| Topic: |
Science > Physics |
| User: |
"Guy Macon http://www.guymacon.com" |
| Date: |
25 Sep 2004 02:38:02 AM |
| Object: |
Heisenberg Uncertainty Principle |
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
Which one of us is mistaken?
.
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| User: "John T Lowry" |
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| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 08:49:26 AM |
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"Guy Macon" <http://www.guymacon.com> wrote in message
news:10la830a59dnuba@news.supernews.com...
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
Which one of us is mistaken?
You are. The Uncertainty Principle doesn't mean what you think
Heisenberg thought it meant. Read it. It's a statement about the
products of measures of SCATTER of pairs of so-called incompatible
(non-commutating) observables. Nothing says you can't measure say
x-position and x-momentum at the same time with arbitrary accuracy. It's
just that the next time you do that, on an identically prepared system,
you're likely to get different answers. And in the long run those
bunches of pairs of observations scatter according to the Uncertainty
Principle. The wave function refers to an ensemble of similarly prepared
systems, not to one exemplar.
John Lowry
Flight Physics
.
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| User: "" |
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| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 07:36:59 PM |
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In article <GHe5d.2787$zG1.2142@newsread3.news.pas.earthlink.net>, "John T Lowry" <jlowry100@earthlink.net> writes:
"Guy Macon" <http://www.guymacon.com> wrote in message
news:10la830a59dnuba@news.supernews.com...
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
Which one of us is mistaken?
You are. The Uncertainty Principle doesn't mean what you think
Heisenberg thought it meant. Read it. It's a statement about the
products of measures of SCATTER of pairs of so-called incompatible
(non-commutating) observables. Nothing says you can't measure say
x-position and x-momentum at the same time with arbitrary accuracy. It's
just that the next time you do that, on an identically prepared system,
you're likely to get different answers. And in the long run those
bunches of pairs of observations scatter according to the Uncertainty
Principle. The wave function refers to an ensemble of similarly prepared
systems, not to one exemplar.
Nope, the wave function does not refer to an ensemble. And yes, every
single entity is described by its wave function.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
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| User: "Y. T." |
|
| Title: Re: Heisenberg Uncertainty Principle |
27 Sep 2004 11:30:05 PM |
|
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Guy Macon <http://www.guymacon.com> wrote in message news:<10la830a59dnuba@news.supernews.com>...
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
Which one of us is mistaken?
As one could have expected, you got a number of half-baked answers.
Unsurprising.
What many people do find surprising is the fact that the Heisenberg
uncertainty principle isn't a statement about the universe, really,
and at most marginally a statement about measurement.
It is really a statement about variables. And how macroscopically
useful variables aren't the cleverest choice when dealing with
microscopic systems.
This here has a quote from Feynman himsef:
http://groups.google.com/groups?as_umsgid=<df160b8f.0407201331.7120f3a4@posting.google.com>
(I hope this is coming though - the link might be wrapped. But I guess
a 'Doc Brown' kinda guy can figure that out, eh? ;) )
cordially
Y.T.
--
Remove YourClothes before you email me.
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| User: "Sam Wormley" |
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| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 09:07:33 AM |
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Guy Macon wrote:
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
Which one of us is mistaken?
The equation holds true
http://scienceworld.wolfram.com/physics/UncertaintyPrinciple.html
.
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| User: "Guy Macon http://www.guymacon.com" |
|
| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 10:05:59 AM |
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--------------------------------
Sam Wormley <swormley1@mchsi.com> says...
The equation holds true
http://scienceworld.wolfram.com/physics/UncertaintyPrinciple.html
(Which page summarizes the equation with "It is not possible to
simultaneously determine the position and momentum of a particle.")
--------------------------------
John T Lowry <jlowry100@earthlink.net> says...
The Uncertainty Principle doesn't mean what you think
Heisenberg thought it meant. Read it. It's a statement about the
products of measures of SCATTER of pairs of so-called incompatible
(non-commutating) observables. Nothing says you can't measure say
x-position and x-momentum at the same time with arbitrary accuracy.
--------------------------------
I am having trouble reconciling the above two statements. Perhaps I
am missing something, but they appear to say different things on the
question of whether I can determine the position and momentum of a
particle at a particular time with arbitrary accuracy. Please forgive
me if I am missing something.
.
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| User: "Old Man" |
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| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 10:25:50 PM |
|
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"Guy Macon" <http://www.guymacon.com> wrote in message
news:10lb2ar2hf5rb85@news.supernews.com...
--------------------------------
Sam Wormley <swormley1@mchsi.com> says...
The equation holds true
http://scienceworld.wolfram.com/physics/UncertaintyPrinciple.html
(Which page summarizes the equation with "It is not possible to
simultaneously determine the position and momentum of a particle.")
--------------------------------
John T Lowry <jlowry100@earthlink.net> says...
The Uncertainty Principle doesn't mean what you think
Heisenberg thought it meant. Read it. It's a statement about the
products of measures of SCATTER of pairs of so-called incompatible
(non-commutating) observables. Nothing says you can't measure say
x-position and x-momentum at the same time with arbitrary accuracy.
--------------------------------
I am having trouble reconciling the above two statements. Perhaps I
am missing something, but they appear to say different things on the
question of whether I can determine the position and momentum of a
particle at a particular time with arbitrary accuracy.
Sure, for a single pair of measurements, you can know
(x, p) to within estimated experimental error, but, via
HUP, the observation of one parameter may interfere
with the observed value the other.
For each measurement, i, determine the position, x_i, and
momentum, p_i, of a particle. Do this N times, calculate
the averages, <x> and <p>, and then calculate the pair-wise
standard deviations of position and momentum.
SD^2 = ( 1 / N) Sum_i { [ ( <p > - p_i ) ( <x > - x_i ) ]^2 }
HUP says SD > hbar regardless of the precision of the
individual measurements.
HUP doesn't exclude the possibility that, for any particular
pair of measurements, to within experimental error,
p_j = < p > and x_j = < x >,
but it won't happen very often unless the estimated experiential
errors exceed those of HUP.
[Old Man]
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| User: "Guy Macon http://www.guymacon.com" |
|
| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 11:44:08 PM |
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Old Man <nomail@nomail.net> says...
Sure, for a single pair of measurements, you can know
(x, p) to within estimated experimental error, but, via
HUP, the observation of one parameter may interfere
with the observed value the other.
*May* intefere, or *will* interfere?
(Assuming that the two parameters are the position and
velocity of a single particle at a particular time.)
.
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| User: "Old Man" |
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| Title: Re: Heisenberg Uncertainty Principle |
26 Sep 2004 01:51:37 AM |
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"Guy Macon" <http://www.guymacon.com> wrote in message
news:10lci8s1pvmsj73@news.supernews.com...
Old Man <nomail@nomail.net> says...
Sure, for a single pair of measurements, you can know
(x, p) to within estimated experimental error, but, via
HUP, the observation of one parameter may interfere
with the observed value the other.
*May* intefere, or *will* interfere?
(Assuming that the two parameters are the position and
velocity of a single particle at a particular time.)
HUP is intrinsic in nature. Measurement is not
causal to HUP. The position and momentum
obtained from a pair of empirical observations don't
necessarily correspond to the quantum state of the
system that existed before the measurements. The
act of measurement can introduce a new quantum
state in which HUP is intrinsic. The wave functions
of the old and new quantum states can be precisely
specified. HUP is intrinsic in both states
Letting, x, signify position and, p, momentum of
an electron in the hydrogen atom ground state, the
function, p = p(x), can't be specified.
The quantum numbers that uniquely describe the
electron wave function is a complete description of
the hydrogen atom. There isn't any additional
information to be had.
The existence of a hydrogen atom ground state of finite
extent demonstrates the intrinsic nature of HUP. the
observed size of the hydrogen atom has naught to do
with the interference of HUP with empirical observation.
[Old Man]
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| User: "Mike" |
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| Title: Re: Heisenberg Uncertainty Principle |
26 Sep 2004 05:15:46 AM |
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"Old Man" <nomail@nomail.net> wrote in message
news:_vudnVP_Ssyb-svcRVn-gw@prairiewave.com...
"Guy Macon" <http://www.guymacon.com> wrote in message
news:10lci8s1pvmsj73@news.supernews.com...
Old Man <nomail@nomail.net> says...
Sure, for a single pair of measurements, you can know
(x, p) to within estimated experimental error, but, via
HUP, the observation of one parameter may interfere
with the observed value the other.
*May* intefere, or *will* interfere?
(Assuming that the two parameters are the position and
velocity of a single particle at a particular time.)
HUP is intrinsic in nature. Measurement is not
causal to HUP. The position and momentum
obtained from a pair of empirical observations don't
necessarily correspond to the quantum state of the
system that existed before the measurements. The
act of measurement can introduce a new quantum
state in which HUP is intrinsic. The wave functions
of the old and new quantum states can be precisely
specified. HUP is intrinsic in both states
Letting, x, signify position and, p, momentum of
an electron in the hydrogen atom ground state, the
function, p = p(x), can't be specified.
The quantum numbers that uniquely describe the
electron wave function is a complete description of
the hydrogen atom. There isn't any additional
information to be had.
The existence of a hydrogen atom ground state of finite
extent demonstrates the intrinsic nature of HUP. the
observed size of the hydrogen atom has naught to do
with the interference of HUP with empirical observation.
[Old Man]
Let me tell you what has happened Old Man, fearing you will again resist
enlightenment.
HUP started as a statement that position and momentum cannot be both
determined at the same time. As experimental accuracy improved and HUP was
falsified, the proponents of a "mind world", turned to Copenhagen hypothesis
and a modified view of HUP dealing with collection of measurements,
observation of interference patterns and which-way information. Now, Afshar
is attacking this hypothesis also, showing that both the pattern and
which-way can be determined.
Next, the "mind world" people will raise the HUP to another level of
abstraction that will probably require 50 more years of progress in
instrumentation accuracy to resolve. Yet, what is, is.
Mike
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| User: "Sam Wormley" |
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| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 10:46:17 AM |
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Guy Macon wrote:
--------------------------------
Sam Wormley <swormley1@mchsi.com> says...
The equation holds true
http://scienceworld.wolfram.com/physics/UncertaintyPrinciple.html
(Which page summarizes the equation with "It is not possible to
simultaneously determine the position and momentum of a particle.")
--------------------------------
John T Lowry <jlowry100@earthlink.net> says...
The Uncertainty Principle doesn't mean what you think
Heisenberg thought it meant. Read it. It's a statement about the
products of measures of SCATTER of pairs of so-called incompatible
(non-commutating) observables. Nothing says you can't measure say
x-position and x-momentum at the same time with arbitrary accuracy.
--------------------------------
I am having trouble reconciling the above two statements. Perhaps I
am missing something, but they appear to say different things on the
question of whether I can determine the position and momentum of a
particle at a particular time with arbitrary accuracy. Please forgive
me if I am missing something.
Nature imposes a fundamental limit on the precision of measurement
between conjugate quantum mechanical variables. Heisenberg was able
to express this mathematically in what we call the "Uncertainty
Principle". No matter what observation or experiment one performs,
the Uncertainty Principle will hold true. The equation says it all.
.
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| User: "" |
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| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 07:44:55 PM |
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In article <dpg5d.116067$D%.17560@attbi_s51>, Sam Wormley <swormley1@mchsi.com> writes:
Guy Macon wrote:
--------------------------------
Sam Wormley <swormley1@mchsi.com> says...
The equation holds true
http://scienceworld.wolfram.com/physics/UncertaintyPrinciple.html
(Which page summarizes the equation with "It is not possible to
simultaneously determine the position and momentum of a particle.")
--------------------------------
John T Lowry <jlowry100@earthlink.net> says...
The Uncertainty Principle doesn't mean what you think
Heisenberg thought it meant. Read it. It's a statement about the
products of measures of SCATTER of pairs of so-called incompatible
(non-commutating) observables. Nothing says you can't measure say
x-position and x-momentum at the same time with arbitrary accuracy.
--------------------------------
I am having trouble reconciling the above two statements. Perhaps I
am missing something, but they appear to say different things on the
question of whether I can determine the position and momentum of a
particle at a particular time with arbitrary accuracy. Please forgive
me if I am missing something.
Nature imposes a fundamental limit on the precision of measurement
between conjugate quantum mechanical variables.
It is not a limit on measurement.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
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| User: "Mike" |
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| Title: Re: Heisenberg Uncertainty Principle |
26 Sep 2004 09:28:35 AM |
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<mmeron@cars3.uchicago.edu> wrote in message
news:bio5d.22$25.1510@news.uchicago.edu...
In article <dpg5d.116067$D%.17560@attbi_s51>, Sam Wormley
<swormley1@mchsi.com> writes:
Guy Macon wrote:
--------------------------------
Sam Wormley <swormley1@mchsi.com> says...
The equation holds true
http://scienceworld.wolfram.com/physics/UncertaintyPrinciple.html
(Which page summarizes the equation with "It is not possible to
simultaneously determine the position and momentum of a particle.")
--------------------------------
John T Lowry <jlowry100@earthlink.net> says...
The Uncertainty Principle doesn't mean what you think
Heisenberg thought it meant. Read it. It's a statement about the
products of measures of SCATTER of pairs of so-called incompatible
(non-commutating) observables. Nothing says you can't measure say
x-position and x-momentum at the same time with arbitrary accuracy.
--------------------------------
I am having trouble reconciling the above two statements. Perhaps I
am missing something, but they appear to say different things on the
question of whether I can determine the position and momentum of a
particle at a particular time with arbitrary accuracy. Please forgive
me if I am missing something.
Nature imposes a fundamental limit on the precision of measurement
between conjugate quantum mechanical variables.
It is not a limit on measurement.
It must be at the end of the day, if the original HUP must hold. The
statement was qualified, as "a fundamental limit on the precision of
measurement between conjugate quantum mechanical variables." Not as a limit
on measurement in general.
I get the impression, there is a lot of word games played in QM.
I agree: "When you argue with a fool, chances are he is doing just the same"
The question here is who are the fools.
Mike
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
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| User: "Sam Wormley" |
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| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 10:50:12 AM |
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Sam Wormley wrote:
Guy Macon wrote:
--------------------------------
Sam Wormley <swormley1@mchsi.com> says...
The equation holds true
http://scienceworld.wolfram.com/physics/UncertaintyPrinciple.html
(Which page summarizes the equation with "It is not possible to
simultaneously determine the position and momentum of a particle.")
--------------------------------
John T Lowry <jlowry100@earthlink.net> says...
The Uncertainty Principle doesn't mean what you think Heisenberg
thought it meant. Read it. It's a statement about the products of
measures of SCATTER of pairs of so-called incompatible
(non-commutating) observables. Nothing says you can't measure say
x-position and x-momentum at the same time with arbitrary accuracy.
--------------------------------
I am having trouble reconciling the above two statements. Perhaps I
am missing something, but they appear to say different things on the
question of whether I can determine the position and momentum of a
particle at a particular time with arbitrary accuracy. Please forgive
me if I am missing something.
Nature imposes a fundamental limit on the precision of measurement
between conjugate quantum mechanical variables.
I should have said nature imposes a fundamental limit on the information
available!
Heisenberg was able
to express this mathematically in what we call the "Uncertainty
Principle". No matter what observation or experiment one performs,
the Uncertainty Principle will hold true. The equation says it all.
.
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| User: "Gregory L. Hansen" |
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| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 07:58:11 AM |
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In article <10la830a59dnuba@news.supernews.com>,
Guy Macon <http://www.guymacon.com> wrote:
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
Which one of us is mistaken?
The Heisenberg uncertainty principle is just more wave mechanics, not so
different from sound waves or whatever waves or anything else. Clap your
hands and do a Fourier decomposition of the sound, what do you get? You
get a whole lot of different frequencies. Your sound wave will be pretty
well localized, but highly dispersed in frequency space. Conversely, if
you create a sound wave with a highly pure single tone, it must be
physically large.
Quantum mechanics is just another wave mechanics. Frequency is related to
momentum, and there's Heisenberg.
There's an old question in the history of quantum mechanics: why doesn't
the electron, accelerating in its orbit about the nucleus, radiate away
all of its energy and fall into the nucleus? The answer is that it has
radiated away all its energy, it has fallen as far into the nucleus as it
can go. Find the kinetic and potential energies of the electron in a
hydrogen atom, use the uncertainty relation to relate momentum to
position, and you'll get the Bohr radius, which equals the radial
expectation value of the electron wavefunction.
The Heisenberg uncertainty principle operates at a fundamental level for
each particle.
--
"We don't grow up hearing stories around the camp fire anymore about
cultural figures. Instead we get them from books, TV or movies, so the
characters that today provide us a common language are corporate
creatures" -- Rebecca Tushnet
.
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| User: "Edward Green" |
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| Title: Re: Heisenberg Uncertainty Principle |
27 Sep 2004 05:44:00 PM |
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(Gregory L. Hansen) wrote in message news:<cj3q13$79c$4@hood.uits.indiana.edu>...
In article <10la830a59dnuba@news.supernews.com>,
Guy Macon <http://www.guymacon.com> wrote:
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
Which one of us is mistaken?
The Heisenberg uncertainty principle is just more wave mechanics, not so
different from sound waves or whatever waves or anything else. Clap your
hands and do a Fourier decomposition of the sound, what do you get? You
get a whole lot of different frequencies. Your sound wave will be pretty
well localized, but highly dispersed in frequency space. Conversely, if
you create a sound wave with a highly pure single tone, it must be
physically large.
Quantum mechanics is just another wave mechanics. Frequency is related to
momentum, and there's Heisenberg.
There's an old question in the history of quantum mechanics: why doesn't
the electron, accelerating in its orbit about the nucleus, radiate away
all of its energy and fall into the nucleus? The answer is that it has
radiated away all its energy, it has fallen as far into the nucleus as it
can go. Find the kinetic and potential energies of the electron in a
hydrogen atom, use the uncertainty relation to relate momentum to
position, and you'll get the Bohr radius, which equals the radial
expectation value of the electron wavefunction.
The Heisenberg uncertainty principle operates at a fundamental level for
each particle.
I have one thing to add to this, Gregory, which might touch on our
disagreement above. Quantum mechanics is just another wave mechanics
_until_ we add one more element to it not in any of those old fogey
wave mechanics -- quantum measurement! Quantum mechanics is plain old
wave mechanics + quantum measurement.
Therefore, qua plain old wave mechanics, we have the reductionist view
that HUP is just a theorem about Fourier transform pairs, applicable
to a single copy of the state vector/wave function. But, you want to
talk about uncertainty in a measurement (the term is presumably there
for some purpose beyond spacing "Heisenberg" and "Principle"), you
have introduced quantum measurement, and the uncertainty in outcomes
of measurements can only be made sense of if we repeat the
measurements on identically prepared systems. Here is your connection
between the properties of the wave function of the individual system,
and the statistics of an ensemble of identically prepared systems:
wave analysis is nice, but wave analysis alone knows nothing about the
additional and logically independent postulates of quantum
measurement.
Sing:
Why can't we be friends!?
Why can't we be friends!?
Why can't we be friends!?
.
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| User: "" |
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| Title: Re: Heisenberg Uncertainty Principle |
27 Sep 2004 06:00:17 PM |
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In article <eca320d0.0409271444.4a4f859@posting.google.com>, (Edward Green) writes:
glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) wrote in message news:<cj3q13$79c$4@hood.uits.indiana.edu>...
In article <10la830a59dnuba@news.supernews.com>,
Guy Macon <http://www.guymacon.com> wrote:
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
Which one of us is mistaken?
The Heisenberg uncertainty principle is just more wave mechanics, not so
different from sound waves or whatever waves or anything else. Clap your
hands and do a Fourier decomposition of the sound, what do you get? You
get a whole lot of different frequencies. Your sound wave will be pretty
well localized, but highly dispersed in frequency space. Conversely, if
you create a sound wave with a highly pure single tone, it must be
physically large.
Quantum mechanics is just another wave mechanics. Frequency is related to
momentum, and there's Heisenberg.
There's an old question in the history of quantum mechanics: why doesn't
the electron, accelerating in its orbit about the nucleus, radiate away
all of its energy and fall into the nucleus? The answer is that it has
radiated away all its energy, it has fallen as far into the nucleus as it
can go. Find the kinetic and potential energies of the electron in a
hydrogen atom, use the uncertainty relation to relate momentum to
position, and you'll get the Bohr radius, which equals the radial
expectation value of the electron wavefunction.
The Heisenberg uncertainty principle operates at a fundamental level for
each particle.
I have one thing to add to this, Gregory, which might touch on our
disagreement above. Quantum mechanics is just another wave mechanics
_until_ we add one more element to it not in any of those old fogey
wave mechanics -- quantum measurement! Quantum mechanics is plain old
wave mechanics + quantum measurement.
Good, very good. Told you you're not an amateur.
Therefore, qua plain old wave mechanics, we have the reductionist view
that HUP is just a theorem about Fourier transform pairs, applicable
to a single copy of the state vector/wave function. But, you want to
talk about uncertainty in a measurement (the term is presumably there
for some purpose beyond spacing "Heisenberg" and "Principle"), you
have introduced quantum measurement, and the uncertainty in outcomes
of measurements can only be made sense of if we repeat the
measurements on identically prepared systems. Here is your connection
between the properties of the wave function of the individual system,
and the statistics of an ensemble of identically prepared systems:
wave analysis is nice, but wave analysis alone knows nothing about the
additional and logically independent postulates of quantum
measurement.
Sing:
Why can't we be friends!?
Why can't we be friends!?
Why can't we be friends!?
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
|
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|
| User: "" |
|
| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 04:14:42 AM |
|
|
In article <10la830a59dnuba@news.supernews.com>, Guy Macon <http://www.guymacon.com> writes:
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
More precisely, "the better defined the position *is*, the less
defined the momentum *is*". It is not a statement about "precise
values existing but unknowable" but about "precise values *not
existing*"
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
|
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| User: "Guy Macon http://www.guymacon.com" |
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| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 09:56:02 AM |
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<> says...
More precisely, "the better defined the position *is*, the less
defined the momentum *is*". It is not a statement about "precise
values existing but unknowable" but about "precise values *not
existing*"
(Light come on over my head)
Got it. That brings a bunch of slightly confusing things I have
read into focus. Thanks!
.
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| User: "" |
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| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 07:42:36 PM |
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|
In article <10lb1o5pvu5a8e2@news.supernews.com>, Guy Macon <http://www.guymacon.com> writes:
mmeron@cars3.uchicago.edu <mmeron@cars3.uchicago.edu> says...
More precisely, "the better defined the position *is*, the less
defined the momentum *is*". It is not a statement about "precise
values existing but unknowable" but about "precise values *not
existing*"
(Light come on over my head)
Got it. That brings a bunch of slightly confusing things I have
read into focus. Thanks!
You're very welcome
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
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| User: "Mike" |
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| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 11:33:30 AM |
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|
wrote in message news:<6Ga5d.16$25.1004@news.uchicago.edu>...
In article <10la830a59dnuba@news.supernews.com>, Guy Macon <http://www.guymacon.com> writes:
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
More precisely, "the better defined the position *is*, the less
defined the momentum *is*". It is not a statement about "precise
values existing but unknowable" but about "precise values *not
existing*"
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
Hi Mati, how can you assert with certainty the epistemological
consequences of the HUP? Specifically, what experiment you can perform
to falsify your statement that "[HUP] is not a statement about
"precise
values existing but unknowable" but about "precise values *not
existing*"?
Let's call your proposition p. Let me know based on whch theory of
knowledge your knowledge that p is justified. As far as I can see,
there is no way to decided between the two alternatives. Any final
resolution must go beyond epistemology and into ontology of spacetime.
Mike
.
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| User: "" |
|
| Title: Re: Heisenberg Uncertainty Principle |
25 Sep 2004 09:02:53 PM |
|
|
In article <9c1b39be.0409250833.34b41dae@posting.google.com>, (Mike) writes:
mmeron@cars3.uchicago.edu wrote in message news:<6Ga5d.16$25.1004@news.uchicago.edu>...
In article <10la830a59dnuba@news.supernews.com>, Guy Macon <http://www.guymacon.com> writes:
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
More precisely, "the better defined the position *is*, the less
defined the momentum *is*". It is not a statement about "precise
values existing but unknowable" but about "precise values *not
existing*"
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
Hi Mati, how can you assert with certainty the epistemological
consequences of the HUP? Specifically, what experiment you can perform
to falsify your statement that "[HUP] is not a statement about
"precise
values existing but unknowable" but about "precise values *not
existing*"?
Let's call your proposition p. Let me know based on whch theory of
knowledge your knowledge that p is justified. As far as I can see,
there is no way to decided between the two alternatives. Any final
resolution must go beyond epistemology and into ontology of spacetime.
From the point of view of physics there is absolutely no difference
between "not existing" and "existing but unobservable". Thus, I feel
perfectly free to limit the term "existing" to entities and/or
situations which can (in principle at least) to be observed. There is
no point to maintain two different terms for things which cannot be
distinguished. YMMV, of course.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
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| User: "Edward Green" |
|
| Title: Re: Heisenberg Uncertainty Principle |
26 Sep 2004 10:14:45 AM |
|
|
wrote in message news:<hrp5d.23$25.1490@news.uchicago.edu>...
In article <9c1b39be.0409250833.34b41dae@posting.google.com>, (Mike) writes:
wrote in message news:<6Ga5d.16$25.1004@news.uchicago.edu>...
In article <10la830a59dnuba@news.supernews.com>, Guy Macon <http://www.guymacon.com> writes:
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
More precisely, "the better defined the position *is*, the less
defined the momentum *is*". It is not a statement about "precise
values existing but unknowable" but about "precise values *not
existing*"
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
Hi Mati, how can you assert with certainty the epistemological
consequences of the HUP? Specifically, what experiment you can perform
to falsify your statement that "[HUP] is not a statement about
"precise
values existing but unknowable" but about "precise values *not
existing*"?
Let's call your proposition p. Let me know based on whch theory of
knowledge your knowledge that p is justified. As far as I can see,
there is no way to decided between the two alternatives. Any final
resolution must go beyond epistemology and into ontology of spacetime.
From the point of view of physics there is absolutely no difference
between "not existing" and "existing but unobservable". Thus, I feel
perfectly free to limit the term "existing" to entities and/or
situations which can (in principle at least) to be observed. There is
no point to maintain two different terms for things which cannot be
distinguished. YMMV, of course.
If we would only limit ourselves to the modest idea that the
uncertainty principle is a statement about the products of the
variances of measurements of certain pairs of variables performed on
ensembles of identically prepared systems, we could avoid this
fruitless conversation altogether. The state of the system is an
input, the observed result is an output. The output is presumably
conditioned in part on this input, but all we know about this
conditioning is the statistical law supplied by quantum mechanics.
We might further take the modest view that the outcome of a
measurement is the outcome of a named physical interaction between a
first system, the measured, and a second physical system, the
apparatus, and thus, while taking the state of the system as an input,
also takes other inputs.
It may be that a statement that the observed does not exist before the
observation is no more profound than the the statement that your yelp
does not exist before I step on your toe.
.
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| User: "Gregory L. Hansen" |
|
| Title: Re: Heisenberg Uncertainty Principle |
26 Sep 2004 08:19:45 PM |
|
|
In article <eca320d0.0409260714.43eb4aaf@posting.google.com>,
Edward Green <spamspamspam3@netzero.com> wrote:
mmeron@cars3.uchicago.edu wrote in message
news:<hrp5d.23$25.1490@news.uchicago.edu>...
In article <9c1b39be.0409250833.34b41dae@posting.google.com>,
eleatis@yahoo.gr (Mike) writes:
mmeron@cars3.uchicago.edu wrote in message
news:<6Ga5d.16$25.1004@news.uchicago.edu>...
In article <10la830a59dnuba@news.supernews.com>, Guy Macon
<http://www.guymacon.com> writes:
A person in another newsgroup (sci.electronics.design, 25
Sep 2004 06:22:09 GMT, <3SE4yuAR6QVBFwRi@jmwa.demon.co.uk> )
told me the following:
"The Heisenberg Uncertainty Principle still exists but it DOESN'T mean
quite what Heisenberg thought it did. ... It IS possible to determine
both position and velocity more precisely that the Heisenberg
Uncertainty Principle stipulates. The Heisenberg Uncertainty Principle
applies to the results of a large number of measurements."
This is different from what I understood about the Heisenberg
Uncertainty Principle. I thought that it applies to individual
particles, and that the more exactly you measure the position
of a particle the less you know about the velocity, and vice versa.
More precisely, "the better defined the position *is*, the less
defined the momentum *is*". It is not a statement about "precise
values existing but unknowable" but about "precise values *not
existing*"
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
Hi Mati, how can you assert with certainty the epistemological
consequences of the HUP? Specifically, what experiment you can perform
to falsify your statement that "[HUP] is not a statement about
"precise
values existing but unknowable" but about "precise values *not
existing*"?
Let's call your proposition p. Let me know based on whch theory of
knowledge your knowledge that p is justified. As far as I can see,
there is no way to decided between the two alternatives. Any final
resolution must go beyond epistemology and into ontology of spacetime.
From the point of view of physics there is absolutely no difference
between "not existing" and "existing but unobservable". Thus, I feel
perfectly free to limit the term "existing" to entities and/or
situations which can (in principle at least) to be observed. There is
no point to maintain two different terms for things which cannot be
distinguished. YMMV, of course.
If we would only limit ourselves to the modest idea that the
uncertainty principle is a statement about the products of the
variances of measurements of certain pairs of variables performed on
ensembles of identically prepared systems, we could avoid this
fruitless conversation altogether. The state of the system is an
input, the observed result is an output. The output is presumably
conditioned in part on this input, but all we know about this
conditioning is the statistical law supplied by quantum mechanics.
But it's not a statement about products of variances of pairs of variables
in ensembles. It's a statement about the wavefunction of each individual
particle. It is the reason atoms have size. It's the reason diffraction
patterns have a larger spacing between peaks when the atoms in the sample
are closer together. Particles have wavelike behavior, that means they
must have uncertainty relations as surely as a sound wave must have a
larger spread in frequency space if you make it short in duration (or
distance). |psi(q)|^2 is determined experimentally over an ensemble, but
it's not an average over classical trajectories.
--
"The preferred method of entering a building is to use a tank main gun
round, direct fire artillery round, or TOW, Dragon, or Hellfire missile to
clear the first room." -- THE RANGER HANDBOOK U.S. Army, 1992
.
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| User: "Edward Green" |
|
| Title: Re: Heisenberg Uncertainty Principle |
27 Sep 2004 05:02:10 PM |
|
|
(Gregory L. Hansen) wrote in message news:<cj7prh$nma$2@hood.uits.indiana.edu>...
In article <eca320d0.0409260714.43eb4aaf@posting.google.com>,
Edward Green <spamspamspam3@netzero.com> wrote:
If we would only limit ourselves to the modest idea that the
uncertainty principle is a statement about the products of the
variances of measurements of certain pairs of variables performed on
ensembles of identically prepared systems, we could avoid this
fruitless conversation altogether. The state of the system is an
input, the observed result is an output. The output is presumably
conditioned in part on this input, but all we know about this
conditioning is the statistical law supplied by quantum mechanics.
But it's not a statement about products of variances of pairs of variables
in ensembles. It's a statement about the wavefunction of each individual
particle.
Granted it tells us something about the identical wave functions of
each individual particle in our ensemble -- where else does the
information come from which enables us to calculate the variances!
And we can interpret the expressions for the variances as statements
about the spread in the spectrum in the appropriate representations.
But...
Are you _really_ telling me that my claim is completely _wrong_, and
that we can't interpret the principle this way?
I'm itching for a cordial fight here -- for which of course I will
have to produce some more references and arguments, and in the course
undoubtedly learn something -- because for the moment I'm fairly well
convinced I'm right.
It is the reason atoms have size. It's the reason diffraction
patterns have a larger spacing between peaks when the atoms in the sample
are closer together. Particles have wavelike behavior, that means they
must have uncertainty relations as surely as a sound wave must have a
larger spread in frequency space if you make it short in duration (or
distance). |psi(q)|^2 is determined experimentally over an ensemble, but
it's not an average over classical trajectories.
Where the hell did I say anything is an average over classical
anything!?
I think you are seeing a bogeyman, Greg. Read what I wrote again
carefully:
the uncertainty principle is a statement about the products of the
variances of measurements of certain pairs of variables performed on
ensembles of identically prepared systems
We're talking about _quantum_ mechanics, and those measurements are
(quantum) measurements performed on ensembles of identically prepared
(quantum) systems, which means, having identical state vectors. In
general the state vector will not be an eigenstate of either conjugate
variable, and so many repeated measurements on identical copies of
this state vector will yield spreads of values. And yea, these
spreads will have variances, and yea, the product of these variances
shall agree with an inequality!
I meant what I said, and I said what I mean. To what part do you
demur?
.
|
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| User: "Gregory L. Hansen" |
|
| Title: Re: Heisenberg Uncertainty Principle |
27 Sep 2004 08:08:18 PM |
|
|
In article <eca320d0.0409271402.6682f33c@posting.google.com>,
Edward Green <spamspamspam3@netzero.com> wrote:
glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) wrote in message
news:<cj7prh$nma$2@hood.uits.indiana.edu>...
In article <eca320d0.0409260714.43eb4aaf@posting.google.com>,
Edward Green <spamspamspam3@netzero.com> wrote:
If we would only limit ourselves to the modest idea that the
uncertainty principle is a statement about the products of the
variances of measurements of certain pairs of variables performed on
ensembles of identically prepared systems, we could avoid this
fruitless conversation altogether. The state of the system is an
input, the observed result is an output. The output is presumably
conditioned in part on this input, but all we know about this
conditioning is the statistical law supplied by quantum mechanics.
But it's not a statement about products of variances of pairs of variables
in ensembles. It's a statement about the wavefunction of each individual
particle.
Granted it tells us something about the identical wave functions of
each individual particle in our ensemble -- where else does the
information come from which enables us to calculate the variances!
And we can interpret the expressions for the variances as statements
about the spread in the spectrum in the appropriate representations.
But...
Are you _really_ telling me that my claim is completely _wrong_, and
that we can't interpret the principle this way?
I'm itching for a cordial fight here -- for which of course I will
have to produce some more references and arguments, and in the course
undoubtedly learn something -- because for the moment I'm fairly well
convinced I'm right.
It is the reason atoms have size. It's the reason diffraction
patterns have a larger spacing between peaks when the atoms in the sample
are closer together. Particles have wavelike behavior, that means they
must have uncertainty relations as surely as a sound wave must have a
larger spread in frequency space if you make it short in duration (or
distance). |psi(q)|^2 is determined experimentally over an ensemble, but
it's not an average over classical trajectories.
Where the hell did I say anything is an average over classical
anything!?
I think you are seeing a bogeyman, Greg. Read what I wrote again
carefully:
The classical average is just something I pulled out of my butt. But it
was there because the uncertainty principle is a deduction of wave
mechanics. If the uncertainty principle doesn't apply to an individual
particle, then the wave mechanics doesn't apply to an individual particle!
Now it's true that you only get a diffraction pattern as the result of
many measurements. But you can take a tight neutron beam with
appropriate collimation, put a cadmium knife edge in it, and start
detecting neutrons where you would not have found any before. If it were
a very weak beam, you could count a single neutron at some angle off the
beam axis and say "Hey, that's not supposed to be there!" Wave mechanics
works with individual particles.
If you sum over an ensemble you can get an average and a variance, and
there would be nothing uncertain about them. The uncertainty goes as
1/sqrt(N), take more measurements. But an "uncertainty" in position is
what allows a single particle to "sample" various points in a crystal and
diffract. An "uncertainty" in position is the reason atoms have a size,
and it's the reason they consist of a nucleus of protons and neutrons
surrounded by an electron cloud rather than a nucleus of electrons
surrounded by a proton and neutron cloud.
the uncertainty principle is a statement about the products of the
variances of measurements of certain pairs of variables performed on
ensembles of identically prepared systems
We're talking about _quantum_ mechanics, and those measurements are
(quantum) measurements performed on ensembles of identically prepared
(quantum) systems, which means, having identical state vectors. In
general the state vector will not be an eigenstate of either conjugate
variable, and so many repeated measurements on identical copies of
this state vector will yield spreads of values. And yea, these
spreads will have variances, and yea, the product of these variances
shall agree with an inequality!
I meant what I said, and I said what I mean. To what part do you
demur?
There's two things we could be thinking about; what the theory of quantum
mechanics says, and relating the theory to measurement. But we know we
can get that diffraction pattern, eventually, by shooting through one
particle at a time. But only if the wavelength is comparable to the
geometrical features you're trying to study. And something like the
Mössbauer effect is wave mechanics applied to a single particle. No
ensemble required, just wondering where the recoil went.
--
"Is that plutonium on your gums?"
"Shut up and kiss me!"
-- Marge and Homer Simpson
.
|
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| User: "Edward Green" |
|
| Title: Re: Heisenberg Uncertainty Principle |
01 Oct 2004 04:17:24 PM |
|
|
(Gregory L. Hansen) wrote in message news:<cjadi2$ma3$1@hood.uits.indiana.edu>...
The classical average is just something I pulled out of my butt. But it
was there because the uncertainty principle is a deduction of wave
mechanics. If the uncertainty principle doesn't apply to an individual
particle, then the wave mechanics doesn't apply to an individual particle!
Actually, we're arguing over completely nothing, except maybe a
question of emphasis. I may have sounded a tad over-reductionist in
my polemic: I was reacting to some typical nonsense of the 'whether
the values are there if we don't measure them' ilk. But, in replying
to a latter post of yours, I'm quite comfortable about a synthesis of
this alleged antithesis we have thrust upon us -- whether the
uncertainty principle lives in the individual wave function, or in
ensemble averages, which by so measuring, end 'em. Of course it's a
silly non-question, but we can give it a high-sounding answer along
the lines of things we can say about the wave equation qua function,
and what we can say about the outcome of experiments -- on the other
side of the quantum measurement divide.
That's my story, and I'm sticking to it!
Now it's true that you only get a diffraction pattern as the result of
many measurements. But you can take a tight neutron beam with
appropriate collimation, put a cadmium knife edge in it, and start
detecting neutrons where you would not have found any before. If it were
a very weak beam, you could count a single neutron at some angle off the
beam axis and say "Hey, that's not supposed to be there!" Wave mechanics
works with individual particles.
If you sum over an ensemble you can get an average and a variance, and
there would be nothing uncertain about them. The uncertainty goes as
1/sqrt(N), take more measurements.
Whoa. Hang on a second there, partner!
You're thinking of a variance as in a sample variance (I think that's
the right term of art), as in the variance in a sample average after N
picks from the same distribution. That does of course go to zero as N
-> 0. And that's _not_ the variance at issue in the experimental side
of the HUP. The variances involved are the variances of the
population distributions themselves -- these can also be estimated,
BTW, as well as the mean, and have their own special rigamarole of
attendant statistical speciality functions.
What you are saying in effect is that if we persist long enough, we
can get arbitrarily accurate estimates of <p>, <x>. Hmm... I can see
where your slight confusion here comes from. The uncertainty in the
estimate of a mean, i.e., in the partially obscuring special
terminology of quantum mechanics, an expectation value, is ... well,
is normally called just that: uncertainty! But that's not the
"uncertainty" in the Heisenberg Uncertainty Principle; that is, on the
post-observational side of the measurement divide, a relation between
population variances. The damned Principle is more accuarately called
the "Heisenberg Variance Inequality". We can know the true population
variances of conjugate observables with 100% accuracy, and they must
satisfy the appropriate inequality.
But an "uncertainty" in position is
what allows a single particle to "sample" various points in a crystal and
diffract. An "uncertainty" in position is the reason atoms have a size,
and it's the reason they consist of a nucleus of protons and neutrons
surrounded by an electron cloud rather than a nucleus of electrons
surrounded by a proton and neutron cloud.
Ok. Now, just possibly that we're on the same page on the
post-observational side, and since I have expressed a cosmic loving
acceptance of the properties of the intact and unobserved wave
function as being fully enfranchised participants in the Great Chain
of Being, we will have no further disagreement! Or maybe not. You
didn't reply to my follow on post, though whether that indicates tacit
acceptance or the onset of boredom, I do not ken.
There's two things we could be thinking about; what the theory of quantum
mechanics says, and relating the theory to measurement. But we know we
can get that diffraction pattern, eventually, by shooting through one
particle at a time. But only if the wavelength is comparable to the
geometrical features you're trying to study. And something like the
Mössbauer effect is wave mechanics applied to a single particle. No
ensemble required, just wondering where the recoil went.
Well, that's a nice example of something or other. :-)
.
|
|
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| User: "Gregory L. Hansen" |
|
| Title: Re: Heisenberg Uncertainty Principle |
01 Oct 2004 07:33:18 PM |
|
|
In article <eca320d0.0410011317.75769d9f@posting.google.com>,
Edward Green <spamspamspam3@netzero.com> wrote:
glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) wrote in message
news:<cjadi2$ma3$1@hood.uits.indiana.edu>...
The classical average is just something I pulled out of my butt. But it
was there because the uncertainty principle is a deduction of wave
mechanics. If the uncertainty principle doesn't apply to an individual
particle, then the wave mechanics doesn't apply to an individual particle!
Actually, we're arguing over completely nothing, except maybe a
question of emphasis. I may have sounded a tad over-reductionist in
my polemic: I was reacting to some typical nonsense of the 'whether
the values are there if we don't measure them' ilk. But, in replying
to a latter post of yours, I'm quite comfortable about a synthesis of
this alleged antithesis we have thrust upon us -- whether the
uncertainty principle lives in the individual wave function, or in
ensemble averages, which by so measuring, end 'em. Of course it's a
silly non-question, but we can give it a high-sounding answer along
the lines of things we can say about the wave equation qua function,
and what we can say about the outcome of experiments -- on the other
side of the quantum measurement divide.
That's my story, and I'm sticking to it!
You may have seen my opinion that the uncertainty relation is the E=mc^2
of quantum mechanics. It gives a quick estimate of the quantum scale of
things, but it contains no new physics, doesn't say anything that's not
contained in the wavefunction and commutation relations, and isn't very
useful for detailed calculations. But it's easy for the layman to pick up
on and discuss. How to interpret the uncertainty principle is really a
question on how to interpret the wavefunction.
The uncertainty principle lives in the wavefunction, not the ensemble
average. There is a difference. It's traditionally considered a relation
between canonically conjugate variables, but the uncertainty principle
between ANY operators A and B, with eigenfunctions a and b, is
<(delta a)^2> <(delta b)^2> = -1/4 \int (psi* [A,B] psi d(tau))^2
If the operators commute, the uncertainty is zero. For example, we could
have a spin wavefunction in L^2 and L_z,
|psi> = |L=1, L_z=1>
Then
delta L^2 * delta L_z = 0
If you go way back, you'll remember calculating the momentum wavefunction
given a Gaussian position wavefunction. And you'll remember that in the
infinite potential well, the shorter the well is, the higher the ground
and other energies were. Those calculations were done for single
particles.
You can imagine a classical ensemble of BBs that will give you a spread in
transverse positions and momenta, say something like
delta x * delta p = (1 cm)*(1 gm cm/s)
But that's not a relation between x and p, it's just delta x and delta
p multiplied together. Pass them through a half centimeter slot, and
those BBs diverging in x are simply removed,
delta x' * delta p' = (1/2 cm) * (1 gm cm/s)
(Adjust the width of the slot and the current density of the BBs so that
the position rms comes out as given.) You can do that with a quantum
ensemble of particles prepared in the identical state for l and l_z,
|psi> = A|1,1> + B|1,0> + C|0,0>
And you can work out a (delta L^2)(delta L_z) for that. Pass them
through some filter that removes, say, all the particles with l_z=1, and
you get (delta L^2)(delta L_z)=0.
But shoot an ensemble of particles with a Gaussian wavefunction at a
potential barrier with a slot, and whatever you take away in delta x will
and must be made up in delta p-- the smaller you make the slot, the more
widely separated the detected particles will be because of the increase in
the transverse delta p. That's because x and p are not independent
variables, X and P don't commute.
--
"Let us learn to dream, gentlemen, then perhaps we shall find the
truth... But let us beware of publishing our dreams before they have been
put to the proof by the waking understanding." -- Friedrich August Kekulé
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| User: "Edward Green" |
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| Title: Re: Heisenberg Uncertainty Principle |
01 Oct 2004 04:22:16 PM |
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I wrote:
That does of course go to zero as N -> 0.
Obviously, I meant "as N -> oo".
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| User: "Guy Macon http://www.guymacon.com" |
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| Title: Re: Heisenberg Uncertainty Principle |
27 Sep 2004 12:24:55 AM |
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Gregory L. Hansen <glhansen@steel.ucs.indiana.edu> says...
But it's not a statement about products of variances of pairs of variables
in ensembles. It's a statement about the wavefunction of each individual
particle.
That is my understanding as well, but I am not even close to being
an expert - I just go by what I read, filtered by my possibly flawed
ability to understand what I am reading.
I do wonder, however, why a minority of what I read seems to say that
the HUP only applies to the statistics of multiple particles while the
majority view seems to be that The HUP applies to individual particles.
Are there two well-respected theories, or is one of those opinions
misinformed?
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| User: "ZZBunker" |
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| Title: Re: Heisenberg Uncertainty Principle |
27 Sep 2004 07:46:07 AM |
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Guy Macon <http://www.guymacon.com> wrote in message news:<10lf91dnjqc263a@news.supernews.com>...
Gregory L. Hansen <glhansen@steel.ucs.indiana.edu> says...
But it's not a statement about products of variances of pairs of variables
in ensembles. It's a statement about the wavefunction of each individual
particle.
That is my understanding as well, but I am not even close to being
an expert - I just go by what I read, filtered by my possibly flawed
ability to understand what I am reading.
I do wonder, however, why a minority of what I read seems to say that
the HUP only applies to the statistics of multiple particles while the
majority view seems to be that The HUP applies to individual particles.
Are there two well-respected theories, or is one of those opinions
misinformed?
The minority and right view is that individual particles
do not exist.
While the majority view is that matrices, concern
something other than Nazi's and low pressure
partial-intelligence quotient spaces, isomorphic
to Feynmann and chemistry spaces.
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