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From: Vermont Skiing Discussion and Snow Reports
[mailto:[log in to unmask]] On Behalf Of Dana Dorsett
Sent: Friday, February 01, 2008 1:37 PM
To: [log in to unmask]
Subject: Re: [SKIVT-L] ????

 

Rachel Rose [[log in to unmask]] writes:

>last itme i checked the laws of physics there was something about not being
able to be in two places at once.

>Maybe that also explain why you haven't seen me. i'm where i am and you're
where you are...not one and the

>same place.

Or maybe you’re rilly rilly tiny and movin’ rilly rilly FAST!?!

Last time I checked the laws of physics: 

Locating a particle in a small region makes the momentum of the particle
uncertain, and conversely, measuring the momentum of a particle precisely
makes the position uncertain.

In quantum mechanics, the position and momentum do not have precise values,
but have a probability distribution. There are no states in which a particle
has both a definite position and momentum. The narrower the probability
distribution is in position, the wider it is in momentum.

A mathematical statement of the principle is that every quantum state has
the property that the root-mean-square (RMS) deviation of the position from
its mean (the standard deviation of the X-distribution):

times the RMS deviation of the momentum from its mean (the standard
deviation of P):

can never be smaller than a small fixed multiple of Planck's constant:

The mathematical statement implies the physical statement. Once an observer
measures the position of a particle with accuracy ΔX, the state of the
particle immediately after the measurement has .

The uncertainty principle is related to the observer effect, with which it
is often conflated. In the Copenhagen interpretation of quantum mechanics,
the uncertainty principle is a theoretical limitation of how small the
observer effect can be. A precise position measurement must alter the
momentum by a large indeterminate amount and vice-versa.

While this is true in all interpretations, in many modern interpretations of
quantum mechanics (many-worlds and variants), the quantum state itself is
the fundamental physical quantity, not the position or momentum. Taking this
perspective, while the momentum and position are still uncertain, the
uncertainty is not just an effect caused by observation, but by any
entanglement with the environment.

So, where the lleh are you (and how fast are you goin’)? 

(Sure wish it were snowing hard instead of R**Nin’ hard! :-(  )

dana

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