Present unknowns

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Chuck and Barbara Burger

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Dec 17, 2002, 11:01:32 PM12/17/02
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In article <asfteu$jcm$1...@lfa222122.richmond.edu>
eb...@lfa221051.richmond.edu wrote:

>By using both the words "unknown" and "unknowable," you seem to be
>suggesting that there's a distinction between them, but I can't figure
>out what the difference between "presently unknown" and "presently
>unknowable" is supposed to be.

Perhaps the distinction between "unknown" and "unknowable"
can be illustrated by the following examples from antiquity as well as the
present.

I. Examples from Antiquity
When Democritus posited his theory of atoms, the answer to the question
of whether or not atoms existed was unknown. It would remain unknowable for
about 2000 years, until technology was sophisticated enough for detection.
The circumference of the earth was also unknown, but was indeed
knowable. It was determined by Eratosthenes about 230 B.C. by means of
measuring and comparing the angles of shadows at different latitudes.

II Examples from the Present
Today, the answer to the question of whether life has ever existed on
Mars, while unknown, is essentially knowable, since there exist appropriate
methods of evaluation.
The nature of dark matter and dark energy, which is currently unknown,
will remain unknowable until appropriate means of detection are
developed.
Barbara Burger

Ahmet Gorgun

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Jan 6, 2003, 10:29:27 PM1/6/03
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"Chuck and Barbara Burger" <bcbu...@rcn.com> wrote:

> When Democritus posited his theory of atoms, the answer to the question
> of whether or not atoms existed was unknown.

And it is still unknown.

> It would remain unknowable for about 2000 years, until technology
> was sophisticated enough for detection.

What was observed with the improving technology was the previously invisible
constituents of what is visible to the unaided eye.

The indivisible and indestructible Democretean primary elements were never
observed.

Ahmet Gorgun

Charles Francis

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Jan 13, 2003, 5:18:00 AM1/13/03
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In message <VjGR9.27646$p_6.2...@bgtnsc04-news.ops.worldnet.att.net>,
Ahmet Gorgun <ago...@att.net> writes

>"Chuck and Barbara Burger" <bcbu...@rcn.com> wrote:

>> When Democritus posited his theory of atoms, the answer to the question
>> of whether or not atoms existed was unknown.

I don't agree. Democritus teacher, Leucippus, posited the theory in
answer to the paradoxes of Zeno, and on the basis of rational thought,
as a way to get around the deep issues regarding the appearance of
infinity in a geometrical background space.

>The indivisible and indestructible Democretean primary elements were never
>observed.

But they have been observed now, electrons, quarks fulfil the role quite
accurately.


Regards

--
Charles Francis


Ahmet Gorgun

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Feb 5, 2003, 3:25:40 PM2/5/03
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"Charles Francis" <cha...@clef.demon.co.uk> wrote:

> Ahmet Gorgun <ago...@att.net> wrote:

> >The indivisible and indestructible Democretean primary elements were never
> >observed.
>
> But they have been observed now, electrons, quarks fulfil the role quite
> accurately.

Are you saying that electron has absolutely no parts and you can prove that it
has absolutely no parts? Otherwise the electron is not the absolutely
indivisible elements that Democritus postulated.

Ahmet Gorgun

Ralph E. Frost

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Feb 7, 2003, 7:46:30 AM2/7/03
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Ahmet Gorgun <ago...@att.net> wrote in message
news:gik%9.18435$rq4.1...@bgtnsc05-news.ops.worldnet.att.net...

> Are you saying that electron has absolutely no parts and you can prove
> that it has absolutely no parts?

The prevailing theory and equations/description are all set up on electrons
being point particles.

What more proof does one need?

[Moderator's note: no compositeness has been seen up to energies
of at least 4 TeV:

http://www.slac.stanford.edu/pubs/snowmass96/PDF/NEW160.PDF

though this paper is from 1996, and the bound may be higher now. - jb]


Arnold Neumaier

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Feb 12, 2003, 6:12:25 AM2/12/03
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"Ralph E. Frost" wrote:

> The prevailing theory and equations/description are all set up on electrons
> being point particles.
>
> What more proof does one need?
>
> [Moderator's note: no compositeness has been seen up to energies
> of at least 4 TeV:

Isn't there a significant difference between pointlike
(= no spatial extension) and composite (= made up of smaller particles)?

I can well conceive of extended (not pointlike) objects that cannot be divided
by any means (indivisible, not composite).
In this sense, an electron can well be regarded as an
extended indivisible particle (with an extension given by the region
where |psi|^2 is significant). More importantly, a photon, which cannot
be localized in space (according to Newton & Wigner),
can hardly be regarded as being pointlike in any geometric sense,
though it is probably indivisible.

Arnold Neumaier

Jeffery

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Feb 12, 2003, 6:12:03 AM2/12/03
to
Charles Francis <cha...@clef.demon.co.uk> wrote in message
news:<oLjTjXAr...@clef.demon.co.uk>...


Well that's not the current view. Today, quarks and electrons are
considered to be 1-dimensional superstrings. Anyway, both Ahmet and
Charles are correct since they mean two different things. Obviously,
the theories of Leucippus and Democritus were not "correct". We have
never had a view of the Universe that was actually true, and we never
will. The purpose of physics is not to find out what's true, since
we'll never be able to do that. The purpose of physics is to think up
possible explanations that could possibly explain what you observe.
You can read "On the Nature of Things" written by Lucretius in the
first century B.C. for a good overview of the various theories of
particle physics in the classical world. You can see how they arrived
at theories through logical reasoning based on observation. Of course,
it's also obvious to us that none of their theories are true. Of
course, our view of the Universe, which is based on superstrings and
M-theory, is not true either, but that's not the point. We've never
had a view of the Universe that was actually true, and we never will.
That's not the purpose of physics. The purpose of physics is to come
up with theories that fit what we observe, and we've been remarkably
successful at doing that.

I don't think Charles and others defending Democritus are saying that
their theory of atoms, the way they imagined them, is actually true.
They were rather speaking in a broad sense, in that Democritus and
others were right in saying that macroscopic matter is made of
constituents too small to be seen, with empty space between them, as
opposed to the prevailing view that macroscopic was composed of
continuous solid matter. So that basic idea turned out to be right,
although obviously their view of the Universe, and their specific
theories, are obviously not correct. They were right in that
macroscopic matter is made of smaller constituents, but Democritus
imagined the smaller constituents being point particles, and today we
call them molecules, which are made of atoms, which are made of
electrons and atomic nuclei, which are made of protons and neutrons,
which are made of quarks, which we now consider to be actually
one-dimensional superstrings.

Jeffery Winkler

http://www.geocities.com/jefferywinkler

Kevin A. Scaldeferri

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Feb 12, 2003, 3:10:29 PM2/12/03
to
In article <8a8c1f93.03020...@posting.google.com>,

Jeffery <jeffery...@hotmail.com> wrote:
>Charles Francis <cha...@clef.demon.co.uk> wrote in message
>news:<oLjTjXAr...@clef.demon.co.uk>...
>
>> In message <VjGR9.27646$p_6.2...@bgtnsc04-news.ops.worldnet.att.net>,
>> Ahmet Gorgun <ago...@att.net> writes
>>
>> >The indivisible and indestructible Democretean primary elements were never
>> >observed.
>>
>> But they have been observed now, electrons, quarks fulfil the role quite
>> accurately.
>
>
>Well that's not the current view. Today, quarks and electrons are
>considered to be 1-dimensional superstrings.

Considered by some.

One should not forget that there is no experimental evidence of this,
nor a workable phenomenological model.

--
======================================================================
Kevin Scaldeferri Calif. Institute of Technology
The INTJ's Prayer:
Lord keep me open to others' ideas, WRONG though they may be.

Squark

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Feb 15, 2003, 2:46:57 AM2/15/03
to
Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
news:<3e43b60b$0$9620$3b21...@news.univie.ac.at>...

> In this sense, an electron can well be regarded as an
> extended indivisible particle (with an extension given by the region
> where |psi|^2 is significant).

This is definitely _wrong_, according to current wisdom, and is a
not uncommon misconception. The wavefunction reflects the
indeterminancy of the particle's location, not it's spatial extension.
A "wavefunction wave" falling upon a screen of detectors can cause
only one detector to fire, not several.

> More importantly, a photon, which cannot
> be localized in space (according to Newton & Wigner),
> can hardly be regarded as being pointlike in any geometric sense,
> though it is probably indivisible.

This is already a much more subtle issue. I didn't form my final
opinion on the subject yet, but a priori it seems hard to imagine
how an object with a single position degree of freedom can be
spatially extended in a local theory. Possibly we're just using
the wrong variables: in 1+1D, the rapidity and the generator of
boosts are canonically conjugate (up to a constant, I think) and the
generator of boosts is the "proper coordinate": the coordinate at
time zero in the particle's own frame. This operator of course has
a (generalized) zero eigenstate which can be interpreted as the
state for which the particle passes through the origin, with full
honesty. In higher dimensions, though, it's more problematic as the
boost generators don't commute...

Best regards,
Squark

------------------------------------------------------------------

Write to me using the following e-mail:
Skvark_N...@excite.exe
(just spell the particle name correctly and change the
extension in the obvious way)

Charles Francis

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Feb 15, 2003, 3:30:04 AM2/15/03
to by lfa222122.richmond.edu id h1DEcDo29041, Thu

In message <8a8c1f93.03020...@posting.google.com>, Jeffery
<jeffery...@hotmail.com> writes

>Charles Francis <cha...@clef.demon.co.uk> wrote in message
>news:<oLjTjXAr...@clef.demon.co.uk>...

>>Democritus teacher, Leucippus, posited the theory in


>>answer to the paradoxes of Zeno, and on the basis of rational thought,
>>as a way to get around the deep issues regarding the appearance of
>>infinity in a geometrical background space.

>> >The indivisible and indestructible Democretean primary elements were never
>> >observed.

>> But they have been observed now, electrons, quarks fulfil the role quite
>> accurately.

>Well that's not the current view. Today, quarks and electrons are
>considered to be 1-dimensional superstrings.

That is only speculation, and it is a speculation which seems to me to
have born remarkably little fruit when one considers all the work which
has been done on it.

>Anyway, both Ahmet and
>Charles are correct since they mean two different things. Obviously,
>the theories of Leucippus and Democritus were not "correct". We have
>never had a view of the Universe that was actually true, and we never
>will.

I think it helps to loosen up a bit on what one means by "correct". It
is probably not within language to be absolute and literal, but if we
merely mean by correct "containing a great deal of truth" that is a far
more reasonable and workmanlike objective.

>The purpose of physics is not to find out what's true, since
>we'll never be able to do that.

I do hate this modern habit of prejudging the issue. We do not know we
will never be able to do that.

>You can read "On the Nature of Things" written by Lucretius in the
>first century B.C. for a good overview of the various theories of
>particle physics in the classical world. You can see how they arrived
>at theories through logical reasoning based on observation.

Actually you can't. Lucretius was a Roman poet writing about two hundred
years after Leucippus and Democritus, and he had little grasp of the
theory and no grasp of the logical problems the theory was intended to
circumvent. The essential idea was that that Zeno had shown that the
concept of "space" was badly flawed, and that there are serious problems
with infinity in physics. The model was intended to do away with that by
disposing of "space", and talking of the "void" meaning a non-existence,
a complete absence of properties. This idea was later picked up by
Descartes, who said that it does not make sense to talk of "space", and
reappears in the orthodox interpretation of quantum mechanics which
prohibits discussion of observable properties (such as position) between
measurements.

The atomic model was also intended to counter Aristotle's idea of
infinite subdivisibility. If there is no infinite subdivision it follows
that there is a smallest indivisible element. In so far as I can see we
have no reason even now to think that these central parts of the
original atomic model are not "correct" (I am not claiming here that
they are proven either).

>I don't think Charles and others defending Democritus are saying that
>their theory of atoms, the way they imagined them, is actually true.

Certainly I don't think that Democritus came up with an absolutely
precise and rigorous scientific theory, correct in every way. For
example when he discusses the "shape" of an atomic particles I would
have to substitute something like "Dirac spinor" and "Vector Boson".


Regards

--
Charles Francis


John Baez

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Feb 15, 2003, 3:34:09 AM2/15/03
to

>Well that's not the current view. Today, quarks and electrons are
>considered to be 1-dimensional superstrings.

I'm sorry, this is misleading. There is not a single piece of
experimental evidence for superstring theory; it's just a line
of research that's currently popular. A string theorist might say
"quarks and leptons are HYPOTHESIZED TO BE 1-dimensional superstrings",
but the phrase CONSIDERED TO BE suggests some sort of consensus
based on experimental evidence, and that doesn't exist.

It's also misleading to speak "the current view", as if there
were such a monolithic thing. Even within superstring theory there
are a large number of specific models battling for acceptance, and
no clear winner yet.


Arnold Neumaier

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Feb 17, 2003, 7:00:37 AM2/17/03
to sci-physic...@moderators.isc.org
Squark wrote:

> Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
> news:<3e43b60b$0$9620$3b21...@news.univie.ac.at>...

> > In this sense, an electron can well be regarded as an
> > extended indivisible particle (with an extension given by the region
> > where |psi|^2 is significant).

> This is definitely _wrong_, according to current wisdom, and is a
> not uncommon misconception. The wavefunction reflects the
> indeterminancy of the particle's location, not it's spatial extension.
> A "wavefunction wave" falling upon a screen of detectors can cause
> only one detector to fire, not several.

But this does not contradict my statement. The latter is a macroscopic
consequence of the particle hitting the screen; the result must be analyzed
in terms of a complicated dynamics. An extended flood also breaks a dam
only at one place, that of least resistance...

To argue that something is _wrong_ (a logical category), one should give
a _logical_ argument, not a handwaving plausibility statement.

Arnold Neumaier

Arnold Neumaier

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Feb 17, 2003, 6:10:35 PM2/17/03
to sci-physic...@moderators.isc.org
Squark wrote:
>
> Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
> news:<3e43b60b$0$9620$3b21...@news.univie.ac.at>...
>
> > In this sense, an electron can well be regarded as an
> > extended indivisible particle (with an extension given by the region
> > where |psi|^2 is significant).
>
> This is definitely _wrong_, according to current wisdom, and is a
> not uncommon misconception. The wavefunction reflects the
> indeterminancy of the particle's location, not it's spatial extension.

It is not just my ideosyncracy, but gives a quite useful and intuitive
geometric picture of microphysics, especially if one wants to
understand the meaning of everything in a relativistic context.
For example, discussing the localization of relativistic particles
in space-time,
D. Marolf and C. Rovelli, Relativistic quantum measurement,
Phys.Rev. D66 (2002) 023510, gr-qc/0203056,
say on p.7 (top right, of the archived version):
... the quantum particle has an intrinsic Compton ``extension''...

Arnold Neumaier

news.verizon.net

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Feb 17, 2003, 6:15:19 PM2/17/03
to
"Ralph E. Frost" <ref...@dcwi.com> wrote in message
news:v43tf2h...@corp.supernews.com...

>
> Ahmet Gorgun <ago...@att.net> wrote in message
> news:gik%9.18435$rq4.1...@bgtnsc05-news.ops.worldnet.att.net...
>
> > Are you saying that electron has absolutely no parts and you can prove
> > that it has absolutely no parts?
>
> The prevailing theory and equations/description are all set up on
electrons
> being point particles.
>
> What more proof does one need?

Let's apply the same logic to celestial mechanics: If we assume that planets
are point particles we can still predict their position with accuracy. From
this it does not follow that planets are indivisible. The same is true for
the electron. How do you prove that electron has no parts?


> [Moderator's note: no compositeness has been seen up to energies of at
> least 4 TeV:
> http://www.slac.stanford.edu/pubs/snowmass96/PDF/NEW160.PDF
> though this paper is from 1996, and the bound may be higher now. - jb]


This reference looks for compositeness of Quarks and Leptons not electrons.

Ahmet Gorgun


[Moderator's note: Electrons are leptons. -TB]

Squark

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Feb 18, 2003, 4:37:12 PM2/18/03
to
Arnold Neumaier <Arnold....@univie.ac.at> wrote in message news:<3e50b4ea$0$14964$3b21...@news.univie.ac.at>...

> But this does not contradict my statement. The latter is a macroscopic
> consequence of the particle hitting the screen; the result must be analyzed
> in terms of a complicated dynamics. An extended flood also breaks a dam
> only at one place, that of least resistance...

But there is no dynamical theory of that sort to account for quantum
phenomena. Would there be one, there would be no need for quantum theory,
as everything would be classical. However, it is apparently impossible to
construct that sort of theory consistently with quantum mutli-particle
effects (i.e. EPR correlations).



> To argue that something is _wrong_ (a logical category), one should give
> a _logical_ argument, not a handwaving plausibility statement.

As I said, I'm only talking about current wisdom. In current theory, the
wavefunction does not express spatial extension and position measurements
always yield a non-ambiguous result. This theory is completely consistent
with experiment, and to counter it you would have to present an alternative.
The later is problematic in view of Bell's theorem, unless you're apt for
de Broglie - Bohm. In de Broglie - Bohm one has a pilot wave which might be
said to posses a spatial extension, but also a particle with a definite
coordinate.

Charles Francis

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Feb 19, 2003, 11:57:19 PM2/19/03
to

In message <3e43b60b$0$9620$3b21...@news.univie.ac.at>, Arnold
Neumaier <Arnold....@univie.ac.at> writes

>. More importantly, a photon, which cannot
>be localized in space (according to Newton & Wigner),
>can hardly be regarded as being pointlike in any geometric sense,
>though it is probably indivisible.

I don't agree with the conclusion, though there are certainly subtle
issues regarding the wave function of the photon. You cannot actually
measure the position of a photon, you can only measure the position of
the electron which absorbed the photon. This does do curious things to
the wave function, but not enough to say that the photon is not
pointlike.

For "pointlike in a geometrical sense" I follow one of the definitions
going back to Euclid, that a point is that which has neither length nor
breadth. This definition I think does hold up, though clearly any
definition which claims that a point has a position fails to make sense
in the quantum domain.


Regards

--
Charles Francis

Squark

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Feb 19, 2003, 11:57:10 PM2/19/03
to
Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
news:<3e50f609$0$14964$3b21...@news.univie.ac.at>...

> It is not just my idiosyncracy, but gives a quite useful and intuitive


> geometric picture of microphysics, especially if one wants to
> understand the meaning of everything in a relativistic context.
> For example, discussing the localization of relativistic particles
> in space-time,
> D. Marolf and C. Rovelli, Relativistic quantum measurement,
> Phys.Rev. D66 (2002) 023510, gr-qc/0203056,
> say on p.7 (top right, of the archived version):
> ... the quantum particle has an intrinsic Compton ``extension''...

One must not confuse the apparent "extended" nature of relativistic
quantum particles with the general notion of indeterminate position in
quantum mechanics. It is true that in relativist quantum mechanics the
notion of position is subtle and problematic, but note the "extension"
is of the size of the Compton wavelength, not the characteristic
length of the |psi(x)^2| distribution.

Oz

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Feb 19, 2003, 11:57:07 PM2/19/03
to
Squark <fii...@yahoo.com> writes

>This is definitely _wrong_, according to current wisdom, and is a
>not uncommon misconception. The wavefunction reflects the
>indeterminancy of the particle's location, not it's spatial extension.
>A "wavefunction wave" falling upon a screen of detectors can cause
>only one detector to fire, not several.

Red rag to a bull, this.

What makes you believe that a 'wavefunction wave' falling on a screen of
detectors causing one to fire excludes the particle from being spatially
extended before then?

If we take a 'free' particle, we can indisputably send it through both
slits and perform many experiments that show it behaves as an extended
wavelike object. The single-photon diffraction pattern is a bit of a
giveaway on that score.

In fact the ONLY time we see it as a pointlike particle is when we
attempt to locate it's precise position. It should not be surprising
that 'locating it's precise position' results in seeing it at a point.
That is what 'locating it's precise position' means, after all.

I have discussed this point here many times and so far nobody has given
me a convincing argument as to why one should not correctly consider a
free diffracting particle as being an extended wave.

IMHO (albeit of a near total ignoramus) the pointlike qualities are a
function of the wavefunction-detector interaction which generally
requires localisation as part of the detection.

--
Oz
This post is worth absolutely nothing and is probably fallacious.
Note: soon (maybe already) only posts via despammed.com will be accepted.


Squark

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Feb 20, 2003, 7:26:12 PM2/20/03
to
Oz <aco...@btopenworld.com> wrote in message news:<b31n73$gbg$1...@panther.uwo.ca>...

> In fact the ONLY time we see it as a pointlike particle is when we
> attempt to locate it's precise position. It should not be surprising
> that 'locating it's precise position' results in seeing it at a point.
> That is what 'locating it's precise position' means, after all.
>
> I have discussed this point here many times and so far nobody has given
> me a convincing argument as to why one should not correctly consider a
> free diffracting particle as being an extended wave.

It all depends on definitions, as always. However, what we might expect
of a physical extended object is, for instance, the possibility the
measure it's state at every point separately. This cannot be done with
the quantum particle. There is no way you can measure the value of the
wavefunction at any given point.
Moreover, if you detect a quantum particle at a certain point, the rest
of the wavefunction "disappears" instantaneously, which would be
"action at a distance" if the wavefunction indeed represented an
extended object, which is another hint at the fact the situation is not
so.

Arnold Neumaier

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Feb 21, 2003, 12:25:28 AM2/21/03
to sci-physic...@moderators.isc.org
Squark wrote:

> Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
news:<3e50b4ea$0$14964$3b21...@news.univie.ac.at>...

> > But this does not contradict my statement. The latter is a macroscopic
> > consequence of the particle hitting the screen; the result must be analyzed
> > in terms of a complicated dynamics. An extended flood also breaks a dam
> > only at one place, that of least resistance...
>
> But there is no dynamical theory of that sort to account for quantum
> phenomena. Would there be one, there would be no need for quantum theory,
> as everything would be classical. However, it is apparently impossible to
> construct that sort of theory consistently with quantum mutli-particle
> effects (i.e. EPR correlations).

No; this has nothing to do with EPR or hidden variables.

There *is* a dynamical quantum theory of multiparticle interaction,
namely the multiparticle Schroedinger equation.
The measurement process is the result of interaction of a single
quantum particle with a quantum multiparticle system (the detector),
and therefore should be described in these terms. Sometimes,
measurement is idealized as instantaneous reduction of the wave packet,
but this is well-known to be inaccurate, and hides what is going on
under the carpet. But sometimes, more realistic scenarios were discussed.

I have seen derivations of the path of a particle in a bubble chamber
(answering the question, 'why do the bubbles describe a path
although the particle has a wave function without well-defined position?'),
and in a similar way one must be able to study the interaction
of a particle with a photographic plate, although I haven't seen
anything about this.

The analogy with a dam is then quite reasonable -
the detector is a specially prepared unstable thermodynamic system with
an energy landscape with multiple local minima at the possible outcomes
of the measurement, and details of the microstate determine into which
of these local minima the system will fall when excited by an incident particle
and dissipating its energy. But it will fall only into one,
of course.



> > To argue that something is _wrong_ (a logical category), one should give
> > a _logical_ argument, not a handwaving plausibility statement.

> As I said, I'm only talking about current wisdom. In current theory, the
> wavefunction does not express spatial extension and position measurements
> always yield a non-ambiguous result.

This is the reduction of the wave packet of the 1930's, which puts
the particle into a position eigenstate, in which |psi|^2 indeed is a
delta function, hence pointlike also according to my recipe.
But it is pointlike only at the idealized measurement instant, not before!
Before the measurement, it is generally not in a position eigenstate,
hence has an extended |psi|^2 distribution, and therefore a spatial
extension. The act of measurement changes the shape of the wave
function, and hence its spatial extension.

But this is all heavily idealized; realistic measurements are neither
instantaneous, as required by von Neumann's orthodox theory, nor do
they localize perfectly in space. Many people think there is no
(nonunitary) reduction of the wave packet at all. There is a thick book
by Wheeler and Zurek (Quantum theory and measurement,
Princeton Univ. Press, Princeton 1983) with collected articles about
all this, displaying the full range of current uncertainty and lack of
wisdom.

Fortunately, there is also more recent stuff, e.g., an excellent book by
Braginsky and Khalili (Quantum measurement, Cambridge Univ. Press,
Cambridge 1992) on _real_ quantum measurements close to actual
(optical) experiments, and they talk for example (p.3 bottom) about

'the photon must have occupied a volume larger than the slit separation.'

I'd take this to be the current wisdom.

Arnold Neumaier

Oz

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Feb 21, 2003, 12:25:24 AM2/21/03
to
Squark <fii...@yahoo.com> writes

>As I said, I'm only talking about current wisdom. In current theory, the
>wavefunction does not express spatial extension and position measurements
>always yield a non-ambiguous result. This theory is completely consistent
>with experiment, and to counter it you would have to present an alternative.

The two slit experiment with single particles refutes your statement.

How does this single particle go through both slits simultaneously?

Oz

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Feb 21, 2003, 2:17:36 PM2/21/03
to
Squark <fii...@YAHOO.COM> writes

>Oz <aco...@btopenworld.com> wrote in message news:<b31n73$gbg$1...@panther.uwo.ca>
>...
>> In fact the ONLY time we see it as a pointlike particle is when we
>> attempt to locate it's precise position. It should not be surprising
>> that 'locating it's precise position' results in seeing it at a point.
>> That is what 'locating it's precise position' means, after all.
>>
>> I have discussed this point here many times and so far nobody has given
>> me a convincing argument as to why one should not correctly consider a
>> free diffracting particle as being an extended wave.
>
>It all depends on definitions, as always.

Indeed.

>However, what we might expect
>of a physical extended object is, for instance, the possibility the
>measure it's state at every point separately.

I'm not sure why you would expect that of a quantised wave.
Measuring it's state inevitably destroys the state, that's a feature of
QM. Not least it localises the particle, how else can you measure a
particle at a point?

>This cannot be done with
>the quantum particle. There is no way you can measure the value of the
>wavefunction at any given point.

Hmmm. Yes, and no. You can do it statistically by preparing particles in
the same state and measuring a lot of them. Actually you have little
choice but to use this method since detecting a particle destroys the
state (and usually the particle). Fortunately preparing a particle in a
given state is often very easy because particles are easily divided into
identical species (electron, photon, etc) so when bound deliver
identical wavefunctions (to first order). Physicists are real good at
preparing particles in required states to order.

>Moreover, if you detect a quantum particle at a certain point, the rest
>of the wavefunction "disappears" instantaneously, which would be
>"action at a distance" if the wavefunction indeed represented an
>extended object, which is another hint at the fact the situation is not
>so.

I'm not sure that this is indeed typically true, not that it would
matter that much if it did.

Take the emission of a photon by an atom. Typically this does not happen
'instantly', in fact the time required is very well known for many types
of emission. Time reverse this and you have an absorption and I can see
no reason why the absorption is 'instant' whilst the emission is 'slow'.
Why should there be any difference in basic mechanism for other
absorbers like silver halide film?

If you then proceed to entangled pairs and cite 'FTL information
transmission' then you have to explain what physical laws are being
broken to make this implausible. For the rest of the universe there is
no instantaneous passage of useful information, no breaking of any of
the conservation laws (quite the contrary) and all is perfectly well
with the world. Why should this be implausible?

A particle formulation, though, has serious problems with self-
interference and big problems when you start putting waves through
polarisers. Sure they can all be overcome by appropriate mathematical
jugglement and the mathematical techniques are well understood and
convenient, but it's much more straightforward to imagine the particle
as a simple quantised wave.

Then you will point to the 'pointlike' electron (say). It's so pointlike
we can diffract it and treat it perfectly happily as a wave. Aha, you
say, but when we fire really short wavelength particles at it we find it
increasingly behaves like a point. Is this so surprising? The wavelength
of a particle is momentum-dependent. The higher the momentum the shorter
the wavelength. The shorter the wavelength the smaller a particle looks.
It's a completely self-fullfilling prophecy that a particle looks
smaller when probed at higher energies. It doesn't contradict wave
formulation, it confirms it.

Aha, you say next, look at the derivation of electron properties
provided by pointlike QED. Surely this proves that electrons are
pointlike? Well, ignoring the cutoff (ie it's NOT a point) my
understanding is that QED is identical (should I say isomorphic or
something?) to wave-based formulations. So one could do the same
integration using a wave formulation, just it's probably very much
easier done following feynman.

Over to you .....

Squark

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Feb 21, 2003, 2:22:40 PM2/21/03
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Arnold Neumaier <Arnold....@univie.ac.at> wrote in message news:<3e538dee$0$14964$3b21...@news.univie.ac.at>...

> the detector is a specially prepared unstable thermodynamic system with
> an energy landscape with multiple local minima at the possible outcomes
> of the measurement, and details of the microstate determine into which
> of these local minima the system will fall when excited by an incident
> particle and dissipating its energy.

But there is no such "microstate"! Such a microstate would be exactly
what is called "hidden variables".

> Before the measurement, it is generally not in a position eigenstate,
> hence has an extended |psi|^2 distribution, and therefore a spatial
> extension. The act of measurement changes the shape of the wave
> function, and hence its spatial extension.

You might have misunderstood my point. I perfectly know and agree
the wavefunction has spatial extension. The only thing I'm claiming
is that the physical object the information about which the
wavefunction represents, i.e. the quantum particle, cannot be
assigned the spatial extension of the |psi^2| distribution.

> But this is all heavily idealized; realistic measurements are neither
> instantaneous, as required by von Neumann's orthodox theory, nor do
> they localize perfectly in space.

As I said, relativistic effects are another issue, but the predict a
finite extension unrelated, in general, to the |psi^2| distribution.
In fact, it proves my point: the distribution is present both in
relativistic and non-relativistic QM, but the problem with describing
the quantum particle as point-like only arises in the relativistic
case.

> Fortunately, there is also more recent stuff, e.g., an excellent book by
> Braginsky and Khalili (Quantum measurement, Cambridge Univ. Press,
> Cambridge 1992) on _real_ quantum measurements close to actual
> (optical) experiments, and they talk for example (p.3 bottom) about
>
> 'the photon must have occupied a volume larger than the slit separation.'
>
> I'd take this to be the current wisdom.

I never read this book, and don't have the possibility to either browse it
or understand in what context was this phrase said. Therefore, you are
putting me in a somewhat unfair position here. In any case, arguing about
whether something is or is not the current wisdom is silly enough, and in
the circumstances it's hard to bring good evidence. Therefore, if you
don't beleive me what I'm saying _is_ current wisdom, I won't engage in an
arguement about it.

Squark

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Feb 22, 2003, 12:59:39 AM2/22/03
to
Oz <aco...@btopenworld.com> wrote in message
news:<b34d84$fpq$1...@panther.uwo.ca>...

> The two slit experiment with single particles refutes your statement.
>
> How does this single particle go through both slits simultaneously?

It doesn't. It goes through one of them, but it is undefined which.

Oz

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Feb 22, 2003, 1:59:49 AM2/22/03
to
Squark <fii...@yahoo.com> writes

>One must not confuse the apparent "extended" nature of relativistic
>quantum particles with the general notion of indeterminate position in
>quantum mechanics. It is true that in relativist quantum mechanics the
>notion of position is subtle and problematic, but note the "extension"
>is of the size of the Compton wavelength, not the characteristic
>length of the |psi(x)^2| distribution.

Hmmm. Is it? Where is the electron in an outer orbital of a heavy atom?
Sure, you can probe for it with a high energy particle but this will
just give you some 'found' position but does not mean the particle was
'there' before it interacted with your probe.

OTOH I would _probably_ agree with you in situations like the S2->S1
orbital transition where psi is roughly a spherical shell because I feel
that the 'recoiling atom' is big and complex enough to result in de-
entanglement (I could be wrong here). In that case I might well consider
'our total knowledge of the position of the photon' to indeed be
spherical (and on average give splendidly accurate results) even though
the emitting atom did indeed recoil 'unobserved' to give a modestly
localised photon (at least in momentum).

There again, I am continually fireballed for this viewpoint.

Oz

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Feb 22, 2003, 1:59:54 AM2/22/03
to
Arnold Neumaier <Arnold....@univie.ac.at> writes:

[NB Note I am in fact stunningly ignorant and not expert]

>No; this has nothing to do with EPR or hidden variables.
>
>There *is* a dynamical quantum theory of multiparticle interaction,
>namely the multiparticle Schroedinger equation.
>The measurement process is the result of interaction of a single
>quantum particle with a quantum multiparticle system (the detector),
>and therefore should be described in these terms. Sometimes,
>measurement is idealized as instantaneous reduction of the wave packet,
>but this is well-known to be inaccurate, and hides what is going on
>under the carpet. But sometimes, more realistic scenarios were discussed.

Cor! I do hope you are an expert because I have been arguing this for
years and being told I am simply ignorant (which is indeed true). Mind
you, you do put it in proper technospeak.

>I have seen derivations of the path of a particle in a bubble chamber
>(answering the question, 'why do the bubbles describe a path
>although the particle has a wave function without well-defined position?'),
>and in a similar way one must be able to study the interaction
>of a particle with a photographic plate, although I haven't seen
>anything about this.

The cloud chamber is a position detector. It must localise the particle
to detect it. The particle must thus have a (reasonably) well-defined
position (to within a few wavelengths).

>The analogy with a dam is then quite reasonable - the detector is a
>specially prepared unstable thermodynamic system with an energy
>landscape with multiple local minima at the possible outcomes of the
>measurement, and details of the microstate determine into which of
>these local minima the system will fall when excited by an incident
>particle and dissipating its energy. But it will fall only into one,
>of course.

Yeeees!!!
Been claiming exactly this for years!
It's worth also pointing out that typically the incoming wave is HUGE
compared to the number of local minima (if you want reasonable detector
efficiency). Consider the size of an absorbing silver halide molecule (a
few hundred pm) with light (of wavelength, let alone |psi^2|, of a few
hundred nm). It's likely (including thickness) that at least billions of
molecules become mutually entangled in a very complex way into a
wavefunction that must time-evolve into one excited silver hailde
molecule if the light is to be detected. Imagining this in a wavelike
formulation is quite easy.

>This is the reduction of the wave packet of the 1930's, which puts
>the particle into a position eigenstate, in which |psi|^2 indeed is a
>delta function, hence pointlike also according to my recipe.

Agreed.

>But it is pointlike only at the idealized measurement instant, not before!
>Before the measurement, it is generally not in a position eigenstate,
>hence has an extended |psi|^2 distribution, and therefore a spatial
>extension.

Agreed but see above.

>The act of measurement changes the shape of the wave
>function, and hence its spatial extension.

Agreed.

>But this is all heavily idealized; realistic measurements are neither
>instantaneous, as required by von Neumann's orthodox theory, nor do
>they localize perfectly in space. Many people think there is no
>(nonunitary) reduction of the wave packet at all. There is a thick book
>by Wheeler and Zurek (Quantum theory and measurement,
>Princeton Univ. Press, Princeton 1983) with collected articles about
>all this, displaying the full range of current uncertainty and lack of
>wisdom.

I'd be tempted to buy it if:

1) I could afford it.
2) I could understand it.

>Fortunately, there is also more recent stuff, e.g., an excellent book by
>Braginsky and Khalili (Quantum measurement, Cambridge Univ. Press,
>Cambridge 1992) on _real_ quantum measurements close to actual
>(optical) experiments, and they talk for example (p.3 bottom) about
>
> 'the photon must have occupied a volume larger than the slit separation.'
>
>I'd take this to be the current wisdom.

Ummm. There might just be one or two people here with a publication list
running into pages who would disagree ....

Trust me on this.

Er, photon thread, anybody?

[Only joking ..]

Arnold Neumaier

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Feb 24, 2003, 3:35:57 AM2/24/03
to

Squark wrote:

> Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
news:<3e538dee$0$14964$3b21...@news.univie.ac.at>...

> > the detector is a specially prepared unstable thermodynamic system with
> > an energy landscape with multiple local minima at the possible outcomes
> > of the measurement, and details of the microstate determine into which
> > of these local minima the system will fall when excited by an incident
> > particle and dissipating its energy.

> But there is no such "microstate"! Such a microstate would be exactly
> what is called "hidden variables".

No; this is a misunderstanding.
In a thermodynamic description there is the classical
macrostate given by a few thermodynamic parameters
(namely the mass density and the temperature, etc), and many,
many microstates (namely quantum density matrices, or wave functions
if you idealize) consistent with this macrostate. Nothing about
hidden variables.

> > Before the measurement, it is generally not in a position eigenstate,
> > hence has an extended |psi|^2 distribution, and therefore a spatial
> > extension. The act of measurement changes the shape of the wave
> > function, and hence its spatial extension.

> You might have misunderstood my point. I perfectly know and agree
> the wavefunction has spatial extension. The only thing I'm claiming
> is that the physical object the information about which the
> wavefunction represents, i.e. the quantum particle, cannot be
> assigned the spatial extension of the |psi^2| distribution.

The particle _is_ the wave function - what else could it be? It has
no properties apart from that represented in the wave function (unless
you assume hidden variables); so one has every right to identify the
two. This is possible since both the particle and the wave function
are conceptual abstractions. The 'reality' is indiscernible...

> > But this is all heavily idealized; realistic measurements are neither
> > instantaneous, as required by von Neumann's orthodox theory, nor do
> > they localize perfectly in space.

> As I said, relativistic effects are another issue, but they predict a


> finite extension unrelated, in general, to the |psi^2| distribution.

What I said has nothing to do with relativistic or not; a
realistic measurement takes time, and this is discussed
by the experts independent of relativity. See, e.g., Wigner, 1976,
in: Wheeler and Zurek, Quantum Theory and Measurement, p. 284:

>>The fact that the measurement is of finite duration introduces
a more serious problem... The existence of this issue
reemphasizes that the quantum-mechanical description of
the measurement ... is a highly idealized description.<<

> In fact, it proves my point: the distribution is present both in
> relativistic and non-relativistic QM, but the problem with describing
> the quantum particle as point-like only arises in the relativistic
> case.

No, it is only that in the relativistic case you are _forced_ to that
conclusion while in the nonrelativistic case you have an option. But
even then, I think, visualization as extended is preferable.

> > Fortunately, there is also more recent stuff, e.g., an excellent book by
> > Braginsky and Khalili (Quantum measurement, Cambridge Univ. Press,
> > Cambridge 1992) on _real_ quantum measurements close to actual
> > (optical) experiments, and they talk for example (p.3 bottom) about
> >
> > 'the photon must have occupied a volume larger than the slit separation.'
> >
> > I'd take this to be the current wisdom.

> I never read this book, and don't have the possibility to either
> browse it or understand in what context was this phrase
> said. Therefore, you are putting me in a somewhat unfair position
> here.

Well, it is worth reading. It has _lots_ of information about
realistic quantum measurement. But for your convenience,
let me quote more extensively:

>>Experiments on the interference and diffraction of light,
when performed with very low intensities, revealed further that an
interference pattern (a classical, pure wave effect) shows up on
a photographic plate only when the number of photons falling on
the plate is very large. Each photon in such an experiment
is _completely_destroyed_ [original italic] (ceases to exist)
by interacting with the plate's silver chloride molecules.
When the photon is destoyed there appears somewhere on the
photographic plate an atom of free silver, which acts as an
embryo from which, by photographic developing, a small seed
of silver will grow. The silver embryo is much smaller than
an electromagnetic wavelength.
This is remarkable. In the interference process (e.g. in the
two-slit experiment of Fig. 1.1), [standard picture] the photon must
have been influenced by the locations of both slits, since the
interference pattern depends on the distance between them. This means
that the photon must have occupied a volume larger than the slit
separation. On the other hand, when it fell on the photographic plate,
the photon must have been localized into the tiny volume of the silver
embryo. Later the terms ''collapse of the wave function'' and
''reduction of the wave packet'' were used to describe such
localization.<<

> In any case, arguing about whether something is or is not
> the current wisdom is silly enough, and in the circumstances
> it's hard to bring good evidence.

Well, I gave good evidence by quoting from a current [1995]
book by experts on quantum measurement. Textbook wisdom is not
current in this case.

> Therefore, if you don't believe me what I'm saying _is_
> current wisdom, I won't engage in an argument about it.

I don't believe you since I think I am better informed, and
since I think judging extension by |psi|^2 also makes much
more sense than claiming a pointlikeness that is operationally
meaningless since it relates to occult properties of physical
objects apart from their state. Current or not, it is _wise_
to consider quantum particles as being extended.

Arnold Neumaier

Oz

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Feb 24, 2003, 8:30:08 PM2/24/03
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Squark <fii...@yahoo.com> writes

>Oz <aco...@btopenworld.com> wrote in message
>news:<b34d84$fpq$1...@panther.uwo.ca>...
>
>> The two slit experiment with single particles refutes your statement.
>>
>> How does this single particle go through both slits simultaneously?
>
>It doesn't. It goes through one of them, but it is undefined which.

That's a most devious and unconvincing explanation.

You have to explain why going through one (but not the other) whilst
'unobserved' gives a diffraction pattern but going through one (when
observed) doesn't. Remembering that we are talking about single particle
diffraction here.

I'm sure there are sufficiently devious explanations for this but occham
forces me to reject them in favour of the simplest:

To diffract it must go through both.

This is effortlessly easy with a wave, heck it even gives the correct
pattern straight off.

Oz

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Feb 24, 2003, 8:31:39 PM2/24/03
to
Squark <fii...@yahoo.com> writes

>Arnold Neumaier <Arnold....@univie.ac.at> wrote in message news:<3e538dee$0
>$14964$3b21...@news.univie.ac.at>...
>> the detector is a specially prepared unstable thermodynamic system with
>> an energy landscape with multiple local minima at the possible outcomes
>> of the measurement, and details of the microstate determine into which
>> of these local minima the system will fall when excited by an incident
>> particle and dissipating its energy.
>
>But there is no such "microstate"!

Eh? You mean you do not accept that silver halide molecules are quantum-
mechanical and exist in a state themselves? And that this state can
time-evolve with an incoming photon?

If I placed a single SH molecule in a light beam I'm sure some smart
physicist or two would be able to characterise the time-evolution of the
absorption of an incoming light quantum eventually. I wouldn't consider
this 'hidden', but 'currently unknown', because in principle it is
knowable.

Probably an individual one only has a small chance of trapping a photon,
but on a film we have billions of them. Billions of local minima
entangled with the incoming photon. All in slightly different states,
all co-evolving together until one gets lucky (or the photon goes
straight though).

>Such a microstate would be exactly
>what is called "hidden variables".

Eh? I have near total ignorance of 'hidden variables' but I don;t think
silver halide film is one of them. Technically I'm sure the required
details could be measured and probably already have been.

>> Before the measurement, it is generally not in a position eigenstate,
>> hence has an extended |psi|^2 distribution, and therefore a spatial
>> extension. The act of measurement changes the shape of the wave
>> function, and hence its spatial extension.
>
>You might have misunderstood my point. I perfectly know and agree
>the wavefunction has spatial extension. The only thing I'm claiming
>is that the physical object the information about which the
>wavefunction represents, i.e. the quantum particle, cannot be
>assigned the spatial extension of the |psi^2| distribution.

I agree in some circumstances (and I gave an example earlier).

Take an idealised electron emitter that emits a spherical distribution
of electrons. Without knowledge of the emission direction we describe it
as a spherical distribution |psi_t^2| and lo and behold everything works
out fine. Some people think this means each electron is spread over a
spherical shell but I don't.

I think we have individual more localised electrons (of order compton
wavelength) following |psi_e^2| but an awful lot of them (typically). We
can even screen out those with selected directions with an aperture.
This means, in almost certainly wrong notation but try and get my gist,
that summing the individual electron wavefunctions should total
|psi_t^2|.

I have a horrible feeling this doesn't quite work, because somewhere we
should need to include a function in |psi_t^2| to express our level of
ignorance. Oh, being realistic also because of my level of knowledge,
and for a whole host of technical reasons well beyond my ken.

What you argue, and I argue above, is a precise analogy to my argument
in the 'photon' threads when I was discussing atoms emitting photons
spherically (yer s2->s1 transition) that were seen by ted 100M years
later. Does it make sense to say it was emitted as a spherical wavefront
for 100M years? The expert opinion was that it does, I am not convinced
(at all).

OTOH if you are talking about a single electron diffraction pattern
where the slits are many wavelengths apart then it is precisely the
compton wavelength that is relevant. You will (eventually) get a
diffraction pattern and it will reflect the electron's compton
wavelength. I would imagine that the proportion of electrons that go
through both slits will decrease drastically as the slit spacing is
increased. To me that gives a measure of the lateral 'size' of the
electron. There isn't much 'electron' many compton wavelengths away from
the 'centre'. Remember, though, that I tried this analogy for 'photon
size' and got thoroughly (and repeatedly) duffed up by the great and the
good.

>> But this is all heavily idealized; realistic measurements are neither
>> instantaneous, as required by von Neumann's orthodox theory, nor do
>> they localize perfectly in space.
>
>As I said, relativistic effects are another issue, but the predict a
>finite extension unrelated, in general, to the |psi^2| distribution.
>In fact, it proves my point: the distribution is present both in
>relativistic and non-relativistic QM, but the problem with describing
>the quantum particle as point-like only arises in the relativistic
>case.

So drop it? Or reformulate it to give the right answers accepting that
it's just a model of the real wave set up for convenient integration.

Or is that too simple?

Arnold Neumaier

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Feb 24, 2003, 8:53:19 PM2/24/03
to

In geometry, one has long left this kind of definitions since
they are circular. Instead, one specifies the axioms that one
wants a point to possess - mathematical properties.

In particular, one asks in the literature for localizability
- clearly, a point should be localizable. In the quantum optic
bilbe of mandel & Wolf, there are several pages devoted to the
impossiblility of localizing a photon (Section 12.11), and there
is also a significant literature about this elsewhere, just
because of its irritating nature.

Arnold Neumaier

Ralph Hartley

unread,
Feb 25, 2003, 5:49:07 PM2/25/03
to
Oz wrote:
> Squark <fii...@yahoo.com> writes
>>Oz <aco...@btopenworld.com> wrote:
>>>How does this single particle go through both slits simultaneously?
>>
>>It doesn't. It goes through one of them, but it is undefined which.

I preffer to say that it goes through one *plus* it goes through the other.
"Plus", as a logical conective, is more of like "or" than like "and" (which
is sort of like "times").

The whole idea of the Hilbert space business is to let you use aritmatic on
things you would normally apply logic to. Logic (at least when applied in
the obvious way) dosen't seem to work in the quantum world, but -
miraculously - aritmatic *does*. The main diference is that numbers can be
negative.

Quantum mechanics, as usually expressed, allows imaginary numbers as well,
but that just makes the equations easier to write (Forier transforms and
all that).

> That's a most devious and unconvincing explanation.

So? Did the universe promise to be straightforward and convincing?

Ralph Hartley

Graham Jones

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Feb 25, 2003, 7:16:16 PM2/25/03
to

In article <b3775a$o33$1...@panther.uwo.ca>, Oz <aco...@btopenworld.com>
writes:

>Arnold Neumaier <Arnold....@univie.ac.at> writes:

[...]


>>There *is* a dynamical quantum theory of multiparticle interaction,
>>namely the multiparticle Schroedinger equation.
>>The measurement process is the result of interaction of a single
>>quantum particle with a quantum multiparticle system (the detector),
>>and therefore should be described in these terms. Sometimes,
>>measurement is idealized as instantaneous reduction of the wave packet,
>>but this is well-known to be inaccurate, and hides what is going on
>>under the carpet. But sometimes, more realistic scenarios were discussed.

>Cor! I do hope you are an expert because I have been arguing this for
>years and being told I am simply ignorant (which is indeed true). Mind
>you, you do put it in proper technospeak.

[...]

You might like Bohmian Mechanics. You will at least find some experts
who are "enemies of your enemies". Here is quote from a recent paper,
which starts by quoting Bell:

"...conventional formulations of quantum theory, and of quantum
field theory in particular, are unprofessionally vague and
ambiguous. Professional theoretical physicists ought to be able
to do better. Bohm has shown us a way." (Bell, 1987)

The problem, in other words, with orthodox quantum theory is not
that it fails to be intuitively founded, but rather that, with
its incoherent babble about measurement, it is not even well
formulated!

Bohmian Mechanics as the Foundation of Quantum Mechanics D. Dürr, S.
Goldstein, and N. Zanghì. arXiv: quant-ph/9511016

You can find this paper and other information about Bohmian Mechanics at
http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/bmstartE.htm

Graham
--
Graham Jones, author of SharpEye Music Reader
http://www.visiv.co.uk
21e Balnakeil, Durness, Lairg, Sutherland IV27 4PT, Scotland, UK

Squark

unread,
Feb 26, 2003, 5:52:31 PM2/26/03
to
Arnold Neumaier <Arnold....@univie.ac.at> wrote in message news:<3e56a7e5$0$14448$3b21...@news.univie.ac.at>...

> Squark wrote:
>
> > Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
> news:<3e538dee$0$14964$3b21...@news.univie.ac.at>...
>
> > > the detector is a specially prepared unstable thermodynamic system with
> > > an energy landscape with multiple local minima at the possible outcomes
> > > of the measurement, and details of the microstate determine into which
> > > of these local minima the system will fall when excited by an incident
> > > particle and dissipating its energy.
>
> > But there is no such "microstate"! Such a microstate would be exactly
> > what is called "hidden variables".
>
> No; this is a misunderstanding.
> In a thermodynamic description there is the classical
> macrostate given by a few thermodynamic parameters
> (namely the mass density and the temperature, etc), and many,
> many microstates (namely quantum density matrices, or wave functions
> if you idealize) consistent with this macrostate. Nothing about
> hidden variables.

If you consider the wavefunction as the "macrostate", the "details of
the microstate" which determine outcome of quantum measurements are
hidden variables. This is because the hidden variables, are, by
definition, unobserved quantities which deterministically determine
the outcome of quantum measurements.

> The particle _is_ the wave function - what else could it be? It has
> no properties apart from that represented in the wave function (unless
> you assume hidden variables); so one has every right to identify the
> two. This is possible since both the particle and the wave function
> are conceptual abstractions. The 'reality' is indiscernible...

Firstly, one cannot identify the two as in a multi-particle system
individual particles have no wavefunctions.

> What I said has nothing to do with relativistic or not; a
> realistic measurement takes time, and this is discussed
> by the experts independent of relativity.

Sorry, I misread "realistic" for "relativistic". Yes, realistic
measurements have various limitations, but I don't think it's
appropriate to draw conclusions from it about the
"pointlikeness", unless you can place a universal limit on the
accuracy such measurements can achieve.

> No, it is only that in the relativistic case you are _forced_ to that
> conclusion while in the nonrelativistic case you have an option. But
> even then, I think, visualization as extended is preferable.

This seems to be a subjective arguement, therefore I can hardly argue
against it.



> > > Fortunately, there is also more recent stuff, e.g., an excellent book by
> > > Braginsky and Khalili (Quantum measurement, Cambridge Univ. Press,
> > > Cambridge 1992) on _real_ quantum measurements close to actual
> > > (optical) experiments, and they talk for example (p.3 bottom) about
> > >
> > > 'the photon must have occupied a volume larger than the slit separation.'
> > >
> > > I'd take this to be the current wisdom.
>
> > I never read this book, and don't have the possibility to either
> > browse it or understand in what context was this phrase
> > said. Therefore, you are putting me in a somewhat unfair position
> > here.
>
> Well, it is worth reading. It has _lots_ of information about
> realistic quantum measurement. But for your convenience,
> let me quote more extensively:
>

> This is remarkable. In the interference process (e.g. in the
> two-slit experiment of Fig. 1.1), [standard picture] the photon must
> have been influenced by the locations of both slits, since the
> interference pattern depends on the distance between them. This means
> that the photon must have occupied a volume larger than the slit
> separation. On the other hand, when it fell on the photographic plate,
> the photon must have been localized into the tiny volume of the silver
> embryo. Later the terms ''collapse of the wave function'' and
> ''reduction of the wave packet'' were used to describe such
> localization.<<

I don't think this introductionary exposure of quantum mechanical
effects contains any attempt to accurately reflect on such issues as
whether the quantum particle is point-like or not. Again, I claim
two things must be distinguished: the point-like quantum particle,
which is a point without location - much like a point in a
non-commutative space, this as a philosophical notion is quite
different from the usual point - and the extended wavefunction.
Therefore, the notion "point-like" applies here in a sense different
from the usual, classical, sense. Nevertheless we would hardly
benefit from abandoning the notion, though it might make our
arguement ill posed: we don't agree on the definitions.



> I don't believe you since I think I am better informed, and
> since I think judging extension by |psi|^2 also makes much
> more sense than claiming a pointlikeness that is operationally
> meaningless since it relates to occult properties of physical
> objects apart from their state. Current or not, it is _wise_
> to consider quantum particles as being extended.

It only remains to me to quote Shakespeare:
"The fool doth think himself wise, but the wise man knows himself
to be a fool."

Squark

unread,
Feb 26, 2003, 5:52:44 PM2/26/03
to
Oz <aco...@btopenworld.com> wrote in message news:<b35u0g$gbo$1...@lfa222122.richmond.edu>...
> Squark <fii...@YAHOO.COM> writes

> >However, what we might expect
> >of a physical extended object is, for instance, the possibility the
> >measure it's state at every point separately.
>
> I'm not sure why you would expect that of a quantised wave.
> Measuring it's state inevitably destroys the state, that's a feature of
> QM.

In QFT, which exactly describes "quantized waves" (at least in the free
case), you can do it (ignoring subtleties, as always :-) ). This is
because operators at space-likes separations commute. And this is what
ensures locality of the whole theory. This, in fact, is the exact
reason I would expect that: locality.

> Hmmm. Yes, and no. You can do it statistically by preparing particles in
> the same state and measuring a lot of them.

Yes, but then you ain't measuring nothing: you prepared the particles in
this state, so you know the wavefunction already. Try doing the same
with an unknown quantum state!

> given state is often very easy because particles are easily divided into
> identical species (electron, photon, etc) so when bound deliver
> identical wavefunctions (to first order).

There's a famous theorem in quantum infomation theory saying that an
unknown quantum state cannot be duplicated. So things are not so
simple :-)

> Take the emission of a photon by an atom.

There's no "action at a distance here". The emission happens in a
single (usually ambiguous, of course) world-point.

> If you then proceed to entangled pairs and cite 'FTL information
> transmission' then you have to explain what physical laws are being
> broken to make this implausible.

There is no passage of information there. As is well known, the
whole beauty of EPR is that it doesn't allow you to transmit
information.

> Then you will point to the 'pointlike' electron (say). It's so pointlike
> we can diffract it and treat it perfectly happily as a wave.

Yes, and nevertheless it still fires a single detector. This
"pointlike" electron is not at all "pointlike" in the classical
sense. Well, what it's doing doesn't really make sense
classically! It's a sort of special "quantum pointlikeness" we're
talking about here, which still allows for the non-pointlike
wavefunction.

Charles Francis

unread,
Feb 26, 2003, 7:13:47 PM2/26/03
to sci-physic...@moderators.uu.net
In message <gik%9.18435$rq4.1...@bgtnsc05-news.ops.worldnet.att.net>,
Ahmet Gorgun <ago...@att.net> writes:

>"Charles Francis" <cha...@clef.demon.co.uk> wrote:

>> Ahmet Gorgun <ago...@att.net> wrote:

>> >The indivisible and indestructible Democretean primary elements were never
>> >observed.
>>
>> But they have been observed now, electrons, quarks fulfil the role quite
>> accurately.

>Are you saying that electron has absolutely no parts and you can
>prove that it has absolutely no parts? Otherwise the electron is not
>the absolutely indivisible elements that Democritus postulated.

Yes I am. The equation for a fundamental indivisible particle was
written down on purely theoretical grounds by Dirac in 1928. This
equation exhibits precisely the observed properties of the electron,
and indeed of the muon, the other leptons, the tau and the neutrinos,
and indeed of the quarks. In the case of gyromagnetic moment it has
the observed properties to at least 11 significant figures.

Regards

--
Charles Francis

--=_Turnpike_te3CmqR7XIX+47uI=
Content-Type: text/plain;charset=us-ascii;format=flowed


Regards

--
Charles Francis

--=_Turnpike_te3CmqR7XIX+47uI=--


Charles Francis

unread,
Feb 26, 2003, 7:13:25 PM2/26/03
to
In message <b3egv0$2sd$1...@lfa222122.richmond.edu>, Oz
<aco...@btopenworld.com> writes

>You have to explain why going through one (but not the other) whilst
>'unobserved' gives a diffraction pattern but going through one (when
>observed) doesn't. Remembering that we are talking about single particle
>diffraction here.
>

>I'm sure there are sufficiently devious explanations for this but Occam


>forces me to reject them in favour of the simplest:
>
>To diffract it must go through both.
>
>This is effortlessly easy with a wave, heck it even gives the correct
>pattern straight off.

Yes, but I should like to see how you change your view when you really
grok ket space, especially as we are working through the two slits
example now. The "wave" which goes through the slits is only a
probability amplitude, and with probabilities we only say things may
happen, we do not say all possibilities happen at once in some measure.

Regards

--
Charles Francis

Oz

unread,
Feb 26, 2003, 7:13:45 PM2/26/03
to
Ralph Hartley <har...@aic.nrl.navy.mil> writes:

>Oz wrote:

>> Squark <fii...@yahoo.com> writes:

>>>Oz <aco...@btopenworld.com> wrote:

>>>>How does this single particle go through both slits simultaneously?

>>>It doesn't. It goes through one of them, but it is undefined which.

>I preffer to say that it goes through one *plus* it goes through the other.
>"Plus", as a logical conective, is more of like "or" than like "and" (which
>is sort of like "times").

Hmmm.

I don't see how 'plus' can equal 'or', nor 'and' equal 'times'.
Unless you chose to define them thus (which is cheating).

I don't see how going through one slit 'plus' going through the other
slit isn't the same as 'going through both slits'.

>The whole idea of the Hilbert space business is to let you use aritmatic on
>things you would normally apply logic to. Logic (at least when applied in

>the obvious way) doesn't seem to work in the quantum world, but -
>miraculously - aritmetic *does*. The main diference is that numbers can be
>negative.

I absolutely agree with that, and have agreed all along.
Equally I don't consider that taking y=x^2 to actually consist of
infinitesimally small slices of size dx means I can't equally take it as
a continuum. No matter how convenient slicing it up into bits is,
mathematically.

>Quantum mechanics, as usually expressed, allows imaginary numbers as well,
>but that just makes the equations easier to write (Forier transforms and
>all that).

>> That's a most devious and unconvincing explanation.

>So? Did the universe promise to be straightforward and convincing?

Absolutely not. I was applying Occam.

John Baez

unread,
Feb 28, 2003, 4:28:07 PM2/28/03
to
In article <b37755$o32$1...@panther.uwo.ca>, Oz
<ozac...@despammed.com> wrote:

>Squark <fii...@yahoo.com> writes

>>One must not confuse the apparent "extended" nature of relativistic
>>quantum particles with the general notion of indeterminate position in

>>quantum mechanics. It is true that in relativistic quantum mechanics the


>>notion of position is subtle and problematic, but note the "extension"
>>is of the size of the Compton wavelength, not the characteristic
>>length of the |psi(x)^2| distribution.

>Hmmm. Is it? Where is the electron in an outer orbital of a heavy atom?
>Sure, you can probe for it with a high energy particle but this will
>just give you some 'found' position but does not mean the particle was
>'there' before it interacted with your probe.

Squark didn't say that a particle has a specific definite location
even when its wavefunction is all smeared out! He's no dope; he
knows quantum mechanics just fine. That's why he mentioned the

"general notion of indeterminate position in quantum mechanics".

Here he's be pointing out, correctly, that this quantum-mechanical
effect has nothing to do with a different effect that comes in only
when you take relativity into account as well.

Namely: if you try to measure the position of a particle very
accurately, you'll need to hit it with stuff of such high momentum
that you'll start creating particle-antiparticle pairs. Since all
particles of a given sort are identical, this makes it impossible
to decide which particle you were measuring the position of!

This other effect becomes important around a distance scale called
the Compton wavelength, which is

hbar/mc

for a particle of mass m, and about 4 x 10^{-13} meters for an
electron.

But even this effect has NOTHING to do with what working particle
physicists mean when they say the electron looks pointlike rather than
extended. SURE, quantum mechanics is true. SURE, relativity matters.
But they're completely used to that. If you tell them about
this stuff they'll say "Ho hum, Oz - we learned all that in school
when we were kids!" They've factored all this into their equations
already.

When they (and I) say the electron is pointlike, they mean that it
doesn't give any indication of being a bound state of other particles...
it doesn't act composite... it acts the way a *fundamental* particle
should when you bounce other particles off it...

... at least down to a certain distance scale - or up to a
certain energy scale, in other words!

But, this distance scale is a lot less than 10^{-13} meters.

To see that the proton is composite, you have to go down to a
distance scale of about 10^{-15} meters. At this distance
scale it acts like a big bag of quarks, virtual quarks and
gluons.

People have gone down quite a bit further and still not seen any
deviations from pointlike behavior on the part of electrons.

(I don't know the the current best figure. Does anyone know?)


Ralph E. Frost

unread,
Feb 28, 2003, 4:27:34 PM2/28/03
to

Charles Francis <cha...@clef.demon.co.uk> wrote in message
news:b3jl7r$qbb$1...@panther.uwo.ca...

> In message <gik%9.18435$rq4.1...@bgtnsc05-news.ops.worldnet.att.net>,
> Ahmet Gorgun <ago...@att.net> writes:
>
> >"Charles Francis" <cha...@clef.demon.co.uk> wrote:
>
> >> Ahmet Gorgun <ago...@att.net> wrote:
>
> >> >The indivisible and indestructible Democretean primary elements were
never
> >> >observed.
> >>
> >> But they have been observed now, electrons, quarks fulfil the role
quite
> >> accurately.
>
> >Are you saying that electron has absolutely no parts and you can
> >prove that it has absolutely no parts? Otherwise the electron is not
> >the absolutely indivisible elements that Democritus postulated.
>
> Yes I am. The equation for a fundamental indivisible particle was
> written down on purely theoretical grounds by Dirac in 1928. This
> equation exhibits precisely the observed properties of the electron,
> and indeed of the muon, the other leptons, the tau and the neutrinos,
> and indeed of the quarks. In the case of gyromagnetic moment it has
> the observed properties to at least 11 significant figures.

And are you saying this was done with no inputs, and it works perfectly for
neutrinos?


Arnold Neumaier

unread,
Mar 3, 2003, 4:07:45 PM3/3/03
to
John Baez wrote:
>
> But even this effect has NOTHING to do with what working particle
> physicists mean when they say the electron looks pointlike rather than
> extended. SURE, quantum mechanics is true. SURE, relativity matters.
> But they're completely used to that. If you tell them about
> this stuff they'll say "Ho hum, Oz - we learned all that in school
> when we were kids!" They've factored all this into their equations
> already.
>
> When they (and I) say the electron is pointlike, they mean that it
> doesn't give any indication of being a bound state of other particles...
> it doesn't act composite... it acts the way a *fundamental* particle
> should when you bounce other particles off it...
>
> ... at least down to a certain distance scale - or up to a
> certain energy scale, in other words!

Well, this is at least a clear definition of how the terminology is used.
So saying 'the electron is pointlike' is simply a convention for
saying 'the electron is indivisible' (at least down to a certain distance
scale), not meaning anything else? But if language provides two different
terms with different associated intuition, isn't it then better to
use these terms differently, especially when there are aspects of the
situation for which one term applies far more than the other?

I think the spin is a clear indicator of non-point behavior;
a point cannot spin.
At distances large compared to the extension of an extended body,
the only indicators of extendedness are the spin (detectable due to
angular momentum conservation) and electromagnetic radiation (which is
long range and gives away oscillation information), but both give no
information about the size of the extension. This holds for
macroscopic bodies as well as for microscopic bodies. Why should we
think these indicators become unreliable simply because the distance
is of the order of 10^{-13} or less, while it is reliable above that scale?

Wigner, in his 1939 classification of elementary particles defines one
as being (for practical purposes) indivisible (and not radiating),
irrespective of it being pointlike or not.
And he proves that the elementary particles in this sense
_all_ have an identical description - as an irreducible projective
representation of the Poincare group, with [in the absense of internal
symmetries] only two characteristic parameters, mass and spin/helicity.

So the fact that the electron or quarks are described in the standard
model by irreducible representations does not allow any inference at
all about their internal structure. We simply treat them as
structureless since this is adequate at the scale of present
experiments. But even if they are truly indivisible this does not
mean that they are pointlike. They are more like fuzzy clouds...

The situation is like in the characterization of [neutral]
stationary vacuum black holes by mass and angular momentum.
Real approximations to black holes will probably have internal
structure that is idealized away since it cannot be observed
without severe dangers for the observer.
And even in their idealized form they have a horizon,
and describing them as pointlike seems inadequate.
But, it seems to me, they are as indivisible as electrons.

Somewhere I read that Kerr holes are indeed related to the Dirac
equation. But I don't remember details.


Arnold Neumaier

Ahmet Gorgun

unread,
Mar 3, 2003, 4:42:46 PM3/3/03
to
"Charles Francis" <cha...@clef.demon.co.uk> wrote:

> ...The equation for a fundamental indivisible particle was


> written down on purely theoretical grounds by Dirac in 1928. This

> equation exhibits precisely the observed properties of the electron...

This argument does not prove that electron is an indivisible elementary
particle.

Here's an equation which explains precisely the motions of point planets:
d^2x/dt^2 + mx/r^3 = 0. It does not follow from this equation that planets
are fundamental elementary particles. The same is true for the electron.

Ahmet Gorgun

Charles Francis

unread,
Mar 4, 2003, 2:18:52 PM3/4/03
to sci-physic...@moderators.isc.org
In message <SDf8a.76979$zF6.5...@bgtnsc04-news.ops.worldnet.att.net>,
Ahmet Gorgun <ago...@att.net> writes

>"Charles Francis" <cha...@clef.demon.co.uk> wrote:
>
>> ...The equation for a fundamental indivisible particle was
>> written down on purely theoretical grounds by Dirac in 1928. This
>> equation exhibits precisely the observed properties of the electron...
>
>This argument does not prove that electron is an indivisible elementary
>particle.

This was not an argument. It was a statement of historical fact.

>Here's an equation which explains precisely the motions of point planets:
>d^2x/dt^2 + mx/r^3 = 0. It does not follow from this equation that planets
>are fundamental elementary particles.

This equation had nothing to do with fundamental particles. What Dirac
did was seek out the equation for a fundamental particle.


Regards

--
Charles Francis

Urs Schreiber

unread,
Mar 4, 2003, 2:24:51 PM3/4/03
to
Arnold Neumaier wrote:

> Somewhere I read that Kerr holes are indeed related to the Dirac
> equation.

Probably here: http://arxiv.org/abs/hep-th/0210103 .

--
Urs.Sc...@uni-essen.de

Charles Francis

unread,
Mar 4, 2003, 2:43:57 PM3/4/03
to

In message <v5r01ta...@corp.supernews.com>, Ralph E. Frost
<ref...@dcwi.com> writes

The inputs are the very general laws of quantum mechanics and special
relativity, and it works perfectly for neutrinos in so far as we are
able to measure properties of neutrinos.

Regards

--
Charles Francis

Oz

unread,
Mar 5, 2003, 2:54:47 PM3/5/03
to
Charles Francis <cha...@clef.demon.co.uk> writes

>Yes, but I should like to see how you change your view when you
>really grok ket space, especially as we are working through the two
>slits example now.

I'm trying. A few examples will probably help.

>The
>"wave" which goes through the slits is only a probability amplitude, and with
>probabilities we only say things may happen, we do not say all possibilities
>happen at once in some measure.

We shall see if it is incompatible with my current viewpoint.
I rather doubt that it will be.

The Bell inequality might do, but so far nobody has been able to
*explain* the details of difference to me. That is I am after the
difference in *mechanism* not a bunch of statistics.

Oz

unread,
Mar 5, 2003, 2:55:57 PM3/5/03
to
Squark <fii...@yahoo.com> writes:

>Oz <aco...@btopenworld.com> wrote in message

>news:<b35u0g$gbo$1...@lfa222122.richm ond.edu>...

>> Squark <fii...@YAHOO.COM> writes
>> >However, what we might expect
>> >of a physical extended object is, for instance, the possibility the
>> >measure it's state at every point separately.
>>
>> I'm not sure why you would expect that of a quantised wave.
>> Measuring it's state inevitably destroys the state, that's a feature of
>> QM.

>In QFT, which exactly describes "quantized waves" (at least in the free
>case), you can do it (ignoring subtleties, as always :-) ). This is
>because operators at space-likes separations commute. And this is what
>ensures locality of the whole theory. This, in fact, is the exact
>reason I would expect that: locality.

I presume that at some point francis will bring this up in the ket
thread. I have to say that the high jargon content means I don't
actually understand what you are saying.

>> Hmmm. Yes, and no. You can do it statistically by preparing particles in
>> the same state and measuring a lot of them.

>Yes, but then you ain't measuring nothing: you prepared the particles in
>this state, so you know the wavefunction already. Try doing the same
>with an unknown quantum state!

I already explained that.

>> given state is often very easy because particles are easily divided into
>> identical species (electron, photon, etc) so when bound deliver
>> identical wavefunctions (to first order).
>
>There's a famous theorem in quantum infomation theory saying that an
>unknown quantum state cannot be duplicated. So things are not so
>simple :-)

Hah! Indeed. See below.

>> Take the emission of a photon by an atom.
>
>There's no "action at a distance here". The emission happens in a
>single (usually ambiguous, of course) world-point.

But it's an unknown world-point, in an unknown direction.

It's a spherical wavefront until you measure the atom recoil, then it's
got a higher accuracy of momentum knowledge. The difference between the
two reflect your knowledge of the photon, both will give (statistically)
the same result. This has been discussed before.

>> Then you will point to the 'pointlike' electron (say). It's so pointlike
>> we can diffract it and treat it perfectly happily as a wave.
>
>Yes, and nevertheless it still fires a single detector.

I already pointed out that 'detection' is a complex QM process designed
to (in this case) that one and only one detector per particle fires.
It's the feature of the QM wave that you either detect (some property)
of the wave or you don't detect it at all. That nobody ever detected
half an electron is unremarkable.

>This
>"pointlike" electron is not at all "pointlike" in the classical
>sense. Well, what it's doing doesn't really make sense
>classically!

>It's a sort of special "quantum pointlikeness" we're
>talking about here, which still allows for the non-pointlike
>wavefunction.

It's the special 'quantum waveness' we are talking about here, which
allows for a quantised wave.

The difference being that a wave can go through both slits, whilst a
particle can't. Unless you allow it to exist as a probability wave that
looks just like the quantum wave, that way you can have half a particle
going through each slit (probably even a whole one through each slit).
A convenient mathematical fiction.

John Baez

unread,
Mar 5, 2003, 8:15:14 PM3/5/03
to
In article <3e5feaf0$0$13932$3b21...@news.univie.ac.at>,
Arnold Neumaier <Arnold....@univie.ac.at> wrote:

>John Baez wrote:

>> When they (and I) say the electron is pointlike, they mean that it
>> doesn't give any indication of being a bound state of other particles...
>> it doesn't act composite... it acts the way a *fundamental* particle
>> should when you bounce other particles off it...
>>
>> ... at least down to a certain distance scale - or up to a
>> certain energy scale, in other words!

>Well, this is at least a clear definition of how the terminology is used.

Great.

>So saying 'the electron is pointlike' is simply a convention for
>saying 'the electron is indivisible' (at least down to a certain distance
>scale), not meaning anything else?

Basically yes - a more precise answer is that when you measure
what happens when you throw electron at each other, the answer
matches that given by some quantum field theory in which the electron
is a fundamental field in the Lagrangian - in particular, the Standard
Model.

>But if language provides two different
>terms with different associated intuition, isn't it then better to
>use these terms differently, especially when there are aspects of the
>situation for which one term applies far more than the other?

In theory yes, but it's not my goal to reform how professional
particle physicists talk. I am happy just to understand what they
are saying, and to have them understand me.

In theory one can often gain precision by using a word in some nonstandard
ways. But, if most of ones target audience doesn't use it that way,
one winds up confusing more people than one helps. Of course this is
not a problem for "internal communications" - e.g. talking to oneself,
or within a small group of friends.


alejandro.rivero

unread,
Mar 6, 2003, 4:39:29 PM3/6/03
to
"Ahmet Gorgun" <ago...@att.net> wrote in message
news:<SDf8a.76979$zF6.5...@bgtnsc04-news.ops.worldnet.att.net>...


> Here's an equation which explains precisely the motions of point planets:
> d^2x/dt^2 + mx/r^3 = 0. It does not follow from this equation that planets
> are fundamental elementary particles. The same is true for the electron.

Spin is the tricky part. If electron were a composite particle, then
it should be possible to see an spin 3/2 state or so. Dirac equation
is about an spin 1/2 particle, thus one can said that this equation
assumes the particle is elementary. Or course, you can also say that it
just represents the lower spin state of a bigger particle.

Arnold Neumaier

unread,
Mar 7, 2003, 4:01:10 PM3/7/03
to
Squark wrote:
>
> Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
> news:<3e50f609$0$14964$3b21...@news.univie.ac.at>...
>
> > For example, discussing the localization of relativistic particles
> > in space-time,
> > D. Marolf and C. Rovelli, Relativistic quantum measurement,
> > Phys.Rev. D66 (2002) 023510, gr-qc/0203056,
> > say on p.7 (top right, of the archived version):
> > ... the quantum particle has an intrinsic Compton ``extension''...

>
> One must not confuse the apparent "extended" nature of relativistic
> quantum particles with the general notion of indeterminate position in
> quantum mechanics.

Indeterminate position only says you cannot locate a particle too accurately;
but of course one can locate it highly reliable within some region.
In fact, just within the region given by its extension. No different from
the location of the Moon, which one cannot give more precise than to the
order of its radius.

> It is true that in relativistic quantum mechanics the
> notion of position is subtle and problematic, but note the "extension"
> is of the size of the Compton wavelength, not the characteristic
> length of the |psi(x)^2| distribution.

The two things are on the same footing, as explained in detail ,e.g., by
L.L. Foldy and S.A. Wouthuysen, Phys. Rev. 78 (1950), 29-36 (the paper
with their transformation of the Dirac equation). In their 21 line
abstract they spend 4 lines on remarking,
``Some light is cast on the question of why a Dirac electron
shows some properties characteristic of a particle of finite
extension by an examination of the relationship between the new
and the conventional position operator.''
In the main text they repeatedly use without shame geometric language.
For example, on p.32 top left, they write:
``Psi' at a given point is constituted from contributions depending
on Psi over a neighborhood of dimensions of the order of a Compton
wave-length of the particle about the point. Thus a wave function
which in the old representation corresponed to a state in which
the particle was definitely located at one point, passes over in
the new representation into a wave function which apparently
corresponds to the particle being spread out over a finite region.''
(Here Psi = relativistic Dirac wave function, Psi' = unitarily transformed
wave function with correct - Pauli - nonrelativistic limit.)

'Extension' - 'being spread out' - 'being located': these are always used
in the sense of the region where |psi(x)|^2 is significant; and
'definitely' refers to the special situation where |psi(x)|^2 is
concentrated at a single point. The Compton wavelength is not the
generic size of the electron but simply the *additional* size of the blurring
due to relativistic effects, namely the minimal size of an optimally
localized particle. But unless measured, particles are usually much
more spread out = extended. For example, in a hydrogen atom, it is the
electron size, not the nucleus, that defines the size of the atom!

Field theory gives more ground for the extended view. In QED, there
are no particles but fields, and the electron field Psi(x) has the
physical meaning that omega(|Psi(x)|^2) is the charge density of an
electron in a state omega, the component j_0 of the conserved
4-current j=omega(Psi_bar gamma Psi). (If there are negative energy
contributions, one has to subtract these.) The current j is the _only_
thing a classical observer (i.e., a macroscopic object for which
a mean field description is adequate) can detect about an electron field,
since this is what couples (in a semiclassical mean field approximation)
to an electromagnetic field. Lots of calculations for real experiments
and real equipment are done in this way, showing that j and hence the
charge density j_0=omega(|Psi(x)|^2) is something tangible.

Now there is at least one case in which quantum field theory is
mathematically well understood, namely for free fields. Thus look
at a pure single particle state in a free spin 1/2 theory, universally
agreed as the right description of a single electron. It defines the
state omega(f) =<psi|f|psi>, where psi is the wave function of the particle.
Lo and behold, it turns out that omega(|Psi(x)|^2) is just the charge
density - and not a probability!!! (For relativistic spin 0 particles
one does not even have a meaningful probability concept.) The probability
interpretation of the Dirac wave function is simply a historical leftover...

Now take any nonzero solution of the free Dirac equation you like
(any of these is a valid wave function) - you'll see that the charge
density always has an extended support, with exception of at most one
moment in time (for special waves only) - this could be the moment
someone has measured its position. At all other times, the particle
is extended, sometimes over regions much bigger than the Compton length.


Having given good physical arguments for, and quoted five different
authors - several of them highly qualified to talk about the issue -
supporting the extendedness of elementary particles, I'd like to see
the facts (or authorities) on which you base your view that particles
are pointlike in some geometric sense different from indivisibility!


Arnold Neumaier

Arnold Neumaier

unread,
Mar 7, 2003, 4:03:03 PM3/7/03
to

I wrote my last mail too quickly and was hence a little sloppy;
sorry!


Arnold Neumaier wrote:
>
> localized particle. But unless measured, particles are usually much
> more spread out = extended. For example, in a hydrogen atom, it is the
> electron size, not the nucleus, that defines the size of the atom!

I meant; unless the position is measured.

> Now there is at least one case in which quantum field theory is
> mathematically well understood, namely for free fields. Thus look
> at a pure single particle state in a free spin 1/2 theory, universally
> agreed as the right description of a single electron. It defines the
> state omega(f) =<psi|f|psi>, where psi is the wave function of the particle.
> Lo and behold, it turns out that omega(|Psi(x)|^2) is just the charge
> density

I meant: it turns out that omega(|Psi(x)|^2) is just the |psi(x)|^2;
hence the squared amplitude is just the charge - and not a probability!

Arnold Neumaier

unread,
Mar 7, 2003, 4:03:31 PM3/7/03
to
Oz wrote:
>
> I'm not sure why you would expect that of a quantised wave.
> Measuring it's state inevitably destroys the state, that's a feature of
> QM. Not least it localises the particle, how else can you measure a
> particle at a point?

There are nowadays many measurements that do not destroy a state.
In particular, nondemolition measurements do not even change the state.
Quantum measurement theory and practice has advanced quite a lot since
the time of von Neumann.

Arnold Neumaier

Ahmet Gorgun

unread,
Mar 7, 2003, 4:12:37 PM3/7/03
to
"Charles Francis" wrote:

> This was not an argument. It was a statement of historical fact.

I must have misunderstood your post. I thought that you were saying:


1. Write down an equation which describes the motions of a material particle
without describing its physical constitution.

2. Test the equation with an experiment.

3. If the equation saves the observations conclude that the assumed particle
is fundamental, elementary and indivisible.

Or, in symbols:

A = a point particle (structure undefined, diameter d = 0)

B(a,b,c,e,f...) = equation

C = fundamental particle (finite diameter, d = not zero, one indivisible
entity)

D = Experiment.

Then,

1. Given: A, B;

2. Test the equation with an experiment

B - D = 0 --> good residuals, equation saves the experiment.

3. Conclusion: A = C.

I say that B - D = 0 does not prove that A = C.

Please correct this interpretation of your statement so that I understand
what you are saying?

Ahmet Gorgun

Arnold Neumaier

unread,
Mar 7, 2003, 4:21:11 PM3/7/03
to
[The following reply from end of February apparently didn't
make it to the net]

Squark wrote:
>
> Arnold Neumaier <Arnold....@univie.ac.at> wrote in message news:<3e56a7e5$0$14448$3b21...@news.univie.ac.at>...


> > The particle _is_ the wave function - what else could it be? It has
> > no properties apart from that represented in the wave function (unless
> > you assume hidden variables); so one has every right to identify the
> > two. This is possible since both the particle and the wave function
> > are conceptual abstractions. The 'reality' is indiscernible...
>
> Firstly, one cannot identify the two as in a multi-particle system
> individual particles have no wavefunctions.

Of course they have; else one couldn't do any quantum physics
without considering the wave function of the universe.
The state of a subsystem is commonly described by the trace
of the the state of a bigger system with respect to all
variables not belonging to the system. This gives a density matrix
which, however, is often to a good approximation of rank 1 and
hence defines the wave function of the subsystem. (If not, one
has to treat the state as a mixture of several wave functions.)

Sometimes, other procedures are used, too. For example, in a hydrogen atom,
you can separate the center of mass motion and end up with a wave function
of the electron (mixed with a little nucleus, reflected in the reduced mass).
Now everyone agrees that the hydrogen atom is an extended object.
Its radius is of the order of the distance from the nucleus at which
|psi(x)|^2 is still large. If not the |psi(x)|^2 of the electron, what then
could determine the atom's size?

> > > > Braginsky and Khalili (Quantum measurement, Cambridge Univ. Press,
> > > > Cambridge 1992) on _real_ quantum measurements close to actual
> > > > (optical) experiments, and they talk for example (p.3 bottom) about

> > This is remarkable. In the interference process (e.g. in the


> > two-slit experiment of Fig. 1.1), [standard picture] the photon must
> > have been influenced by the locations of both slits, since the
> > interference pattern depends on the distance between them. This means
> > that the photon must have occupied a volume larger than the slit
> > separation. On the other hand, when it fell on the photographic plate,
> > the photon must have been localized into the tiny volume of the silver
> > embryo. Later the terms ''collapse of the wave function'' and
> > ''reduction of the wave packet'' were used to describe such
> > localization.<<
>
> I don't think this introductionary exposure of quantum mechanical
> effects contains any attempt to accurately reflect on such issues as
> whether the quantum particle is point-like or not.

Other people use similar language in the middle of technical discussions.
For example, the standard quantum mechanics textbook by Messiah says
(at least in the German version, from which I translate; the original
is French, which I cannot read) in 20.5.8:
``In the nonrelativistic limit, the Dirac electron is described
not by a point charge but ... extension.''
(The German version of Bjorken and drell contains a similar remark after
(4.18), but the English version is formulated differently. So at least the
translators thought the electron to be extended.)

If it is so suggestive that people use it (by slip of the mouth, you'd have
to assume), then because it is the geometrically natural way of thinking
about what the formulas mean.

> Again, I claim two things must be distinguished: the point-like quantum
> particle, which is a point without location

why a point???

> - much like a point in a non-commutative space, this as a philosophical
> notion is quite different from the usual point -

Please provide details; I haven't seen _anywhere_ a definition of what
a point in a non-commutative space is. Since a non-commutative space
is a purely mathematical concept, there should be a precise definition
of a point, without the usual phiosophical difficulties associated with
reality. Fuzzy definitions in mathematics are meaningless.

> and the extended wavefunction.
> Therefore, the notion "point-like" applies here in a sense different
> from the usual, classical, sense.

in _which_ different sense? You haven't made it precise.

> Nevertheless we would hardly
> benefit from abandoning the notion, though it might make our
> arguement ill posed: we don't agree on the definitions.

I haven't seen you give a definition; so how can I agree?

> > I don't believe you since I think I am better informed, and
> > since I think judging extension by |psi|^2 also makes much
> > more sense than claiming a pointlikeness that is operationally
> > meaningless since it relates to occult properties of physical
> > objects apart from their state. Current or not, it is _wise_
> > to consider quantum particles as being extended.
>
> It only remains to me to quote Shakespeare:
> "The fool doth think himself wise, but the wise man knows himself
> to be a fool."

I know I am a fool ;-) scoring close to 200 points on the crackpot index
http://math.ucr.edu/home/baez/crackpot.html

Arnold Neumaier

Squark

unread,
Mar 7, 2003, 4:28:15 PM3/7/03
to
Oz <aco...@btopenworld.com> wrote in message news:<b45kod$dvb$1...@panther.uwo.ca>...

> Squark <fii...@yahoo.com> writes:
> >Yes, but then you ain't measuring nothing: you prepared the particles in
> >this state, so you know the wavefunction already. Try doing the same
> >with an unknown quantum state!
>
> I already explained that.

I'm not quite sure I know what you're talking about.



> >There's no "action at a distance here". The emission happens in a
> >single (usually ambiguous, of course) world-point.
>
> But it's an unknown world-point, in an unknown direction.

That's what I meant by ambiguous. So what?

> >Yes, and nevertheless it still fires a single detector.
>
> I already pointed out that 'detection' is a complex QM process designed
> to (in this case) that one and only one detector per particle fires.
> It's the feature of the QM wave that you either detect (some property)
> of the wave or you don't detect it at all. That nobody ever detected
> half an electron is unremarkable.

It is remarkable. When you detect the electron at a given point, you
cannot detect it at another even though its wavefunction was non-zero
there. This means the "wave" supposedly disappeared there once you
performed the measurement. This is "action at a distance" and it also
has problems when considering different frames of reference in special
relativity. That's why the wave interpretation is physically unsound
(again, it's still a matter of interpretation, so you are free to
choose your side, but mind the facts). That's also the problem
physicists had on the turn of the 19/20 centuries. That the electron
behives neither as a classical particle nor as a classical wave.
What I'm saying is that it's a "quantum particle" i.e. something that
has a point-like location, but only in a freaky "quantum" sense. Just
like a "quantum group" is both like and unlike a real group.



> The difference being that a wave can go through both slits, whilst a
> particle can't.

It doesn't go through both slits, it goes through either one, but it
is undetermined which :-)

Arnold Neumaier

unread,
Mar 7, 2003, 4:40:19 PM3/7/03
to
John Baez wrote:
>
> In article <3e5feaf0$0$13932$3b21...@news.univie.ac.at>,
> Arnold Neumaier <Arnold....@univie.ac.at> wrote:
>
> >So saying 'the electron is pointlike' is simply a convention for
> >saying 'the electron is indivisible' (at least down to a certain distance
> >scale), not meaning anything else?
>
> Basically yes - a more precise answer is that when you measure
> what happens when you throw electron at each other, the answer
> matches that given by some quantum field theory in which the electron
> is a fundamental field in the Lagrangian - in particular, the Standard
> Model.
>
> >But if language provides two different
> >terms with different associated intuition, isn't it then better to
> >use these terms differently, especially when there are aspects of the
> >situation for which one term applies far more than the other?
>
> In theory yes, but it's not my goal to reform how professional
> particle physicists talk. I am happy just to understand what they
> are saying, and to have them understand me.

So it is consitent to call an electron pointlike _and_ extended
in space. Strange terminology...

It seems to me that most paradoxes in quantum mechanics
are based on imprecise language inviting conflicting conclusions,
and cleaning up the language helps avoiding being misled by intuition.

After the paradoxes of set theory were discovered, mathematicians
worked hard to rectify the situation and after understanding how
to resolve the difficulties they reformed the way they were talking
about sets. Not to their disatvantage.

In physics, people don't seem to care. Maybe physics derive an
advantage from the fogginess of current quantum concepts since
it makes the subject mysterious and hence attractive for young
people? But it also attracts fancy New Age misinterpretations
like many worlds, which seems a dubious gain.

Arnold Neumaier

Oz

unread,
Mar 10, 2003, 2:39:11 AM3/10/03
to sci-physic...@moderators.isc.org

Squark <fii...@yahoo.com> writes

>It is remarkable. When you detect the electron at a given point, you
>cannot detect it at another even though its wavefunction was non-zero
>there.

It was non-zero there. It was non-zero there before it was detected.
It became zero during the process that resulted in a detection.
Remember it's a great big wave.

>This means the "wave" supposedly disappeared there once you
>performed the measurement.

Of course. The moving photon is now no more, instead we have an exited
atom in an orbital somewhere on the emulsion.

>This is "action at a distance"

Hardly. It's a great big wave, remember. The wavefunction time-evolves
when it interacts with the billions of potentially absorbing orbitals in
the emulsion.

>and it also
>has problems when considering different frames of reference in special
>relativity.

Tough. Doubtless entangled particles give even more of a problem.
There it can be over kilometers.

>That's why the wave interpretation is physically unsound
>(again, it's still a matter of interpretation, so you are free to
> choose your side, but mind the facts).