Quantum Theory

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Quantum Theory

• By Brian Williams

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Blackbody Radiation

• Around the turn of the 20th century, physicists
  were studying the total energy carried by all of
  the electromagnetic radiation inside an oven at a
  given temperature
• Using classical physics, scientists came up with
  a ridiculous answer, infinity!
• Max Planck came up with a solution- energy can
  only be emitted in small packets, called quanta,
  and the energy of each wave is determined by its
  frequency

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Light- Particle or Wave?

• Particle
• First thought of by Newton, who suggested that
  light was made up of little bullets
• Later verified by Einstein in his Photoelectric
  Effect
• Energy of each photon is given by Ehf

• Wave
• First proposed by Christian Huygens, a colleague
  of Newtons
• Verified by Thomas Young in 1803, using a
  modified version of the double-slit experiment

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Double-Slit Experiment

• When one slit is opened, the photons appear
  directly in line with that slit
• But when both slits are opened, the photons form
  an interference pattern
• This result holds even if you there is only one
  photon in the system at any given time
• Works with electrons as well!!
• De Broglies hypothesis- lambda h/p

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Mathematical Interpretations

• In the early 20th century, scientists were
  looking for a mathematical construct that could
  describe atomic systems
• In 1925, Erwin Schrodinger wrote down the
  equation shown on the left, which is known as the
  Schrodinger equation
• Around the same time, Werner Heisenberg developed
  matrix mechanics, an equally valid method
• Later, Paul Dirac showed that the two were
  equivalent

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Particle in a Box

• The Schrodinger equation can be used to solve for
  the probabilities, not the actual position of the
  particle
• Once you get the wave equation, you can square it
  to get a probability density of where the
  particle might be
• Quantum mechanics can only tell you the
  statistical probabilities of certain outcomes or
  positions, not because of any flaw in the theory,
  but because this is the way nature works!
• In order to know for certain where the particle
  is, you must observe it
• Which brings us to our next question..

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Where was the particle?

• If you know where the particle is now, at
  position C,do you know where it was right before
  you looked at it?
• 3 common interpretations
• 1. Realist position- Advocated by Einstein,
  among others. The particle was always at C.
  The position of the particle was never
  indeterminate, but was merely unknown to the
  experimenter
• 2. Orthodox interpretation- Advocated by Niels
  Bohr. The particle wasnt really anywhere. The
  act of measurement (looking at it) forced the
  particle to decide on a definite position.
  Observations not only disturb the particle, they
  produce it
• 3. Agnostic interpretation- Advocated by
  Wolfgang Pauli. Asserts that this question is
  metaphysical and cannot be answered, its a silly
  question that should not even be bothered with.
• So, which is correct?

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Schrodingers Cat

• Imagine a cat inside a steel chamber, along with
  this device. In a Geiger counter there is a tiny
  bit of radioactive substance, so small that
  perhaps in the course of one hour one of the
  atoms decays, but also, with equal probability,
  perhaps none if it happens, the counter tube
  discharges and through a relay releases a hammer
  which shatters a small flask of hydrocyanic acid,
  thus killing the cat
• Now, without opening the lid of the box, is the
  cat alive or dead?
• Yes.

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A Few Quotes to Ponder

• Albert Einstein- God does not play dice with the
  Universe.
• Neils Bohr- Albert, stop telling God what to
  do!
• Bohr- Anyone who says that they can contemplate
  quantum mechanics without becoming dizzy has not
  understood the concept in the least.
• Richard Feynman- There was a time when the
  newspapers said that only twelve men understood
  the theory of relativity. I do not believe there
  ever was such a time. There might have been a
  time when only one man did because he was the
  only guy who caught on, before he wrote his
  paper. But after people read the paper a lot of
  people understood the theory of relativity in one
  way or another, certainly more than twelve. On
  the other hand, I think I can safely say that no
  one understands quantum mechanics.

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The End