesis that the laws of physics prevent time travel on all but microscopic scales. The permissibility of time travel is represented mathematically by the existence of closed timelike curves in some solutions to the field equations of general relativity. The chronology protection conjecture should be distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting the causal violation[1] (also known as chronology violation).

In a 1992 paper, Hawking uses the metaphorical device of a "Chronology Protection Agency" as a personification of the aspects of physics that make time travel impossible at macroscopic scales, thus apparently preventing time paradoxes. He says:

“It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the universe safe for historians.”

The Unification of Physics

Quantum field theory (QFT) and general relativity (GR) describe the physics of the Universe with astounding accuracy within their own domains of applicability. However, these two theories contradict each other. For example, the uncertainty principle of QFT is incompatible with GR. This contradiction, and the fact that QFT and GR do not fully explain observed phenomena, have led physicists to search for a theory of "quantum gravity" that is both internally consistent and explains observed phenomena just as well as or better than existing theories do.

At the time the book was written, "superstring theory" had emerged as the most popular theory of quantum gravity, but this theory and related string theories were still incomplete and had yet to be proven in spite of significant effort (this remains the case as of 2020). String theory proposes that particles behave like one-dimensional "strings", rather than as dimensionless particles as they do in QFT. These strings vibrate in many dimensions. Instead of 3 dimensions as in QFT or 4 dimensions as in GR, superstring theory requires a total of 10 dimensions. The nature of the six "hyperspace" dimensions required by superstring theory are difficult if not impossible to study, leaving countless theoretical string theory landscapes which each describe a universe with different properties. Without a means to narrow the scope of possibilities, it is likely impossible to find practical applications for string theory.

Alternative theories of quantum gravity, such as loop quantum gravity, similarly suffer from a lack of evidence and difficulty to study.

Hawking thus proposes three possibilities:

  1. There exists a complete unified theory that we will eventually find;
  1. The overlapping characteristics of different landscapes will allow us to gradually explain physics more accurately with time

  2. There is no ultimate theory.

The third possibility has been sidestepped by acknowledging the limits set by the uncertainty principle. The second possibility describes what has been happening in physical sciences so far, with increasingly accurate partial theories.

Hawking believes that such refinement has a limit and that by studying the very early stages of the Universe in a laboratory setting, a complete theory of Quantum Gravity will be found in the 21st century allowing physicists to solve many of the currently unsolved problems in physics.

Conclusion

Hawking states that humans have always wanted to make sense of the Universe and their place in it. At first, events were considered random and controlled by human-like emotional spirits. But in astronomy and in some other situations, regular patterns in the workings of the universe were recognized. With scientific advancement in recent centuries, the inner workings of the universe have become far better understood. Laplace suggested at the beginning of the nineteenth century that the Universe's structure and evolution could eventually be precisely explained by a set of laws, but that the origin of these laws was left in God's domain. In the twentieth century, quantum theory introduced the uncertainty principle, which set limits to the predictive accuracy of future laws to be discovered.

Historically, the study of cosmology (the study of the origin, evolution, and end of Earth and the Universe as a whole) has been primarily motivated by a search for philosophical and religious insights, for instance, to better understand the nature of God, or even whether God exists at all. However, most scientists today who work on these theories approach them with mathematical calculation and empirical observation, rather than asking such philosophical questions. The increasingly technical nature of these theories have caused modern cosmology to become increasingly divorced from philosophical discussion. Hawking expresses hope that one day everybody would talk about these theories in order to understand the true origin and nature of the Universe, and accomplish "the ultimate triumph of human reasoning".

Glossary

  • Anthropic principle: We see the universe the way it is, because if it were different we would not be here to observe it.
  • Anti-particle: Each type of matter particle has a corresponding antiparticle; When they collide, they annihilate eachother, leaving only energy.
  • Big bang: The singularity at the beginning of the universe.
  • Big crunch: The singularity at the end of the universe.
  • Black hole area theorem: Ignoring the quantum mechanics, the surface of a black hole can only grow with time.
  • Casimir effect: The attractive pressure between two flat, parallel metal plates placed very near each other in a vaccuum.
  • Chandrasekhar limit: The maximum possible mass of a cold star. If you go above the mass, it MUST collapse into a black hole.
  • Conservation of energy: The law of science that states: Energy can neither be crated or destroyed.
  • Dark energy: An unknown form of energy which is accelerating the expansion of the universe.
  • Dark matter: Matter in galaxies, clusters, and possibly between clusters, that cannot be observed directly but can be detected by its gravitational effect. (90% of the mass of the universe is)
  • Duality: When two different theories lead to the same physical result.
  • Edwin Hubble: American Astronomer who discovered that galaxies where (red)-shifting away from Earth.
  • Einstein-Rosen bridge: A tube in space-time linking two black holes (wormhole)
  • Electromagnetic force: The force between two particles with an electric charge.
  • Event horizon: The boundary of a black hole.
  • Exclusion principle: The idea that two identical spin-1/2 particles cannot have both the same position and velocity.
  • Friedmann models: Based on general relativity, these models predict that the universe will eventually collapse in on itself in a "big crunch".
  • Gamma rays: Electromagnetic rays of very short wavelength, produced in radioactive decay or by collisions of elementary particles.
  • General relativity: Einstein's theory based on the idea that the laws of science should be the same for all observers, no matter how they are moving. It also explains the force of gravity in terms of the curvature of a four-dimensional space-time.
  • Geodesic: The shortest (or longest) path between two points.
  • Gravitational waves: Ripples in the curvature of space.
  • Inflation: The theory that space expanded rapidly in the early universe.
  • Information paradox: The information that goes into a black hole seems lost, but this contradicts the laws of quantum mechanics.
  • Microwave background radiation: The radiation from the glowing of the hot early universe, now so greatly red-shifted that it appears as microwaves
  • Naked singularity: A space-time singularity not surrounded by a black hole/event horizon.
  • Neutrino: An extremely light (possible massless) particle.
  • Neutron: An uncharged particle, similar to a proton. (Half of the particles in an atomic nucleus)
  • Neutron star: A cold star, supported by the explusion principle replusion between neutrons
  • No boundary condition: The idea that the univers is finite but has no boundary (in imaginary time).
  • Nucleus: The center of an atom (Protons + neutrons).
  • Photon: A quantum of light.
  • Planck's quantum principle: The idea that light (or any other wave) can be emitted or absored only in discrete quanta, whose energy is proportional to their wavelength.
  • Proton: A positively charged particle.
  • Pulsar: A rotating neutron star that emits regular pulses of radio waves.
  • Quantum: The indivisible unit in which waves may be emitted or absorbed.
  • Quantum mechanics: The theory developed from Planck's principle and Heisenberg's uncertainty principle.
  • Quark: A (charged) particle. (Photons and neutrons are each composed of three quarks).
  • Red shift: The reddening of light from a star that is moving aways from us, due to the Doppler effect.
  • Singularity: A point in space-time at which the space-time curvature becomes infinite.
  • Space-time: The four-dimensional space whose points are events.
  • Special relativity: Einstein's theory based on the idea that the laws of science should be the same for all observers, no matter how they are moving, in absence of gravity.
  • Spin: A property of elementary particles, related to, but not identical to , the everyday concept of spin.
  • String theory: A theory of physics in which particles are described as waves on strings. Strings have length but no other dimension.
  • Uncertainty principle: One can never be exactly sure of both the position and and the velocity of a particle.
  • Wave/particle duality: In quantum mechanics, there is no disinction between waves and particles; because they behave the same.
  • White dwarf: A stable cold star