Please note that the phenomenon of 'cat states of the human brain' covers both two possible results of a single observable (Schrödinger's cat) and two different observables (the product rule). In the context of "Physics of Cognition", the 'remnant from the cat' is 'John' having two superposed 'jackets', |dead cat> and |live cat>. The note below is at
Date: Tue, 27 Jun 2000 15:49:19 -0400
From: "Dimiter G. Chakalov" <dchakalov@email.com>
[Dimi Chakalov] In a recent quant-ph/0006116, Ulrich Mohrhoff wrote: "It should be noted, however, that there isn't any possible world in which the product rule is "violated", for there isn't any possible world in which Q_A Q_B is measured. (...) What is measured in the possible world in which both beepers are in place, is not Q_A Q_B but Q . The product rule is "violated" only by combinations of counterfactual statements that refer to different possible worlds" [Ref. 1]. If by Q_A we imply "living cat" and by Q_B "dead cat", we get the famous Schroedinger's cat paradox [Ref. 2]. I will try to show that the human brain can perceive 'cat states' of 'both alive and dead', thanks to a 'remnant from the cat' which can never be subjected to the so-called collapse, being the Platonic idea http://members.xoom.com/_XMCM/mindbrain/time.html#apple of a cat *per se*. In cognitive psychology, there is a well-known example of those 'cats states': two black contours of two human faces leaving a white space between them, which can be perceived as a vase as well. (Regrettably, I cannot submit the picture here.) Depending on what we choose to see, we can either see "two black faces" (on white background) or a white "vase" (on black background). Contrary to the basic principles of QM, if we choose to see a white "vase", we do NOT collapse the alternative option, "two black faces" on white background. It stays in our mind ready to be actualized on demand. Needless to say, the process is fully reversible -- we can switch from "vase" to "two black faces", and back to "vase". (Please also keep in mind that all this takes place in a bundle of nearly 100 billion neurons, and in all brains of the readers of these lines.) We simply keep in our mind -- that is, in our brain -- the whole picture of two superposed states, "vase" and "two black faces", and the process of actualization (not "collapse") of one of these states is generating the psychological time arrow. This holistic image serves as a 'remnant' from both "vase" and "two black faces". It is neither strictly "vase" nor strictly "two black faces". It is something NEW that has emerged from the superposition of "vase" and "two black faces". Figuratively speaking, it is like a 'forest' emerging from the superpositions of two (or more) 'trees', http://listserv.arizona.edu/cgi-bin/wa?A2=ind0003&L It goes without saying that this 'forest' or 'remnant from the cat' is not presented in QM [Ref. 3], simply because it is a linear theory. If we want to develop a background-free quantum gravity, however, we may need just that 'remnant from the cat' with respect to which the 'trees' acquire their real and actualized (not "collapsed") values. We definitely need new ideas about time, http://listserv.arizona.edu/cgi-bin/wa?A2=ind0003&L Kind regards, Dimi Chakalov
References [Ref. 1] Ulrich Mohrhoff. Objective probabilities,
quantum counterfactuals, and the ABL rule: Apropos of Kastner's comment. Ulrich Mohrhoff: "It should be noted, however,
that there isn't any possible world in which the product rule is "violated",
for there isn't any possible world in which Q_A Q_B is measured. While
Q_A is measured in the possible world in which *only* F_A is in place,
Q_B is measured in the possible world in which *only* F_B is in place.
Thus is it *logically* impossible for both Q_A and Q_B to be measured in
the same world. (...) What is measured in the possible world in which both
beepers are in place, is not Q_A Q_B but Q . The product rule is "violated"
only by combinations of counterfactual statements that refer to different
possible worlds. ...."There is only one time, the fourth dimension of space-time.
There is not another time in which the present "advances" through space-time
as if space-time itself -- rather than our mental picture of it -- were
a persisting and unchanging whole. ...."In quantum-mechanical context,
the same error makes us think of a quantum "state" W(t) as an instantaneous
state -- something that evolves continuously in an intrinsically and infinitely
differentiated time until it "collapses" -- mysteriously rather than self-evidently
-- into a different "state". This fairy tale compounds two mistakes. It
treats W (t) as an actual state of affairs rather than as a probability
measure, for only an actual state of affairs can exist in time; the probability
of being found at the time t is not something that exists at the time t
, anymore than the probability of being found in box A is something that
exists in box A . Apart from this category mistake, it treats the parameter
t as representing a "continuum" of intrinsically distinct instants, at
each of which the corresponding "state" W(t) "obtains". In reality, t is
the *specified* time of an actually or counterfactually performed measurement.
If we use W(t) to assign Born probabilities to the possible outcomes of
a specific future measurement, we assume that this measurement is made,
and we assume that it is made at the time t. W(t) is good for only *one*
time t . Once the measurement is made and its result is taken into account,
W(t) has to be replaced by a different probability measure W'(t) , for
reasons that are obvious rather than mysterious. ...."If we could bring
ourselves to stop imagining an instantaneous present that advances continuously
from t_1 to t_2 , it would no longer be impossible for us to see that there
isn't any particular time t between t_1 and t_2 that is real for the particle,
anymore than the distinction between A and its complement in A\cup B\cup
C is real for the particle. A particular (but not necessarily exact) time
is real for a system if and only if it is the indicated time of possession
of an indicated property. Times supervene on facts, just like positions.
If between t_1 and t_2 the particle lacks indicated properties, *a fortiori*
it lacks indicated times, and this is the same as saying that a particular
intermediate time does not exist for the particle. Time is differentiated
by property-indicating events. It is a set of temporal relations between
such events. If between two such events e_1 and e_2 there isn't any other
such event, then the time between the two events is "empty", in the sense
that between e_1 and e_2 there isn't anything that is temporally related
to e_1 or e_2 ; there is only the relation between e_1 and e_2 . Least
of all is there an instantaneous objective present or state that moves
continuously from e_1 to e_2 in an infinitely differentiated time. This
infinitely (and intrinsically) differentiated time is a pure figment of
our imagination, as is the idea of an infinitely and intrinsically differentiated
space."
[Ref. 2] J. Finkelstein. Does Schrodinger's
Cat Know Something That Schrodinger Does Not Know?
[Ref. 3] Erast B. Gliner. Relativistic Quantum
Non-Locality.
"Abstract "The controversy between relativistic causality and quantum non-locality can be resolved by establishing the general relativistic background of quantum non-locality." ============================================
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