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The Origin
of the Universe
    and the
Arrow of Time

                       Sean Carroll
                    California Institute
                      of Technology
                  preposterousuniverse.com
What is Time?

A label on points in the
universe, just like space.

Time helps us locate things.




                                   [Jason Torchinsky]
We measure time using clocks:
repetitive, predictable motions.




                                   [Sara Petagna, Flickr]
Biological rhythms -- our pulse, breathing,
nervous system -- are (somewhat) reliable clocks.
They allow us to feel the passage of time.




             [Pattie Lee, Flickr]
A profound difference between time and space:
     time has a direction, space does not.




                                      [NASA]
The arrow of time
points from the
past to the future.

Things change, in
consistent ways,           time

throughout the universe.




               time               time
Just as organisms
change and evolve,
so do stars, and so
does the universe.




                      [Sky & Telescope]
1 second: hot, smooth plasma.
380,000 years: ripples in a smooth background
1010 years: stars and galaxies.
1015 years: black holes and rocks.
10100 years: empty space (forever).
There is no arrow of time in
          the fundamental laws of nature.




                               time




Interactions between       The arrow of time only
simple objects (atoms,     emerges when there
billiard balls) are        are many moving parts.
perfectly reversible.
What really happens as time passes?
 The world gets messier -- more disorderly.




                                                 [Charles Mallery]


                     time




We can clean things up, but that takes effort;
        it doesn’t happen by itself.
Disorder in the universe increases with time.
Disorder is measured
           by Entropy. Messier,
           less-organized things
Entropy


           have higher entropy.




                                                     Time

               The Second Law of Thermodynamics:
          entropy increases with time (in closed systems).
Growth of entropy is responsible
                  for all the aspects of the arrow of time.

                                            Life and death
                                            Biological evolution
                                            Memory
                                            Cause and effect
[Roger Penrose]                             The “flow” of time

            Without the arrow of time, the universe
               would be in thermal equilibrium --
            everything static, nothing ever changing.
Ludwig Boltzmann, 1870’s:

Entropy counts the number
of ways we can re-arrange
a system without changing
                                         [Martin Röll,
its basic appearance.                     Wikimedia]




 low entropy:                 high entropy:
 delicately                   all mixed up
 ordered




                       time
Boltzmann’s idea explains why entropy tends to go up:
        there are more ways to be high-entropy
                 than to be low-entropy.
                                                                   all possible
                                                                   arrangements
                                                                   of some system




But why did the entropy
start out so low?
                                      low entropy
A question about
the early universe!

                                                    high entropy

                      regions denote
                      arrangements
                      that look the same
This includes ideas like
causality and even free will.

We can reconstruct the
past from the present only
by appealing to a low-
entropy boundary condition.


          possible                                         possible
           pasts                                           futures



              correct reconstruction
low-entropy
    past
                                         what we know
                                       about the present
The origin of the arrow of time is cosmological.

Entropy was low near the Big Bang. Our initial conditions
were finely-tuned, “unnatural.” Nobody knows why.


today -- galaxy distribution             future -- emtpy space
(14 billion years): lumpy and sparse     (100 billion years): dilute and cold
medium entropy                           high entropy




                                            early -- microwave background
                                            (380,000 years): smooth and dense
                                            low entropy
Why was the early universe so “unnatural”?

      Could the whole universe just
        be a random fluctuation?
Boltzmann, 1895:
maybe there is a multiverse mostly in
high-entropy equilibrium, and our
galaxy is just a random fluctuation.




                   Boltzmann’s multiverse



    The anthropic principle: in a big universe, we
    will only observe those parts that are
    hospitable to the existence of intelligent life.
Boltzmann wasn’t the first to suggest this scenario.

“For surely the atoms did not hold
council, assigning order to each, flexing
their keen minds with questions of place
and motion and who goes where.

But shuffled and jumbled in many ways,
in the course of endless time they are
buffeted, driven along, chancing upon
all motions, combinations.

At last they fall into such an arrangement
as would create this universe…”

               -- Lucretius, De Rerum Natura, c. 50 BC.
In 1931, Sir Arthur Eddington
explained why we cannot be
just a random fluctuation.

Fluctuations are rare, and large
fluctuations are very rare.



                       This scenario predicts that we
                       should be the minimum possible
                       fluctuations -- “Boltzmann Brains.”


    [New York Times]
Skeptical
voices are
important.
Perhaps the answer is to be found before the Big Bang.



                     General relativity predicts its
                     own downfall at the moment of
                     the Big Bang. Needs to be
                     replaced by something better.

                     There could be spacetime before
                     the Big Bang, and many possibilities
                     are currently being pursued.
    [Getty Images]
A high-entropy universe would look like empty space.

That’s where our
universe is headed.

But in the presence of
vacuum energy, even
empty space has a
nonzero temperature.



                         Fields will constantly be
 background
                         gently fluctuating, even
 space                   though space is “empty.”
Einstein says that space and time are dynamical;
   they will have their own fluctuations.




We can even imagine forming a new bubble of
spacetime -- a baby universe.

Baby universes start out small, with low entropy;
then they expand and cool, creating an arrow of time.

Just like the Big Bang.
Baby universes cost zero energy to produce.

A bubble could form in this room and we’d never know.


The universe is like an
eternal bubble-making
machine. It will
never turn off.


 Each new bubble increases the entropy of the
 larger multiverse. That’s the difference between
 this scenario and Boltzmann’s; entropy grows
 forever, rather than jiggling near a maximum.
This can happen in both directions in time.




Evolving empty space to the past, we would also see
baby-universes created; their arrow of time would be
reversed with respect to ours. The multiverse can be
perfectly time-symmetric; we just don’t see all of it.
The multiverse business
is obviously speculative.



What’s important is:

You remember the past and not the future because
the early universe had a very low entropy.

Understanding why is a profound challenge
for modern cosmology.

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The Origin of the Universe and the Arrow of Time

  • 1. The Origin of the Universe and the Arrow of Time Sean Carroll California Institute of Technology preposterousuniverse.com
  • 2. What is Time? A label on points in the universe, just like space. Time helps us locate things. [Jason Torchinsky]
  • 3. We measure time using clocks: repetitive, predictable motions. [Sara Petagna, Flickr]
  • 4. Biological rhythms -- our pulse, breathing, nervous system -- are (somewhat) reliable clocks. They allow us to feel the passage of time. [Pattie Lee, Flickr]
  • 5. A profound difference between time and space: time has a direction, space does not. [NASA]
  • 6. The arrow of time points from the past to the future. Things change, in consistent ways, time throughout the universe. time time
  • 7. Just as organisms change and evolve, so do stars, and so does the universe. [Sky & Telescope]
  • 8. 1 second: hot, smooth plasma.
  • 9. 380,000 years: ripples in a smooth background
  • 10. 1010 years: stars and galaxies.
  • 11. 1015 years: black holes and rocks.
  • 12. 10100 years: empty space (forever).
  • 13. There is no arrow of time in the fundamental laws of nature. time Interactions between The arrow of time only simple objects (atoms, emerges when there billiard balls) are are many moving parts. perfectly reversible.
  • 14. What really happens as time passes? The world gets messier -- more disorderly. [Charles Mallery] time We can clean things up, but that takes effort; it doesn’t happen by itself. Disorder in the universe increases with time.
  • 15. Disorder is measured by Entropy. Messier, less-organized things Entropy have higher entropy. Time The Second Law of Thermodynamics: entropy increases with time (in closed systems).
  • 16. Growth of entropy is responsible for all the aspects of the arrow of time. Life and death Biological evolution Memory Cause and effect [Roger Penrose] The “flow” of time Without the arrow of time, the universe would be in thermal equilibrium -- everything static, nothing ever changing.
  • 17. Ludwig Boltzmann, 1870’s: Entropy counts the number of ways we can re-arrange a system without changing [Martin Röll, its basic appearance. Wikimedia] low entropy: high entropy: delicately all mixed up ordered time
  • 18. Boltzmann’s idea explains why entropy tends to go up: there are more ways to be high-entropy than to be low-entropy. all possible arrangements of some system But why did the entropy start out so low? low entropy A question about the early universe! high entropy regions denote arrangements that look the same
  • 19. This includes ideas like causality and even free will. We can reconstruct the past from the present only by appealing to a low- entropy boundary condition. possible possible pasts futures correct reconstruction low-entropy past what we know about the present
  • 20. The origin of the arrow of time is cosmological. Entropy was low near the Big Bang. Our initial conditions were finely-tuned, “unnatural.” Nobody knows why. today -- galaxy distribution future -- emtpy space (14 billion years): lumpy and sparse (100 billion years): dilute and cold medium entropy high entropy early -- microwave background (380,000 years): smooth and dense low entropy
  • 21. Why was the early universe so “unnatural”? Could the whole universe just be a random fluctuation?
  • 22. Boltzmann, 1895: maybe there is a multiverse mostly in high-entropy equilibrium, and our galaxy is just a random fluctuation. Boltzmann’s multiverse The anthropic principle: in a big universe, we will only observe those parts that are hospitable to the existence of intelligent life.
  • 23. Boltzmann wasn’t the first to suggest this scenario. “For surely the atoms did not hold council, assigning order to each, flexing their keen minds with questions of place and motion and who goes where. But shuffled and jumbled in many ways, in the course of endless time they are buffeted, driven along, chancing upon all motions, combinations. At last they fall into such an arrangement as would create this universe…” -- Lucretius, De Rerum Natura, c. 50 BC.
  • 24. In 1931, Sir Arthur Eddington explained why we cannot be just a random fluctuation. Fluctuations are rare, and large fluctuations are very rare. This scenario predicts that we should be the minimum possible fluctuations -- “Boltzmann Brains.” [New York Times]
  • 26. Perhaps the answer is to be found before the Big Bang. General relativity predicts its own downfall at the moment of the Big Bang. Needs to be replaced by something better. There could be spacetime before the Big Bang, and many possibilities are currently being pursued. [Getty Images]
  • 27. A high-entropy universe would look like empty space. That’s where our universe is headed. But in the presence of vacuum energy, even empty space has a nonzero temperature. Fields will constantly be background gently fluctuating, even space though space is “empty.”
  • 28. Einstein says that space and time are dynamical; they will have their own fluctuations. We can even imagine forming a new bubble of spacetime -- a baby universe. Baby universes start out small, with low entropy; then they expand and cool, creating an arrow of time. Just like the Big Bang.
  • 29. Baby universes cost zero energy to produce. A bubble could form in this room and we’d never know. The universe is like an eternal bubble-making machine. It will never turn off. Each new bubble increases the entropy of the larger multiverse. That’s the difference between this scenario and Boltzmann’s; entropy grows forever, rather than jiggling near a maximum.
  • 30. This can happen in both directions in time. Evolving empty space to the past, we would also see baby-universes created; their arrow of time would be reversed with respect to ours. The multiverse can be perfectly time-symmetric; we just don’t see all of it.
  • 31. The multiverse business is obviously speculative. What’s important is: You remember the past and not the future because the early universe had a very low entropy. Understanding why is a profound challenge for modern cosmology.