User:Bob K31416/EPR/sandbox

Outline of present form of article

Lead

 * dichotomy: either measurement affects other system or wave function not complete
 * challenge to Copenhagen
 * EPR thought experiment implied contradiction in Copenhagen
 * Einstein's struggles/protests re Copenhagen defines reality by measurements
 * garbled paradox explanation- hidden variables, local realism (not to be confused with philosophical realism; see Bell inequality, Bell test experiments, and counterfactual definiteness), contradiction, but not inconsistent, does not contradict causality, Bell says it does, violates classical intuitions

Quantum mechanics and its interpretation

 * quantum mechanics has been used successfully
 * interpretations of quantum mechanics, mainly of a philosophical nature, have been controversial
 * measurements not deterministic
 * wave function collapse (Copenhagen)
 * Einstein opposed Copenhagen - QM incomplete
 * von Neumann, Bohm advocated hidden variables but not Einstein
 * EPR paper
 * experiment implies knowing measurement result before measurement; implies reality
 * reality local
 * reality only influenced by backward light cone
 * Einstein said EPR paper didn't express his views well

Description of the paradox

 * quantum entanglement used to show separate parts of system, measurements: nonlocal behavior

Simple version

 * described by Greene, used by Einstein to show existence of hidden variables
 * positron and electron from pion decay
 * spins opposite (i.e. total spin zero)
 * measuring spin about one axis, then it can't be measured about another axis [sic]
 * suppose measure electron spin about x-axis, then positron's spin about x-axis known
 * since positron's spin now known without it being measured, it must have had that spin all along
 * Then measure positron spin about y-axis so that it had a definite spin about x and y axes before measurement - implies hidden variable according to some interpretations

Measurements on an entangled state

 * source emits electron-positron pairs
 * electron goes to destination A and positron to B
 * total spin is zero (i.e. spins opposite)
 * consider case of electron and positron entangled
 * superposition of two spin states relative to z-axis: (I) electron +z, positron -z and (II) electron -z, positron +z
 * a measurement yielding electron +z, results in collapse into 2-particle spin state I with positron -z.
 * similarly if electron -z with positron +z.
 * same for x-axis with states Ia, IIa and spins +x, -x
 * x-spin and z-spin are incompatible observables, Heisenberg uncertainty principle, can't have definite values simultaneously
 * suppose measurement of electron is +z so that state I now with positron +z
 * a measurement of positron x-spin would be equally probable to yield +x or -x
 * might expect that measurement of positron x-spin could only have one result since positron hasn't been disturbed [sic]
 * but positron x-spin should not be certain
 * what positron knows
 * paradox summed up
 * when electron and positron spins are measured about the same axis, one is + and the other -, implies they are linked in either of two ways:
 * created with opposite spin (hidden variable)
 * spin of one made opposite when spin of other measured (entanglement)
 * when measured about different axes, electron about x-axis implies positron about x-axis, then either of two possibilities for the positron:
 * its y-spin is no longer certain
 * it has a definite spin already about a second axis—a hidden variable.
 * EPR paper used momentum instead of spin
 * real experiments used polarization of photons

Locality in the EPR experiment

 * principle of locality - physical processes occurring at one place should have no immediate effect on the elements of reality at another location
 * consequence of special relativity - if information transmitted faster than c then causality violated
 * "usual rules for combining quantum mechanical ?and classical? descriptions violate the principle of locality without violating causality" since information not transmitted
 * according to EPR paper, violation of locality implies QM not a complete theory

A proposed opening of the article for the more general reader

The EPR paradox, Einstein–Podolsky–Rosen paradox, or EPR argument, is a topic in quantum physics and the philosophy of science regarding  measurements of microscopic systems (such as individual photons, electrons or atoms) and the description of those systems by the methods of quantum physics. More specifically it concerns various versions and consequences of a thought experiment where two systems interact with each other and then are separated so that they presumably don't interact any more. Then in the thought experiment, a property of one of the systems is measured and the possible effect of this measurement on the other separated system is considered, along with the consequences of the possible effect.