From Eternity to Here:
The Quest for the Ultimate Theory of Time

Sean Carroll

Table of Contents


  1. Prologue

    The nature of time, the importance of entropy, and the role of cosmology.

Part One: Time, Experience, and the Universe

  1. The Past is Present Memory

    Time has different meanings: a label on different moments, the duration between events, and a medium of change. We can think of the past, present, and future as equally real.

  2. The Heavy Hand of Entropy

    The direction of time is governed by the Second Law of Thermodynamics: in a closed system, entropy only increases or stays the same. Entropy measures the disorder of a system.

  3. The Beginning and End of Time

    The evolution of the universe through time, beginning with a hot, dense Big Bang (which may not be the true beginning), expanding and forming stars and galaxies, eventually accelerating into emptiness.

Part Two: Time in Einstein's Universe

  1. Time is Personal

    Einstein’s Special Theory of Relativity. You can’t go faster than the speed of light; you stay within a light cone in spacetime. Time measures the duration elapsed along different trajectories.

  2. Time is Flexible

    Einstein’s General Theory of Relativity. Spacetime is curved, which we experience as gravity. The curvature of spacetime underlies black holes and the expansion of the universe.

  3. Looping Through Time

    Closed timelike curves would allow you to visit the past without violating the rules of relativity. A time machine of this sort doesn’t necessarily lead to paradoxes, but might be impossible to create according to the laws of physics.

Part Three: Entropy and Time's Arrow

  1. Running Time Backwards

    The fundamental laws of physics, as we understand them, conserve information: the future and past can be predicted and retrodicted from perfect knowledge of the present state. Microscopic processes are reversible.

  2. Entropy and Disorder

    Ludwig Boltzmann discovered our modern understanding of entropy: the number of ways microscopic constituents can be arranged to form the same macroscopic system. It’s natural for entropy to increase, but only if we assume a “Past Hypothesis” that entropy started very low.

  3. Information and Life

    The growth of entropy powers our experience of life: the ability to remember the past, to metabolize free energy, and to process information. Maxwell’s Demon illustrates the connection between entropy and information.

  4. Recurrent Nightmares

    A finite system spends most of its time in high-entropy equilibrium, with occasional fluctuations to lower entropy. A finite universe that lasts for all time would behave just that way, and most observers would be disembodied “Boltzmann brains.”

  5. Quantum Time

    Quantum mechanics says that what we can observe is much less than what exists. The act of observation seems to be irreversible. One interpretation is that the irreversibility is only apparent, as we exist in “branches of the wave function” that lose touch with other branches.

Part Four: From the Kitchen to the Multiverse

  1. Black Holes: The Ends of Time

    Stephen Hawking showed that black holes aren’t completely black: they emit radiation. That implies that they have entropy, and that they will eventually evaporate away. Black holes provide a crucial clue to the connection between entropy and gravity.

  2. The Life of the Universe

    Near the Big Bang, the entropy of the universe was extremely low. It grew as the universe expanded, as gravity pulled matter together to form stars, galaxies, and black holes. But it remains much smaller than it could be; a state of truly high entropy would look like empty space.

  3. Inflation and the Multiverse

    The smooth state of the early universe can be explained by inflation – a period of high-energy acceleration at very early times. But inflation itself requires that the universe began in a state of even lower entropy; by itself, it doesn’t answer our questions. It does open a new possibility in the form of eternal inflation and the multiverse.

  4. The Past Through Tomorrow

    There are a number of possible explanations of our observed arrow of time, including fundamentally irreversible laws and a boundary condition outside the laws of physics. To explain the arrow using only reversible laws requires that we situate the universe we observe within a time-symmetric multiverse. This and other speculative scenarios are topics of ongoing research.

  5. Epilogue

    The origin of the universe and the arrow of time are major unsolved problems in our understanding of the natural world. But there is every reason to expect that they will someday be understood using the laws of physics. The quest to answer these questions helps make it all meaningful.

Appendix:  Math

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