Orbitals and Reality (yet again)

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