Present unknowns
Chuck and Barbara Burger
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
> 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
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
"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
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
"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
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
Kevin A. Scaldeferri
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
>>
>> >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
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
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
>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
> 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
>
> Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
> news:<3e43b60b$0$9620$3b21...@news.univie.ac.at>...
>
> > In this sense, an electron can well be regarded as an
> > extended indivisible particle (with an extension given by the region
> > where |psi|^2 is significant).
>
> This is definitely _wrong_, according to current wisdom, and is a
> not uncommon misconception. The wavefunction reflects the
> indeterminancy of the particle's location, not it's spatial extension.
It is not just my ideosyncracy, but gives a quite useful and intuitive
geometric picture of microphysics, especially if one wants to
understand the meaning of everything in a relativistic context.
For example, discussing the localization of relativistic particles
in space-time,
D. Marolf and C. Rovelli, Relativistic quantum measurement,
Phys.Rev. D66 (2002) 023510, gr-qc/0203056,
say on p.7 (top right, of the archived version):
... the quantum particle has an intrinsic Compton ``extension''...
Arnold Neumaier
news.verizon.net
news:v43tf2h...@corp.supernews.com...
>
> Ahmet Gorgun <ago...@att.net> wrote in message
> news:gik%9.18435$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
> 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
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
> 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
>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
> 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
> 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
>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
>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
> 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
> 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
>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
[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
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
>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
>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
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
>>>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
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
> 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
> 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
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
<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
>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
<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
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
>
> 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
> ...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
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
> Somewhere I read that Kerr holes are indeed related to the Dirac
> equation.
Probably here: http://arxiv.org/abs/hep-th/0210103 .
Charles Francis
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
>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
>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
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
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
>
> > 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
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
>
> 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
> 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
> 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
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
> 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
>
> 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
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).
Minding the facts is about all I can do, being quite unable to cope with
the maths, as you know.
>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.
I am not talking about a classical wave.
I am talking about a quantum 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.
Ah, so your pointlike quantum particle behaves as a wave.
My wave behaves as a quantised wave.
>> 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 :-)
This doesn't mesh well with single photon diffraction patterns. If it's
a pointlike particle then it goes through one or the other, even if you
don't know which one. I would be happy if your pointlike particle went
through both, but then you have a problem considering it indivisible.
Charles Francis
Ahmet Gorgun <ago...@att.net> writes
>Please correct this interpretation of your statement so that I understand
>what you are saying?
Ok
>I thought that you were saying:
>1. Write down an equation which describes the motions of a material particle
>without describing its physical constitution.
No. Dirac wrote down an equation for the motions of a fundamental
particle
>2. Test the equation with an experiment.
>3. If the equation saves the observations conclude that the assumed particle
>is fundamental, elementary and indivisible.
No. Conclude that the assumed fundamental particle exists, and that the
observed particle is an instance of it.
Regards
--
Charles Francis
Charles Francis
writes:
>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.
The Bell inequality is quite difficult to explain in language, and the
math requires quite a reasonable level of competence in dealing with
spin and multiparticle states. If I were to try and sum it up, I think I
would say that the difference is that in the quantum domain there is an
absence of mechanism. For example when we deal with entangled states, it
is not because the particles are physically entangled, but because the
physical mechanisms do not exist which are required to discuss their
separation. Only when the particles interact with other matter does it
become possible to say where they are, and only when you can say where
they are can you describe them as apart.
Regards
--
Charles Francis
Squark
> 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?
> > 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.)
A density matrix and a wavefunction are two different things.
> 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).
No, it's just that the energy eigenstates factorize that way.
> 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?
Imagine a classical analogy: the solar system. The distance between the
planets and the sun determines the size, but it has nothing to do with
the size of the planets themselves.
> 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.)
There's again the question of what they meant here. It is at least not
certain they were referring to the "size" of the |psi^2| distribution.
> 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.
You think it's natural. I think the non-commutative geometry view is
natural.
> > Again, I claim two things must be distinguished: the point-like quantum
> > particle, which is a point without location
>
> why a point???
Because
1) As it has a single "position-type" degree of freedom
(it's coordinates).
2) The physics thus described are local, in an appropriate sense.
> 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.
The non-commutative space is a mathemtical notion, while the "point" is
a philosophical way of thought which, in my view, provides the optimal
view on quantum mechanics. Just as we can pretend non-commutative
spaces are usual ones, here we pretend the non-commutative phase space
is a usual one. As in the former case there is no real space having
the non-commutative algebra as a function algebra, and nevertheless
all sorts of usual geometric constructions "work", in the later case
the phase-space "doesn't exist" and yet answers on meaningful physical
questions can be retrieved. Now, an electron is a point-like particle
in approximately the same way a projective module over a
non-commutative algebra is a vector bundle: it isn't in the usual
sense, but it is in some weird related sense.
Jeffery
Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
news:<3e68c286$0$14706$3b21...@news.univie.ac.at>...
[unnecessary quoted text deleted by moderator]
> 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.
There really is no fogginess. I don't think the language is imprecise.
What is extended in space is the wavefunction which can identified
with the probability of detecting an electron which is traditionally
viewed as a point particle. It's only pop science writers who "make
the subject mysterious".
Jeffery Winkler
Oz
I would like to consider this.
I doubt this would work for detecting which slit a particle went
through. So it must only happen when it 'doesn't matter'.
Could you give some examples?
John Baez
Arnold Neumaier <Arnold....@univie.ac.at> wrote:
>John Baez wrote:
>> 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 consistent to call an electron pointlike _and_ extended
>in space. Strange terminology...
Actually particle physicists say the electron is pointlike, while
its wavefunction is extended in space.
Here's why: when they say the electron is pointlike, they mean
that the electron wavefunction can be written as a function on R^3,
the elements of which are *points* in everyday geometrical space.
Contrast this with a string, say, whose wavefunction is a function
on Maps(S^1,R^3), the elements of which are *loops* in everyday
geometrical space. A string is not considered pointlike. Nor is
a proton, whose wavefunction is also not a function on R^3.
You may not like this terminology, but it's fairly unambiguous,
and it's good to know if you want to talk to particle physicists.
>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.
Sure: there are no paradoxes in quantum mechanics other than those
brought on by sloppy thinking... and a key cause of sloppy thinking
is sloppy talk!
But working particle physicists are not the ones foaming at the
mouth over "quantum paradoxes". They may not be good philosophers,
but they know enough to stay out of trouble! The people who get
in trouble are usually people who philosophize a lot and don't do many
calculations or experiments. People like this need to talk extremely
carefully to stay out of trouble... and most of them don't succeed.
>In physics, people don't seem to care.
Sure we care. I care! But the people who care the most either focus
on calculations and experiments, *or* focus on talking in *extremely*
careful ways... and these ways of talking don't do well in noisy
environments like newsgroups or stores that sell books on pop physics.
To talk carefully, you have to spend a lot of time defining your terms
precisely. Doing this in public is like seeing how many pennies you
can balance in a stack when you've got 50 drunks dancing a polka in
the same room! Talking about the interpretations of quantum mechanics
seems to positively *attract* the conceptually disorganized! So,
people who want to think carefully prefer to fade into the background.
>Maybe physics derives an
>advantage from the fogginess of current quantum concepts since
>it makes the subject mysterious and hence attractive for young
>people?
Maybe. When I was a kid I thought the "Tao of Physics" was great;
it got me interested in physics... and then I learned physics and
realized this book was baloney.
>But it also attracts fancy New Age misinterpretations
>like many worlds, which seems a dubious gain.
If you put 50 copies of Roland Omnes' "The Interpretation of Quantum
Mechanics" and 50 copies of Deepak Chopra's "Quantum Healing" in your
local Borders and Noble bookstore, which do you think is going to sell
faster? I know the answer, because I've seen which one these bookstores
stock! But if you're serious, you just screen out all that noise and
focus on the good stuff.
(By the way, there's nothing inherently "New Age" about the many worlds
interpretation, though it can be pushed in that direction, and personally
I prefer to ignore the "many worlds" stuff and think about Everett's
relative state interpretation, of which "many worlds" arose as a kind
of popularization - as can be seen from reading Everett's thesis and
the other essays in "The Many Worlds Interpretation of Quantum Mechanics",
edited by DeWitt and Graham.)
Squark
Oz <aco...@btopenworld.com> wrote in message news:<xQ7DcZAO...@btopenworld.com>...
> 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.
> >This means the "wave" supposedly disappeared there once you
> >performed the measurement.
>
> 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.
In an ideal measurement, this evolution is instantaneous and over all
space.
> >and it also
> >has problems when considering different frames of reference in special
> >relativity.
>
> Tough.
Tough, but the non-locality is the reason. The instantaneous evolution
is thus everywhere simultaneous. But in which frame?
> I am not talking about a classical wave.
> I am talking about a quantum wave.
I don't quite see what you mean by a "quantum wave". The quantization
of wave dynamics would yield a QFT. Is that what you mean?
> >It doesn't go through both slits, it goes through either one, but it
> >is undetermined which :-)
>
> This doesn't mesh well with single photon diffraction patterns. If it's
> a pointlike particle then it goes through one or the other, even if you
> don't know which one.
If it's a classical pointlike particle.
uv
>There really is no fogginess. I don't think the language is imprecise.
>What is extended in space is the wavefunction which can identified
>with the probability of detecting an electron which is traditionally
>viewed as a point particle. It's only pop science writers who "make
>the subject mysterious".
but John Baez just said in <b467f2$m10$1...@glue.ucr.edu> on what I take to
be essentially a similar matter
>>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.
Now in http://www.utm.edu/research/iep/w/wittgens.htm we find
"Similarities between Wittgenstein's work and that of Derrida are now
generating interest among continental philosophers, and Wittgenstein may
yet prove to be a driving force behind the emerging post-analytic school
of philosophy" and Kripke certainly owes a lot to Wittgenstein IMHO. We
can ignore Derrida if we choose (some would say, at our peril) and
virtually every high energy physics scientist probably does, but we
can't ignore Kripke unless we just want to forget formal logic. I
suppose this is bringing us several steps away from mathematics and of
course to some, even Bayes is a lost cause.
I would have thought that Baez is right for many purposes, depends how
much we want to think it through, but we end up putting the blind eye to
the telescope if we take it to the point where we totally ignore, for
example, that simple quantum problems like the fact that Schrodinger Cat
paradox are only explained physically, AFAIK, by something at least as
complicated as a MWI or otherwise (probably largely) useless
many-universes. To do that is practically begging for a latterday
Derrida to fill the gap.
- uv
Views on physics, many worlds and other topics
Last updated 19th Feb 2003
http://www1.freewebs.com/uvuv/musings.html
Oz
>Imagine a classical analogy: the solar system. The distance between the
>planets and the sun determines the size, but it has nothing to do with
>the size of the planets themselves.
That entirely depends on how big you are.
If you are some 1B miles across then the orbital distance of the planets
may be highly relevant to your chances of a collision.
John Baez
Oz <ozac...@despammed.com> wrote:
>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.
Oh, so you believe in collapse as a physical process? Sigh...
Jeffery
Charles Francis <cha...@clef.demon.co.uk> wrote in message news:<zbTVnrDe...@clef.demon.co.uk>...
We use inelastic scattering experiments to determine if a particle is fundamental.
Jeffery
Squark
> Squark <fii...@yahoo.com> writes
> >Imagine a classical analogy: the solar system. The distance between the
> >planets and the sun determines the size, but it has nothing to do with
> >the size of the planets themselves.
> That entirely depends on how big you are.
>
> If you are some 1B miles across then the orbital distance of the planets
> may be highly relevant to your chances of a collision.
This is irrelevant to the point.
The original point was that the size of the atom could only come
from the size of the electron, and I contradicted this by
demonstrating a system which doesn't work that way (which is
quite trivial, the "size" of a complex object always depends on
the distances between the constituents). I.e., one can have a
system of several point-like objects having finite size.
Charles Francis
writes:
>>Squark <fii...@yahoo.com> writes
I don't know Oz, there I am in the other thread trying to teach you that
collapse is only a change in the calculation of a probability when a
condition becomes known, so that you will be able to walk safely through
the newsgroup without getting blasted by wizardly fireballs, and here
you go, blundering about as usual, and all he can do is sigh. I think he
didn't toast you because he wants to deprive me of my breakfast.
Regards
--
Charles Francis
Urs Schreiber
fii...@yahoo.com (Squark) wrote in message news:<939044f.03031...@posting.google.com>...
> Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
> news:<3e67386d$0$13160$3b21...@news.univie.ac.at>...:
[...]
> > 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.
>
> The non-commutative space is a mathemtical notion, while the "point" is
> a philosophical way of thought [...]
Why don't you mention maximal ideals?
A commutative manifold M may be identified with the set of maximal
ideals of the algebra of functions over it. Any function that vanishes
precisely on a given subset S of M generates the ideal of functions
that vanish at least on that subset. The smaller S the bigger the
ideal. The extreme case where S contains only a single point
corresponds to maximal ideals of the function algebra.
Once the notion of a point has thus been identified with an algebraic
notion it carries over to the the non-commutative setting. Therefore
it is usually said that a point in a noncommutative space is a maximal
ideal of the respective noncommutative algebra. Of course this algebra
need not have any non-trivial ideals at all, in which case the
geometry it describes is "pointless".
I don't understand, though, how this should be relvant to your
discussion, since the configuration space of the electron is
commutative (usually...).
Arnold Neumaier
Squark wrote:
>
> > Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
> >news:<3e56a7e5$0$14448$3b21...@news.univie.ac.at>...
> > 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.)
>
> A density matrix and a wavefunction are two different things.
A rank 1 density matrix is the same as a wave function, more precisely,
it is isomorphic to the ray determined by the latter. And in much of
quantum physics we have really density matrices because real systems
are dissipative, but we treat them for convenience as rank 1, i.e.,
as 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).
>
> No, it's just that the energy eigenstates factorize that way.
This is one way to look at it, but my way of looking at it is equally adequate,
and has the advantage to generalize to molecules with more than one nucleus,
where there is no exact factorization, and the Born-Oppenheimer approximation
is employed just to get the (multiparticle) wave function of the electrons.
This is equivalent to the projection formalism I alluded to in my previous mail,
including the rank 1 approxiamtion needed to get rid of the density matrix.
If the nuclei were infinitely heavy, they would disappear from the problem,
and projection would result exactly in the electron wave function.
With a finite mass nuclei, the projected electron wave function is
slightly different, but agrees with the result of the separation of variables
to an accuracy of around the (tiny) quotient electron mass/nucleus mass.
In case of several electrons, the wave function is multidimensional and no
longer
conveys direct size information, but one can still compute the charge density of
the electron field, which is in fact what all quantum chemistry calculations do.
And this charge density defines the size of the system.
> > 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?
>
> Imagine a classical analogy: the solar system. The distance between the
> planets and the sun determines the size, but it has nothing to do with
> the size of the planets themselves.
But this is different - planets don't show diffraction phenomena, so their size
is rightly small; whereas by assigning an electron pointsize causes paradoxes in
visualization. Assingning an electron a cloud stucture defined by the charge
density doesn't and hence deserves to be preferred.
> > 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.''
>
> There's again the question of what they meant here. It is at least not
> certain they were referring to the "size" of the |psi^2| distribution.
But it is certain that they meant _something_ and that they _explicitly_ say
that the electron is _not_ a point charge. Once you think relativistically,
this point of view is essentially forced upon use; only in the nonrelativistic
case one may avoid it (although i think one shouldn't).
In Foldy's work which I quoted elsewhere, it _is_ clear from the context that
they deduce the lack of pointlikeness from the "size" of the |psi^2|
distribution.
> I think the non-commutative geometry view is natural. [...]
> The non-commutative space is a mathematical notion, while the "point" is
> a philosophical way of thought which, in my view, provides the optimal
> view on quantum mechanics.
A point is a mathematical notion as well; at least since Euclid.
> Just as we can pretend non-commutative spaces are usual ones,
But this is meaningless. Non-commutative spaces are not observed in nature
but only in mathematics, and in mathematics things without a precise
definition are meaningless. There is no pretense in mathematics.
> here we pretend the non-commutative phase space
> is a usual one. As in the former case there is no real space having
> the non-commutative algebra as a function algebra, and nevertheless
> all sorts of usual geometric constructions "work",
Many, but not all. In particular nothing related to points!!!
What makes non-commutative spaces attractive to many is precisely
the fact that they are pointless ;-)
> in the later case the phase-space "doesn't exist"
This is not true. There is a well-defined notion of quantum phase space
via Wigner's function, though the interpretation as a probability
density is not possible. In contrast, in noncommutative geometry
there is _no_ well-defined notion of a point.
> and yet answers on meaningful physical
> questions can be retrieved. Now, an electron is a point-like particle
> in approximately the same way a projective module over a
> non-commutative algebra is a vector bundle: it isn't in the usual
> sense, but it is in some weird related sense.
I reject notions that are meaningful only in a weird sense.
Science progresses by clear notions, not by weird ones.
Arnold Neumaier
Oz
Squark <fii...@yahoo.com> writes
>
>Oz <aco...@btopenworld.com> wrote in message news:<xQ7DcZAO1ja+EwGI@btopenworld
>.com>...
>> 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.
>> >...
>> >This means the "wave" supposedly disappeared there once you
>> >performed the measurement.
>> >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.
>
>In an ideal measurement, this evolution is instantaneous and over all
>space.
I think you just defined what you consider an ideal measurement.
1) How do you know the evolution is instantaneous and over all space.
2) Everyone is perfectly happy with ftl behaviour of entangled pairs. So
any apparent ftl behaviour within the wavefunction of a single particle
is hardly a surprise.
3) You accept that an excited atom emitting a photon typically doesn't
do it instantly, and presumably you also believe the reverse. Why do you
expect a silver atom to behave qualitively differently?
>> >and it also
>> >has problems when considering different frames of reference in special
>> >relativity.
>>
>> Tough.
>
>Tough, but the non-locality is the reason. The instantaneous evolution
>is thus everywhere simultaneous. But in which frame?
This is outside my knowledge envelope. (much is).
However I wouldn't expect something that operates in a manner that isn't
modelled by SR to be described in the same language as SR. As far as I
can see there are two events, emission and detection, and these
certainly obey SR (and probably GR).
>> I am not talking about a classical wave.
>> I am talking about a quantum wave.
>
>I don't quite see what you mean by a "quantum wave". The quantization
>of wave dynamics would yield a QFT. Is that what you mean?
I have no idea, but given that smart and knowledgeable people find QFT
challenging, I rather doubt it's somewhere I will ever get to go. Which
is sad.
>> >It doesn't go through both slits, it goes through either one, but it
>> >is undetermined which :-)
>>
>> This doesn't mesh well with single photon diffraction patterns. If it's
>> a pointlike particle then it goes through one or the other, even if you
>> don't know which one.
>
>If it's a classical pointlike particle.
Ah. Well if you allow a divisible pointlike particle then it's not a
problem, but the description then becomes a wave.
Arnold Neumaier
Oz wrote:
>
> Arnold Neumaier <Arnold....@univie.ac.at> writes
>
> >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.
>
> I would like to consider this.
> I doubt this would work for detecting which slit a particle went
> through.
Yes, in this case, it won't work; this is not a nondemolition
measurement.
> Could you give some examples?
For example, in a quantum computer, you want to read your data
without destroying them; so you must be careful in your
measurements.
Details are quite technical, and instead of explaining I give
you some references. The first paper on the subject appears to be
V.B. Braginsky, Y.I. Vorontsov and K.S. Thorne,
Science 209 (1980), 547-557.
For relations to quantum computing, see, e.g.,
quant-ph/9704028, quant-ph/0203130, cond-mat/0202082
Arnold Neumaier
Gavin Collings
ba...@galaxy.ucr.edu (John Baez) wrote in message news:<b4m67k$eg2$1...@glue.ucr.edu>...
> Oh, so you believe in collapse as a physical process? Sigh...
... and you believe it is non-physical?
I read that you don't want to be drawn on this, but (he continues
hoping that you will be) isn't it true that, according to Bell's
inequality and a belief in reality, the collapse isn't simply an
uncovering of a pre-existing state. i.e. making a measurement affects
the system physically; it affects the results of other measurements
made remotely (in the sense of SR). Doesn't this imply some sort of
physical process? (Even if you believe it is a gross form of
collusion).
Are there any interpretations of QM (positivism aside) that don't
regard it as a physical process? As I understand it, these are some
of the intepretations of collapse (feel free to correct these): -
Copenhagen - don't ask
Transactional - A transaction is a physical process
Many Worlds - Splitting the Universe (sounds physical)
Feynman Diagrams - Takes virtual particle paths very physically,
but as far as I know, leaves collapse as a
mystery.
Bohm (non-local) - Relies on non-local signalling in a
preferred frame to descramble the probability
in "collapsed" parts of the wavefunction
I've also seen arguments (associated with the the Bohm approach, but
presumably more widely applicable) that appeal to the non-separability
of apparatus and experiment and insist that the apparatus be included
in the whole wavefunction. To me this argument indicates
more of a collusional World than a faster-than-light signalling one.
(Not being totally happy that signalling implies ordering and that
that ordering may be ambiguous in other Lorentz frames.)
One of the biggest surprises to me when I learnt QM was that the
wavefunction for multiple particles is not separable. (e.g. psi( p1,
p2 ) instead of psi1( p1 ) and psi2( p2 )). This in itself seems to
indicate some sort of fundamental connectedness and it doesn't seem
like too much of a leap to insist that apparatus particles should be
included along with the experiment.
Exactly what form this connectedness might take, though, baffles me.
I saw your reference to Roland Omnes book. I don't have a copy; is
there anything online describing his ideas?
Gavin Collings
Oz
Arnold Neumaier <Arnold....@univie.ac.at> writes
>But it is certain that they meant _something_ and that they _explicitly_ say
>that the electron is _not_ a point charge. Once you think relativistically,
>this point of view is essentially forced upon use; only in the nonrelativistic
>case one may avoid it (although i think one shouldn't).
>In Foldy's work which I quoted elsewhere, it _is_ clear from the context that
>they deduce the lack of pointlikeness from the "size" of the |psi^2|
>distribution.
This is slightly off-topic.
Thinking relativistically in QM (which I know nothing about).
What is the big problem here. there seems to be one but I don't know
what it is. I get the impression that the ket formalism is better suited
to this, but why?
Ahmet Gorgun
"Charles Francis" wrote:
> No. Dirac wrote down an equation for the motions of a fundamental
> particle
I am looking at Dirac's papers "The Quantum Theory of the Electron," parts I
and II, but I don't see an assumption of a fundamental particle. In fact the
word "fundamental" does not occur in these papers. On the contrary it
appears that Dirac is imagining the electron to have structure when he
writes that his dynamical variables alpha "may be regarded as describing
some internal motion of the electron...."
> No. Conclude that the assumed fundamental particle exists, and that the
> observed particle is an instance of it.
Since Dirac never assumes or discusses that his theory requires a
*fundamental* particle, this conclusion is not justified.
Ahmet Gorgun
Squark
> Squark wrote:
> > A density matrix and a wavefunction are two different things.
> A rank 1 density matrix is the same as a wave function, more precisely,
> it is isomorphic to the ray determined by the latter. And in much of
> quantum physics we have really density matrices because real systems
> are dissipative, but we treat them for convenience as rank 1, i.e.,
> as wave functions.
Obviously, I knew all of that. My point was that your original claim was
that the electron is a wavefunction.
> > No, it's just that the energy eigenstates factorize that way.
>
> This is one way to look at it, but my way of looking at it is equally
> adequate,
It isn't because it only applies to energy eigenstates rather than all
states.
> ...but one can still compute the charge density of the electron
> field, which is in fact what all quantum chemistry calculations >
> do. And this charge density defines the size of the system.
Yes, electrodynamics derived from this charge density is only an
approximation.
> > Imagine a classical analogy: the solar system. The distance
> > between the planets and the sun determines the size, but it has
> > nothing to do with the size of the planets themselves.
> But this is different - planets don't show diffraction phenomena, so
> their size is rightly small;
Your point was that there's no way for the atom to have size without
the electron having size. The solar system is a counterexample.
> whereas by assigning an electron pointsize causes paradoxes in
> visualization. Assingning an electron a cloud stucture defined by
> the charge density doesn't and hence deserves to be preferred.
I don't see the physical meaning of the notion "paradoxes in visualization".
> But it is certain that they meant _something_ and that they
> _explicitly_ say that the electron is _not_ a point charge.
Putting things out of context in never a good thing.
> Once you think relativistically,
> this point of view is essentially forced upon use;
I already stated many times why this is a wholly different matter.
> In Foldy's work which I quoted elsewhere, it _is_ clear from the
> context that they deduce the lack of pointlikeness from the "size"
> of the |psi^2| distribution.
As I said, there are two notions of pointlikeness lurking here:
"Classical pointlikeness" & "quantum pointlikeness".
> > I think the non-commutative geometry view is natural. [...] The
> > non-commutative space is a mathematical notion, while the "point"
> > is a philosophical way of thought which, in my view, provides the
> > optimal view on quantum mechanics.
> A point is a mathematical notion as well; at least since Euclid.
If you haven't noticed, I was talking about _the_ point :-)
> > Just as we can pretend non-commutative spaces are usual ones,
> But this is meaningless. Non-commutative spaces are not observed in
> nature but only in mathematics, and in mathematics things without a
> precise definition are meaningless. There is no pretense in
> mathematics.
Non-commutative spaces have a precise definition. They are observed as
phase spaces in nature de facto, e.g. in quantum mechanics.
> Many, but not all. In particular nothing related to points!!!
> What makes non-commutative spaces attractive to many is precisely
> the fact that they are pointless ;-)
Let's not start confusing terminology. No location can be assigned
to an electron in a general state, but it is the quantization of
a point-like object rather than of an extended one. In particular,
the number of degrees of freedom it carries cannot describe an
extended object (for the later, an infinite amount is needed
because of locality).
> This is not true. There is a well-defined notion of quantum phase
> space via Wigner's function, though the interpretation as a
> probability density is not possible.
This is confusing terminology again. This is a "phase space" in a
non-classical sense. Again, it is the phase-space of a point-like object.
> I reject notions that are meaningful only in a weird sense.
> Science progresses by clear notions, not by weird ones.
I don't see the contradiction between the two properties :-)
Mike Mowbray
> Are there any interpretations of QM (positivism aside)
> that don't regard [collapse] as a physical process?
> As I understand it, these are some of the intepretations
> of collapse (feel free to correct these): -
>
> Copenhagen - don't ask
> Transactional - A transaction is a physical process
> Many Worlds - Splitting the Universe (sounds physical)
> Feynman Diagrams - Takes virtual particle paths very physically,
> but as far as I know, leaves collapse as a
> mystery.
> Bohm (non-local) - Relies on non-local signalling in a
> preferred frame to descramble the probability
> in "collapsed" parts of the wavefunction
There's also a couple of other newer interpretations:
Ithaca - only correlations have physical reality;
that which they correlate does not.
(So things like affecting someone in
Andromeda instantaneously via EPR are
not elements of reality.)
Amherst - we don't need an interpretation and collapse
is a fiction. QM is actually fine as long as
you treat records, memory, etc, correctly as
quantum states. [My summary only. For details,
see quant-ph/0210104]
- MikeM.
Charles Francis
Collings <gavin.c...@airbus.com> writes
>ba...@galaxy.ucr.edu (John Baez) wrote in message
>news:<b4m67k$eg2$1...@glue.ucr.edu>...
>> Oh, so you believe in collapse as a physical process? Sigh...
>... and you believe it is non-physical?
>
>I read that you don't want to be drawn on this
I'll be drawn on it, however.
>but (he continues
>hoping that you will be) isn't it true that, according to Bell's
>inequality and a belief in reality, the collapse isn't simply an
>uncovering of a pre-existing state. i.e. making a measurement affects
>the system physically; it affects the results of other measurements
>made remotely (in the sense of SR). Doesn't this imply some sort of
>physical process? (Even if you believe it is a gross form of
>collusion).
True, but the way in which the measurement affects the physical state is
not modelled by collapse. That is to say we do not start off with a
physical wave function which is acted on by a physical process which
causes it to collapse. We start of with a probability of a result if a
measurement were to be done. Just like drawing coloured balls out of a
bag the change in probability is the result of a physical process, but
does not model that physical process.
>Are there any interpretations of QM (positivism aside) that don't
>regard it as a physical process? As I understand it, these are some
>of the intepretations of collapse (feel free to correct these): -
>
> Copenhagen - don't ask
Copenhagen is centred on the idea of complementarity. That quantum
particles really have both wave and particulate aspects. Shut up and
Calculate evolved from it, via orthodoxy. Orthodoxy is not "shut up and
calculate" but more like "many ordinary ideas break down, so that is why
we can't talk about them"
>I saw your reference to Roland Omnes book. I don't have a copy; is
>there anything online describing his ideas?
I am not keen on Omnes, and prefer Bub, D'Espagnat, Home. On my somewhat
cursory reading of Omnes I found him claiming an interpretation, but he
first carefully defines his terms so that "interpretation" means that
which we can say, so that what ever he manages to say then becomes his
interpretation. I call that pretty cheesy, and I note that Omnes does
not claim interpretation in his later work.
Regards
--
Charles Francis
Arnold Neumaier
> Thinking relativistically in QM (which I know nothing about).
>
> What is the big problem here. there seems to be one but I don't know
> what it is.
Relativistic QM has as symmetry group not the Heisenberg group
with 6 generators p_k, q_k but the Poincare group with 10
generators p_\mu and M_{\mu\nu}. This causes all sorts of
problems when you try to create nontrivial dynamics in spacetime.
This is independent of the representation used. Traditionally
one uses field theory in the Heisenberg representation, and for
lack of know-how more or less forgets about the Hilbert space.
Muddy waters for anyone looking for clarity...
Arnold Neumaier
Arnold Neumaier
Arnold Neumaier wrote:
>
> 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).
To move the discussion back from the muddled waters of ambiguous
terminology to things closer to mathematical physics,
I want to summarize my point of view, reflecting the discussion of
this thread (and the related one on the spinning electron).
There seems to be a consensus that it is meaningful to treat
the electron as an undivisible particle. From a mathematical point
of view, an undivisible particle is described classically by a
transitive Hamiltonian representation of the Poincare group, as
classified by Arens, and quantum mechanically by an irreducible
unitary representation of the Poincare group. (For an electron,
we get classically a phase space R^6 x S^2, and quantum mechanically
a representation by the solutions of the free Dirac equation.)
The identification undivisible - transitive - irreducible is
essentally Wigner's characterization of 'fundamental quantum systems',
i.e., systems which can be regarded as a single entity for the
purpose of a theory at a specified level of detail. In this sense,
a nucleus is a fundamental system in quantum chemistry,
but not in nuclear physics.
Indivisibility means on an operational level that there is not
the slighest experimental evidence that the description as a
fundamental quantum system would not be adequate in some circumstances.
Clearly this is dependent on the resolution of the state of the art
in experimenting and might change with time. Currently, the criterion
is satisfied for quarks and leptons, and in particular for
the electron, which is the most common lepton.
The disagreement is about the geometric implications of
indivisibility, and whether the designation 'pointlike' for an
indivisible particle is adequate. If 'pointlike' is taken as
synonymous with 'indivisible' (as suggested by John Baez),
then everything is clear cut; but in this case the term 'pointlike'
is devoid of geometric meaning and can as well be dispensed with.
It does nothing for an intuitive understanding of quantum physics,
except that it confuses the geometric intuition in discussions of
situations like double slit experiments.
Those who are happy with such a confusing situation may stop reading
here. But those, who think like me that good intuitive
understanding requires an adequate geometric justification for
the usage of geometric terms, may question the pointlikeness of
indivisible particles on good physical grounds. Indeed, several
well-known physicists gave explicit reasons why electrons (and photons)
cannot be regarded as pointlike. But for the defense of
pointlikeness I couldn't find a single significant argument in the
literature; those who assert it do it in a hand-waving way.
To discuss the situation clearly, one needs to agree what an electron
'is'. On the most fundamental level - quantum field theory -,
all that exists are quark fields, lepton fields, and gauge fields
(including electromagnetic and gravitational interaction), and the
'state of the universe', in which expectations are to be taken and
probabilities to be calculated. Among them is an electron field
psi(x), which gives rise via a Wigner transform to a phase-space
function W(x,p) (4x4-matrix valued, with complex entries, not
operators), which is measurable; it is the fundamental object
in the statistical mechanics of plasmas (and satisfies in the
usual approximate treatment a Vlasov- or Boltzmann-type equation),
and in quantum chemistry (where the usual approximations give
Hartree-Fock or, relativistically, Dirac-Fock equations).
psi(x) itself is - as anticommuting field - unobservable; only
products of an even number of field operators are physical.
In the classical limit, the trace of W(x,p) becomes the electron
density in phase space, and its integral over p the electron density
in configuration space. In a classical theory, a point is
characterized by the fact that it traces a path in phase space, its
world line. In a classical field theory, this path shows as a singular
solution with support on the world line.
To justify a pointlike nature of an electron, one would therefore
have to show that W(x,p) (or at least the integral of trace W(x,p)
over p) may have singular solutions concentrated on a path,
at least in the asymptotic limit where one would expect
free electrons as part of a scattering state.
For free field theories, where one can reduce field theory to
noninteracting particles, the configuration space electron density
(= integral of trace W(x,p) over p) becomes in a pure single
particle state just |psi(x)|^2. The wave function must satisfy a
free Dirac equation. But there are no solutions to the free Dirac
equation whose support is on a world line.
Thus the concept of a world line (and hence of a point at all
instants of time) does not make sense for free relativistic electrons.
For interacting electrons the situation is more complicated, but
at least for singe electrons in an external field, the configuration
space electron density in a pure state with wave function psi
is still given by |psi(x)|^2. And then even in the nonrelativistic
case, where the Schr"odinger equation defines psi(x)=psi(t,x1,x2,x3),
there are generally no solutions whose support is on a world line.
Thus the concept of a world line (and hence of a point at all
instants of time) does not make sense for interacting nonrelativistic
electrons.
Being not a point, it is clear that an electron must be extended.
And on the same ground as that the size of the sun is defined by the
radius within which its mass density is appreciable, the natural
definition of the size of an electron is the radius within which
its electron density is appreciable. In the case where the electron
can be described by a pure state, this is the radius within which
|psi(x)|^2 is appreciable. In particular, the size of the electron
in a hydrogen atom in the ground state is of the order of the Bohr
radius.
Fuzzified notions of a point (such as "quantum pointlikeness")
that do not have an unambiguous mathematical meaning
are in my view a form of confused thinking; they do not help in
clarifying the issue.
Arnold Neumaier
Gavin Collings
> I'll be drawn on it, however.
I was hoping someone would be.
> True, but the way in which the measurement affects the physical state is
> not modelled by collapse. That is to say we do not start off with a
> physical wave function which is acted on by a physical process which
> causes it to collapse. We start of with a probability of a result if a
> measurement were to be done. Just like drawing coloured balls out of a
> bag the change in probability is the result of a physical process, but
> does not model that physical process.
I hope I'm not taking your analogy too literally, but the point is that it's
not like drawing coloured balls out of a bag. You can't say that the balls
have a definite colour in any real sense until they are measured. In fact
(assuming shape and colour don't commute) if you measured the shape of a
ball it would exist as a superposition of different colours after the
measurement. Thus by choosing to measure colour (or shape), you determine
the type of state that exists after the measurement. In other words, the
collapse occurs differently (physically) depending on the type of
measurement you make. I would say that the collapse models exactly the way
the measurement affects the physical state.
Bell/Aspect confirmed that all this works even for widely separated (in an
SR sense) entangled particles. So if you take two entangled balls and
separate them and then measure the colour of one of them, you will affect
the physical state of the distant ball. ie. make it collapse colourwise
rather than shapewise. To me this implies collusion (the particle "knows"
how it's going to be measured), communication across time (e.g.
Transactional Interpretation), denying reality between measurements
(Copenhagen), or some type of faster than light signalling (Bohm). I'm not
sure I distinguish between the first two interpretations really. I don't
want to deny reality. I'm unhappy with signalling as it seems to require a
preferred frame and introduces asymmetry between two different measurements.
The problem with my preferred option (TI/collusion) is that is seems to
require a gross level of determinism (there are photons on their way from
distant stars that have "already" arranged their transactions with the
electrons in the retina of my unborn grandson)...
I suppose it could be that entanglement is only a short term phenomenon and
invoke some type of decoherence argument that would prevent the seeming
inevitability of my grandson's skyward glance. The Aspect experiment,
certainly, involved only very short durations. Do you know of any other
experiments that have been performed that place any limits on the amount of
time entanglement may persist?
I'm also quite interested in the idea that maybe the implied entanglement of
the entire Universe somehow places restrictions on what "transactions" may
be viable. ie. we see a fully deterministic process as probablistic because
although each individual transaction may have only one option open to it,
the quantum noise (someone posted a reference to an article about this the
other day) gets in our way.
> I am not keen on Omnes, and prefer Bub, D'Espagnat, Home.
What do they have to say?
Gavin Collings
John Baez
In article <473f427f.03031...@posting.google.com>,
Gavin Collings <gavin.c...@airbus.com> wrote:
>ba...@galaxy.ucr.edu (John Baez) wrote in message
>news:<b4m67k$eg2$1...@glue.ucr.edu>...
>> Oh, so you believe in collapse as a physical process? Sigh...
> ... and you believe it is non-physical?
Sigh...
>I read that you don't want to be drawn on this, but (he continues
>hoping that you will be) isn't it true that, according to Bell's
>inequality and a belief in reality, the collapse isn't simply an
>uncovering of a pre-existing state. i.e. making a measurement affects
>the system physically; it affects the results of other measurements
>made remotely (in the sense of SR).
The reason I avoid this sort of discussion is that:
1) I don't know what you mean by "a belief in reality",
2) I don't know what you mean by "simply an uncovering of a
pre-existing state",
3) I don't know what you mean by "affects the results of other measurements",
4) Even if you explain what you mean, I still probably won't
understand what you mean,
and worst of all, to be perfectly frank:
5) I'm not sure I want to know what you mean.
As for 1) and 2), I strenuously avoid expressions like "a belief
in reality" or "simply an uncovering of a pre-existing state".
I think expressions like this do little but cause confusion.
Here's why:
People can usually agree about the results of an experiment.
But, they can't always agree about what is "really going on" -
this is where the fights start. The reason is that, especially
in arguments about quantum mechanics, the word "really" tends
to acquire the bizarre meaning of "as opposed to what we see",
or "before we look".
There's not really any good way to figure out what's going on
before we look to see what's going on! It's a bit like the guy
who stays awake all night wondering if the refrigerator light is
on when the door is shut. But it's even worse, because at least
that guy could drill a hole in the back of the refrigerator and
peek in the hole. We're even more stuck, because even peeking
is against the rule.
As for 3), I have my own definition of what "affects" means.
In particular, if something you do over there "affects"
the results of my experiments, I should be able to notice it
without talking to you. I should see a different probability
distribution of outcomes when I repeat my experiment, depending
on what you are doing over there.
This is not the case in the experiment described by Bell and
performed by Aspect. We perform the experiment over and over;
regardless of what you over there do to your photon, I will
see the same probability distribution of results when I measure
anything about my photon. I can't use what I see to guess
what you're doing. So, according to my definition, you haven't
"affected" me.
There are other definitions of "affect" according to which what
you do *does* affect my results in this experiment. But I don't
like these other definitions because according to them, quantum
mechanics says you can instantly "affect" someone millions of
lightyears away... BUT, there's no way for them to notice it
until you talk to them, millions of years later! I don't think
that's a very useful definition of the word "affect".
>Doesn't this imply some sort of physical process?
Here's the next problem: I don't know what you mean by "physical
process". I know what *I* mean, but since I don't know what you
mean, I feel that if I answer the above question without defining
this term, I stand a very good chance of having you misunderstand
me. And I'm too tired now to define this term, having just spent
about 15 minutes defining the word "affects".
(My original "Sigh..." was addressed to Oz, whom I like to pester
just for the fun of it, so I wasn't too worried about miscommunicating
back then.)
Gavin Collings
news:<b4vorv$2t5$1...@panther.uwo.ca>...
Thanks, I've been reading.
> There's also a couple of other newer interpretations:
>
> Ithaca - only correlations have physical reality;
> that which they correlate does not.
> (So things like affecting someone in
> Andromeda instantaneously via EPR are
> not elements of reality.)
I'm not so comfortable with this - it seems to go half way to
Copenhagen by denying just some of the reality (anything that isn't a
correlation).
On the track of this I came across an article recommending a view of
"objective probability". This seems to have some merit, particularly
when thinking of single particle interference patterns, and seems to
concur with Feynmans view of photons with spinning arrows on them, but
I'd see it more as a positive step than an interpretation.
> Amherst - we don't need an interpretation and collapse
> is a fiction. QM is actually fine as long as
> you treat records, memory, etc, correctly as
> quantum states. [My summary only. For details,
> see quant-ph/0210104]
Interesting, it make a good attempt to include experimenters, log
books as part of the system. I think that this is probably essential
in any complete picture, but I'm unhappy when it starts talking about
superpositions of experimenters and log books while deriving the most
important results. To me this is reminiscent of the Many Worlds
interpretation (which I don't like).
Gavin Collings
Charles Francis
Ahmet Gorgun <ago...@att.net> writes:
>"Charles Francis" wrote:
>> No. Dirac wrote down an equation for the motions of a fundamental
>> particle
>I am looking at Dirac's papers "The Quantum Theory of the Electron," parts I
>and II,
Regrettably I do not have these papers, I have what I was taught about
Dirac's argument by one of Dirac's students, and a copy of The
Principles of QM.
>but I don't see an assumption of a fundamental particle. In fact the
>word "fundamental" does not occur in these papers.
I don't believe it did. In fact a limitation of the original argument
pointed out by Prof Goddard is that superficially it makes it seem that
all particles should obey the Dirac equation, not only fundamental ones.
Clearly that is wrong. Also, in the original context, it does not appear
to allow for fundamental vector bosons, and that is wrong too.
Nevertheless Dirac's original argument does apply to a class of
fundamental particles, and gives measurable predictions for the
properties of those particles, and particles with precisely those
properties are observed.
>On the contrary it
>appears that Dirac is imagining the electron to have structure when he
>writes that his dynamical variables alpha "may be regarded as describing
>some internal motion of the electron...."
Dirac uses that phrase in The Principles of Quantum Mechanics. However
there is a big difference between the idea that a particle has structure
and the idea that it is divisible. But in any case I do not think any
modern physicists think of spin as an internal motion. It has more to do
with the way in which the electron couples to the photon in interaction.
Dirac's argument only shows that there must be a spin index, not the
underlying meaning of spin, and Dirac is quite clear in his use of this
phrase: the argument is in the mathematics, this phrase is just a
heuristic aid to conceptualisation.
>> No. Conclude that the assumed fundamental particle exists, and that the
>> observed particle is an instance of it.
>Since Dirac never assumes or discusses that his theory requires a
>*fundamental* particle, this conclusion is not justified.
No "since" about it. This is scarcely relevant. If you would understand
the argument you would find it in the mathematics, not in the absence of
a word in the discussion of mathematics. Particularly the absence of a
word in a discussion by a physicist noted equally for his parsimonious
use of words and high level of understanding of mathematics.
Regards
--
Charles Francis
Charles Francis
In message <b502dc$m8q$1...@newsg3.svr.pol.co.uk>, Gavin Collings
<gcol...@sitedynamics.co.uk> writes
>
>"Charles Francis" <cha...@clef.demon.co.uk> wrote in message
>news:b4vos9$2t7$1...@panther.uwo.ca...
>
>> not modelled by collapse. That is to say we do not start off with a
>> physical wave function which is acted on by a physical process which
>> causes it to collapse. We start of with a probability of a result if a
>> measurement were to be done. Just like drawing coloured balls out of a
>> bag the change in probability is the result of a physical process, but
>> does not model that physical process.
>
>I hope I'm not taking your analogy too literally, but the point is that it's
>not like drawing coloured balls out of a bag. You can't say that the balls
>have a definite colour in any real sense until they are measured.
I'm afraid you are taking my analogy too literally. I just meant
ordinary classical balls with definite colours. When you pull a yellow
ball out of the bag the probability that it is yellow collapses and
becomes 1. Classical laws of probability theory arise when there is a
classical random variable, in this case colour. Quantum laws of
probability arise when the variable is created in the measurement. But
in both cases the probability is changed by doing the measurement.
>
>> I am not keen on Omnes, and prefer Bub, D'Espagnat, Home.
>
>What do they have to say?
They discuss the different interpretations and find them all lacking.
Regards
--
Charles Francis
Daryl McCullough
ba...@galaxy.ucr.edu (John Baez) says...
>The reason I avoid this sort of discussion is that:
>
>1) I don't know what you mean by "a belief in reality",
>
>2) I don't know what you mean by "simply an uncovering of a
> pre-existing state",
>
>3) I don't know what you mean by "affects the results of other measurements",
>
>4) Even if you explain what you mean, I still probably won't
> understand what you mean,
>
>and worst of all, to be perfectly frank:
>
>5) I'm not sure I want to know what you mean.
Okay, I've successfully managed to avoid discussions about the
philosophy of quantum mechanics for...oh, maybe five years now.
I'm not going to break my streak now, but I would like to make
a metacomment about it.
Basically, it seems to me that those people who have thought long
and hard about the philosophy of quantum mechanics have pretty
much all come to the conclusion that nothing worthwhile will come
of it. That's probably true. But the 5 points that John lists
above to me seems to be an after-the-fact justification for why
the questions about the meaning of quantum mechanics were nonsensical
to begin with. I don't think that's quite fair.
Yes, it's true that asking whether something is "real" or "physical"
doesn't mean anything precise. But those labels do affect the attitudes
of scientists towards their subject matter. I may be indulging in
historical revisionim here, but wasn't it a common belief among
physicists in the nineteenth century that "atoms" were just a
facon de parler? They were a conceptual tool that could be used to
provide a mechanism behind the laws of thermodynamics, but they
shouldn't be taken too seriously. The observable things were
temperature, pressure, viscosity, etc.
But thinking of atoms as real (as opposed to mathematical abstractions)
turns out to have consequences, such as Brownian motion. I doubt whether
Einstein's explanation of Brownian would ever have occurred to someone
who thought of atoms as just calculation tools.
I don't think that it is a priori obvious that thinking about the
reality of the wave function, and the reality of wave function collapse
is an ignorant or pointless thing to do. It just seems that way in
hindsight.
--
Daryl McCullough
Ithaca, NY
John Baez
[quant-ph/0210104]
>Interesting, it make a good attempt to include experimenters, log
>books as part of the system. I think that this is probably essential
>in any complete picture, but I'm unhappy when it starts talking about
>superpositions of experimenters and log books while deriving the most
>important results.
What's wrong with that? You think there's an footnote in the laws
of quantum mechanics saying that physicists are exempt? :-)
No: the world is quantum mechanical, so everything, including you and
your log book, can be put in a superposition of states. If you want
to know why the world seems the way it does, you need to take this into
account. It's not easy getting used to it, but you're a quantum-mechanical
entity just like the rest of us.
Mike Mowbray
Gavin Collings wrote:
> Mike Mowbray wrote:
>> [...]
>> Ithaca - only correlations have physical reality;
>> that which they correlate does not.
>> (So things like affecting someone in
>> Andromeda instantaneously via EPR are
>> not elements of reality.)
> I'm not so comfortable with this - it seems to go half
> way to Copenhagen by denying just some of the reality
> (anything that isn't a correlation).
I'm not sure what the problem is here. For me, "A" more
comfortable than "B" if "A" leads to fewer inconsistencies
and paradoxes (assuming experiment cannot decide absolutely
between the two). But if "B" is better aligned with my
worldview, then I should probably change my worldview to
be more aligned with "A" until something better comes along,
or experimental capabilities improve.
>> Amherst - we don't need an interpretation and collapse
>> is a fiction. QM is actually fine as long as
>> you treat records, memory, etc, correctly as
>> quantum states. [...see quant-ph/0210104]
> Interesting, it make a good attempt to include experimenters,
> log books as part of the system. I think that this is
> probably essential in any complete picture, but I'm unhappy
> when it starts talking about superpositions of experimenters
> and log books while deriving the most important results.
> To me this is reminiscent of the Many Worlds
> interpretation (which I don't like).
If experimenters, etc, are to be treated properly as quantum
states, there's not much choice but to have superpositions.
A central point of the Amherst interpretation (IIUC) is
that we don't need to invoke the non-unitary evolution
involved in "collapse" ideas to make sense of QM.
But it occurs to me that one should also keep in mind the
phenomenon of decoherence - whereby such quantum
superpositions (off-diagonal interference terms in the
density matrix) have been shown to decohere (ie disappear)
extremely quickly due to interaction with a thermal
environment such as (eg) the ubiquitous soft photon background.
The interaction causes non-unitary evolution of the
off-diagonal terms making them decay rapidly. There's some
very recent work on this by Ford et al in quant-ph/0301054
and quant-ph/0301057. If these ideas survive scrutiny, they
could well resolve most of the old chestnut Schrodinger-Cat
paradoxes.
- MikeM.
Gavin Collings
news:<b5ahk...@drn.newsguy.com>...
> But thinking of atoms as real (as opposed to mathematical abstractions)
> turns out to have consequences, such as Brownian motion. I doubt whether
> Einstein's explanation of Brownian would ever have occurred to someone
> who thought of atoms as just calculation tools.
I don't know about the historical accuracy of all this, but this is
the reason behind my interest.
> I don't think that it is a priori obvious that thinking about the
> reality of the wave function, and the reality of wave function collapse
> is an ignorant or pointless thing to do. It just seems that way in
> hindsight.
I think I would go further than this. Haven't physicists actually
spent a good deal of time over the last few decades thinking about
physical systems describing the reality of wave functions? What else
is a Feynman diagram? Just a calculation tool? Maybe some would say
yes, but the lines and nodes are described in terms of physical
particles.
I read an article the other day about Feynman hyperdiamonds. This is
extremely compelling to me: A discretisation of physics with very
simple rules (I was always concerned by the classical smoothness
wavefunctions in what was described to me before as a discrete
theory), a lattice aligned with light like curves that could
conceivably provide a natural limit on speed, an infrastructure that
could provide (space-like) connectivity between events, an explanation
of what mass means, a fundamental link between matter and
space-time...
I think it pays to look beneath the surface.
Gavin Collings
Squark
> Arnold Neumaier wrote:
>
> To move the discussion back from the muddled waters of ambiguous
> terminology to things closer to mathematical physics,
> I want to summarize my point of view, reflecting the discussion of
> this thread (and the related one on the spinning electron).
As one of the main participants of the discussion, and one that
has argued against Arnold's point of view, it is in place that I
summarize my own.
Apparently, the arguement was a mixture of true physical
disagreements with such of merely terminology, hence I shall
attempt to separate them by giving clear definitions.
Arnold claims the electron (and other fundumental particles) is
not pointlike as it cannot be assigned a definite pointlike
location in space and a world-curve in spacetime. Taking
pointlike in this sense I completely agree with him.
Indeed, in classical physics, the above is the only meaning one
can assign to the term "pointlike". In quantum physics, however,
the situation in this regard is more ambiguous.
One the one hand, one can stick with the classical definition,
and demand that the mathematical model for a pointlike object
includes a definite function x(t) translating time into position.
In this sense, practically no quantum system is pointlike.
On the other hand, one can "quantize" the notion and demand x(t)
exits not as a c-function, but as function from the timeline to
the algebra of quantum observables. This is a "quantization"
because the classical x(t) is essentially a function from the
timeline to the classical algebra of observables.
Thus, if we accept the formula
(*) pointlike =
having a single indepedant position-type observable
then the electron, and indeed all fundumental particles is
definitely pointlike when treated non-relativistically.
Relativistically the matter is somewhat obscure, so I won't make
any sharp claim in this regard, however I have to emphasize the
idenitification of the typical scale of the rho(x,x) distribution
(where rho is the given particle's density matrix) with the
particle size is certainly impossible in any sense analogous to
the above.
Thus, although the non-relativistic quantum particle doesn't
posses a definite position at each moment of time, it "has"
position _in precisely the same sense_ it "has" energy, momentum,
angular momentum etc.
Also, we have to note (*) is not equivalent to usual, classical,
pointlikeness even classically if we don't demand the given
theory is local (the rigid body is a counterexample). However,
the current wisdom does say nature is local (again, in an
appropriate sense, as here all of the Bell jazz comes in). So,
global locality is an implicit assumption in (*).
One could also offer a more sophisticated definition, which is
also somewhat sharper (though, as an unavoidable cost, applicable
to a more limited scope of models - fortunately, most of the
interesting models are within this scope):
An entity is called local when its creation operators a*_i(x) at
any point of space x commute with all obserables localized in a
space volume excluding the point x. Here i is an index in some
internal state space.
A definition of "entity" might be a collection of creation
operators a*_i(x) together with a conjugate collection of
annihilation operators a_i(x) and number operators N(S) assigned
to every open set S, obeying the algebra
[a_i(x), a*_j(x)] = delta_ij
[N(S), a*_i(x)] = 1 when x belongs to S and 0 othewise
[N(S), a_i(x)] = -1 when x belongs to S and 0 othewise
Here I assume the "i" index runs over an orthonormal basis in
the internal space (which could include spin, colour etc.)
In this sense also, the electron and all other fundumental
particles are pointlike when treated nonrelativistically (those
particles got to have positive rest-mass to be treated
nonrelativistically, so the above definition of "entity" avoid IR
problems).
Gavin Collings
> In article <473f427f.03031...@posting.google.com>,
> Gavin Collings <gavin.c...@airbus.com> wrote:
>
> [quant-ph/0210104]
>
> What's wrong with that? You think there's an footnote in the laws
> of quantum mechanics saying that physicists are exempt [from being
> in superpositions of states]? :-)
No, but I thought that Bohr did.
> No: the world is quantum mechanical, so everything, including you and
> your log book, can be put in a superposition of states. If you want
> to know why the world seems the way it does, you need to take this into
> account. It's not easy getting used to it, but you're a quantum-mechanical
> entity just like the rest of us.
It is also my preference that physicists should not occupy a special
position in any physical theory. However, extrapolating upwards would
mean that the entire Universe is in a superposition of states
restricting you to the MWI.
Really, I was implicitly expressing a preference for interpretations
that avoid superpositions of states and collapse (e.g. transactional).
And when I described collapse as a physical process, I didn't really
mean some obscure mechanism using FTL signalling, I was thinking more
of a collusional or atemporal process, but a process nonetheless.
(This probably differs from your definition of "physical process").
I felt the paper avoided the issue of collapse a little, rather than
explained it as unnecessary. In the World of experiments and
(repeated) measurements, we get a definite result that is repeated, we
do not just record the fact that repeated measurements are equal. And
as you know, it is the obtaining of a particular result and whether
that fact is important that seems to provoke most heated debate.
Still, I was encouraged that an attempt had been made to formalize the
measurement process within the framework of QM, I just don't think
that it's the entire answer.
Gavin Collings
Ilja Schmelzer
gavin.c...@airbus.com (Gavin Collings) writes:
> Are there any interpretations of QM (positivism aside) that don't
> regard it as a physical process? As I understand it, these are some
> of the intepretations of collapse (feel free to correct these): -
> Copenhagen - don't ask
I would prefer to distinguish minimal interpretation (don't ask) and
Copenhagen (there is a collapse).
> Transactional - A transaction is a physical process
> Many Worlds - Splitting the Universe (sounds physical)
But only sounds, SCNR.
> Feynman Diagrams - Takes virtual particle paths very physically,
> but as far as I know, leaves collapse as a
> mystery.
I like Feynman, but Feynman Diagrams are descriptions of terms in
pertubation theory, not an interpretation.
> Bohm (non-local) - Relies on non-local signalling in a
> preferred frame to descramble the probability
> in "collapsed" parts of the wavefunction
Here is the main reason for my reply here: Sorry, but there is no
collapse in Bohmian theory, and therefore there are no collapsed parts
of the wavefunction.
> I've also seen arguments (associated with the the Bohm approach, but
> presumably more widely applicable) that appeal to the non-separability
> of apparatus and experiment and insist that the apparatus be included
> in the whole wavefunction.
Yep. This is realized in Bohmian theory. There is a global
wavefunction which never collapses.
Ilja
--
I. Schmelzer, <il...@ilja-schmelzer.net>, http://ilja-schmelzer.net
Squark
news:<473f427f.03032...@posting.google.com>...
> I read an article the other day about Feynman hyperdiamonds.
What are those and where is the article?
Best regards,
Squark
[Moderator's note: here's one reference:
http://www.innerx.net/personal/tsmith/Sets2Quarks7.html
- jb]
Gavin Collings
Mike Mowbray <mi...@despammed.com> wrote in message news:<3E792EDF...@despammed.com>...
> Gavin Collings wrote:
> >
> > I'm not so comfortable with this - it seems to go half
> > way to Copenhagen by denying just some of the reality
> > (anything that isn't a correlation).
>
> I'm not sure what the problem is here. For me, "A" more
> comfortable than "B" if "A" leads to fewer inconsistencies
> and paradoxes (assuming experiment cannot decide absolutely
> between the two). But if "B" is better aligned with my
> worldview, then I should probably change my worldview to
> be more aligned with "A" until something better comes along,
> or experimental capabilities improve.
Well, yes, you've got a point. But if you're a "realist" then it's an
all or nothing thing.
> If experimenters, etc, are to be treated properly as quantum
> states, there's not much choice but to have superpositions.
... unless you believe in some classical/quantum barrier or
decoherence with scale. In other words, you could treat the micro
properties of the experimental apparatus (the electron in the geiger
counter) as part of the quantum system without involving the entire
macro World.
> But it occurs to me that one should also keep in mind the
> phenomenon of decoherence - whereby such quantum
> superpositions (off-diagonal interference terms in the
> density matrix) have been shown to decohere (ie disappear)
> extremely quickly due to interaction with a thermal
> environment such as (eg) the ubiquitous soft photon background.
> The interaction causes non-unitary evolution of the
> off-diagonal terms making them decay rapidly. There's some
> very recent work on this by Ford et al in quant-ph/0301054
> and quant-ph/0301057. If these ideas survive scrutiny, they
> could well resolve most of the old chestnut Schrodinger-Cat
> paradoxes.
I had a quick skim through. It seems quite important to understand;
limits (time/temperature or otherwise) on the persistence of entangled
states can have quite a profound effect on your outlook on the
Universe! Have any experimental limits been set on the persistence of
entangled states? Light from distant stars, perhaps?
Gavin Collings
Charles Francis
writes
>No: the world is quantum mechanical, so everything, including you and
>your log book, can be put in a superposition of states. If you want
>to know why the world seems the way it does, you need to take this into
>account. It's not easy getting used to it, but you're a quantum-mechanical
>entity just like the rest of us.
It never fails to amaze me that physicists who should know better fall
for this trivial misconception. Quantum mechanics EXCLUSIVELY studies
the relationships found in measurement of a quantum system by an
apparatus (which is why it cannot say anything about what happens
between measurements). Neither I nor my log book can be described as a
measurement by an apparatus, and neither I nor my log book can be put
into a superposition of states. At least, I can, but only by the
imbibing of large quantities of alcohol.
Regards
--
Charles Francis
Mike Mowbray
> Mike Mowbray <mi...@despammed.com> wrote
> (in the context of Mermin's Ithaca interpretation of QM):
>> Gavin Collings wrote:
>>> I'm not so comfortable with this - it seems to go half
>>> way to Copenhagen by denying just some of the reality
>>> (anything that isn't a correlation).
>> I'm not sure what the problem is here. For me, "A" more
>> comfortable than "B" if "A" leads to fewer inconsistencies
>> and paradoxes (assuming experiment cannot decide absolutely
>> between the two). But if "B" is better aligned with my
>> worldview, then I should probably change my worldview to
>> be more aligned with "A" until something better comes along,
>> or experimental capabilities improve.
> Well, yes, you've got a point. But if you're a "realist"
> then it's an all or nothing thing.
I do like to think I'm a "realist", but the question is:
what does "reality" consist of? We only ever observe/measure
correlations between one state and another, so the Ithaca
interpretation's assertion that only correlations have physical
reality seems "realist" enough for me. All the things that we
infer the correlations to be between (the "correlata") are
artifacts of our theoretical models (which is a polite way of
saying "figments of our imagination").
>> If experimenters, etc, are to be treated properly as
>> quantum states, there's not much choice but to have
>> superpositions.
> ... unless you believe in some classical/quantum barrier
> or decoherence with scale. In other words, you could treat
> the micro properties of the experimental apparatus (the
> electron in the geiger counter) as part of the quantum
> system without involving the entire macro World.
Belief has no place in hardcore science. Such distinctions
or scales require some further explanation or mechanism for
how/why they exist. This is an extra complexity, and therefore
such philosophies can be rejected under Occam's razor (in the
absence of experimental evidence showing the extra complexity
to be essential).
>> But it occurs to me that one should also keep in mind the
>> phenomenon of decoherence - whereby such quantum
>> superpositions (off-diagonal interference terms in the
>> density matrix) have been shown to decohere (ie disappear)
>> extremely quickly due to interaction with a thermal
>> environment such as (eg) the ubiquitous soft photon background.
>> The interaction causes non-unitary evolution of the
>> off-diagonal terms making them decay rapidly. There's some
>> very recent work on this by Ford et al in quant-ph/0301054
>> and quant-ph/0301057. If these ideas survive scrutiny, they
>> could well resolve most of the old chestnut Schrodinger-Cat
>> paradoxes.
> I had a quick skim through. It seems quite important to
> understand; limits (time/temperature or otherwise) on the
> persistence of entangled states can have quite a profound
> effect on your outlook on the Universe!
Right. A large part of the "Measurement Problem" in QM
evaporates.
> Have any experimental limits been set on the persistence
> of entangled states? Light from distant stars, perhaps?
We don't get measurable entanglement effects in light from
distant stars, afaik. At lab-scale, one of the problems in
quantum computing is to prevent decoherence long enough to
get results. But I'm not familiar with the details.
The rapidity of environmental decoherence is a function of
the strength of the interaction and the energy-momentum of
the environmental particles. So I imagine photon entangled
states would persist much longer in a bath of soft photons
than, say, electron entangled states. But now I'm starting
to speculate, so I should stop. :-)
- MikeM.
Squark
> If experimenters, etc, are to be treated properly as quantum
> states, there's not much choice but to have superpositions.
>
> ...whereby such quantum
> superpositions (off-diagonal interference terms in the
> density matrix) have been shown to decohere (ie disappear)
> extremely quickly due to interaction with a thermal
> environment such as (eg) the ubiquitous soft photon background.
This is not accurate. It's true that the off-diagonal terms of the
experimenter's (say) density matrix disappear, but that's only
because he gets his state "measured" by the thermal bath (if I
understand correctly). I.e., the state transforms from one of the
type
|environment> (x)
(|experimenter in state 1> + |experimenter in state 2>)
to one of the type
|enviroment in state A> (x) |experimenter in state 1> +
|enviroment in state B> (x) |experimenter in state 2>
The universe is still "in a superposition".
Best regards,
Squark
Arnold Neumaier
> Arnold Neumaier <Arnold....@univie.ac.at> wrote in message
> news:<3e731978$0$14190$3b21...@news.univie.ac.at>...
> > To move the discussion back from the muddled waters of ambiguous
> > terminology to things closer to mathematical physics,
> > I want to summarize my point of view, reflecting the discussion of
> > this thread (and the related one on the spinning electron).
> As one of the main participants of the discussion, and one that
> has argued against Arnold's point of view, it is in place that I
> summarize my own.
Of course, I don't agree with you, but have nothing new to say
to defend my position. But your view is poorly stated and needs
clarification:
> Thus, if we accept the formula
>
> (*) pointlike =
> having a single indepedendent position-type observable
>
> then the electron, and indeed all fundamental particles is
> definitely pointlike when treated non-relativistically.
In this sense, in all of nuclear physics and in all effective
field theories, the proton would be pointlike, too, since it
is described by a single indepedendent position-type observable.
But few nuclear physicists would agree with you since they argue
that their complicated form factors are a proof of not-pointlike
structure - and the knowledge of these form factors actually
predated the discovery of their divisibility (i.e., of quarks).
Thus they didn't equate
three position degrees of freedom = pointlike = indivisible
I consider their arguments sound since it is not based on spooky quantum
interpretations but on criteria that even survive a classical
limit, where the energy dependence of the form factors produces
nonhamiltonian behavior which casts doubt on the existence of
world lines in the classical limit.
> A definition of "entity" might be a collection of creation
> operators a*_i(x) together with a conjugate collection of
> annihilation operators a_i(x) and number operators N(S) assigned
> to every open set S, obeying the algebra
>
> [a_i(x), a*_j(x)] = delta_ij
I guess you mean
[a_i(x), a*_j(y)] = delta_ij delta(x-y),
since otherwise nonrelativistic second quantization would not
fit into your description.
> [N(S), a*_i(x)] = 1 when x belongs to S and 0 otherwise
> [N(S), a_i(x)] = -1 when x belongs to S and 0 otherwise
I guess you mean
[N(S), a*_i(x)] = a*_i(x) when x belongs to S and 0 otherwise
[N(S), a_i(x)] = -a_i(x) when x belongs to S and 0 otherwise
since these are the formulas that usually hold.
Arnold Neumaier
Gerard Westendorp
John Baez wrote:
> In article <473f427f.03031...@posting.google.com>,
> Gavin Collings <gavin.c...@airbus.com> wrote:
>
> [quant-ph/0210104]
>
>
>>Interesting, it make a good attempt to include experimenters, log
>>books as part of the system. I think that this is probably essential
>>in any complete picture, but I'm unhappy when it starts talking about
>>superpositions of experimenters and log books while deriving the most
>>important results.
>>
>
> What's wrong with that? You think there's an footnote in the laws
> of quantum mechanics saying that physicists are exempt? :-)
Perhaps there is an important distinction here between a conscious
being and a dead object.
If a conscious being like me is in a superposition of
having seen Schrodinger's cat dead and having seen Schrodinger' s cat
dead, how would I perceive being in such a state?
I think the answer is I would perceive to be in only one of the sub-
states that make up the superposition. I will leave it at that for the
moment, for fear of the moderators wrath.
Gerard