Re: chaos and uncertainty (was seti@home is SORTA WORKING)

Christopher Maloney (
Fri, 16 Jul 1999 23:52:17 -0400

Rob Harris Cen-IT wrote:
> > QM says if I measure the position x, there is a range of
> > values that it can take, and there is no way for me to predict the
> > outcome of the experiment beforehand.
> >
> OK - after all, that's why we're taking the measurement.....
> > Let's say I measure the
> > position and come up with a value of 2. *Now*, if I measure the
> > position again right away, QM says that I am guaranteed to get the
> > same value, 2.
> >
> the same time position ? Surely if you take another reading at a
> later time - no matter how small the timescale, we can expect a slight
> change in the reading due to system progression...?
> Alternatively - are you talking REALLY small time scales? I mean, viewing
> the progression of time as a quantized sequential transition from one time
> "position" to another, rather than an analogue, constant progression? If so,
> and you are saying that the second reading is taken within the same time
> chunk, then I follow you.

I'm just saying that there's no theoretical problem measuring the position twice in a row, but there is a problem if you try to measure position and them momentum.

> > Thus, for example,
> > to measure the position of an electron, you have to bounce a
> > photon off of it.
> >
> With our current technology.

That's why I used the phrase "for example". I was trying to show how the theory manifests itself in one particular example of an experimental setup.

This is analogous to the question often asked by people not familiar with relativity, "Yeah, but *why* can't something go faster than light? What stops it?" One might imagine a rocket with a propulsion system that accelerates it for an indefinite period of time. What stops that rocket from accelerating past the speed of light. One explanation would be (and I don't pretend this is the best one) that as the rocket goes faster, it increases in mass, such that the same propulsive force accelerates it less. The mass increases without limit as the speed of light is approached, so it's never possible to actually get up to that speed.

See? The theory says something's impossible, and we find that the experimental setups we contrive have behaviors which validate the theory.

> > But these are just
> > manifestations of the underlying theory, which says,
> > unequivocally, that you cannot simultaneously know both
> > observables.
> >
> What is the basis for this premise?

The math. I thought the sound metaphor was a good one. Didn't it make sense to you?

> > The theoretical limit of this uncertainty is
> > defined by Plank's constant, hbar.
> >
> What do you (everyone) think about this? It seems to me that the
> obvious way to avoid the uncertainty principle is to use non-intrusive
> methods of measurement.

No such thing.

> For instance, determining the composition of stars
> by detecting photons from it. You can get all the photons you want without
> actually affecting the star's composition - you could have a legion of
> photon-munchers eating the photons as soon as they leave the star's surface,
> and you wouldn't affect the star's composition in any way.

I'm not sure "composition" has an uncertainty relation.

> Also, I don't buy the double measurement commutability thing. Surely
> the critical factor involved in commutability in this case is whether the
> first measurement affects the system. Well, whether you're measuring
> position with a photon (which will alter the system by 1 photon of whatever
> energy and velocity), THEN another position measurement, or position THEN
> momentum, the disruption has occurred at the point of the original
> measurement, making the nature of the intended secondary measurement
> irrelevant - The system was already disrupted by the first measurement.
> I could be off track here due to my lack of understanding of wave
> functions, and their properties and implications. What do you all think?

Yes, you should pick up a text on QM. It's not that difficult, and it's well worth learning, IMHO. Think of the sound metaphor. It's really more than a metaphor, as QM describes particles by these functions, which are exactly analogous to a sound wave. Non-commuting observables are basically Fourier transforms of each other. With a sound wave, you can use either an pressure amplitude vs. time or an energy amplitude vs. frequency function to get a complete description. But YOU CANNOT devise a wave that will give you an *exact* time of occurence and an exact frequency for a given sound wave.

> Rob.
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Chris Maloney

"Knowledge is good"
-- Emil Faber