seeger@beach.cis.ufl.edu (F. L. Charles Seeger III) (01/30/89)
There was some demand for posting this to comp.arch. The clincher was
that our friends in Australia don't get the sci.physics group. Hope
that no one is too upset over the cross-posting.
In this posting I will give a summary of five papers that collectively
show that nature is non-local, i.e. that there are faster-than-light
connections. However, these papers do NOT indicate that it is possible to
either travel or communicate at FTL speeds. It is my current (amateur)
opinion that FTL travel is not possible, though FTL communication is an
open question for a restricted set of conditions. Subsequent postings
will consider the possiblities of FTL communication. The papers in
this posting should be considered "classic" papers in quantum physics.
IMHO, all professional physicists should be familiar with them. Certainly,
no one unfamiliar with them should be allowed near a quantum mechanics
class (except students, of course).
I envision perhaps three more postings. One will be a brief intro to
quantum mechanics, mostly covering terminology and a few concepts.
[If anyone wants to help ...] Another will cover the work of the
Sussex group (Clark, Widom, Prance, etc.). [Are any of these people on
the net?? I believe that Widom is/was at Northeastern in Boston.
Anyone in the U.K. listening?] The last will cover the quantum conditions
required of an FTL circuit, courtesy of a physicist from one of the
national labs.
I hope that you enjoy it.
Chuck
--
Charles Seeger 216 Larsen Hall
Electrical Engineering University of Florida
seeger@iec.ufl.edu Gainesville, FL 32611
=============================================================================
A. Einstein, B. Podolsky and N. Rosen, "Can Quantum-Mechanical
Description of Physical Reality Be Considered Complete?"
_Physical_Review_, vol. 47, pp. 777-780 (15 May 1935).
This paper is the original formulation of the classic EPR Paradox. In
this paper, it is argued that quantum mechanics can not be a complete
theory of nature, but should be supplemented by additional ("hidden")
variables that restore locality and causality. The specification of
these variables would predetermine the measurement of any observable,
though the measurements would agree with quantum predictions because of
the statisitical distribution of the hidden variables. It can be said
that this was Einstein's best attempt at showing QM to be an incomplete
theory. Recall the famous quote, "I cannot believe that God plays dice
with the universe." Einstein admitted that quantum theory correctly
described all known experiments, but maintained that it was an incomplete
theory, leaving "open the question of whether or not such a description
exists."
The basic idea of the EPR Paradox is to use information obtained from
one particle to infer the properties of another particle, where the two
particles had undergone a special type of interaction in the past and had
not been influenced by anything else between their interaction and their
measurement. The interaction of the particles is special in the sense
that some property must be known about the combined system of two particles,
though it is not known about the particles individually until it is
measured.
Specifically, this paper considered the case of measuring the momentum and
position of the particles. In QM lingo, momentum and position are
"non-commuting operators." This means that any attempt to measure both
of these "observables" simultaneously is subject to the Heisenberg
uncertainty principle, i.e. both cannot be simultaneously measured to
arbitrary precision. [This paper uses the QM formalisms of wave-functions,
operators, eigenvalues, eigenfunctions, operators, non-commutation and
reducing the wave packet, now better known as collapsing the wave function.
I will try to post a brief introduction to these concepts and notations
in preparation for a more detailed posting of what QM criteria an FTL
communication circuit probably needs to meet.]
Now, consider two particles that interact and separate, in such a way that
we know exactly the total momentum of the two particle system and their
initial separation (this is allowed by QM). Then, after the particles
separate, we measure the momentum of one particle. Since the total momentum
is already known, then we also know the momentum of the other particle.
Next, we measure the position of the first particle. Though this "disturbs"
the momentum of the first particle (to conform with uncertainty), it SHOULD
NOT affect the momentum of the distant particle. Now, we know BOTH the
position (by calculation using the initial separation) and momentum of the
distant particle, in violation of the uncertainty principle. This
contradiction is used to "prove" that quantum theory was incomplete, i.e.
"the quantum-mechanical description of reality given by the wave function
is not complete."
In fact, as is shown by the Aspect experiment, the measurement of one
particle DOES affect the distant particle, and it does so instantly (without
speed-of-light delays). This is some sort of "action at a distance" that
conflicts with our "normal" relativistic ideas of causality.
=============================================================================
D. Bohm and Y. Aharonov, "Discussion of the Experimental Proof for
the Paradox of Einstein, Rosen and Podolsky," _Physical_Review_,
vol. 108, p. 1070 (1957).
This paper reformulates the EPR Paradox in terms of spin one-half particles
formed in the singlet spin state and allowed to move freely apart in
opposite directions. This is the formulation that Bell starts with in
the next paper. This paper also suggests that the measurement system be
reconfigured while the particles are in flight, so that its state can be
more safely abstracted from the state of the particles. Note that Bohm
was in the hidden variable theory camp.
I don't think I can improve on this:
"We consider a molecule of total spin zero consisting of two atoms, each of
spin one-half. ... The two atoms are then separated by a method that does not
influence the total spin. After they have separated enough so that they
cease to interact, any desired component of the spin of the first particle (A)
is measured. Then, because the total spin is still zero, it can immediately
be concluded that the same component of the spin of the other particle (B)
is opposite to that of A."
"In quantum theory, a difficulty arises, in the interpretation of the above
experiment, because only one component of the spin of each particle can have
a definite value at a given time. ... the quantum theory still implies that
no matter which component of the spin of A may be measured the same component
of the spin of B will have a definite and opposite value when the measurement
is over. ... there will then be no correlations between the remaining
components of the spins of the two atoms. Nevertheless, before the
measurement has taken place (even while the atoms are still in flight) we are
free to choose ANY direction as the one in which the spin of particle A (and
therefore of particle B) will become definite."
"... But it does not explain why particle B (which does not interact with
A or with the measuring apparatus) realizes its potentiality for a definite
spin in precisely the same direction as that of A. ...
One could perhaps suppose that there is some hidden interaction between
B and A, or between B and the measuring apparatus, which explains the above
behavior. Such an interaction would, at the very least, be outside the
scope of the current quantum theory. Moreover, it would have to be
instantaneous, because the orientation of the measuring apparatus could
very quickly be changed, and the spin of B sould have to respond immediately
to the change. Such an immediate interaction between distant systems would
not in general be consistent with the theory of relativity.
The result constitutes the essence of the paradox of Einstein, Rosen, and
Podolsky."
Later in the paper, it is suggested that, rather than using atoms, it would
be more practical to use photons. Specifically, the positon-electron
annihilation is suggested, where the particles are given off with opposite
momentum and with orthogonal polarization. An experiment involving the
scattering of the photons is considered and is shown "that this experiment
is explained adequately by the current quantum theory which implies distant
correlations, of the type leading to the paradox of ERP, but not by any
reasonable hypotheses implying a breakdown of the quantum theory that
could avoid the paradox of ERP." However, the sensitivity of the experiment
is less than desirable. [I don't know why they interchanged Podolsky's
and Rosen's initials.]
=============================================================================
J. S. Bell, "On the Einstein Podolsky Rosen Paradox," _Physics_,
vol. 1, no. 3, pp. 195-200 (1964).
Bell starts with the EPR Paradox formulation of Bohm and Aharonov. From
this he derives mathematical relations that are incompatible with quantum
mechanical predictions, based on a physically reasonable condition of locality.
These differences provide the basis for experimental testing of the competing
theories. He outlines how his formulation is generalizable (invoking the
notion of observable operators).
Bell suggested more direct measurements of the particles' spins, perhaps
by Stern-Gerlach magnets. Measurement of a component of one particle's
spin would determine the same component of the other particle's spin to
be opposite. But, consider measuring a different component of the second
particle's spin. Then, statistical predictions can be made using both
the quantum theory and the "local" or "hidden variable" theory for the
expectation value of the product of the two spin components. The two
approaches give different predictions of the amount of correlation of the
two distant spin components as a function of the angle between them.
This is embodied in "Bell's inequality," a violation of which implies
non-locality. The predictions of the two theories differed in functional
form, such that "the quantum mechanical expectation value cannot be
represented, either accurately or arbitrarily closely" by the hidden
variable formulation.
"In a theory in which parameters are added to quantum mechanics to determine
the results of individual measurements, without changing the statistical
predictions, there must be a mechanism whereby the setting of one measuring
device can influence the reading of another instrument, however remote.
Moreover, the signal involved must propogate instantaneously, so that such
a theory could not be Lorentz invariant."
[I'm not satisfied with this description, but I'm not sure how to do
this without reproducing the equations and the derivation. Actually,
I find this to be a pretty slick sort of development. My hat is off
to John Stewart Bell!]
=============================================================================
J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, "Proposed
Experiment to Test Local Hidden-Variable Theories," _Physical_Review
Letters_, vol. 23, no. 15, pp. 880-884 (13 Oct 1969).
This paper generalizes Bell's mathematical formulation into a form that
applies to realizable experiments. It then proposes an experiment to
decisively test between quantum mechanics and the local hidden-variable
theories. The suggested experiment is based on the polarization of photon
pairs emitted from excited calcium atoms.
=============================================================================
A. Aspect, J. Dalibard and G. Roger, "Experimental Test of Bell's
Inequalities Using Time-Varying Analyzers," _Physical_Review_Letters_,
vol. 49, no. 25, pp. 1804-1807 (20 Dec 1982).
This paper reports the results of an experiment of the type suggested by
Clauser, Horne, Shimony and Holt, with a measurement system that varied
while the photons were in flight. Results agreed well with quantum
predictions, but violated Bell inequalities by 5 standard deviations.
This experiment involved the use of fast optical switches to direct the
incident light to one of two polarizers, each having a different orientation.
Bell's inequalities are generalized in manner similar to that of the
Clauser, Horne, Shimony and Holt paper, making allowance for the four-way
coincident counting. This was done under the assumption that the two
switches are random and uncorrelated. Both the time scale of the switching
and the lifetime of the intermediate level of the cascade (that produces
the photons) were small compared to the separation of the two switches
(10 ns and 5 ns compared to 40 ns for light to traverse the separation).
Hence, a detection event and the corresponding change of orientation on
the other side had a space-like separation.
The optical switching was accomplished using acousto-optical interactions
with an ultrasonic standing wave in water, produced by the interference
of counter-propogating waves generated by transducers driven in phase
at 25 MHz. The correlated photon pairs, at 422.7 and 551.3 nm, were
obtained from the cascade emission from excited calcium ions. The
four double-coincidence-counting circuits had coincidence windows of 18 ns.
Collection efficiencies in this experiment were lower than previous ones
due to the more complicated optics. A typical counting run lasted
12,000 s.
Measurements were taken with the polarizers positioned to give the greatest
difference between quantum theory and Bell's inequalities. Two runs were
performed to test the inequalities. The result was S = 0.101 +/- 0.020,
which violates the inequality S <= 0 by five standard deviations. In
contrast, for the solid angles and polarizer efficiencies used in the
calculations, quantum theory predicts S = 0.112. Another run was carried
out with different orientations, with all measurements giving excellent
agreement with quantum theory predictions. The switching control was, in
fact, quasiperiodic, but the two switches were driven by different
generators at different frequencies. [I didn't bother deriving what S
is, I just wanted to show some numbers. S is calculated using the four
coincidence counting rates and the counting rates with the polarizers
removed.]
=============================================================================
Now, the reason why this FTL quantum connection is not useful for FTL
communication. Though the measurement of one particle affects the
distant particle by collapsing its wave function, a person measuring the
distant particles still sees a random distribution of states. Only when
the measured data from both measurement sights are brought together, at
subluminal speeds, are the correlations of the two sets of random data
apparent. So, there seems to be no useful FTL application here. There
may be another [stay tuned!], but it does depend on another sort of
FTL quantum connection. That's why I wanted to put this one on a firm,
I hope, foundation.
=============================================================================
Additional References
N. Bohr, "Can Quantum-Mechanical Description of Physical Reality Be
Considered Complete?" Physical Review, vol. 48, pp. 696-702
(15 Oct 1935).
J. S. Bell, "On the Problem of Hidden Variables in Quantum Mechanics,"
Reviews of Modern Physics, vol. 38, no. 3, pp. 447-452 (July 1966).
D. Bohm and J. Bub, "A Proposed Solution of the Measurement Problem
in Quantum Mechanics by a Hidden Variable Theory," Reviews of Modern
Physics, vol. 38, no. 3, pp. 453-469. "A Refutation of the Proof by
Jauch and Piron that Hidden Variables Can be Excluded in Quantum
Mechanics," pp. 470-475.
C. A. Kocher and E. D. Commins, "Polarization Correlation of Photons
Emitted in an Atomic Cascade," Physical Review Letters, vol. 18,
no. 15, pp. 575-577 (10 April 1967).
A. Aspect, "Proposed Experiment to Test the Nonseparability of Quantum
Mechanics," Physical Review D, vol. 14, no. 8, pp. 1944-1951
(15 Oct 1976).
A. Aspect, "Experiences Basees Sur les Inegalites de Bell," Journal
de Physique, Colloque C2, vol. 42, no. 3, pp. C2-63-80 (mars 1981).
(In French).
A. Aspect, P. Grangier and G. Roger, "Experimental Test of Realistic
Local Theories via Bell's Theorem," Physical Review Letters,
vol. 47, no. 7, pp. 460-463 (17 Aug 1981).
A. Aspect, P. Grangier and G. Roger, "Experimental Realization of
Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of
Bell's Inequalities," Physical Review Letters, vol. 49, no. 2,
pp. 91-94 (12 July 1982).
=============================================================================
--
Charles Seeger 216 Larsen Hall
Electrical Engineering University of Florida
seeger@iec.ufl.edu Gainesville, FL 32611firth@sei.cmu.edu (Robert Firth) (01/30/89)
In article <19718@uflorida.cis.ufl.EDU> seeger@iec.ufl.edu (F. L. Charles Seeger III) writes: >In this posting I will give a summary of five papers that collectively >show that nature is non-local, i.e. that there are faster-than-light >connections. However, these papers do NOT indicate that it is possible to >either travel or communicate at FTL speeds. It seems appropriate that this followup should be cross-posted also; my apologies to anyone this offends. As an addendum to Mr Seeger's excellent list of references on the issue of non-local interactions in quantum mechanics, here are two papers that do indeed claim the effect can be used to transmit information faster than light: N Herbert: Foundations of Physics vol 12 p 1171 (1982) [see also Herbert: Quantum Reality - Beyond the New Physics] Summary: Two correlated particles are prepared and allowed to separate. One is subjected to a measurement against a basis set; it is supposed that the other will then be in an eigenstate of that same basis set. Information is transferred by choosing one basis set or another; it is asserted that the receiver can detect which basis set is used (even though the specific eigenstate itself gives no information) A Datta, D Home, A Raychaudhuri: Physics Letters A vol 123 p 4 (1987) Summary: Two particles are prepared by a decay method that violates CP invariance. The resulting wave functions exhibit a weak interaction term whose eigenstates are nonorthogonal. It is asserted that a measurement that casts one particle into a given eigenstate therefore has an effect on the observed statistical distribution of the eigenstates of the other.
tja105@phys0.anu.oz (Tim Allen) (02/03/89)
In article <8373@aw.sei.cmu.edu>, firth@sei.cmu.edu (Robert Firth) writes: > A Datta, D Home, A Raychaudhuri: Physics Letters A vol 123 p 4 (1987) > The claim made in this paper, namely that FTL communication is possible, was soundly refuted by Michael Hall, from my department, also in Phys. Lett. A, though I can't remember the issue and he didn't come in to work today so I can't ask him. -- -------------------------------------------------------------------------------- Tim Allen ACSNET: tja105@phys0.anu.oz Dept of Theor Phys,RSPhysS,ANU Ash nazg durbataluk Ash nazg gimbatul Ash nazg thrakataluk Agh burzum ishi krimpatul ________________________________________________________________________________ D