Re: If particles could be split up infinitely...

Hello Lucy,

You have observed that electrons, photons, and other so-called "fundamental particles" do not behave like billiard balls, nor like fluids, nor like anything else we're familiar with in the big world.

You're wondering if this strangeness is due to a flaw in reasoning---maybe the assumption of pointlike electrons/quarks/photons is wrong?

If you read up on the various "classical" quantum physics experiments, like the Stern-Gerlach Experiment and the double-slit experiment, and the study of simple atoms, there are two things worth noticing. First, it's important to notice that the electrons behave like waves. The wavelike aspect of the electron leads to diffraction (interference) in the two-slit experiment, and to the "standing-wave" aspect of electron orbits in Bohr's atoms. You don't need to know anything about the "inner workings" of the electron in order to give it a wavelike nature. After all, physicists have seen wavelike behavior in large things like sodium atoms, as well as protons, neutrons and even pions (which are all complex assemblages of quarks and gluons). Amazingly, even large molecules like buckyballs have a wavelike nature.

The other surprising thing in quantum mechanics experiments, is the fact that each particle seems to "randomly" choose how to behave. In the double-slit experiment, each electron crashes into the detector in one (and only one) location; the locations appear to be randomly chosen from just the right distribution, so that (after many measurements) the electrons can be seen to show interference behavior. In the Stern-Gerlach experiment, an atom whose spin was originally pointing in a particular direction, will "randomly" select a direction when a certain type of measurement is made.

In the traditional interpretation, the randomness is a perfectly reasonable consequence of something called "wavefunction collapse". However, some theorists (including Einstein, in the early days) wondered if maybe the process is not random at all. Imagine that inside of (for example) the spinning Stern-Gerlach atom has some internal structure, some strange clockwork that we can't see, churning very fast---imagine that the atom has a little internal stopwatch, counting the seconds and milliseconds and femtoseconds. Imagine that, when you make a measurement on the atom, it consults its stopwatch and says "If the twentieth digit on my watch is an even number, I'll jump left; if it is an odd number, I'll jump right". Since the watch's behavior is invisible to us, and unmeasurable to our clumsy instruments, we'll think that the atom is behaving randomly; in fact, it is behaving deterministically. This sort of reasoning is called a hidden variable theory. Hidden variable theories can be made to work, although they end up being very complicated and "nonlocal". And, as desired, a hidden variable theory may be able to describe quantum mechanics without any true randomness.

OK, does that clarify your thinking on the subject? It sounds like you're proposing a hidden variable theory. Your analogy with the bacteria is pretty good---the behavior of a large clump of bacteria (seen through a looking-glass) might be inexplicably weird, in spite of very simple behavior on the level of single bacteria. Another good analogy would be the behavior of atoms; imagine how complex and mysterious the periodic table appeared, before we knew about the electron shells that give it its shape. (Nowadays, we can (to some extent) derive the properties of all atoms, using only Schrodinger's equation!)

So. That's all I have to say about the physics---now (as quantum mechanics discussions tend to) we have to segue into philosophy. There is no experiment whatsoever, in "classical" quantum mechanics, which gives an unreasonable result: there is no need for hidden variables to "fix" some underlying problem. The various different interpretations of quantum mechanics---Copenhagen, hidden variable (or Bohm), and many-worlds---are designed to give the same, entirely accurate description of all measurements; their differences are essentially philosophical. I personally am a fan of the many-worlds interpretation; I think it is the most "elegant". Many physicists think the same of Copenhagen. I've never in my life met a Bohmian, except in odd back alleys of the Internet. If you learn more about it, you can decide for yourself which interpretation you prefer.

Finally, I should put in a word in defense of "fundamental particles". You mentioned "scale levels" in your question, and that's a very important thing to think about. In your bacteria example, the confusing activity of a cluster of bacteria is not due to quarks, or quantum mechanics, or even chemistry; it is due to the individual bacteria, which must be small enough to escape discovery and big enough to have an influence you can see. When we say (for example) that an "electron is blurred out" when it orbits an atom, it is very different than saying that an amoeba is blurry and structureless under a cheap microscope. With a better microscope, we can look closer and see the substructure. The substructure turns out to be resonsible for the amoeba's size, mass, and apparent smoothness.

If you focus in more closely on an electron---using a higher-energy probe, or smashing it into something at high energy---you still just see a pointlike object, blurred only by the laws of quantum mechanics and by your measurement. Since the electron still looks pointlike at 0.01 femtometers, you cannot say that "substructure" would cause blurriness for an electron stuck to an atom, where the scale is closer to 1 angstrom (100,000 femtometers). That doesn't mean that the electron has no substructure, but it does mean that substructure isn't responsible for the 1-angstrom blurriness of the atom. The quantum behavior in the double-slit experiment may play out over very large distances, like millimeters; nothing going on "inside the electron" below 0.01 femtometers will have any effect. That's what we mean when we say that electrons, muons, quarks, and neutrinos are "fundamental"---only that we can't break them up, or see inside them, with the highest-energy experiments available.

Indeed, physicists do still search for electron and quark substructure, or new interactions/relationships between them. They may, for example, turn out to be strings, if we look closely enough.

OK, that's been a long-winded answer. I hope this has been useful and interesting to you---let us know if you have any other questions.

Cheers, -Ben