## Tuesday, April 16, 2013

### An Atom Drawn To Scale

From here.

Maju said...

Why do they insist on drawing electrons as dots when a string would be more consistent with their uncertain "movement". What's wrong with drawing them as "orbital" strings?

andrew said...

In the Standard Model, electrons are for most purposes "point-like" and even coming up with sizes involves some theoretical assumptions. An orbital string representation has issues too because to some extent the motion of an electron from point A to point B is via all paths from point A to point B and not just one path.

The main point of this drawing is to illustrate that essential point that most of an atom is empty space.

Maju said...

But doesn't the electron always belong to an specific orbit, maybe not a line but a sphere in any case. It never goes from point A to point B via the nucleus for example, being at certain distance from it determined by the quantum value n. At least that's what I learned in school. Only when the electron gains or loses quantum values of energy ("virtual" photons) it changes its "orbit" or quantum state.

So why not a sphere?

Maju said...

For example this graph shows the probability of a hydrogen electron in cross section:

http://en.wikipedia.org/wiki/File:Hydrogen_Density_Plots.png

... implying spheres or toruses (depending on the quantum state). So shy not to treat the whole probability function as an object instead of imagining "solid objects" that are not tangible nor measurable at all?

andrew said...

"At least that's what I learned in school."

For purposes of doing real world chemistry that model works very well most of the time. But, it is possible to know more or less precisely where an electron is at a given time at the cost of not knowing its speed and direction, so a point-like representation has its virtues. At any given measurement, it can be pinned down, so imaging it as merely a probability distribution has its own problems.

Also, the way that you determine the path of an electron from point A to point B actually does include paths through the nucleus, paths at faster than the speed of light and all other sorts of possibilities you wouldn't expect. Most importantly this includes paths the would seem to be prohibited by matter-energy conservation as long as neither point A nor point B violates those conditions - the phenomena, which is called quantum tunnelling is absolutely essential to the functioning of every electronic device containing a transistor. Mathematically, the path of an electron looks more like a series of short range teleportation hops from one detection to the next than it does like a continuous single path from a point A to a point B.

Interpreting this is a challenge and one of the big theoretical issues in quantum physics is the fact that you can't simultaneously have a world that is "causal" (everything in the future is caused by something in a permanently fixed past), "local" (an electron must take some continous path to get from point A to point B), and "real" (an electron is an "object" that stays in existence at all times) and still be consistent with the equations of quantum mechanics. You need to sacrifice at least one of them to get a conception of reality that matches the way experiments observe the world to actually behave. The most conventional solution is to assume reality (most of the time) and causality (all of the time), while usually sacrificing locality (most of the time). But, other heuristic worldviews that sacrifice different assumptions (or a mix of them) can be equivalent when expressed in equation form.

The "orbitals" used to describe electron shells are really closer to being localized properties of particular electrons associated with their momentum than they are with genuine physical locations, although on average over reasonable periods of time (fractions of seconds big enough to measure with an Olypmic stopwatch, for example) the descriptions become equivalent for most purposes.

A related issue about the nature of particles like an "electron" is the "in" or "of" debate. Normally, we think of particles as discrete things that are contained IN space-time, but it may be that it is more accurate to think of them as excitations OF little corners of space-time. It is not at all obvious it particles are really separate and distinct from the background or are just a special state or phase of the backgground.

Maju said...

Alright, thanks. A pretty good lesson you gave me here.

Andrew Oh-Willeke said...

If you read just one book on established quantum mechanics that strikes a good balance between too much dilution of important points and too much technical detail for a non-physicist to understand (and is short with illustrations), I would strongly recommend "QED" by Richard Feynmann.