24
Lectures
30
minutes/lecture
1.
Why Time Is a Mystery
Begin your study of the physics of time with these questions: What is a clock? What does it mean to say that “time passes”? What is the “arrow of time”? Then look at the concept of entropy and how it holds the key to the one-way direction of time in our universe.
1.
Why Time Is a Mystery
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13.
Boltzmann Brains
One possible explanation for order in the universe is that it is a random fluctuation from a disordered state. Could the entire universe be one such fluctuation, now in the process of returning to disorder? Investigate a scenario called “Boltzmann brains” that suggests not.
13.
Boltzmann Brains
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2.
What Is Time?
Approach time from a philosophical perspective. “Presentism” holds that the past and future are not real; only the present moment is real. However, the laws of physics appear to support “eternalism”—the view that all of the moments in the history of the universe are equally real.
2.
What Is Time?
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14.
Complexity and Life
Discover that Maxwell’s demon from lecture 10 provides the key to understanding how complexity and life can exist in a universe in which entropy is increasing. Consider how life is not only compatible with, but is an outgrowth of, the second law of thermodynamics and the arrow of time.
14.
Complexity and Life
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3.
Keeping Time
How do we measure the passage of time? Discover that practical concerns have driven the search for more and more accurate clocks. In the 18th century, the problem of determining longitude was solved with a timepiece of unprecedented accuracy. Today’s GPS navigation units rely on clocks accurate to a billionth of a second.
3.
Keeping Time
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15.
The Perception of Time
Turn to the way humans perceive time, which can vary greatly from clock time. In particular, focus on experiments that shed light on our time sense. For example, tests show that even though we think we perceive the present moment, we actually live 80 milliseconds in the past.
15.
The Perception of Time
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4.
Time’s Arrow
Embark on the quest that will occupy the rest of the course: Why is there an arrow of time? Explore how memory and aging orient us in time. Then look at irreversible processes, such as an egg breaking or ice melting. These capture the essence of the one-way direction of time.
4.
Time’s Arrow
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16.
Memory and Consciousness
Remembering the past and projecting into the future are crucial for human consciousness, as shown by cases where these faculties are impaired. Investigate what happens in the brain when we remember, exploring different kinds of memory and the phenomena of false memories and false forgetting.
16.
Memory and Consciousness
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5.
The Second Law of Thermodynamics
Trace the history of the second law of thermodynamics, considered by many physicists to be the one law of physics most likely to survive unaltered for the next thousand years. The second law says that entropy—the degree of disorder in a closed system—only increases or stays the same.
5.
The Second Law of Thermodynamics
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17.
Time and Relativity
According to Einstein’s special theory of relativity, there is no such thing as a moment in time spread throughout the universe. Instead, time is one of four dimensions in spacetime. Learn how this “relative” view of time is usefully diagramed with light cones, representing the past and future.
17.
Time and Relativity
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6.
Reversibility and the Laws of Physics
Isaac Newton’s laws of physics are fully reversible; particles can move forward or backward in time without any inconsistency. But this is not our experience in the world, where the arrow of time is fundamentally connected to irreversible processes and the increase in entropy.
6.
Reversibility and the Laws of Physics
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18.
Curved Spacetime and Black Holes
By developing a general theory of relativity incorporating gravity, Einstein launched a revolution in our understanding of the universe. Trace how his idea that gravity results from the warping of spacetime led to the discovery of black holes and the big bang.
18.
Curved Spacetime and Black Holes
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7.
Time Reversal in Particle Physics
Explore advances in physics since Newton’s time that reveal exceptions to the rule that interactions between moving particles are fully reversible. Could irreversible reactions between elementary particles explain the arrow of time? Weigh the evidence for and against this view.
7.
Time Reversal in Particle Physics
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19.
Time Travel
Use a simple analogy to understand how a time machine might work. Unlike movie scenarios featuring dematerializing and rematerializing, a real time machine would be a spaceship that moves through all the intervening points between two locations in spacetime. Also explore paradoxes of time travel.
19.
Time Travel
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8.
Time in Quantum Mechanics
Quantum mechanics is the most precise theory ever invented, yet it leads to startling interpretations of the nature of reality. Probe a quantum state called the collapse of the wave function that may underlie the arrow of time. Are the indications that it shows irreversibility real or only illusory?
8.
Time in Quantum Mechanics
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20.
Black Hole Entropy
Stephen Hawking showed that black holes emit radiation and therefore have entropy. Since the entropy in the universe today is overwhelmingly in the form of black holes and there were no black holes in the early universe, entropy must have been much lower in the deep past.
20.
Black Hole Entropy
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9.
Entropy and Counting
After establishing in previous lectures that the arrow of time must be due to entropy, begin a deep exploration of this phenomenon. In the 1870s, physicist Ludwig Boltzmann proposed a definition of entropy that explains why it increases toward the future. Analyze this idea in detail.
9.
Entropy and Counting
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21.
Evolution of the Universe
Follow the history of the universe from just after the big bang to the far future, when the universe will consist of virtually empty space at maximum entropy. Learn what is well founded and what is less certain about this picture of a universe winding down.
21.
Evolution of the Universe
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10.
Playing with Entropy
Sharpen your understanding of entropy by examining different macroscopic systems and asking, which has higher entropy and which has lower entropy? Also evaluate James Clerk Maxwell’s famous thought experiment about a demon who seemingly defies the principle that entropy always increases.
10.
Playing with Entropy
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22.
The Big Bang
Explore three different ways of thinking about the big bang—as the actual beginning of the universe; as a “bounce” from a symmetric version of the universe on the other side of the big bang; and as a region that underwent inflationary expansion in a much larger multiverse.
22.
The Big Bang
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11.
The Past Hypothesis
Boltzmann explains why entropy will be larger in the future, but he doesn’t show why it was smaller in the past. Learn that physics can’t account for this difference except by assuming that the universe started in a state of very low entropy. This assumption is called the past hypothesis.
11.
The Past Hypothesis
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23.
The Multiverse
Dig deeper into the possibility that the big bang originated in a multiverse, which provides a plausible explanation for why entropy was low at the big bang, giving rise to the arrow of time. But is this theory and the related idea of an anthropic principle legitimate science or science fiction?
23.
The Multiverse
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12.
Memory, Causality, and Action
Can physics shed light on human aspects of the arrow of time such as memory, cause and effect, and free will? Learn that everyday features of experience that you take for granted trace back to the low entropy state of the universe at the big bang, 13.7 billion years ago.
12.
Memory, Causality, and Action
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24.
Approaches to the Arrow of Time
Use what you have learned in the course to investigate a range of different possibilities that explain the origin of time in the universe. Professor Carroll closes by presenting one of his favorite theories and noting how much remains to be done before conclusively solving the mystery of time.
24.
Approaches to the Arrow of Time
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24
Lectures
30
minutes/lecture
1.
Fundamental Building Blocks
Scientists now have a complete inventory of the universe, which is composed of three basic constituents: Ordinary matter includes every kind of particle ever directly observed; dark matter consists of massive particles known only because of their gravitational effects; and dark energy is a smoothly distributed component that whose density does not change as the universe expands.
1.
Fundamental Building Blocks
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13.
WIMPs and Supersymmetry
Weakly interacting massive particles (WIMPs) are ideal candidates for what comprises dark matter. WIMPs may have their origins in supersymmetry, which posits a hidden symmetry between bosons and fermions, and predicts a host of new, as-yet-unobserved particles, including WIMPs.
13.
WIMPs and Supersymmetry
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2.
The Smooth, Expanding Universe
Imagine looking into a clear night sky with perfect vision. What would you see? This lecture surveys the visible universe—from the stars in our galaxy to the cloudy patches called nebulae that astronomer Edwin Hubble proved are galaxies in their own right—and Hubble's discovery that the universe is expanding.
2.
The Smooth, Expanding Universe
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14.
The Accelerating Universe
In the late 1990s, two groups of astronomers found to their astonishment that the expansion of the universe is speeding up rather than slowing down. Such behavior can't be explained by any kind of matter and suggests the existence of an entirely new component: dark energy.
14.
The Accelerating Universe
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3.
Space, Time, and Gravity
Einstein taught us that space and time can be combined into spacetime, which has the ability to evolve and grow. Indeed, what we think of as gravity is just a manifestation of the curvature of spacetime. To find things in the universe—including dark matter and dark energy—all we have to do is to map out this curvature.
3.
Space, Time, and Gravity
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15.
The Geometry of Space
Precise measurements of the cosmic microwave background let us measure the total energy density of the universe by observing the geometry of space. We find that the energy in matter alone is not enough, confirming the need for dark energy.
15.
The Geometry of Space
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4.
Cosmology in Einstein's Universe
The expansion of the universe is governed by its spatial curvature and energy density, both of which have specific ways of changing as the universe grows. These features are related to each other by Einstein's general theory of relativity, which can be used to model the past and possible future of the universe.
4.
Cosmology in Einstein's Universe
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16.
Smooth Tension and Acceleration
Dark energy is smoothly distributed throughout the universe and its density is nearly constant, even though the universe is expanding. Unlike gas under pressure in a container, dark energy is a kind of "negative pressure"—or tension—that imparts an accelerated expansion to the universe.
16.
Smooth Tension and Acceleration
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5.
Galaxies and Clusters
Applying the laws of dynamics to galaxies and galaxy clusters, we find that more matter is required to account for their motions than can be observed. Some of the missing mass is hot gas; however, this is still not enough, and we need to invoke some new kind of particle in galaxies and clusters: dark matter.
5.
Galaxies and Clusters
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17.
Vacuum Energy
The density and distribution of dark energy remain the same across all of spacetime, but what exactly is dark energy? There are many possibilities, the simplest of which is vacuum energy—an constant amount of energy in every cubic centimeter of space itself. Vacuum energy is equivalent to Einstein's idea of the cosmological constant.
17.
Vacuum Energy
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6.
Gravitational Lensing
Another way to detect invisible matter is to use light as a probe of the gravitational field. Passing through curved spacetime, the path of a light ray is deflected due to gravitational lensing. Lensing demonstrates the existence of gravitational fields where there is essentially no ordinary matter.
6.
Gravitational Lensing
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18.
Quintessence
Another idea about dark energy is that it results from a new field in nature, analogous to the electromagnetic field but remaining persistent as the universe expands. This field is called quintessence. It would be observationally distinguishable from the cosmological constant.
18.
Quintessence
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7.
Atoms and Particles
We peer into the atom to discover the constituents of ordinary matter: nuclei and electrons. Nuclei are made of protons and neutrons, which in turn are made of quarks. Electrons and quarks are examples of fermions, or matter particles. There are also bosons, or force-carrying particles, such as photons and gluons.
7.
Atoms and Particles
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19.
Was Einstein Right?
We have inferred the existence of dark matter and dark energy from the gravitational fields they cause. In this lecture, we explore proposals that a modified theory of gravity might allow us to dispense with the need for invoking dark stuff. However, this turns out to be very difficult in practice.
19.
Was Einstein Right?
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8.
The Standard Model of Particle Physics
In the 1960s and 1970s, physicists developed a comprehensive theory of known fermions and bosons. Now called the standard model, this theory fits an impressive amount of data, but it leaves two crucial puzzles: the hypothetical Higgs boson and the graviton, the carrier of the gravitational force.
8.
The Standard Model of Particle Physics
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20.
Inflation
Before we had observational evidence that the universe is accelerating, cosmologists considered the possibility of a period of rapid acceleration at very early times—a scenario known as inflation.
20.
Inflation
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9.
Relic Particles from the Big Bang
Armed with the core principles of particle physics, we know enough about the early universe to predict how many of each type of particle should be left over from the Big Bang. These "relic abundances" are crucial to understanding the origin of dark matter and light elements.
9.
Relic Particles from the Big Bang
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21.
Strings and Extra Dimensions
We know about the dark sector because of gravity, and string theory is an ambitious attempt to unify gravitation with the other forces of nature into a theory of everything. String theory promises a theory of quantum gravity, but it also predicts extra, unseen spatial dimensions that are difficult to test.
21.
Strings and Extra Dimensions
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10.
Primordial Nucleosynthesis
The process of nucleosynthesis describes how protons and neutrons were assembled into light elements during the first few minutes after the Big Bang. We can observe these primordial elements today and check on Einsteinian cosmology and a stringent constraint on theories of dark matter.
10.
Primordial Nucleosynthesis
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22.
Beyond the Observable Universe
The speed of light and the age of the observable universe are finite. That means we can't see the whole universe because our vision can only stretch so far. The "multiverse"—a hypothesis of regions where conditions are very different from those we see in our observable universe—may help explain properties of dark energy.
22.
Beyond the Observable Universe
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11.
The Cosmic Microwave Background
About 380,000 years after the Big Bang, the universe had cooled sufficiently for electrons and nuclei to combine into atoms allowing light to travel much more freely. The relic photons from this era are visible to us today as the cosmic microwave background, which holds clues to the composition and structure of the universe.
11.
The Cosmic Microwave Background
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23.
Future Experiments
Astronomers are designing new observatories to probe the acceleration of the universe and other cosmic phenomena. Physicists are also looking forward to new experiments that will dramatically improve our understanding of particles and forces, and how ordinary matter fits in with dark matter and dark energy.
23.
Future Experiments
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12.
Dark Stars and Black Holes
Candidates for dark matter include small, dark stars called Massive Compact Halo Objects (MACHOs) and black holes. Such objects are ultimately composed of ordinary matter, of which there just isn't enough to account for the dark matter. We are forced to conclude that the dark matter is a new kind of particle.
12.
Dark Stars and Black Holes
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24.
The Past and Future of the Dark Side
The concordance cosmology is an excellent fit to a variety of data, but it presents us with deep puzzles: What are dark matter and dark energy? Why do they have the densities they do? Our own universe seems unnatural to us. That's good news, as it is a clue to the next level of understanding.
24.
The Past and Future of the Dark Side
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