[aik]

From the "Completeness of Quantum Theory" chapter (on one theory of the determinability of quantum systems): "If an atom has a probability of one half of radioactive decay over an hour, then all that really means is that its wave function describes an ensemble of many different atomic systems, half of which decay in an hour. Whether one particular atom in the ensemble will decay in one hour is definitely determinable. However we will not be able to discern it if all we know is the quantum wave associated with it. Whether it decays or not depends upon properties of that system that have been smoothed away by the quantum wave and thus are unknown to us. It is our ignorance of these smoothed away properties that makes a probabilistic assertion the best we can do."

HN, what does "Whether it decays or not depends upon properties of that system that have been smoothed away by the quantum wave" mean?! What properties exactly, and smoothed away how? Just by the fact that observing the system causes a change within the system and therefore changes the quantum waves?

[mechanical_fish]

I was quite confused by this statement, because it just looks wrong. Upon consulting the text you are citing, I figured out why: This is the author's summary of Einstein's position on the determinability of quantum systems, and Einstein was wrong, famously wrong. This statement is about how Einstein thought the world worked, not about how the world actually works.

This statement you quote has often been called by the jargon name "hidden variables theory". You're asking: What are these hidden variables? Well, Einstein could never find them, and later work has shown that this is because they don't exist. Read the end of the chapter first. ;)

Incidentally, at first glance this chapter doesn't look like light reading.

[othermaciej]

Technically, the only thing that is known not to exist is local hidden variables. There are non-local hidden variable theories which are consistent with all known experiments. Unfortunately, they are also not distinguishable by experiment from more mainstream interpretations of QM.

Here is an example of a non-local hidden variable theory: http://en.wikipedia.org/wiki/Bohm_interpretation

[blatherard]

As I understand it, Einstein was arguing that quantum theory was basically incomplete. That it provided a statistical view of unknown, underlying deterministic processes.

To say that properties "have been smoothed away" means that the particular statistical measures that quantum theory was using were losing the fine-grained detail necessary for understanding particular events. It's not that the "quantum wave" is literally smoothing things in the world, but that the theory of the "quantum wave" is disregarding particular facts.

Imagine that we described human populations without having the ability to observe individual sex characteristics, or individual human interactions. We might say things like "a human has a 10% chance of splitting into two humans over the course of a 20 year span." In this case, our statistics "smooth away" differences such as sex, and the interactions of specific humans over time, leaving us with a probabilistic statement. We might start reading the apparent non-determinism as a fact of nature, rather than as a problem with our knowledge.

[amalcon]

Einstein's view was more or less that there is some state contained in each particle that determines its quantum effects. We do not, however, have access to that state, so we instead do all work with statistical approximations of that state. The statistical approximations encompass all unknown information, and thus "smooth it over".

He put forth this theory before the EPR experiments (he's the E); these experiments made that interpretation unlikely. Specifically, the EPR experiments showed that the state (if any) is probably non-local.