Subject: Orbitals and Reality (yet again)

From: "Phil Hultin" <hultin{at}cc.umanitoba.ca>
Date: Mon, 31 Jan 2005 20:18:15 -0600

<Please forgive the length of this one>

I think the analogy of the trajectory of a Newtonian object's motion is
useful, albeit imprecise.

The problem with a lot of the comments that have been posted since that
analogy was suggested is that a lot of people are still confusing the
"observation of the ball as it moves through its trajectory" with
"observation of the trajectory".  It is indeed impossible to observe a
trajectory, but common experience proves that it is possible to observe a
ball in flight, and to deduce from this the notion of its trajectory.  A
trajectory is an abstract conception that links a ball's position at time
"t" with its position at time "t + .delta.t".  Note that if we as humans
were not capable of perceiving time as having sequence, the notion of a
trajectory would be meaningless to us.

I have been reading "Alice" to my son, and I note that Lewis Carroll
addresses this kind of paradox in both "Wonderland" and "Looking-Glass".
What is the relationship between a thing and its name?  Consider this
dialogue from Chapter 8 of "Looking-Glass":

"The name of the song is called "HADDOCKS' EYES."' 

`Oh, that's the name of the song, is it?' Alice said, trying to feel
interested. 

`No, you don't understand,' the Knight said, looking a little vexed. `That's
what the name is CALLED. The name really IS "THE AGED AGED MAN."' 

`Then I ought to have said "That's what the SONG is called"?' Alice
corrected herself. 

`No, you oughtn't: that's quite another thing! The SONG is called "WAYS AND
MEANS": but that's only what it's CALLED, you know!' 

`Well, what IS the song, then?' said Alice, who was by this time completely
bewildered."

Alice is right - what IS the song?  We cannot observe a song, all we can
observe is a series of pressure fluctuations as a function of time.  The
concept of "song" is something quite different, although obviously it has
some connection to the physical observable.  And then, what do we CALL what
we observe as opposed to what the thing itself actually IS?

What does this have to do with orbitals?  Well, we can certainly observe a
cloud of electrons, at least indirectly.  I am less sure that we can observe
a single electron out of this cloud, but for the sake of argument let's just
say that we (or Villeneuve et al) can.  If we then observe that this
electron is detectable in some places but not in others (within the limits
of our ability to see electrons), can we then say we have "observed an
orbital"?

Well, no we cannot.  However, we can certainly deduce that something
orbital-like might exist, just as we can deduce the existence of a
trajectory.

Is the similarity of Villeneuve et al's electron distribution to a
Hartree-Fock orbital purely coincidence?  Well, again this question depends
on how one understands the word "coincidence".  It is entirely possible for
the observation and the model to "coincide" purely by chance, with
absolutely no logical or causative connection - this is what some people
posting on this list are using coincidence to mean.

On the other hand, it is also possible, as I maintained in my first posting
on this subject, that our theory has captured some "real" aspect of
electronic behaviour, despite its obvious inaccuracies and imprecisions.  Is
this coincidence in the sense that there is absolutely no logical or
causative relationship?  I don't think that it necessarily is.  After all,
our theory is based on spectroscopic measurements leading to energies, and
it is also based on some understanding of particle physics.  Is it
impossible that maybe some part of orbital-based quantum theory "got it
(partly) right"?  I hope not.

Dr. Philip G. Hultin

Associate Professor of Chemistry,

University of Manitoba

Winnipeg, MB

R3T 2N2

hultin{at}cc.umanitoba.ca

http://umanitoba.ca/chemistry/people/hultin