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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