There are the laws of QM, and there is something that is governed by them.
But what are the laws of QM and what is it that is governed by them?
According to the quantum Platonists, the laws are "dynamical" equations
such as the Schroedinger equation, and what is governed by them is the
state vector. The reason why I call them "Platonists" is that, like Plato,
they introduce two kinds of reality, a superior one (what *is*, the state
vector) and an inferior one (what *appears*, the classical). According to
quantum Aristotelians like yours truly, there is only one kind of reality:
The laws are correlations, and what is governed by them (the correlata) is
facts - actual events or states of affairs. [1]Those who believe with Dieter Zeh (paper posted on 15 Feb) and Wojciech
Zurek (summary posted on 25 Feb) that decoherence is the key to
the "emergence of classicality" are Platonists. Zeh: "While decoherence
transforms the formal 'plus' of a superposition into an effective 'and' (an
*apparent* ensemble of new wave functions), this 'and' becomes an 'or' only
with respect to a subjective observer." Zurek establishes an "effective
classicality," which allows information gathering systems "in a completely
quantum universe" to share the impression of an objective world.
Aristotelians find this hard to swallow. QM is an empirical theory
abstracted from and tested in the world of facts. Its formalism
encapsulates the correlations between actual events. If attaching ultimate
reality to a particular tool of this formalism (the state vector) leads to
the conclusion that facts or actual events possess only an inferior,
intersubjective, and ultimately illusory kind of reality, then it must be
wrong to attach ultimate reality to the state vector.
Zeh: "...nonlocality must be part of reality. So why not simply accept the
reality of the wave function?"
While the reality of the wave function implies nonlocality, nonlocality
does not imply the reality of the wave function.
Zeh: "Can something that ... keeps solid bodies from collapsing itself be
unreal?"
Certainly not. But what is it that keeps a body from collapsing? Not the
state vector but the indefiniteness of the relative positions of the body's
material constituents. The proper way of dealing with indefinite variables
is to make counterfactual probability assignments [2,4], and the obvious
way of making room for (nontrivial) probabilities leads straight to the
formalism of QM [3]. This formalism is the expression of an objective
indefiniteness *in terms of its consequences in the world of facts*. The
indefiniteness that fluffs out matter is real, the correlations through
which the indefiniteness becomes manifest in the world of actual events are
real, but to attribute a superior kind of reality to the algorithm that
encapsulates the correlations is absurd, or so it seems to this
Aristotelian.
Zeh: "After this preparation, the [nonlocal] state 'exists but is not
there'. Or in similar words: the physical state is *ou topos* (at no
place)..."
The "physical state" is at no place for the same reason that the
probability for something to happen or exist in a given region is not
something that happens or exists in that region. The " physical state"
exists in the same sense in which a probability algorithm "exists".
Moreover, if it is at no place, it should also be at no time. And indeed,
the state vector assigns probabilities to sets of possible events on
condition that exactly one event from exactly one set happens at a *given*
time. The time dependence of a quantum "state" is not the time dependence
of something that exists and evolves in time but a dependence on the
*specified* time of an actually or counterfactually performed measurement.
According to Zeh the (local) components of a (nonlocal)
superposition "exist" (his quotes) simultaneously.
It would be more correct to say that a particle exists in different places
(or goes through different slits) simultaneously. What exists is the
particle, not the state vector. If an electron is detected behind the slit
plate, and if the detection implies that it has passed through the slit
plate, then it has passed through the slit plate. And if nothing indicates
the particular slit (L or R) taken by the electron then "the electron went
through both slits simultaneously". Note that the statement in quotes is
not a conjunction of two propositions ("it went through L" and "it went
through R"), for this conjunction is true only if the electron's passage
through L and its passage through R are both indicated, which is never the
case. What that statement affirms is (i) that the electron went through
L&R - the regions defined by the two slits considered as a single region -
and (ii) that the electron did not go through a particular slit (because
nothing indicates that it did).
Zeh: "So what lets events and measurement results appear actual rather than
virtual? In order to answer this question we must... take into account the
realistic environment of the quantum system. We may then convince ourselves
by means of explicit estimates that a macroscopic pointer cannot avoid
becoming strongly entangled with its environment by an uncontrollable
avalanche of interactions..."
If one confines actuality to appearences, as Zeh does, letting something
appear actual is the same as letting something appear. Since only what
exists in some sense can be made to appear, Zeh implies that a virtual
measurement result has some kind of reality of its own. Yet a "virtual"
measurement result is nothing but the result of a counterfactually
performed measurement. It is not something that exists in any but a
counterfactual sense. That is, it exists only in a possible world different
from ours, and such a world exists nowhere but in our imagination. It is
not something that can be made to appear (actual). It can only be made
actual, in the sense that the measurement can be performed and the result
can be obtained.
Zeh's statement that "a macroscopic pointer cannot avoid becoming strongly
entangled with its environment by an uncontrollable avalanche of
interactions" is a statement of correlations. It doesn't say what is the
case but only what would be the case if certain conditions were fulfilled.
It asserts that the environment contains a huge number of pointers (in a
generic sense) whose positions become strongly correlated with the position
of the macroscopic pointer in question, in the sense that *if* the
positions of all those environment pointers *were* measured then they
*would* consistently indicate the position of that macroscopic pointer. In
order to get from this counterfactual statement to a factual statement
(rather than in order to understand "what lets events and measurement
results appear actual rather than virtual") we need to "take into account
the realistic environment of the quantum system". In other words, we need
actual events. If the "realistic" environment *does* indicate the position
of the macroscopic pointer then (and only then) does that pointer have the
indicated position.
This should make it clear that quantum-mechanical statements - probability
assignments or statements of correlations - derive their meaning from the
correlata - actual events or measurement results. (This is equally true if
the probabilities are counterfactually assigned to the results of
unperformed measurements, in which case the probability assignments
formally express an objective indefiniteness.) Hence if the correlata are
appearances, QM deals with correlations between appearances, and if the
correlata are bona fide facts, QM deals with correlations between such
facts. Pick your choice - QM doesn't make it for you.
We cannot ask what makes something become, or come to appear as, a fact,
for there is nothing but facts, correlations between facts, and properties
or values indicated by facts - there is nothing that could become, or come
to appear as, a fact. But we need to ask, how is the *extrinsic* nature of
positions consistent with the *intrinsic* nature of the positions of
macroscopic objects (macroscopic positions, for short)? (See my comments
posted on 28 Feb.) How can we conceive of all macroscopic positions as
factual per se (and hence as capable of indicating something) even though
they too are possessed only because, and only to the extent that, they are
indicated?
The key to the answer is that macroscopic positions are the sharpest
positions in existence. As a consequence, their fuzziness cannot evince
itself through unpredictable position-indicating facts, since this would
require detectors with sharper positions. Hence the possessed (indicated)
positions of macroscopic objects evolve predictably, in the sense that
every position-indicating fact is consistent with what can be predicted on
the basis of previous position-indicating facts and a classical law of
motion - except, of course, when they indicate the unpredictable positions
of microscopic objects. A macroscopic object can therefore be thought of as
*by itself* following a trajectory that is neither exact nor manifestly
fuzzy. Its (not manifestly fuzzy) position is intrinsic in the sense of
being effectively detached from the events by which it is indicated.
Because it is only effectively detached from these events, we cannot
attribute to each individual macroscopic position an independent reality.
What constitutes a free-standing, self-contained reality is the entire
system of mutually indicating macroscopic positions, together with whatever
else they indicate. [2,4,5]
[1] U. Mohrhoff, Two theories of decoherence, quant-ph/0108002.
[2] U. Mohrhoff, What quantum mechanics is trying to tell us, Am. J. Phys.
68, 728 (2000); quant-ph/9903051.
[3] U. Mohrhoff, Why the laws of physics are just so, quant-ph/0202149.
[4] U. Mohrhoff, The world according to quantum mechanics (Or the 18 errors
of Henry P. Stapp), Secs. 7-9, to appear in Found. Phys.; quant-ph/0105097
[5] U. Mohrhoff, Making sense of a world of clicks, quant-ph/0202148.
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