o rly? [updated! Ack, need help in Quantum Physics]

[andylawcc]

Originally posted by: Jeff7

That brings up something else that is semi-relevant: a perpetual motion machine. Such a device could never be observed. Doing so would require that some matter or energy beam be reflected off of the device to allow observers a glimpse of the miraculous machine. But that would mean that it is no longer self-perpetuating, as it would then have an outside source of energy. Oops, you just effectively destroyed the perpetual motion machine by observing it!

another good, layman-style explanation.

Originally posted by: andylawcc
okay Jeff7 it doesn't have to be that long ;P

That's what she sa!!!!......aw nevermind.[/quote]

;p

 

[Born2bwire]

One thing to note about the Uncertainty Principle. It does not mean that everything cannot be measured precisely. The basic representation of the principle relates the uncertainty in measuring momentum and position at the same time. Mathematically, this is shown by proving that the position and momentum operators do not commute. However, there are observables that do commute, meaning that you can measure them together accurately. One example is the spin (internal angular momentum) of the electron in a hydrogen atom. Theoretically, we can measure the square of the total spin and the spin along the z-axis. We can also measure the angular momentum of the hydrogen atom along the z-axis and its z position at the same time. Though it's easy to say that we can measure these observables, it's another thing do it in practice.

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This is the mathematical representation of the uncertainty principle. What it means is that the product of the standard deviation in position and momentum of a measurement (if done at the same time) can only be as low as hbar/2. What this means is that if you were to take an ensemble (large amount of measurements on identically prepared systems) of a system, the momentum and position measurements will have a spread. The measure of the spread is the standard deviation. We can force a system to have a very precise range of possible positions (I guess maybe like a quantum dot well). The resulting ensemble of position measurements will be bunched close together, meaning a small deviation in position. But then the momentum measurements would have a large spread. Thus, while we may be able to determine the position of the particle in the system to a high degree, the certainty of its momentum is very poor.