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Answer To Question Number 1...

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Posted by Mark on September 26, 2001 18:54:05 UTC

The uncertainty you're referring to is not the "position/momentum" uncertainty; rather it is the "energy/time" uncertainty principle. This is the principle that states that we cannot know both the exact energy of a system and the duration in time for which it was measured.

The energy uncertainty is associated with time, and the momentum uncertainty is associated with space. If we view just the "space like" qualities, then we are referring to momentum, while the "time like" qualities are referring to energy. Does this help you out with your second question at all? I'm not going to go in depth in answering your second question because I had a hard time understanding and interpreting what exactly you meant. Perhaps you could reword it..?

To answer your first question, the vacuum is teeming with tiny little "virtual particle pairs", which are allowed to "come from nothingness" and return to "nothingness" so long as they don't exist long enough to be noticed. By the way, when I refer to "nothingness", I am referring to the absence of matter; granted space-time itself is not "nothingness" per se. Anyway, physicists like to refer to this phenomenon as "borrowing" energy from the vacuum, which has to be paid back in an amount of time small enough that conservation of energy is not violated. All this is possible via the Heisenberg energy/time uncertainty relation. In effect ... if we keep narrowing down the duration of time, closer and closer to zero, than our knowledge of the duration of time gets closer and closer to EXACT accuracy (we know it to be zero). Just like in the position/momentum uncertainty ... where the act of narrowing down to more confined locations of space gave indeterminate momenta... so too do we get indeterminate energy in shorter spans of time. The shorter the time span, the more energy that's aloud to exist because of our inability to measure it, (nature isn't able to notice that the energy existed). This causes the vacuum to be full of tiny particles that erupt into existence, only to annihilate before they could have been said to "exist". It is surprising, that due to the odd nature of quantum activities, that these little particles can actually effect the momenta of other matter that "actually do exist". This is one of the aspects of the standard model, (the model that explains the interactions of particles), which includes virtual particles as the "force carriers".

Does that answer your first question alright? Here are a couple of technical pieces of information... The lower bound to uncertainty is reliant upon: 1/2 h-bar (h-bar is Planck's Constant divided by 2π), which is h/4π.
And also, if you believe uncertainty to be an intrinsic property of matter and reality ... there is a name for this. It's called the Copenhagen Interpretation of quantum physics.

As far as your third question goes, it was not through philosophical inspiration that led Heisenberg to the discovery of uncertainty. It was through painstaking resolution of paradoxical results of experiments and interpretaion of existing mathematical models. I belive Einstein may have been the first to sugget squaring the wave function of a light particle, to get a probability distribution of possible positions. From then on, the search for a model explaining particle/wave duality led to many important advances including uncertainty.

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