| Topic: |
Science > Physics |
| User: |
"Wate" |
| Date: |
25 Apr 2006 08:05:11 PM |
| Object: |
HUP misunderstood (ping Bilge, Gregory...) |
What do you think of the Ensemble Interpretation concerning
the HUP:
To the few uncranked left here. I came across the so called
Ensemble Interpretation in
http://www.anasoft.co.uk/quantummechanics/
Do you guys agree with the following part:
Heisenberg's Uncertainty Principle
The Heisenberg's Uncertainty Principle, HUP, is often misunderstood
to imply that individual simultaneous position and momentum
measurements can not be made. This is false.
The HUP is a statistical statement, as is all of Quantum Mechanics.
It is a statement about the standard deviations of momentum and
position, not about individual measurements. Standard deviations are
calculated from calculating the root mean square of many individual
measurements. It says nothing about an individual measurement,
indeed Jauch (1993) performs such a measurement that is much
more precise than that would otherwise be indicated by HUP. Indeed,
HUP is not even a statement about simultaneous measurements.
The HUP is about the prediction of a state given the current position
and momentum. It is predictions that are constrained by HUP, not
measurements.
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| User: "Sam Wormley" |
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| Title: Re: HUP misunderstood (ping Bilge, Gregory...) |
25 Apr 2006 08:18:17 PM |
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Wate wrote:
What do you think of the Ensemble Interpretation concerning
the HUP:
Uncertainty Principle
http://scienceworld.wolfram.com/physics/UncertaintyPrinciple.html
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| User: "Edward Green" |
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| Title: Re: HUP misunderstood (ping Bilge, Gregory...) |
26 Apr 2006 06:12:45 PM |
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Wate wrote:
What do you think of the Ensemble Interpretation concerning
the HUP:
To the few uncranked left here.
I'm studying to be a crank, but I haven't passed my qualifying yet.
Can I play?
I came across the so called Ensemble Interpretation in
http://www.anasoft.co.uk/quantummechanics/
The so-called "so-called Ensemble interpretation" is nothing new; it is
rather the most neutral and cautious interpretation available (perhaps
another way of saying the correct one). What we are really deriving,
given the probabilistic interpretation of the state vector, is a
relation between the standard deviations of two measurement
(probability) distributions obtained from the same state vector, under
different measurements. The "ensemble" is simply a population having
the indicated distribution. This is all probability theory 101.
Do you guys agree with the following part:
Heisenberg's Uncertainty Principle
The Heisenberg's Uncertainty Principle, HUP, is often misunderstood
to imply that individual simultaneous position and momentum
measurements can not be made. This is false.
The HUP is a statistical statement, as is all of Quantum Mechanics.
That's painting with a spackle brush.
It is a statement about the standard deviations of momentum and
position, not about individual measurements. Standard deviations are
calculated from calculating the root mean square of many individual
measurements. It says nothing about an individual measurement,
OK, ok, that much is true. The horse is dead already!
Now we get to the iffy parts.
indeed Jauch (1993) performs such a measurement that is much
more precise than that would otherwise be indicated by HUP.
I'd like to know exactly what that means. What did Jauch do?
Indeed,
HUP is not even a statement about simultaneous measurements.
Did the horse sigh, that it needed another smack?
The HUP is about the prediction of a state given the current position
and momentum. It is predictions that are constrained by HUP, not
measurements.
This doesn't sound correct, but to attempt exegesis would violate the
law that it is not worth the effort to try to explicate a passage if it
is going to take more than an order of magnitude more words than the
original to exhaust the possibilities -- unless we are writing the
Talmud.
Let's go back to the beginning. For a so-called pure state (the
possibility of additional uncertainty before the state vector raises an
additional complication), the state vector describes the system as
completely as possible. It particular, the state vector determines the
probability distribution of measurements we could perform on the
system. When physicists deal with probabilities, they often like to
append the word "ensemble", which perhaps indicates that they are
frequentists. We will allow them this word of power.
Now, when things have probability distributions, they also have things
like means, variances, and standard deviations, which are properties of
the probability distributions (when they exist). Things like the
outcome of position and momentum measurements are just ordinary
distributed things in this regard, and have these other things -- or,
more correctly "thingies" -- along with them. And it was good. And
furthermore, clever mathematical physicist types were able to establish
that some of these thingies, obeyed some relations like "the product of
this thingie and that thingie is always at least equal to this constant
thing, for any possible state vector". And it was very good.
Now, what does this mean? It means just what we said it means.
However, if you wish to relate these profundities to experiment -- to
operationalize them -- you might have resort to ensembles of
identically prepared systems, whose sample statistics obey -- in the
famous infinite limit -- the relations we have obtained for the joint
probability distribution, which in turn is determined by friend state
vector. The "ensemble" interpretation is just short hand for this
operationalization of the relationships in probability derived from the
state vector. Nothing new here.
Now we know a minimum interpretation that is rigorously correct, given
the model (quantum mechanics), its postulated relation to experiment,
and our cleverness. There are, however, a number of things we can say,
which may or may not be meaningful or true, which _sound_ like they
might be true, given the choice of the word "uncertainty". Some of
these might be the "wrong" interpretations of the Heisenberg
Uncertainty Principle our protagonists are lambasting. I agree with
them that the so-called "ensemble interpretation" is in fact the
minimal correct interpretation of the relationships. I'm not sure
offhand if any of the other things we might say which might sound like
they might be true are actually wrong or not, but I am sure that it
_is_ wrong to accept any of them as meaningful or true without careful
operationalization and connection with the fundamental interpretation.
Wrong, and very sloppy.
This is why I am somewhat surprised, after a correct (if triumphal)
beginning, that the passage ends
"The HUP is about the prediction of a state given the current position
and momentum. It is predictions that are constrained by HUP, not
measurements."
....because at best this claim contains one or more of the somethings
which sound like they might be made true given careful
operationalization and connection with what is known to be true, but is
unmotivated by the previous material, and is a good candidate for one
of the bad confused views they seek to eradicate! Perhaps this section
of Genesis was written by a different author.
(I seem to have violated my own rule).
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