Jim and Bill,
I only just caught the continuation of this thread. Let me give you my explanation of the Heisenberg Uncertainty Relation and then my interpretation of what Peikoff is saying and see what you think.
Heisenberg states that you can only measure (in the usual meaning of measure; i.e. with instruments) the position and the momentum of a subatomic particle to accuracies that satisfy his uncertainty relation. The classical reason for this is found in most Modern Physics books.
In order to measure the position of something, you have to probe it with, for example, light with a wavelength smaller than the position accuracy desired. Now, the momentum of light is inversely proportional to its wavelength, so the smaller the wavelength (and so the more accurate a position measurement) the greater the momentum of the probe. This will affect the subatomic particle’s momentum, due to the collision of the light and the particle. So, if the particle’s momentum was known prior to the probe, it is now uncertain by an amount given by the momentum exchange during the collision. So, basically, the measurement disturbs that which is being measured. It can be shown that the product of the uncertainty of the momentum and the uncertainty of the position of the particle cannot be less than h/4pi.
What I think Peikoff is saying, and what I think is true, is that this problem of measuring something extremely small is an epistemological problem. That is, it says nothing about whether the subatomic particle has a precise trajectory and obeys causality when not being measured. That would be a metaphysical statement and Heisenberg had no justification for saying that based on his uncertainty relation. Hence Peikoff’s statement quoted by Jim: “Our ignorance of certain measurements, however, does not affect their reality or the consequent operation of nature.”
Thanks,
Glenn
(Edited by Glenn Fletcher on 11/08, 8:15am)
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