REQUEST answer(s) to 4 questions
Tom Cervenka
questions would be much appreciated.
1) Can a "unified theory of everything" end reductionist inquiry? How?
2) Do the "unusual" findings of quantum theory potentially
indicate that some "classical" formal systems, say logic, are insufficient
to explore all truths.
3) In layman's terms, what are the implications of quantum theory for the
observed/observer relationship? Do any such implications only hold for
subatomic particles?
4) How is it possible for elementary particles to acccount for higher
order complexity? At the sub-atomic level, what happens to the
information necessary to maintain higher order phenomena, such as
Disneyland, Marylyn Monroe, or peanut butter? Is this information
conserved at the level of the "smallest" elementary particle? Is it
conserved in their interactions?
- Tce...@psych.ualberta.ca -Tom
Joshua B. Scott
: Any answers, opinions, or insights into any of the following
You smoke way tooooooooo much crack. :) Q1.Maybe.Q2.Maybe.Q3.MaybeQ4.They
don't account for the complexity. Assuming a great deal aren't you. Pass
the pipe.
God, hahaha
Jacques Distler
tce...@ice.psych.ualberta.ca (Tom Cervenka) wrote:
> Any answers, opinions, or insights into any of the following
> questions would be much appreciated.
>
> 1) Can a "unified theory of everything" end reductionist inquiry? How?
Why would I want to? You got something against "reductionist inquiry"?
> 2) Do the "unusual" findings of quantum theory potentially
> indicate that some "classical" formal systems, say logic, are insufficient
> to explore all truths.
No. Every formal system starts with a set of axioms. If those axioms resemble
the "real world", then it's a useful vehicle for exploring (certain facets of)
reality. Quantum Mechanics, too, can be axiomatized and, because it more
closely resembles the way the world really works, is a more useful vehicle
than
Classical Physics.
> 4) How is it possible for elementary particles to acccount for higher
> order complexity? At the sub-atomic level, what happens to the
> information necessary to maintain higher order phenomena, such as
> Disneyland, Marylyn Monroe, or peanut butter? Is this information
> conserved at the level of the "smallest" elementary particle? Is it
> conserved in their interactions?
You wrote this on a *computer*, right? Was the information content of your
message contained in each individual bit of data sent down the Internet?
And finally, we get to:
> 3) In layman's terms, what are the implications of quantum theory for the
> observed/observer relationship? Do any such implications only hold for
> subatomic particles?
Wow! That's an off-the-deep-end question, but quantum measurement theory
does that to even relatively level-headed individuals.
Seriously, "Reduction of the Wave Packet", an oft-cited axiom which posits
a central role for the Observer in Quantum Mechanics, is one of the
silliest ideas in Physics.
All together now, WITH FEELING:
"Reduction of the Wave Packet" is not time-reversal invariant (for nigglers,
it ain't CPT-invariant, either). As such, it has NO PLACE as an axiom of
our microscopic theory of the world. The microphysics IS time-reversal
invariant.
The source of the irreversibility that we commonly associate with the
measurement process is exactly the same as the source of all
irreversibility in
physics -- the behaviour of large complex system which happen to be prepared
(thank heavens for initial condition!) in initial states of low entropy (few
micro states corresponding to the initial macro state).
The prototype for such a measuring apparatus is a large number of harmonic
oscillators
prepared initially in their ground states, which for some period of time
("the measurement") are coupled to the system under study in some
particularly relevant way. We ("the observer") see whether the total
occupation number has gone from low to high ("a detection") during the
course of the measurement.
Naturally, since we measure only the total occupation number, the
subsequent evolution is incoherent (we traced over a large number of
quantum microstates).
No mystical "Reduction of the Wave Packet", just good 'ole statistical
mechanics at work, keeping the arrow of time pointed in the right
direction,
and degrading quantum coherence as it goes.
Sorry if that was more long-winded and technical an answer than you were
seeking, but I wanted this article to have some nonzero information
content.
Jacques Distler
Kevin Sterner
>Any answers, opinions, or insights into any of the following
>questions would be much appreciated.
>
>1) Can a "unified theory of everything" end reductionist inquiry? How?
Maybe, in a sense, at least as far as fundamental physics goes. If a
theory is complete and accounts for all the data, you can't ask "why
is it so", since no additional data gives you any additional handle
you can use to test any "grander" unification. Reductionism will still
work in all other fields, though.
>2) Do the "unusual" findings of quantum theory potentially
>indicate that some "classical" formal systems, say logic, are insufficient
>to explore all truths.
Considering that logic (i.e. mathematics) *led* us to the quantum theory,
I should say not. Goedel's incompleteness theorem tells us that any
specific logical system is incomplete, but that has nothing to do with
quantum weirdness.
>3) In layman's terms, what are the implications of quantum theory for the
>observed/observer relationship? Do any such implications only hold for
>subatomic particles?
The implication is that observing disturbs the observed. The disturbances
that might be dominant at the quantum level are too small to be noticed
at a macroscopic level, but they are certainly there.
>4) How is it possible for elementary particles to acccount for higher
>order complexity? At the sub-atomic level, what happens to the
>information necessary to maintain higher order phenomena, such as
>Disneyland, Marylyn Monroe, or peanut butter? Is this information
>conserved at the level of the "smallest" elementary particle? Is it
>conserved in their interactions?
Consider a cellular automaton, such as Conway's "Life". The rules of
interaction are trivial, but the systems that can be made out of these
rules can be arbitrarily complex. Does this bother you?
As for information being conserved, well, it isn't.
-- K.
--------------------------------------------------------------------------------
Kevin L. Sterner | U. Penn. High Energy Physics | Smash the welfare state!
--------------------------------------------------------------------------------
Arun Ram-Mohan
>Any answers, opinions, or insights into any of the following
>questions would be much appreciated.
>
>1) Can a "unified theory of everything" end reductionist inquiry? How?
I doubt a Theory of Everything will end any inquiry at all.
There was an article in Scientific American recently that discussed
this far better than I ever could.
Matt McIrvin
Jacques Distler <dis...@utpapa.ph.utexas.edu> wrote:
>
>"Reduction of the Wave Packet" is not time-reversal invariant (for nigglers,
>it ain't CPT-invariant, either). As such, it has NO PLACE as an axiom of
>our microscopic theory of the world. The microphysics IS time-reversal
>invariant.
Actually, the versions of it in some interpretations *are*
time-reversal invariant, in a sense. All you have to do is find an
observable of which the initial state is an eigenstate, and if you
measure that, the probability of getting the initial state given the
final state is the same as the probability of getting the final state
given the initial state in the original measurement.
Finding the observable for the reverse process would be, of course,
the hard part (which is just statistical mechanics at work again).
I don't like "reduction of the wave packet" either, but my reason is
basically that it's unnecessary, and that I haven't heard any
conditions for the special "reduction" physics that sound plausible
to me.
--
Matt 01234567 <-- Indent-o-Meter
McIrvin ^ Harnessing tab damage for peaceful ends!
Jacques Distler
(Matt McIrvin) wrote:
> In article <distler-1809...@slip-10-9.ots.utexas.edu>,
> Jacques Distler <dis...@utpapa.ph.utexas.edu> wrote:
> >
> >"Reduction of the Wave Packet" is not time-reversal invariant (for nigglers,
> >it ain't CPT-invariant, either). As such, it has NO PLACE as an axiom of
> >our microscopic theory of the world. The microphysics IS time-reversal
> >invariant.
>
> Actually, the versions of it in some interpretations *are*
> time-reversal invariant, in a sense. All you have to do is find an
> observable of which the initial state is an eigenstate, and if you
> measure that, the probability of getting the initial state given the
> final state is the same as the probability of getting the final state
> given the initial state in the original measurement.
>
> Finding the observable for the reverse process would be, of course,
> the hard part (which is just statistical mechanics at work again).
Well, yes, in this special case "reduction of the wave packet" gives a
reversible statement. But that's not what happens for general initial and
final states. And, in any case, the *relevant* feature of "reduction" is
that in
general it *does* do something irreversible to the system.
> I don't like "reduction of the wave packet" either, but my reason is
> basically that it's unnecessary, and that I haven't heard any
> conditions for the special "reduction" physics that sound plausible
> to me.
Of course it's irrelevant to doing real physics, but as part of "the
interpretational framework" of QM, it sucks. Not just on the physical
grounds I cited, but also because it leads *directly* to a whole lot of
mushy thinking about the role of consciousness in QM (ie, no mere
mechanical piece of apparatus can reduce a wave packet; that takes an
"observer").
Think about the "Schroedinger's Cat" paradox if you doubt that having a
reasonable alternative to "reduction of the wave packet" is worthwhile.
In the statistical interpretation, of course, there is no paradox.
Jacques Distler
Saul Youssef
|>(Matt McIrvin) wrote:
|>
|> I don't like "reduction of the wave packet" either, but my reason is
|> basically that it's unnecessary, and that I haven't heard any
|> conditions for the special "reduction" physics that sound plausible
|> to me.
|
|
|Of course it's irrelevant to doing real physics, but as part of "the
|interpretational framework" of QM, it sucks. Not just on the physical
|grounds I cited, but also because it leads *directly* to a whole lot of
|mushy thinking about the role of consciousness in QM (ie, no mere
|mechanical piece of apparatus can reduce a wave packet; that takes an
|"observer").
|
When you flip a coin and see the result "heads", your probability
distribution has just "collapsed" from (1/2,1/2) to (1,0). Does this
mean that something special happened to the coin to change it's "state"
from (1/2,1/2) to (1,0), but only when you looked at it? Should you
worry about how conscious you have to be for this to happen or invent
dynamical mechanisms to cause (1/2,1/2) to evolve into (1,0)? Should
you reject this "collapse" because any such mechanism would have to
be non-local? Perhaps your observation of the coin creates a
copy of the entire universe where you see "tails"?[*] Notice that
this entire mass of confusion is cause by one mistaken assumption:
that (1/2,1/2) is the "state of the coin." Once you realize that
(1/2,1/2) just represents what you happen to know about the the coin,
all of the problems evaporate. Perhaps, then, it is the quantum
mechanical version of this simple[**] mistake that causes your unhappiness
with collapse, causes people to think that quantum mechanics has something
to do with consciousness, world splitting, etc., etc., etc.
Cheers,
Saul Youssef
[*] People actually believe this -- no kidding! Actually, these are all
meant as retorical questions. The answers are supposed be "No."
[**} Simple but dangerous; so simple that the idea can be absorbed
without any awareness that something is being assumed.
Jacques Distler
Youssef) wrote:
> When you flip a coin and see the result "heads", your probability
> distribution has just "collapsed" from (1/2,1/2) to (1,0). Does this
> mean that something special happened to the coin to change it's "state"
> from (1/2,1/2) to (1,0), but only when you looked at it? Should you
> worry about how conscious you have to be for this to happen or invent
> dynamical mechanisms to cause (1/2,1/2) to evolve into (1,0)? Should
> you reject this "collapse" because any such mechanism would have to
> be non-local? Perhaps your observation of the coin creates a
> copy of the entire universe where you see "tails"?[*] Notice that
> this entire mass of confusion is cause by one mistaken assumption:
> that (1/2,1/2) is the "state of the coin." Once you realize that
> (1/2,1/2) just represents what you happen to know about the the coin,
> all of the problems evaporate.
If you think that the (quantum mechanical) coin really is either heads or
tails, and that (1/2,1/2) merely represents our ignorance of which it is,
then you are a believer in hidden variable theories. This is certainly a
self-consistent position. And indeed, it has no need for "collapse of the
wave function", or any of its alternatives. Unfortunately, it is also
WRONG, for it runs afoul of the Bell's Theorem. That is, in slightly more
complicated experiments, it gives predictions in conflict with those of
Quantum Mechanics.
Jacques
Saul Youssef
Dear Jacques,
The idea that a wavefunction represents what you know about a system
rather than it's "state" actually goes all the way back to Heisenberg
(see his "Physics and Philosophy") and is an interpretation of standard
quantum theory without hidden variables. His basic point is just that
you don't have to worry about *how* collapse happens since it's only a
change in your description of the system in response to your finding out
something (as in the coin example above). I think that a generation or
two ago, many physicists knew of this idea, but it seems to have been
almost forgotten. Maybe because you can't write any more papers about it!
Strangely or un-strangely enough, you actually can assume that
a quantum mechanical coin is either heads or tails, but you don't know
which, provided you're willing to mess around with probability theory
(and it's consistent with Bell's theorem). There are all sorts of
consequences of this idea which you can see in e.g. hep-th/9406184 and it's
references if you're interested.
Regards,
Saul Youssef
Joe Lavelle
>If you think that the (quantum mechanical) coin really is either heads or
>tails, and that (1/2,1/2) merely represents our ignorance of which it is,
>then you are a believer in hidden variable theories. This is certainly a
>self-consistent position. And indeed, it has no need for "collapse of the
>wave function", or any of its alternatives. Unfortunately, it is also
>WRONG, for it runs afoul of the Bell's Theorem. That is, in slightly more
>complicated experiments, it gives predictions in conflict with those of
>Quantum Mechanics.
>
>Jacques
correlated pennies is not easy to visualize. Another
to see this is to recall that quantum states obey a superposition principle.
Probabilities arising from mere ignorance of actual conditions do not.
Think of the double slit experiment, which Feynman said was the only myster
of QM.
Jacques Distler
Youssef) wrote:
> The idea that a wavefunction represents what you know about a system
> rather than it's "state" actually goes all the way back to Heisenberg
> ...........
> I think that a generation or
> two ago, many physicists knew of this idea, but it seems to have been
> almost forgotten. Maybe because you can't write any more papers about it!
No, because now we know about Bell's theorem and its successors which rule
out this interpretation.
>
> Strangely or un-strangely enough, you actually can assume that
> a quantum mechanical coin is either heads or tails, but you don't know
> which, provided you're willing to mess around with probability theory
> (and it's consistent with Bell's theorem). There are all sorts of
> consequences of this idea which you can see in e.g. hep-th/9406184 and it's
> references if you're interested.
Yes, "mess around with probability theory" is certainly an adequate description
of what you do in you paper, but you still are forced to abandon as well
most reasonable notions of locality in order to evade the stronger
versions of Bell's Theorem.
The "trouble" with Bell's Theorem in its original form is that it says
that hidden variable theories predict that a certain experiment will yield
a certain result X% of the time, whereas quantum mechanics predicts that
this result will obtain Y% of the time. Perhaps, one imagines, if one
monkeyed with the laws of probability, one could turn "X%" into "Y%" and
obtain agreement with quantum mechanics.
Unfortunately, the Greenberger, Horne, Shimony & Zeilinger [Ann. Phys. 58
(1990) 1131] version of the theorem affords one no such luxury, as it
says: hidden variable theories predict one result 100% of the time,
whereas QM predicts that it occurs 0% of the time.
You dismiss their work by saying that their notion of locality is suspect.
Well... Here is a rendition (mostly for the edification of the readers of this
newsgroup) of their result, due to Sidney Coleman (to whom I profusely
apologize for mangling his lucid and witty explication), which will, I
hope lay the point of contention in sharp relief.
Consider a central site which, at regular intervals simultaneously
dispatches three objects to three widely-separated measuring stations. At
each measuring station, the operator can perform one of two different
measurements (call them
"measurement A" and "measurement B"), each of which can yield one of two
results (call them +1 or -1).
Now, these objects could be blood samples, and the measuring stations
could be testing them either for AIDS ("A") or Hepatitis ("B"), or these
objects could be spin 1/2 particles, and some component of their spins are
being measured.
Whatever the details, the operators of the measuring stations independently
choose which of the two measurements to make (perhaps by flipping a coin),
and the measurements, occuring simultaneously at widely-separated
locations, can have no causal effect on one another.
They perform many, many measurements, recording their data in a form that
looks like:
.
.
.
AAB = +++
BAA = --+
AAA = ---
ABA = -+-
BBA = ++-
.
.
.
Consider first the subset of the data in which two of the measuring
stations measure "A", and one measures "B". There are three such possible
configurations
("AAB", "ABA" and "BAA"), and a remarkable regularity is found in the
measurements: For each of these configurations, the product of the three
measurements (remember, each is +1 or -1) turns out to be +1 in all cases.
Evidently, the blood samples are correlated in some way. Whenever two of
them are measured for AIDS, and the third for Hepatitis, one finds that
either just one sample tests positive, or all three test positive. Note
this happens 100% of the time; no exceptions!
Now, imagine for a moment that we could perform all three test sets
("AAB", "ABA" and "BAA") on the same three blood samples. We can't
actually do this, but, at least for blood samples, we don't doubt that
each blood sample actually IS either positive or negative for AID and for
Hepatitis, regardless of whether we measure it or not.
So, if we were to perform all three tests sets, and multiply the results
together, we would get
AAB = 1
ABA = 1
x BAA = x 1
--- ---
BBB = +1
Note that, since A gets measured twice for each sample, the actual value
of A (+1 or -1) drops out, and we get a prediction for the set of "BBB"
measurements, namely that the product should always be +1.
Let me belabour this point, since this is the point on which we part company.
It doesn't matter what the value of A would be measured to be. It is either
+1 or -1, and in either case, (-1)^2=(+1)^2=+1.
Maybe the probability that A is measured to be +1 is 1+i\sqrt{3} (if you
happen to like complex probabilities). WE DON'T CARE. A^2 is always +1, so
the product of the "BBB" measurements is ALWAYS +1. No probability
distributions were envoked in coming to this conclusion, so no conceivable
modifications of the laws of probabilities can change it.
No, if you want to wriggle out of this conclusion, you really have to deny
that the blood sample actually IS either positive or negative for each
disease, REGARDLESS of what tests are performed on it. If I have
understood anything of what you are saying, this is one thing you would
not want to deny.
So what does Quantum Mechanics predict (for those of you who have been
patiently following along)? Drum roll..........
Quantum Mechanics Predicts that the product of the "BBB" measurements is
ALWAYS -1. Not for blood samples, mind you, but for spin 1/2 particles.
Those who care will be pleased to learn that the three spin 1/2 particles are
prepared in the state (which has total angular momentum 3/2):
1 / | ^ ^ ^ \ | | | | \ \
--- | | | | | / - | v v v / |
\/ 2 \ /
and "A" corresponds to measuring \sigma_y and "B" corresponds to measuring
\sigma_x for each particle. I leave it as an exercise to the reader to
verify that quantum mechanics indeed predicts the above results.
The essential point is, I hope, clear. Classical reasoning give one answer
100% of the time. No probabilities (complex or otherwise) were involved in
the calculation. Quantum mechanics predicts the other answer 100 percent
of the time.
I doubt this will do much to sway you, but I hope that the other readers
of this newsgroup find the preceeding discussion enlightening, as Bell's
Theorem seems to be something of an FAQ hereabouts.
Jacques Distler
Michael Clive Price
<365cdo$7...@scunix2.harvard.edu>
<distler-3009...@slip-2-14.ots.utexas.edu>
<36l0mg$o...@news.scri.fsu.edu>
Date: Thu, 06 Oct 94 12:01:06 GMT
Reply-To: pr...@price.demon.co.uk
X-Newsreader: Demon Internet Simple News v1.29
Lines: 52
Saul, you argue a good case, but you didn't mention complex probability
once :-)
> [*] People actually believe [in many-worlds] -- no kidding!
Yup, no kidding. Other worlds or complex probabilities. I know which
I prefer!
******** from my FAQ ********
4) Extended Probability [M]. A bold theory in which the concept of
probability is "extended" to include complex values [Y]. Whilst
quite daring, I am not sure if this is logically permissable, being
in conflict with the relative frequency notion of probability, in
which case it suffers from the same criticism as quantum logic.
Also it is unclear, to me anyway, how the resultant notion of
"complex probability" differs from the quantum "probability
amplitude" and thus why we are justified in collapsing the complex-
valued probability as if it were a classical, real-valued
probability.
[M] W Muckenheim _A review of extended probabilities_ Physics
Reports Vol 133 339- (1986)
[Y] Saul Youssef _Quantum Mechanics as Complex Probability Theory_
hep-th 9307019
*******************************
Michael Price pr...@price.demon.co.uk
Saul Youssef
|> The idea that a wavefunction represents what you know about a system
|> rather than it's "state" actually goes all the way back to Heisenberg
|> ...........
|
|
|No, because now we know about Bell's theorem and its successors which rule
|out this interpretation.
|
theory is OK, with or without Bell. You can find a discussion in
Cramer's RMP article ca. late 1970's (I can find the reference with
some effort, it's the same paper where he introduces the "transactional
interpretation.")
|
|...you still are forced to abandon as well
|most reasonable notions of locality in order to evade the stronger
|versions of Bell's Theorem.
|
I would probably disagree with this, depending on what you meant
by "most reasonable notions of locality."
|
|The "trouble" with Bell's Theorem in its original form is that it says
|that hidden variable theories predict that a certain experiment will yield
|a certain result X% of the time, whereas quantum mechanics predicts that
|this result will obtain Y% of the time. Perhaps, one imagines, if one
|monkeyed with the laws of probability, one could turn "X%" into "Y%" and
|obtain agreement with quantum mechanics.
|
Actually, this is sort of right. The point is that you need
standard probability theory in addition to Bell's explicit assumptions to
get the prediction "X%" in the first place (the result is actually an
inequality, as I'm sure you know).
|
|Unfortunately, the Greenberger, Horne, Shimony & Zeilinger [Ann. Phys. 58
|(1990) 1131] version of the theorem affords one no such luxury, as it
|says: hidden variable theories predict one result 100% of the time,
|whereas QM predicts that it occurs 0% of the time.
|
|You dismiss their work by saying that their notion of locality is suspect.
No, I'm not criticising their idea of locality.
I haven't discussed the spin version of GHZ's result, but I can't resist
just one thing...
|
| ...[Sidney Coleman's rendition of the spin version of GHZ deleted]...
|
|
|No, if you want to wriggle out of this conclusion, you really have to deny
|that the blood sample actually IS either positive or negative for each
|disease, REGARDLESS of what tests are performed on it. If I have
|understood anything of what you are saying, this is one thing you would
|not want to deny.
|
Actually, this *is* something that I would want to deny. Being
able to assign values to a set of propositions which agrees with
experiment is equivalent to their "supporting standard probabilities".
Not all sets of propositions have this property. This is the result
of theorem 1, but I have found out that this was worked out long ago by
Aurthur Fine in Phys.Rev.Lett. 48(1982)291.
|
|I doubt this will do much to sway you, but I hope that the other readers
|of this newsgroup find the preceeding discussion enlightening, as Bell's
|Theorem seems to be something of an FAQ hereabouts.
|
We'll see how things go.
I've posted this also to sci.physics and I suggest that we move over
there since this doesn't have much to do with particle physics as such.
Saul Youssef
Saul Youssef
| Mike Price writes:
|
|Saul, you argue a good case, but you didn't mention complex probability
|once :-)
|
|> [*] People actually believe [in many-worlds] -- no kidding!
|
|Yup, no kidding. Other worlds or complex probabilities. I know which
|I prefer!
|
| ******** from my FAQ ********
|4) Extended Probability [M]. A bold theory in which the concept of
|
I'll settle for "bold" for the time being :-) I think I'm going to
shut up and work out more consequences to make sure it's also "not wrong"!
Saul
Jacques Distler
Dreiner) wrote:
>I agree that
> the one-shot experiments are very nice, but have they actually
> been performed yet?
No. It's not clear (to me) how easy it would be to prepare 3 particles in the
desired initial state. So this may just be a very pretty gedanken experiment.
> Aren't the Aspect experiments the best we have to date?
So far.....
Herbert Dreiner
I just read your very nice explanation of the 3 particle one-shot
experiments to distinguish between QM and hidden-variable
theories.
However you start out on this discussion in order to respond
to the "statistics" critique of the Bell theorem. I agree that
the one-shot experiments are very nice, but have they actually
been performed yet?
Herbi Dreiner
Sven the Moose
: |In article <36l0mg$o...@news.scri.fsu.edu>, you...@scri.fsu.edu (Saul
: |Youssef) wrote:
: |
: |> When you flip a coin and see the result "heads", your probability
: |> distribution has just "collapsed" from (1/2,1/2) to (1,0). Does this
: |> mean that something special happened to the coin to change it's "state"
: |> from (1/2,1/2) to (1,0), but only when you looked at it? Should you
: |> worry about how conscious you have to be for this to happen or invent
: |> dynamical mechanisms to cause (1/2,1/2) to evolve into (1,0)? Should
: |> you reject this "collapse" because any such mechanism would have to
: |> be non-local? Perhaps your observation of the coin creates a
: |> copy of the entire universe where you see "tails"?[*] Notice that
: |> this entire mass of confusion is cause by one mistaken assumption:
: |> that (1/2,1/2) is the "state of the coin." Once you realize that
: |> (1/2,1/2) just represents what you happen to know about the the coin,
: |> all of the problems evaporate.
: |
: |If you think that the (quantum mechanical) coin really is either heads or
: |tails, and that (1/2,1/2) merely represents our ignorance of which it is,
: |then you are a believer in hidden variable theories. This is certainly a
: |self-consistent position. And indeed, it has no need for "collapse of the
: |wave function", or any of its alternatives. Unfortunately, it is also
: |WRONG, for it runs afoul of the Bell's Theorem. That is, in slightly more
: |complicated experiments, it gives predictions in conflict with those of
: |Quantum Mechanics.
: |
: |Jacques
I think that the major point to make is that the QM state is a description of
a STATISTICAL ENSEMBLE and not a single particle/coin (i.e. the
probabilities only refer to a countably infinite number of trials
of EXACTLY the same experiment, prepared in EXACTLY the same
fasgion). You cannot apply any other interpretation without some sort of
contradiction.
SVEN