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The EPR paradox arises in a thought
experiment which shows that quantum mechanics leads to very
counter-intuitive and paradoxical consequences. It is named after Einstein, Podolsky,
and Rosen, who published the idea in 1935. It is also referred to as the EPRB paradox after Bohm, who improved the formulation of the thought experiment.
The paradox defined
The EPR paradox draws attention to a phenomenon predicted by quantum mechanics known as quantum entanglement, in which measurements on spatially separated quantum systems can
instantaneously influence one another. As a result, quantum mechanics violates a principle formulated by Einstein, known as the
principle of locality or local realism, which states that changes performed on one physical system should have no
immediate effect on another spatially separated system.
The principle of locality is persuasive, both in intuitive grounds and because it seems at first sight to be a natural
outgrowth of the theory of special relativity. According to
relativity, information can never be transmitted faster than the speed of
light, or causality would be violated. Any theory which
violates causality would be deeply unsatisfying, and probably internally inconsistent. However, a detailed analysis of the EPR
scenario shows that quantum mechanics violates locality without violating causality, because no information can be transmitted
using quantum entanglement.
Nevertheless, the principle of locality appeals powerfully to physical intuition, and Einstein, Podolsky and Rosen were
unwilling to abandon it. They suggested that quantum mechanics is not a complete theory, just an (admittedly successful)
statistical approximation to some yet-undiscovered description of nature. Several such descriptions of quantum mechanics, known
as "local hidden variable theories" were proposed.
These deterministically assign definite values to all the physical quantities at all times, and explicitly preserve the principle
of locality.
Of the several objections to the prevailing interpretation of the quantum mechanics spearheaded by Einstein, the EPR paradox
was the subtlest. It is at present considered to have been unsuccessful, the existence of hidden variables having been refuted
experimentally and the EPR "paradox" taken to be fully resolved within the current interpretation of the theory. The belief that
entanglement is a real phenomenon has led to a radical shift in thinking about 'what is reality' and what is a 'state of a
physical system'. First, a review of the history:
How the EPR paradox affects our understanding of particles
Before 1936, the generally accepted view was that a particle, such as an electron, has a position and a momentum but
'we cannot know both' at the same time. This view is present in a typical textbook explanation of the Heisenberg uncertainty principle. In such an explanation, the 'more exactly we measure the position', the 'more
we disturb the particle' and its momentum becomes that much less certain. The numerical measure of uncertainty satisfies
Heisenberg's principle, but this (local realistic) interpretation is no longer accepted in professional circles (it still lives
in popular books).
The shift was caused by the EPR thought experiment, which has shown how to measure the property of a particle, such as a
position, without disturbing it. In today's terminology, we would say that they did the determination by measuring the
state of a distant but entangled particle. According to
quantum mechanics, the state of our particle will instantly change even though we did not disturb it in any local way. It is
called a paradox, since it conflicts with our classical intuition —specifically, with the principle of locality.
The very concept of 'entanglement' also conflicts with our intuition the same way. One possibility is that quantum mechanics
is wrong. However, experiments have been interpreted as showing that entanglement does occur, and applications in the fields of
quantum cryptography and quantum computation are currently under development. In quantum
cryptography, an entangled signal is sent down a communications channel making it impossible to intercept and rebroadcast that
signal without leaving a trace. In quantum computation, entangled states allow simultaneous computations to occur in one
step.
We could argue that the EPR paper 'discovered' entanglement. The concept, also called 'nonlocal behaviour' and 'quantum
weirdness' has no classical analogy. It is the fact that QM
treats two particles, which interacted in the past (and so became entangled) and then separated spatially (i.e., 'flew
apart'), as one object. When one such particle is changed, the other will change too (instantly). Einstein called this behavior
'spooky action at a distance', and considered it
unacceptable. Before it was accepted as real and inevitable by most physicists, one escape route had to be closed, namely the
possible existence of 'hidden parameters'.
John Bell is currently considered to have closed that escape route. The setup of the EPR experiment and Bell's
theorem are described in separate pages. Here we proceed historically and first describe Bohm's contributions and then
explain the conceptual meaning of the hidden parameter using a parable of color.
Further explanation using color
Bohm substituted measurement of spin coordinates for measurement of momentum and position. The classical analogy of spin of a
photon is polarization of light, which is quite familiar. However, the mathematical description of this property in quantum
mechanics is complex. The experiment measuring spin is, however, easier than the original EPR setup.
We now describe the concept of EPR using the words 'red' and 'cyan' for 'spin up' and 'spin down':
- Imagine that a single white particle splits into two, one cyan and one red. (Here the color (spin) is conserved and
red+cyan=white).
- One flies left, one right, and we do not know which is which.
- When Alice, on the left, will notice (measure) that her particle is red, she will instantly know that Bob's measurement on
the right, far far away, will be cyan.
- "So!", you may say: "there is no paradox here!". The one which went left was always red, the one which went right was always
cyan. Alice just did not know which was the case, until she did her measurement. There is no need for any 'instant
synchronisation at a distance', no need for spooky action."
- That is indeed an intuitive explanation of the experimental result, and we call it a 'hidden parameter' hypothesis.
Why hidden? Because when you look at the mathematical quantity, which according to QM describes the 'state' of that particle,
it does not have that color there. It has a possibility of red, and possibility of cyan. These possibilities or 'potentia' for
one component of spin (an angle of polariser) are complementary to such potentia for another component (another angle of
polariser). Because they are complementary, just like position and momentum, they cannot both be determined at the same time. QM
says they do not both exist. Potentia is converted to pure state, red or cyan, when we measure it. Instantly, the other,
entangled particle, has its potentia jump to cyan or red. To avoid that weirdness, hidden parameter theory says it was there, it
was red for x-component and cyan for y-component, (violating Heisenberg's principle) and we just were not able to see it. It was
hidden.
Our intuition leads us to believe that these hidden particle states must exist, because otherwise we would have to admit the
'spooky action at distance' which Einstein disliked. Bohm disliked it too and so he constructed a hidden parameter theory which
did agree with the experiment and gave the same results as QM. However, an early mathematical proof by Von Neumann said that Bohm's supposed 'local realistic' theory was
impossible.
Bell disliked 'action at distance' (also known as 'nonlocality') as well.
He investigated and discovered two things:
- that von Neumann's proof was wrong.
- that Bohm's theory was actually non-local.
Eventually, he corrected von Neumann's error and generalised von Neumann's proof to a whole class of theories.
And so, in 1964, John
Stewart Bell did show that the whole class of theories known as hidden variable theories, are, if they are to agree with the quantum-mechanical prediction for
ideal experiments, either non-local or have to satisfy Bell's inequality. Quantum mechanics predicts that the inequality is not satisfied.
Experiments have been conducted that apparently confirm that the predicted action at distance does happen and is indeed instant
(or at least faster than light).
Modern perspectives on the EPR paradox
Today, most physicists agree that local hidden variable theories are untenable and that the principle of locality does not
hold. Therefore, the EPR paradox would only be a paradox because our physical intuition does not correspond to physical
reality.
However, the book is not closed yet on this issue. The QM experiments are different from experiments on a macroscopic scale,
which are directly accessible to our senses. In QM we can count the clicks of a Geiger counter or the spots on a photographic plate and those results have to be interpreted by some
abstract reasoning. There are assumptions explicitly made or hidden
and effects (experimental loopholes) which may be just artifacts
of today's measuring devices or fundamental limits not fully accounted for by today's theory. The topic remains active -- there
may yet be ways of escaping the logic of Bell's theorem. Some people
continue to investigate local realist theories exploiting the defects in actual experiments, others the possibility of Bell's
original assumptions having been flawed [1] .
References
- A. Einstein, B. Podolsky, and N. Rosen: Can quantum-mechanical description of physical reality be considered
complete? Physical Review 47, 777
(1935).
- Bell, J.S.: On the Einstein-Poldolsky-Rosen paradox. Physics 1, pp. 195-200 (1965)
- Hardy, L.: Nonlocality for 2 particles without inequalities for almost all entangled states. Physical Review Letters
71: (11) pp. 1665-1668 (1993)
- Sakurai, J.J.: Modern Quantum Mechanics. Addison-Wesley, USA 1994, pp. 174-187, 223-232
- Thompson, C. H.: The Chaotic Ball: An Intuitive Analogy for EPR Experiments , Foundations of Physics Letters 9, 357 (1996).
External links
See also
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