From: scerir (scerir@libero.it)
Date: Sun Jun 08 2003 - 12:28:46 MDT
"Physics in Action" wrote:
<Perhaps the deepest mystery in all of physics is quantum non-locality -
the ability of two distant systems to instantaneously know about each other.
Non-locality means that two particles in a quantum system can be
"entangled" such that the state of one particle affects the state of the
other, regardless of how far apart they are. As well as challenging our
common sense, non-locality suggests that the ultimate speed limit - the
speed of light - is violated. Einstein spent many years worrying about
this problem because such "superluminal" interactions seem to be
incompatible with special relativity.>
But this is, at least, a bit confusing.
In their long debate both Einstein and Bohr
made subtle but important errors, after the famous
EPR paper, but also before (discussing those gedanken
experiments, in 1927 and also later).
But let us stay with the entangled particles.
EPR wrote that "if, without in any way disturbing
a system, we can predict with certainty (i.e. with
probability equal to unity) the value of a physical
quantity, then there exists an element of physical
reality corresponding to this physical quantity."
They discussed a composite system, composed of
two entangled, but separated, subsystems, and they
made the point that the precise value of 'any'
observable of subsystem 1 is 'real' because it can be
predicted - without disturbing subsystem 1
itself - by measuring the precisely correlated
observable of the separated, and entangled, subsystem 2.
Now, quantum mechanics cannot predict precise values
fot two non-commuting observables (i.e. two such observables
of subsystem 1 cannot have simultaneous reality). Hence
- EPR say - quantum mechanics is not "complete".
(The EPR paper was written by Podolski alone, Einstein
was just interested in the physical point, the so called
quantum 'non-separability', and not much in the logical
point above).
Well, Bohr responded that until the experimental
procedure is specified, there is a possibility of
"an influence on the very conditions which define
the possible types of predictions regarding the future
behavior of the system." In other words, since mutually
exclusive experimental procedures are needed to
measure non-commuting observables, the prediction
of the precise values of the two non-commuting
observables is impossible (hence they are not
real at the same time). In other words, the EPR
experimental setup precludes, by itself, a complete
description of subsystem 1 (or subsystem 2) in
isolation. (Btw, this semi-obscure position by Bohr
- many important authors did not understand what
he was trying to say - is of course invalid
in the context of MWI.)
Then why did it appear to EPR that non-commuting
observables of subsystem 1 may be "predicted"
(without disturbing subsystem 1) by measuring
the entangled subsystem 2? There is a conceptual error,
here. Subtle, subtle, and conceptual.
Actually it can be shown that each subsystem is in a
"mixed state" and one can only "predict" with certainty
that *if* an apparatus 2 measures the value an observable
of the subsystem 2 *then* we can deduce, or infer, the value
for the correspondent observable of subsystem 1.
But this is a *conditional* probability and not a "prediction"
for the complete knowledge of the quantum state of the subsystem 1.
These conditional probabilities are, thus, not properties
of subsystems alone but, rather, properties of the composite
system. That is to say that the measurement of subsystem 2,
by apparatus 2, has no effect on the state of subsystem 1
alone.
We can also say that the EPR scheme always involves a comparison
of subsystem 1 and 2. Or, to say it in better terms,
EPR involves a conparison of records of apparatus 1
(measuring subsystem 1) and apparatus 2 (measuring
subsystem 2). And there is no reason, in orthodox quantum
mechanics, to suppose that the measurement of subsystem 2,
by apparatus 2, has any effect on subsystem 1, and
viceversa. Such an effect ("passion at a distance",
after Albert Shimony) would violate special relativity,
but the only possible effect here is the relationship
between apparata 1 and 2, and the comparison
of records stored in apparata 1 and 2. Which are not
superluminal.
(It can be shown why subsystems 1 and 2 are "mixed states",
and also why EPR scheme does not require any "collapse" or
"projection postulate".)
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