Lecture 16 Quantum Tunnelling by chenmeixiu

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									  Lecture 16


Quantum Tunnelling
       Heisenberg‟s 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
          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!
                 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
Quantum Tunnelling Animation
Example of Quantum Tunnelling:
         Radioactivity
                   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
      Applications of Quantum Tunnelling

   Scanning tunnelling microscope


   Tunnel diode




   Josephson junction
Scanning Tunnelling Microscope
Iron Atoms on Copper
35 Xenon Atoms on Nickel
If Planck‟s constant were much larger...
A can toppling over due to quantum
     fluctuations of its position




                               33
     Have to wait about 1010        years!!
               Quantum Teleportation

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

                                         51
                        1 part in 1010


   But quantum teleportation has been achieved for
    photons




                                                 “Beam me up”
Discourse on Quantum Weirdness

      Einstein‟s moon


      Schrödinger‟s cat


      EPR paradox
             Einstein‟s 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
                   Schrödinger‟s 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 …
          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
     Other Interpretations to the Rescue?

   Bohm: Quantum potential


   Wigner, Penrose: Human consciousness


   von Neumann, Wheeler: Participatory universe


   Everett, Deutsch: Many-worlds interpretation
   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?
         Delayed Choice Experiment




Expt carried out now will determine whether each photon,
   billions of years ago, behaved like a particle or wave
           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
    Einstein-Podolsky-Rosen (EPR) Paradox

   Decay of pion




   Electron and positron have opposite spins
                 EPR Paradox (cont‟d)

   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)
 Non-Locality of Quantum Mechanics




Events in Region A                      Events in Region B
 instantaneously                         instantaneously
 dependent upon                          dependent upon
events in Region B                      events in Region A

                     widely separated
                         regions




       Einstein: “Spooky action at a distance”
    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
                  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.”
                   Further Reading

   J. Horgan, Quantum Philosophy
    Scientific American (July 1997)


   R.E. Crandall, The Challenge of Large Numbers
    Scientific American (Feburary 1997)

								
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