[OT[: Heisenberg Uncertainty Principle

[Guy Macon]

There is an interesting thread that I started in sci.physics with
the title "Heisenberg Uncertainty Principle." Think of it as a
non-expert getting a second opinion...

 

[Jonathan Kirwan]

On Sun, 26 Sep 2004 22:30:24 -0700, Guy Macon <http://www.guymacon.com> wrote:

There is an interesting thread that I started in sci.physics with
the title "Heisenberg Uncertainty Principle." Think of it as a
non-expert getting a second opinion...

I read it. So, have you learned anything from it?

Jon

 

[Guy Macon]

Jonathan Kirwan <jkirwan@easystreet.com> says...

Guy Macon <http://www.guymacon.com> wrote:

There is an interesting thread that I started in sci.physics with
the title "Heisenberg Uncertainty Principle." Think of it as a
non-expert getting a second opinion...

I read it. So, have you learned anything from it?

Yes.

 

[Paul Hovnanian P.E.]

Guy Macon wrote:

There is an interesting thread that I started in sci.physics with
the title "Heisenberg Uncertainty Principle." Think of it as a
non-expert getting a second opinion...

You have told us where your article is, but not when you posted it. ;-)

--
Paul Hovnanian mailtoaul@Hovnanian.com
note to spammers: a Washington State resident
------------------------------------------------------------------
Happily doing the work of 3 Men ... Moe, Larry & Curly

 

[Kevin Aylward]

Jonathan Kirwan wrote:

On Sun, 26 Sep 2004 23:08:24 -0700, Guy Macon
http://www.guymacon.com> wrote:

Jonathan Kirwan <jkirwan@easystreet.com> says...

Guy Macon <http://www.guymacon.com> wrote:

There is an interesting thread that I started in sci.physics with
the title "Heisenberg Uncertainty Principle." Think of it as a
non-expert getting a second opinion...

I read it. So, have you learned anything from it?

Yes.

It would be interesting to know exactly what. I'll be more generous
about my reply than you:

I noted Gregory's response was congruent to the one I chose to write.
Old Man got into some other details (but not incompatible ones, I
believe.) If you are interested in the math, I'd recommend "Basic
Quantum Mechanics" from the Oxford Physics Series. And for a general
comment on what HUP means here, see pages 22 and 23. Another place
to go is Feynman undergrad Lectures on Physics, vol III, chapter 2,
page 2-2ff. (And most of the rest of that volume, as well.)

There are two different 'uncertainty' concepts being discussed, by
the way. One is the uncertainty principle itself, which can be seen
as a necessary outcome of applying the correspondence principle to
Newtonian and quantum mechanics. The other is the uncertainty
relation. It is here that is found the uncertainty inequality I
mentioned, which is imposed because for any real numbered wavelength,
the squared length vector is always real and non-negative. The
quadratic solution then forces the important further restriction on
the uncertainties of two observables (X and Y) for the same state.
Here, generally, if the two observables do not commute (XY-YX is
non-zero), then the uncertainty of X and the uncertainty of Y cannot
both be made arbitrarily small __simultaneously__.

I will have to disagree here. My Bible is the Ballentine text book. In
this book it explains in detail, that HUP isn't even about simultaneous
measurements at all.

"Quantum Mechanics, A Modern Development" ISBN981-02-4105-4 - Leslie E.
Ballentine,

p.225
"...One must have a repeatable preparation procedure corresponding to
the state p which is to be studied. Then on each one of a large number
of similarly prepared systems, one performs a single measurement (either
Q od O). The statistical distributions of the results are shown as
histograms, and the root mean square half-widths or the two
distributions deltaQ and deltaP, are indicated in fig. 8.2. The theory
predicts that the product of these two half-widths can never be less
then hbar/2, no matter what state is considered."

The issue with much of what is written about HUP, is that it is usually
based on un-rigorous definitions, and hand waving.

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[Kevin Aylward]

Guy Macon wrote:

There is an interesting thread that I started in sci.physics with
the title "Heisenberg Uncertainty Principle." Think of it as a
non-expert getting a second opinion...

A 3rd opinion.

http://www.anasoft.co.uk/quantummechanics/On the Postulates of Quantum
Mechanics.pdf

Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

 

[Jonathan Kirwan]

On Mon, 27 Sep 2004 18:15:46 GMT, "Norm Dresner" <ndrez@att.net> wrote:

The observable operaters, X an P don't commute, this is not the same.
According to the ensemble interpretation, X and P only have relevance
statistically, not to individual particles, so HUP says nothing about
individual particles.

The observables X & P for a single particle are non-commuting.

That's the understanding I've taken.

Jon

 

[Norm Dresner]

"Kevin Aylward" <salesEXTRACT@anasoft.co.uk> wrote in message
news:8ST5d.96521$U04.11571@fe1.news.blueyonder.co.uk...

Norm Dresner wrote:
"Guy Macon" <http://www.guymacon.com> wrote in message
news:10lfkldrs62qc3a@news.supernews.com...

..if the two observables do not commute (XY-YX is non-zero), then
the uncertainty of X and the uncertainty of Y cannot both be made
arbitrarily small __simultaneously__.

In the case of the position and velocity of a single subatomic
particle, do the two observables commute? Is XY-YX zero in
that case?

We live in a 3-D space. That means that there are three independent,
mutually perpendicular coordinate axes that you can construct at a
point. Actually there are an infinite number of these triads, all
related by various rotations. Choose any one of them. The HUP
implies that for each of these directions individually, the
components of position and velocity of a single particle do not
commute.

The observable operaters, X an P don't commute, this is not the same.
According to the ensemble interpretation, X and P only have relevance
statistically, not to individual particles, so HUP says nothing about
individual particles.

The observables X & P for a single particle are non-commuting.

That is, for, say, an electron, the position along the,
say, X-axis and the velocity component along the X-axis are
non-commuting observables. Same with Y-axis and Z-Axis. But the
inter-axis variables are commuting. That is, you can simultaneously
measure the positions on the three coordinate axes with unlimited
precision -- or the three velocities; or the X-position and the
Y-velocity, or ... It's the corresponding velocities and positions
that don't commute and hence are limited by the HUP.


I think you have missed the point of the thread. Its about the *correct*
interpretation of HUP. The summary is here,
http://www.anasoft.co.uk/quantummechanics/index.html.

I know the correct interpretation of HUP. I studied it in graduate school.

Norm