David Gerdes

1
The Physics of
Nothing

• David Gerdes
• Department of Physics
• University of Michigan
• March 15, 2003

2
Why is there Something Rather than Nothing?

• the darkest question in all philosophy.
  (William James)
• This problem can tear the individuals mind
  asunder. (A.C.B. Lovell)
• Each of us is grazed by this questions hidden
  power. (Martin Heidegger)
• What is it that breathes fire into the equations
  and makes a universe for them to describe? Why
  does the universe go to all the bother of
  existing? (Stephen Hawking)

3
The Vacuum in Antiquity
Earth, Air, Fire, Water, and Void.
Nature abhors a vacuum.
A vacuum is a hell of a lot better than some of
the stuff nature replaces it with.
What is, is. What is not, is not.
Aristotle (384-322 BC)
Tennessee Williams (1911-1983)
Parmenides (5th c. BC)
Buddha (6th c. BC)
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The debate on the nature of space also engaged
some of the greatest minds of the Enlightenment
Space is the sensorium of God. It is absolute,
existing apart from matter.
Gottfried Wilhelm Leibniz (1646-1716)
Space is relative and must be thought of as a set
of relationships between material objects.
Isaac Newton (1642-1727)
5
Summary of the Vacuum in Classical Mechanics

• The passive stage on which the play of force
  and motion is acted out.
• Space is static and unchanging.
• Geometry is Euclidean.
• Time marches according to an absolute, universal
  clock.

6
Electromagnetic Waves and the Ether

• We are familiar with many types of waves water
  waves, sound waves, waves on a rope or slinky.
• In each of these cases, the wave needs some
  medium (water, air, a slinky) in which to
  propagate.
• In 1863, James Clerk Maxwell showed that light is
  an electromagnetic wave.
• Obviously, light should propagate in a physical
  medium too. This medium was dubbed the
  luminiferous ether.

James Clerk Maxwell (1831-1879)
7
Searching for the Ether

• The ether had the strange property that, despite
  being some type of structure that allowed the
  propagation of light, it did not produce any
  frictional drag on the motion of mechanical
  objects.
• In fact, it could not be directly detected at
  all. It was massless and invisible.
• But there was a way to look for it indirectly

8
The Michelson-Morley Experiment (1887)

• Maxwell predicted that light should travel at
  speed c 299,792,458 m/s in the
  rest frame of the ether.
• Earth is moving around the sun at about 30,000
  m/s. If the ether exists, we would expect to
  measure values for the speed of light that differ
  by roughly this amount, depending on whether the
  light is traveling along our direction of motion
  or perpendicular to it.
• But Michelson and Morley found that the speed of
  light was always the same, independent of its
  direction or the state of motion of the observer.
  ? death knell for the ether.

9
Despite this inconvenient result, many physicists
were slow to appreciate the fact that something
momentous had happened

• The most important fundamental laws and facts
  of physical science have all been discovered, and
  these are now so firmly established that the
  possibility of their ever being supplanted in
  consequence of new discoveries is exceedingly
  remote Our future discoveries must be looked for
  in the sixth place of the decimals.

-- Albert Michelson, 1894
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The Special Theory of Relativity (1905)

• Einstein elevated the Michelson-Morley null
  result into a fundamental principle of nature

The speed of light is constant, independent of
the motion of the source or the observer.
This required him to treat space and time as
a single entity
Space
Time
Spacetime
Albert Einstein (1879-1955)
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The General Theory of Relativity (1916)

• Extension of special relativity to include
  gravity.
• Matter warps spacetime falling object follow
  straight lines in curved, 4-dimensional
  spacetime.
• Space tells matter how to move matter tells
  space how to curve.

12
General Relativity and the Universe

• Einstein attempted to find solutions to his
  equations that described the complete spacetime
  shape of the universe.
• Much to his consternation, he discovered that he
  could not find static solutions they all
  described a universe that was either expanding or
  contracting.
• Since this was clearly nonsense, Einstein
  modified his equations, adding a term that
  corresponded to the energy of the vacuum. He
  called this term the cosmological constant.

13
Doh!
14
1929 The Universe is Expanding
Edwin Hubble (1889-1953)
Age of universe 14 billion years
Chagrined, Einstein called the cosmological
constant my greatest blunder.
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Summary of the Vacuum in Relativity

• Active player in the dynamics of physics.
• Space can change. In fact a static universe is
  hard to achieve. The dynamics of spacetime
  determines the fate of the universe (Big Chill or
  Big Crunch).
• Geometry can be non-Euclidean.
• Space and time are intertwined.

16
The Quantum Leap

• Relativity abolished the distinction between the
  seemingly independent concepts of space and time.
• Meanwhile, quantum mechanics was doing the same
  thing for the seemingly independent concepts of
  particles and waves.

17
Waves
Particles

• Localized in space.
• Cant bend around corners.
• Have a definite momentum.
• Cant pass through each other.

• Spread out in space.
• Can bend around corners.
• Usually contain a range of different momenta.
• Can combine (interfere) constructively or
  destructively.

18
Quantum Uncertainty
The wavelike nature of particles is summarized in
the famous Heisenberg Uncertainty Principle,
which states that position and momentum cannot be
known to arbitrary precision simultaneously
Werner Heisenberg (1901-1976)
Niels Bohr (1885-1962)
(?x)?(?p) gt h
NB Copenhagen at Ann Arbor Performance Network,
March 20 April 13.
h is Plancks constant, a fundamental constant of
nature.
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Implications for Particles
In classical physics, there is an exact
relationship between the masss position and its
energy
Consider a mass that can oscillate up and down on
a spring
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The Quantum Oscillator

• Classically, at x0, the energy is zero.
• Therefore, the momentum is zero too.
• But this would violate the Heisenberg uncertainty
  principle!
• Therefore, the quantum oscillator cannot be
  completely at rest. Allowed energies, En, are

The minimum possible energy for the quantum
oscillator is E0 ½ hf.
En (n ½ )hf (n0,1,2)
This is called the zero point energy.
f oscillation frequency
21
Quantum Fields

• Relativity meets quantum mechanics everything is
  an oscillator!
• Each type of particle (photon, electron,) is
  described by a field that fills all space.
• At each point in space, the field has the ability
  to oscillate at any frequency.
• Mechanical analogy a 3-D lattice of connected
  springs.

Richard Feynman (1918-1988)
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Empty space the oscillators move with their
random quantum fluctuations.
Particle present a traveling disturbance in the
lattice.
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Summary of the Quantum Vacuum

• Filled with fields corresponding to each type of
  particle.
• Think of the field as describing the potential
  for particles to exist.
• Quantum fluctuations of the fields, even when no
  particles are present, mean that the vacuum
  contains a sea of virtual particles.

24
A Force from Nothing the Casimir Effect

• The vacuum is seething with quantum fluctuations
  of the electromagnetic field.
• We can classify these fluctuations by the
  wavelengths of the corresponding photons.
• Free space all wavelengths allowed.
• Between two mirrors only discrete wavelengths
  are allowed.

Hendrik Casimir (1909-2000)
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Prediction (1948) A weak attractive force
between the two mirrors
Measured in 1996
S. K. Lamoreaux, PRL 78, 5 (1997).
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The Energy of Nothing An Embarrassing Result

• Given the quantum nature of the vacuum, its no
  longer obvious that the energy density of the
  vacuum is zero.
• We can try to calculate the vacuum energy
  density, ?vac, by adding up the zero-point
  energies of all the quantum oscillators that make
  up the fields.

27
Surprise! The Expansion of the Universe is
Accelerating!

• Stunning convergence of recent results.
• Type Ia supernovae.
• Observations of the cosmic microwave background
  radiation (echo of the Big Bang).

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Type Ia Supernovae A Standard Candle for
Measuring Cosmic Distances
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Survey of Many Type 1a Supernovae at high
redshiftPerlmutter et al., 1998Riess et al.,
1998The Universe was expanding more slowly in
the distant past!
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Dark Energy

• The vacuum appears to have a nonzero energy
  density that is propelling the accelerating
  expansion of the Universe.
• Most recent data (Feb. 2003)
• This result implies that nearly ¾ of the energy
  density of the universe resides not in matter or
  radiation but in the vacuum itself!
• The cosmological constant Einsteins greatest
  legacy?
• Come to Prof. Katie Freeses SMP talks on April 5
  and 12 for many more details.

?vac 0.73 ? 0.04
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Conclusion Much Ado about Nothing

• The vacuum is a dynamic place
• Space and time are intertwined.
• Curved by matter this curvature affects motion.
• A roiling sea of virtual particles created by
  quantum fluctuations that follow from the
  uncertainty principle.
• Contains a nonzero energy density that makes up
  70 of the energy of the Universe. The nature of
  this dark energy is almost completely unknown.
• The dark energy propels the accelerating
  expansion of the universe.

Perhaps the hottest topic in physics right now.
32
Thanks!

• The Demo Lab staff Warren Smith, Bonnie Evans,
  Mark Kennedy, Angela Plagemann.
• Carol Rabuck
• Ted and Ann Annis

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