Philosophy of Physics

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Philosophy of Physics

• Week X
• The Copenhagen Interpretation

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Making sense of superposition

• The state of a system is represented by a vector
  ? in a Hilbert space H.
• Measurement outcomes are always eigenvalues, a1,
  a2, corresponding to the eigenvectors, a1, a2,
• The probability of getting a particular outcome,
  say a2, depends on the amount of overlap of the
  state vector ? with the eigenvector a2.
• When ? does not exactly correspond to any
  eigenvector, its in a superposition of
  eigenstates.
• Whats going on?
• Mathematically, superpositions are easy to
  understand its just basic linear algebra.
• What do the mean, physically?

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• Consider the spin of a photon.
• Will it make it through a Polaroid filter
  oriented in the x direction?
• If it does, then it has spin up in the
  x-direction if not, then it has spin down in
  the x direction.

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• Is the system really one way or the other (ie,
  really spin up or really spin down in the
  x-direction)?
• And will measuring tell us which?
• Or is it neither until it is measured?

a1
?
(a1,?)
a2
(a2,?)
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Stern-Gerlach

• For a nice presentation, see http//phet.colorado
  .edu/simulations/sterngerlach/SG_1.swf

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Some Views

• Those who are not shocked when they first come
  across quantum theory cannot possibly have
  understood it. -- Niels Bohr.
• If you are not completely confused by quantum
  mechanics, you do not understand it. -- John
  Wheeler.
• It is safe to say that nobody understands quantum
  mechanics.
• -- Richard Feynman.
• If quantum theory is correct, it signifies the
  end of physics as a science. -- Albert Einstein.
  
• I do not like quantum mechanics, and I am sorry
  I ever had anything to do with it. -- Erwin
  Schrödinger.
• Quantum mechanics makes absolutely no sense. --
  Roger Penrose.

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Should We Just Give UP ?

• The above quotes suggest that maybe the best
  thing is to give up. Dont try to make sense of
  the QM.
• However, nobody likes a quitter, a whiny
  complainer, an intellectual coward.
• Better to go down in flames.
• On the other hand, we will see why those famous
  scientists were so pessimistic.

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Interpretations

• Minimal statistical interpretation
• Predict observation
• Dont try to do more
• Deep understanding is impossible dont even try
• Realism
• Science gives us a true description of reality
• Measurements discover an independent reality
• Anti-realism (one version)
• The world is not independent from us
• Measurements (in some sense) create, rather than
  reveal what is already the case.

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Original Schrödinger interpretation

• Problems
• Electrons are localized particles while ? is
  spread out
• ? is complex, many dimensional, thus, cannot be a
  wave in ordinary space
• ? is discontinuous on measurement

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Original Born Interpretation

• According to Max Born ? is a probability wave.
  It describes the probability density of an
  ensemble of electrons it is not a physical wave.
• ?2dx is the probability of being in the region
  dx.
• Electrons have positions and momenta at all times.

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Problems with (original) Born

• Single electron (or photon) shows interference
  effects. (They can be slowed to one a day, not
  hitting each other.)
• How can a non-physical probability wave interfere
  with itself?

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• The Schrödinger interpretation is ontological in
  that ? describes an independent world.
• The Born interpretation is epistemic in that ?
  describes the state of our knowledge/ignorance of
  the world.
• Neither interpretation works. (But the
  Schrödinger equation and the Born rule are OK.)
• The Copenhagen interpretation is a blend of the
  two. ? is about the world and about our knowledge
  of the world.

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Niels Bohr (18851962)

• Danish, born in Copenhagen
• Son of prominent Prof of physiology
• Student of Høffding who introduced him to Kant,
  Kierkegaard, James
• 1913 Bohr atom
• 1922 Nobel Prize
• Denmark built him the Institute for Theoretical
  Physics a Mecca for physics in the 1920s and
  30s.
• A kind of father figure for Heisenberg, and
  others who spent much time in Copenhagen.
• 30 year fight with Einstein over QM
• His view is known as the Copenhagen
  Interpretation.

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Bohrs Basic Idea

• Classical physics has a kind of priority, even
  though it isnt true, at least not true in the
  micro-realm.
• But we can only understand things with the help
  of common sense concepts, even though many common
  sense beliefs are false.
• The ideas of classical physics involve a kind of
  common sense and we are forced to use those
  concepts when trying to understand the
  micro-world.

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Common Sense

• Some common sense beliefs might be right, some
  wrong.
• Some of them might be innate, some learned.
• Things we have learned (some right, some wrong)
• If the earth were round, then Australians would
  fall off.
• Sun doesnt move through the sky we turn.
• Things dont come naturally to rest conservation
  of momentum/energy.
• Innate beliefs (some right, some wrong)
• Objects have colours and smells.
• The primary/secondary property distinction
  (accepted by philosophy, physics, and
  psychology), says objects have properties such as
  mass, charge, velocity, etc., but colours,
  tastes, smells, etc. are produced by the mind.
• Innate (but possibly unavoidable)
• The world consists of objects that have
  properties.

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Common Sense (Continued)

• Here are some assumptions we all make, at least
  in ordinary circumstances.
• The world consists of definite objects.
• A bird is distinct from the air it flies in
• A tree is distinct from the ground
• A photon is distinct from a polaroid filter
• These objects are distinct and our concepts of
  these things are also distinct.

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Contrasts
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Some Main Bohr principles

• These points are all disputable. Bohr was not a
  clear writer most find him very obscure.
• 1. All experience is to be accounted for by
  means of classical concepts.
• By classical, Bohr meant the concepts of
  classical physics, which he took to be
  refinements of common sense concepts.
• We cannot avoid these concepts and must use them
  when we describe our experience of the
  micro-realm.

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• For example location in space, location in time,
  momentum, mass, etc.
• We need these concepts in order to have
  meaningful experience.
• We also need them for communication.
• Without them we could experience nothing.
  (Everything would be a buzzing, blooming
  confusion. James)
• Parallels with Kant?
• We contribute causation when we experience A
  causing B
• We contribute space when we see objects in space.

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• 2. The application of any concept depends on the
  presence of suitable physical conditions.
  Micro-objects have properties only in relation to
  the macro-world.
• For instance, a photon has a spin component in
  the x-direction (ie, spin up or spin down), iff
  there is a macro-device (ie, a polaroid filter)
  to which it is appropriately related.
• Without such a setup, there would be no spin at
  all.
• In such a setup (ie, a measurement in the
  x-direction), there are no spin components in the
  y-direction (neither up nor down).

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• In the beam of light, a photon has a position in
  the x-direction (ie, at the hole in the screen),
  but it has no momentum in the x direction. (NB.
  Not zero momentum, but no momentum.)

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• 3. There is a finite quantum of action associated
  with the measuring process in the micro-world.
  This quantum of action links the micro-system and
  the macro-measuring device into an indivisible
  and uncontrollable unity.
• It is here that causation begins to break down
  and determinism fails.

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• 4. The concepts of classical physics (eg,
  position, momentum) are not all simultaneously
  applicable. Which of a pair of complementary
  concepts is applicable depends on the whole
  physical arrangement.
• If you are measuring spin in the x-direction,
  then you cannot measure it in the y-direction.
  If you are measuring position in the x-direction,
  then you cannot measure momentum in the
  x-direction.

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Werner Heisenberg (1901-1976)

• Matrix mechanics 1925
• Uncertainty principle 1927
• Nobel prize 1932
• Many contributions after that

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Heisenberg on the uncertainty principle
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• How should we understand this?
• Realist as mere ignorance position and momentum
  both exist, but we can only know one. After all,
  how can we disturb the momentum unless there is
  a momentum to disturb. Heisenbergs thought
  experiment presupposes realism.
• Bohr type anti-realist ontologically if there
  is a position, then no momentum exists.

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Heisenbergs account

• If one wants to clarify what is meant by
  position of an object, for example, of an
  electron, he has to describe an experiment by
  which the position of an electron can be
  measured otherwise this term has no meaning at
  all. --Heisenberg
• He seems to claim that ignorance in principle of
  X implies the non-existence of X (ie, a form of
  verificationism)

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• Heisenberg introduced the term observables for
  the properties of quantum entities, eg, position,
  momentum, spin, etc. are observables. Why
  (according to someone like Heisenberg) is path
  or trajectory not an observable (and hence, not
  a legitimate concept)?
• (First, ask yourself, What is a path?)

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Heisenberg on determinism

• According to most people, QM is not
  deterministic. Why?
• Heisenberg characterizes determinism or the
  principle of causality as follows If we have
  exact knowledge of the present, then the future
  can be calculated.
• H says this is false, since we cannot have exact
  knowledge of the present.
• Is this a good argument? No.
• But H might perhaps say knowledge of the
  present is meaningless, so the causal principle
  is not applicable.

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Later Heisenberg

• When a quantum system is in a state of
  superposition of eigenstates of, say, momentum,
  then it has no momentum, but it has a potential
  for various different momenta.

a1
?
(a1,?)
a2
(a2,?)
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• Reality consists of potentials that become
  actualized in measurements.
• potential actual
• The idea is from Aristotle (acorns are potential
  oak trees).

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• How is potentiality turned into actuality?
• This the same as asking How does the wave
  function collapse?
• And this is equivalent to asking How does reality
  become determinate?
• Heisenberg hasnt solved any problem at all, just
  put it in a new form.

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Schrödingers cat

• This problem arises from two key assumptions.
• QM applies to both micro- and macro-objects
• Measurement is a physical process hence it
  should be described by QM

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Measurement

• Lets suppose a photon has the property spin in
  the x direction and there are two possible
  outcomes up and down. Its called a two-state
  system.
• A measuring device to measure this might be a
  polaroid filter with a photosensitive detector
  that flashes green or red depending on whether
  the photon passed the filter or not.
• Thus, the measuring device is also a two-state
  system.

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• We can represent the photon as in a state ?p u
  d.
• The measuring device also has two eigenstates, g
  and r for green flash and red flash.
• Features of QM imply that the correct
  representation of the photon and the measuring
  device is the so-called tensor product ?pm ?p
  ? ?m. This, too, is a vector in a Hilbert space,
  constructed out of the photons and the measuring
  devices separate Hilbert spaces.
• In general, ?pm (u ? g) (d ? r).
• This means, the measuring device also goes into a
  state of superposition.

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• The consequence is bizarre.
• A cat is in a box with a radio-active atom if it
  decays, the cat will be poisoned. All are hidden
  from view.
• Is the cat alive or dead before looking?
• Or is the cat neither (ie, in a state of
  superposition?
• It seems to be the latter.

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• In other words, the cat seems to be in a state
  of superposition of being alive and dead
• ?atomcat (energeticatom ? alivecat)
  (decayedatom ? deadcat)

energetic ? alive
?atomcat
decayed ? dead
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Responses

• Schrödinger this is absurd QM is wrong (or at
  least the Copenhagen interpretation is wrong).
• Bohr (?) there is a difference between the
  micro- and the macro- worlds QM applies only to
  the micro-.
• Decoherence The cat does go into a state of
  superposition, but only for a very short time, so
  dont worry.
• Wigner Conscious minds are crucial.

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Eugene Wigner (1903-1995)

• Promoter of symmetry in physics
• Nobel prize 1963
• Developed the view of von Neumann and others that
  consciousness is what collapses the wave function.

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Two questions

• Do macroscopic objects such as cats really go
  into superpositions?
• Yes, QM applies to big and small (there is only
  one physical world)
• When we look we only see eigenstates, never
  superpositions. How is this possible? What
  collapses the wave function?

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• None of these measuring devices can collapse the
  wave function, ie, put the system into one of the
  eigenstates.
• Yes, it happens. How?
• Wigner We need something to which QM does NOT
  apply when measuring.
• It would have to be non-physical, since QM
  applies to everything physical
• Are there any obvious candidates? Yes, the mind.
• It is consciousness that makes measurements, that
  collapses the wave function, that makes reality
  determinate.

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Ridiculous?

• Entails mind-body dualism.
• Is dualism plausible?
• Be tolerant QM is very weird, so give serious
  consideration to views that seem very farfetched.
• Note that the rivals are just as farfetched.

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Delayed choice

• John Wheeler (an outstanding physicist and friend
  of Wigner) proposed an even weirder possibility
  changing the past.

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• Wheeler We have a choice between wave
  detecting and
• particle detecting devices
• If we choose the interference detector
  (wave), the state will be
• ?top ?bottom, which is a superposition.
• If we choose the particle detector, the
  state will be one of either
• ?top or ?bottom, neither of which is a
  superposition.
• The experimental arrangement determines the
  state.
• BUT, the photon passed the galaxy long ago
  the choice of which
• experimental setup to have is delayed until
  after the photon is on
• its way.

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• It is wrong to think of the past as already
  existing in all detail. The past is theory.
  The past has no existence except as it is
  recorded in the present. By deciding what
  questions our quantum registering equipment shall
  put in the present we have an undeniable choice
  in what we have a right to say about the past.
• Wheeler
• Thus, our present choices create past reality.
  Our choice today determines whether the photon
  went one way or went both ways billions of years
  ago.

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Further Reading

• A very nice book is Murdoch, Niels Bohrs
  Philosophy of Physics
• A good online survey http//plato.stanford.edu/en
  tries/qm-copenhagen/
• A brief biography of Bohr can be found at
  http//www-groups.dcs.st-and.ac.uk/history/Mathem
  aticians/Bohr_Niels.html
• A longer biography is Pais, Niels Bohrs Times
  in Physics, Philosophy, and Polity
• There is a short film clip of some of the main
  people at the famous Solvay Conference in 1927
  http//216.120.242.82/greensp/video.html (Some
  of the names are mispronounced.)
• Michael Frayn, Copenhagen is a wonderful play
  about a meeting between Heisenberg and Bohr in
  Nazi-occupied Denmark.

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Further Reading (more)

• Heisenberg, Physics and Philosophy
• Wigner, Symmetries and Reflections (chapters on
  quantum measurement)
• Online survey http//plato.stanford.edu/entries/q
  m-copenhagen/
• The measurement problem http//plato.stanford.edu
  /entries/qt-measurement/
• Schrödingers Cat http//en.wikipedia.org/wiki/Sc
  hroedingers_cat
• Consciousness http//en.wikipedia.org/wiki/Consci
  ousness_causes_collapse
• Wikipedia articles on Heisenberg
• http//en.wikipedia.org/wiki/Heisenberg
• and on Wigner
• http//en.wikipedia.org/wiki/Wigner and
• http//en.wikipedia.org/wiki/Wigner27s_friend
• and on Wheeler
• http//en.wikipedia.org/wiki/John_Archibald_Wheel
  er