Quantum Tunnelling

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Lecture 16

• Quantum Tunnelling

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Heisenbergs Uncertainty Principle involving
energy and time

• If our measurement lasts a certain time Dt, then
  we cannot know the energy better than an
  uncertainty DE

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Imagine the Roller Coaster ...

• Normally, the car can only get as far as C,
  before it falls back again
• But a fluctuation in energy could get it over the
  barrier to E!

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Quantum Tunnelling

• A particle borrows an energy DE to get over a
  barrier
• Does not violate the uncertainty principle,
  provided this energy is repaid within a certain
  time Dt
• The taller the barrier, the less likely
  tunnelling would occur

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Quantum Tunnelling Animation
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Example of Quantum Tunnelling Radioactivity
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Concept of Half-Life

• 13N has a half-life of 10 min
• Consider a sample of 13N
• After 10 min, half of the 13N atoms would have
  decayed and half would not have decayed
• After another 10 min, half of the remaining 13N
  atoms would have decayed and half would not
• Probabilistic process can never predict exactly
  when a given atom would decay

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Applications of Quantum Tunnelling

• Scanning tunnelling microscope
• Tunnel diode
• Josephson junction

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Scanning Tunnelling Microscope
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Iron Atoms on Copper
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35 Xenon Atoms on Nickel
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If Plancks constant were much larger...
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A can toppling over due to quantum fluctuations
of its position
Have to wait about 101033 years!!
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Quantum Teleportation

• Probability that in your lifetime, you would find
  yourself teleported onto the surface of Mars,
  reassembled, and at least momentarily alive

1 part in 101051

• But quantum teleportation has been achieved
  forphotons

Beam me up
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Discourse on Quantum Weirdness

• Einsteins moon
• Schrödingers cat
• EPR paradox

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Einsteins Moon

• Does the moon exist if nobody is looking at it?
• Copenhagen interpretation NO! The moon exists
  only in terms of probability wave functions
• Only when observed do these wave functions
  collapse to definite states
• Conflict between objective and subjective
  realities

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Schrödingers Cat

• One atom of 13N and a detector
• If atom decays, detector activates a hammer
  which breaks a glass containing poison gas
• Everything inside a box, together with a cat,
  and seal it

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After 10 minutes has passed, just before we open
the box...

• Copenhagen interpretation The cat exists in a
  probabilistic state of being 50 alive and 50
  dead
• Our act of observation collapses the wave
  function and determines its fate instantly

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Other Interpretations to the Rescue?

• Bohm Quantum potential
• Wigner, Penrose Human consciousness
• von Neumann, Wheeler Participatory universe
• Everett, Deutsch Many-worlds interpretation

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Recall Double-slit experiment with electron gun
and detector
Can we try to trick the electron, by closing
one slit after it has passed through the wall?
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Delayed Choice Experiment
Expt carried out now will determine whether each
photon, billions of years ago, behaved like a
particle or wave
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Many-Worlds Interpretation

• Each quantum process will split the universe into
  two or more universes
• All the possible universes exist, but none can
  communicate with another

Many-worlds FAQ
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Einstein-Podolsky-Rosen (EPR) Paradox

• Decay of pion

• Electron and positron have opposite spins

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EPR Paradox (contd)

• Let the electron and positron fly very far apart
  
• Measure the spin of one of them, say the electron
• This would instantaneously determine the spin of
  the positron
• Experimentally verified by Aspect (1982)

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Non-Locality of Quantum Mechanics
Events in Region B instantaneously dependent
upon events in Region A
Events in Region A instantaneously dependent
upon events in Region B
widely separated regions
Einstein Spooky action at a distance
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Does this contradict special relativity?

• In other words, can this be used to transmit
  messages faster than light?
• NO! Because outcome is completely probabilistic
• We would never know in advance whether the
  electron is going to be spin up or down

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Quotes to ponder

• Niels Bohr Anyone who is not shocked by
  quantum theory has not understood it.
• Richard Feynman I think I can safely say
  that nobody understands quantum mechanics.

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Further Reading

• J. Horgan, Quantum PhilosophyScientific American
  (July 1997)
• R.E. Crandall, The Challenge of Large Numbers
  Scientific American (Feburary 1997)