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Measurement, as you said, is how we best try to isolate a charteristic of whatever we are measuring; how it is in relation to otherthings in a similar environment.

I guess in a quantum sense, measuring is the act of introducing a known level of entropy into a system to graph that system's changed form, to piece together a picture of it's initial form.

except that there is an almost unadultered state, isn't there? When measurement is not taking place, all states exist superimposed and can be described by a wave function. This is what I mean by artificial, and I disagree, in quantum especially everything is about the artificial, about the 'observer imposed'. The whole, without an observer there is no reality. Although here I think it's just semantics. When I say artificial I don't mean 'made by humans' I mean imposed by an observer, and not of the environment. That is, with this definition, a measurement is artificial and changes the un-intruded superposition of states existing together.

but a measurement doesn't have to occur to callapse the wave function. In his Feynman Lectures, Feynman says 'the mere possibility of a determining the outcome collapses the wave function'. For example, if we have two identical particles (two electrons) which we shoot at each other and collide then there are two different ways that they could fly off (per say). If we place a detector at each side, because we cannot distinguish one electron from the other, then we'll never be able to detect which outcome was chosen. Thus the wave function is not collapsed and the pattern we get is one with interferance. If however we collide a proton and an electron, then we can easily detect the outcome, thus there is no wave function. The mere possibility of detecting the outcome has already collapsed the wave function, even before we made the measurement. So that saying a measurement is anything that collapses the wave function is an insufficient definition.

um, this maybe the just the layman in me speaking (self educated) but I always thought that measurement was just a piece of data that is recorded about either an event or distance.

I'm sure someone will be able to correct me if what I'm trying to say goes awry.

In the last lecture of QM, the professor went over what constitutes as a "measurement" in the two-slit experiment. Measurements - in this context, anything that could change the outcome of the experiment prematurely - could be entirely unintentional, and be a product of impurities in the experimental apparatus (as opposed to the experimental design). In an extremely loose and vague sense, he offered the following quick interpretation:

Say you fire a particle with very well-defined momentum at a two-slit setup. For the sake of argument, assume that it has some wavefunction component |+> coming out of the top slit, and some component |-> from the bottom slit, so that their addition creates the entire wavefunction, and accounts for the interference pattern we always see. This is the ideal experiment.

But this ideal experiment neglects the presence of, well...the rest of the universe. So, to the top slit, we assign the state |+>|U+> to the top slit (U+ denoting the rest of the...universe acting on the top slit) and assign |->|U-> to the bottom slit. So (neglecting normalization for the moment), when we add these up and try to calculate |psi|^2, instead of the usual interference pattern, we get an extra term of
Re{<-|+>}
If no "measurement" has been made, the second term will be 0 and we get our interference pattern back. If a total measurement has been made - that is, if the state is now decoherent - the second inner product will be 1.

Now, I'm not saying that the second inner product is at all easy or possible to compute. But it *will* be between 0 and 1, and gives us a scale on which to formulate the idea of a "measurement." The professor also said that research has confirmed that it is possible to influence the system in such a way as to make a "partial measurement", where that inner product is neither 0 nor 1. I'm not sure where such things will be useful, but I thought that this more intuitive way of defining a measurement was particularly appealing.

well that is only a definition of length, what about other properties like spin, mass, charge. Surely spin and charge have nothing to do with the spacetime continuum.

What poweroutage means is that certain quantities, such as spin and charge, and mass in some cases, can only come in discreet amounts. For example, spin can only come in multiples of 1/2: 0, 1/2, -1/2, 1, -1, 3/2, etc.

And unfortunately, there is more to a measurement than simply determining the value of some observable quantity.