Relativity and Quantum Mechanics

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Lecture 19

• Relativity and Quantum Mechanics

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Domains of Physics
Speed
c
Relativistic Quantum Mechanics
Relativistic Cosmology
Relativity
c/10
Quantum Mechanics
Classical Mechanics
Newtonian Cosmology
Size
Nucleus (10-14 m)
Atom (10-10 m)
Galaxy (1020 m)
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Paul Dirac (1902-84)

• First to try to combine quantum mechanics with
  special relativity
• Obtained the relativistic version of
  Schrödingers equation in 1928
• Known as the Dirac equation

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The Dirac Equation

• Appears to have solutions with negative energies
• Vacuum consists of a sea of such
  negative-energy particles
• Dirac identified holes in this sea as
  antiparticles, with opposite charge to normal
  particles
• He (wrongly) identified the antiparticle of the
  electron with the proton

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Positron Antiparticle of the Electron

• Discovered in cosmic rays by Carl Anderson in
  1932
• Has the same mass as the electron but positive
  charge

Anderson saw a track in a cloud chamber left by
something positively charged, and with the same
mass as an electron
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Every particle has an antiparticle

• 1955 antiproton
• 1960 antineutron
• 1965 anti-deuteron
• 1995 anti-hydrogen atom (only 9 produced!)
• The photon is its own antiparticle!

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What if we bring a particle and antiparticle
together?
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Particle Antiparticle Annihilation / Creation

• A particle can annihilate with its antiparticle
  to form gamma rays
• An example whereby matter is converted into pure
  energy by Einsteins formula E mc2
• Conversely, gamma rays with sufficiently high
  energy can turn into a particle antiparticle
  pair

Particle antiparticle tracks in a bubble
chamber
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How much antimatter is there in the universe?

• Cannot tell just by looking
• But if there are antimatter stars and galaxies,
  then their boundaries with normal matter will be
  sources of gamma rays
• We do not detect such gammarays in significant
  amounts? universe is mainly made up of matter

A possible cloud of antimatter at the centre of
our galaxy?
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Why is there so little antimatter in the universe?

• A very small asymmetry between particles and
  antiparticles is predicted by the weak force
• During the big bang, for every billion antimatter
  particles produced, there were a billion and one
  matter particles
• This one matter particle out of a billion is all
  that is left today!

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Uses of Antimatter

• Present Positron Emission Tomography (PET)
• Future Antimatter propulsion?
• problems with manufacture and storage

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How PET Works

• A short-lived radioactivesubstance such as 18F
  is injected into the bloodstreamas glucose
• It would decay by emitting apositron, which
  would annihilatewith an electron in the blood to
  produce gamma rays
• Gamma rays fly off in oppositedirections into
  the detectors. This enables the location of the
  original electron to be pinpointed

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PET Images of the Brain
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Quantum Field Theory

• Modern replacement of Diracs theory by Feynman
  and others
• A relativistic version of quantum theory in which
  the number of particles is not fixed
• since Emc2 means energy can be converted into
  particles and vice versa

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Antiparticles and Backward Time Travel

• Feynman discovered that a particle going
  backwards in time is mathematically equivalent
  to an antiparticle going forwards in time

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Closed Timelike Curve

• Such a CTC is equivalent to an electron-positron
  pair created at A and annihilated at B

time
B ?
electron
positron
? A
space
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What is a vacuum?

• Space with nothing in it
• Energy of vacuum is therefore zero
• But isnt this inconsistent with the energy-time
  uncertainty principle?

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Vacuum not really a vacuum?

• Energy of the vacuum can fluctuate
• By E mc2, energy is equivalent to matter
• Energy fluctuations can appear as additional
  particles, called virtual particles

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Virtual Particles
No law of physics is violated if virtual
particles annihilate within a certain time
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Casimir Effect

• Put two metal plates in a vacuum
• Only virtual particles of certain wavelengths can
  appear between the plates, while those of any
  wavelength can appear on the outside
• Result is a net force pushing the plates together

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Black Hole Evaporation

• Caused by virtual particles appearing just
  outside the event horizon
• A virtual particle could cross the event horizon
  and thus will not be able to annihilate with
  its partner
• To ensure energy conservationescaping particle
  must turn into a real particle with positive
  energy, while trapped particle carries negative
  energy into the black hole