The agreed picture is, that the electron is n o t smeared out. Otherwise also its charge would be smeared out and the electrostatic energy of atoms came out completely wrong. As far as I remember the stories arround history that I was told in QM lessons, Schrödinger first considered the electrons smeared out according to the wave function and then changed this mind in view of the electrostatic argument mentioned above. Note that, when you are speaking about the 2s orbital you are speaking about a stationary state. It's a standing wave - no need for the electron to hop accross the node. To conclude: the electron is a point particle, the motion of which is discribed by a wave function (notice that the wave function is always time-dependent, even if the time-dependence is oscillatory as in 'stationary' states. So, 'motion' is always an applicable notion).

Charles,

it is a self-suggesting idea that non-localized nature of atomic stationary electron states arises from some kind of fuzzy structue of space. This seems to be a bad idea, however. At least down to 10⁻18 m space is a uniform and regular arena for all the virtual processes that create the 'anomalous' part of the magnetic moment of electrons in atoms.

Francis,

shaking stochastically cells of space back and forth with a mean amplitude of 10-18 m would make the computed value of the anomalous magnetic moment of the electron disagree with the measured value. Admittedly a bit more indirect than the usage of a meter stick.

Charles,

I spoke of a measured value of the anomalous magnetic moment. So there is a measurement in the game. This measurement fits perfectly the theoretical predictions resulting from the evaluation of Feynman integrals (belonging to Feynman diagrams). Since these integrals go over a part of Minkowski spacetime and assume for this the well-known structure of a pseudo-Riemannian space, one concludes that deviations from this pseudo-Riemannian structure are negligible over distances characteristic for the features of the functions to be integrated. This is an indirect measurement of the graininess of spacetime. From analysis of propagation of star light with a similar logic even stronger limits for graininess of spacetime were obtained. As always, physical reasoning leads to not more than a working hypothesis. If it is a weak one, there will soon come someone who presents a more convincing one. He is welcome. Simply saying that the working hypothesis is 'meaningless' is not enough.

@Charles

if, as you say: "space is an emergent construct, not a prior in the sense of Newtonian absolute space," What happens with the idea of the nuclear atom?

This conception is really antique, as it was proposed by de Broglie. Please take a look to: "Problems of Atomic Dynamics", by Max Born, Dover Pub., in particular at Lecture 10. There, Born cites Einstein: ". . . The true laws of nature are relations between magnitudes which must be fundamentally observable." And continues its introduction to quantum theory: ". . . we have certainly introduced, as fundamental constituents, magnitudes of very doubtful observability, as, for instance, the position, velocity, and period of the electron. What we really want to calculate by means of our theory and can be observed experimentally, are the energy levels and the emitted light frequencies derivable from them. . . . On the other hand, no one has been able to give a method for the determination of the period of an electron in its orbit or even the position of the electron at a given instant. There seems to be no hope that this will ever become possible."

No! It is at the mere formulation of Matrix Quantum Mechanics. In 1925-25 series of lectures that Max Born presented at the Massachusetts Institute of Technology.

"At the time I began this course lectures, Heisenberg´s first paper on the new quantum theory had just appeared. Here his masterly treatment gave the quantum theory an entirely new turn. The paper of Jordan and myself, in which we recognized the matrix calculus as the proper formulation of Heisenberg´s ideas, was in press, and the manuscript of a third paper by the three of us was almost completed¨

¨. . . In closing I should like to add a few general remarks. The first concerns the question of whether it is possible to visualize the laws of physics as formulated in this new manner and whether the processes in the atom can be conceived to exist in space and time . . . . it already seems certain that the usual conceptions of space and time are not rigorously compatible with the character of the new laws."

This text is a wonderful example of why the exposition of great ideas by the creators, are the most transparent an inspiring. Incidentally, at the last part of its preface, M. Born tell us:

"I wrote the original test in German. . . .; finally, Dr. M. S. Vallarta went carefully through the complete text in order to verify the formulas and make the English idiomatic."

Don Manuel Sandoval Vallarta is one of the founders of the tradition of Physics Science in México.

Charles F.:

You are welcome!

The important question is that we never stop wondering and exploring!

Philip, your statement that "I find it easier to say that the electron is the orbital. It is a smeared out object." does not survives a more careful thinking.

1. Certainly it is not possible to identify the orbital with the smeared electron. What property would be represented by the value of the orbital ? density ? charge density ? No way: orbitals in general do have sign! and may even be complex!

2. can we identify the density probability (square modulus of the orbital) with the smeared electron ? nope! the square modulus does not contain the whole information contained in the orbital.

3. if the electron would be a smeared object, why we never observed a fraction of electron ? Apparently all measurements up to now have shown either zero or one electron. Nothing in between.

So, the very early ideas by de Broglie and Schroedinger have been demonstrated untenable and wavefunctions are there just to provide the density probability and a probability current of finding the electron *at* a given point. In non-relativistic quantum mechanics the possibility of localizing an electron is absolutely unlimited.