Subject: Re: CCL:orbitals and reality

From: khinsen -()- cea.fr
Date: Tue, 1 Feb 2005 12:05:39 +0100

On 01.02.2005, at 00:14, Eric Scerri wrote:

> Many useful things are unobservable!
>
> The question was indeed whether one can observe an orbital.
> I don't think anybody really doubts the usefulness of the concept.
>
> Electrons and nuclei are at least observable in principle.
> The usual understanding is that orbitals are not.

Electrons and nuclei are not observable, its some of their properties  
that are. The position, velocity, energy, charge, etc. of an electron  
are observables. Other properties, such as its wave function, are not  
observables. When we say "electrons are observable", this is really  
just a shorthand for saying "electrons have observable properties".

Note also that the status of a quantity as an "observable" is part of  
the model, not of "reality". The model of an electron with all the  
properties listed in physics textbooks is the outcome of a long process  
of experimentation and model making. There is no operation that allows  
to establish the list of all observable properties of an electron. They  
might become more numerous in the future, but future research might  
also lead us to abandon the concept of the electron, or at least  
downgrade its status in our understanding of nature.
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Konrad Hinsen
Laboratoire Leon Brillouin, CEA Saclay,
91191 Gif-sur-Yvette Cedex, France
Tel.: +33-1 69 08 79 25
Fax: +33-1 69 08 82 61
E-Mail: khinsen -()- cea.fr
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From: Tom Sundius <sundius^at^pcu.helsinki.fi>
Date: Tue, 1 Feb 2005 14:07:19 +0200 (EET)

On Tue, 1 Feb 2005 khinsen^at^cea.fr wrote:

> Electrons and nuclei are not observable, its some of their properties that 
> are. The position, velocity, energy, charge, etc. of an electron are 
> observables. Other properties, such as its wave function, are not 
> observables. When we say "electrons are observable", this is really just a 
> shorthand for saying "electrons have observable properties".
...

I agree completely. I would also like to add that you have to take
Heisenberg's uncertainty relation into account. Thus the motion of
electrons and nuclei cannot be compared to the classical motion of
"balls in flight", as was suggested earlier in this discussion.
The quantum world is very different from the "classical world", that
is why it is not possible directly to "observe" a wave function.

Tom Sundius
University of Helsinki, Dept of Physical Sciences   phone +358-9-191 50672
P.O.Box 64, FIN-00014 Helsinki, Finland             fax   +358-9-191 50610
+++ for we know in part, and we prophesy in part +++

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From: Aaron Deskins <ndeskins %a% purdue.edu>
Date: Tue, 01 Feb 2005 08:52:16 -0500

Not to be too pedantic, but what is an example of an observable? When we 
say we observe something, are we not just observing its properties? For 
example I may say, "I see a red book." Actually I'm only observing its 
properties. The book has the properties of interacting with visible 
light to make it appear red. I've only observed its light-related 
properties. If I touch the book, I have observed its mass-related 
properties. Are not all observables based on its properties?

khinsen %a% cea.fr wrote:

> properties listed in physics textbooks is the outcome of a long 
> process  of experimentation and model making. There is no operation 
> that allows  to establish the list of all observable properties of an 
> electron. They  might become more numerous in the future, but future 
> research might  also lead us to abandon the concept of the electron, 
> or at least  downgrade its status in our understanding of nature.
> --

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From: khinsen_at_cea.fr
Date: Tue, 1 Feb 2005 15:52:31 +0100

> Not to be too pedantic, but what is an example of an observable? When  

I was using that term in the technical sense of quantum theory, i.e. a  
quantity represented by a Hermitian operator. The position of an  
electron for example.

> properties. Are not all observables based on its properties?

That's exactly what I wanted to say in my post as well!
--
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Konrad Hinsen
Laboratoire Leon Brillouin, CEA Saclay,
91191 Gif-sur-Yvette Cedex, France
Tel.: +33-1 69 08 79 25
Fax: +33-1 69 08 82 61
E-Mail: khinsen_at_cea.fr
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From: Nicolas Ferré <nicolas.ferre = = = up.univ-mrs.fr>
Date: Tue, 01 Feb 2005 10:44:53 +0100

Hum ...
I only said 1-e orbitals and trajectories are analog as human mind 
creations ! Useful but not measurable.

In Hartree-Fock theory, a two-electrons system can be *approximately* 
described by some linear combinations of one-electron orbitals. But the 
correlation lacks.
In classical mechanics, the combined trajectories of two interacting 
objects can be written as the sum of the trajectories f(r_i) of each 
individual object, but some physics also lack: collisions between the 
two objects for instance. In this case, we need to add an explicit 
dependance of f in r_i and r_ij.
That means that looking at one individual classical trajectory in a 
two-objects system is meaningless if we are interested in describing the 
whole behavior of the system.
In the same way, any QC theory based on 1-electron functions is an 
approximate theory, helpful but always lacking some features !

Now, can these 1-electron functions capture *some* physics of what is 
the behavior of a single electron in the field of some other particles ? 
Some, certainly. But does it mean we can measure them ? I don't think 
so, even less than the true full wavefunction that describes the 
simultaneous behavior of all the interacting particles.

Alan Shusterman a icrit :
> I find the introduction of the trajectory analogy interesting, but I 
> think it is inappropriate to equate trajectories with orbitals (maybe I 
> misunderstood the analogy?).
> 
> I would use trajectories this way:
> 1. let a classical trajectory be analogous to a complete wave function 
> (not an orbital)
> 2. and suppose we have a complicated system so that the trajectory (like 
> a complete wave function) cannot be expressed analytically
> 3. in this case, we will try to model the trajectory with a combination 
> of simpler analytical functions, like short line segments
> 4. the line segments are analogous to orbitals
> 
> Now we can return to the question of what can be measured. We might 
> claim that a measurement teaches us something about the trajectory. 
> However, it seems misguided to claim a measurement tells us the length 
> or direction of the line segments. We only invented the line segments as 
> a tool for approximating the trajectory.
> 
> Granted, it's not a perfect analogy. But consider one more thing: as we 
> approach the limiting situation of an infinite number of infinitely 
> short line segments, our trajectory model does approach the actual 
> trajectory. On the other hand, the limiting situation of an infinite 
> number of orbitals only approaches the Hartree-Fock limit (a model) and 
> never the actual wave function. It seems very strange to say we have 
> measured orbitals.
> 
> -Alan
> 

-- 
  Dr. Nicolas Ferre'
  Laboratoire de Chimie Theorique et de Modelisation Moleculaire
  UMR 6517 - CNRS Universite' de Provence
  Case 521 - Faculte' de Saint-Jerome
  Av. Esc. Normandie Niemen
  13397 MARSEILLE Cedex 20 (FRANCE)
  Tel : (+33)4.91.28.27.33              Fax : (+33)4.91.28.87.58

  Please avoid sending me Word or PowerPoint attachments.
  See http://www.gnu.org/philosophy/no-word-attachments.html

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From: Guosheng Wu <wu_guosheng2002 !v! yahoo.com>
Date: Tue, 1 Feb 2005 08:12:16 -0800 (PST)

> > observables. 

>> When we say "electrons are observable", this is really

The last statement should also be true for wave function?!  And that
Nature paper did observe some properties of the wave function of N2.  

Of course we know QM is different from CM, but what is the difference
between the wave of electron and the wave of light?  In some sense the
exact solution of wave function for a molecule of course has very
meaningful property of the system, such as H atom, harmonic vibrator,... 
do not bother me with complicated molecules! In principle that's the same
thing, please forget about multi-electron system for a second, NOW some
folks are talking about any kind of wave function!   

As I mentioned last time, exact solution of wave function is the
probability amplititude, it is not <<nothing but something strange in our
mind>>, it's very meaningful stuff.  Certainly b/c the nature of QM
especially the principle of uncertainty, it's absolute value may not mean
much, especially when it's a complex function, but things like |psi|, or
just psi itself when it's real like H atom, or <psi|psi|psi>, <psi|psi>
(density) or <psi|H|psi>,.... each one is meaningful, and observable for
simple systems!  I guess in the future experiments would definitely
provide better answers to some of the listers, and it's the advantage of
experiment that might be able to provide useful and meaningful tool to
help the validataion of QM theories for complicated system, where the
exact solution of SE is terribly difficult. 

It might be better for us to check some graduate-level Quantum mechanics
book carefully, not Quantum chemistry book, definitely not any kind of
book like quantum organic chemistry, if there may be any.

BTW, can not we find something more meaningful to discuss instead of this
"Orbitals and reality"? 

Thanks for reading.

-Guosheng Wu 

		
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Do you Yahoo!? 
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From: khinsen)at(cea.fr
Date: Tue, 1 Feb 2005 18:12:37 +0100

> The last statement should also be true for wave function?!  And that

Before introducing linguistic shorthands about observable aspects of  
wavefunctions, we'd better make sure we understand and agree on all  
those aspects!

> Nature paper did observe some properties of the wave function of N2.

Fine, but that's something entirely different from what I described  
before. I used "observable" as a technical term from quantum theory,  
i.e. a quantity represented by a Hermitian operator. This is not the  
same as the common language meaning of "something that can be  
observed". The latter is quite vague as it can apply to both objects  
("a brick is observable") and properties (the colour of a brick is  
observable") and leaves the notion of "observation" open to  
interpretation (and this is a tricky one in quantum theory).

> between the wave of electron and the wave of light?  In some sense the

The nature of the field associated with the wave. In the case of light,  
it's the electric and magnetic field, which are observables (in quantum  
field theory). In the case of a wave function of an electron, it is a  
non-observable quantity (again within the framework of quantum theory).

> simple systems!  I guess in the future experiments would definitely

Obviously many quantities derived from the wave function can be  
obtained experimentally. But that is not the same as observing the wave  
function itself.
--
------------------------------------------------------------------------ 
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Konrad Hinsen
Laboratoire Leon Brillouin, CEA Saclay,
91191 Gif-sur-Yvette Cedex, France
Tel.: +33-1 69 08 79 25
Fax: +33-1 69 08 82 61
E-Mail: khinsen)at(cea.fr
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