Tuesday, December 07, 2010

Dear Fellow Quantum Mechanics

I try not to frequently highlight still-unpublished arXiv manuscripts. Some of them are crap and have no place else where they can go. But often, I would find something written by prominent physicists that simply demand to be mentioned. This is one such example.

Jeremy Bernstein has written an entertaining, but at the same time, rather informative view on quantum mechanics, especially on the "measurement problem". You have to read the entire article to get his argument. Along the way, he clarified the uncertainty principle based on what Heisenberg has written:

The uncertainty principle refers to the degree of indeterminateness in the possible present knowledge of the simultaneous values of various quantities with which the quantum theory deals; it does not restrict, for example, the exactness of a position measurement alone or a velocity measurement alone. Thus suppose that the velocity of a free electron is precisely known, while the position is completely unknown. Then the principle states that every subsequent observation of the position will alter the momentum by an unknown and undeterminable amount such that after carrying out the experiment our knowledge of the electronic motion is restricted by the uncertainty relation. This may be expressed in concise and general terms by saying that every experiment destroys some of the knowledge of the system which was obtained by previous experiments.
This formulation makes it clear that the uncertainty relation does not refer to the past: if the velocity of the electron is at first known and the position then exactly measured the position for times previous to the measurement may be calculated. Thus for the past times ΔxΔp is smaller than the usual limiting value, but this knowledge of the past is of a purely speculative character, since it can never (because of the unknown change in momentum caused by the position measurement) be used as an initial condition in any calculation of the future progress of the electron and thus cannot be subjected to experimental verification. It is a matter of personal belief whether such a calculation concerning the past history of the electron can be ascribed any physical reality or not.

You will note that this is consistent with my earlier blog entry on the misconception of the HUP.

Still, the most fascinating aspect of this article is Bernstein's assertion about the observer based on Dyson's writing:

My second general conclusion is that the ``role of the observer'' in quantum mechanics is solely to make the distinction between past and future. The role of the observer is not to cause an abrupt ``reduction of the wave-packet'', with the state of the system jumping discontinuously at the instant when it is observed. This picture of the observer interrupting the course of natural events is unnecessary and misleading. What really happens is that the quantum-mechanical description of an event ceases to be meaningful as the observer changes the point of reference from before the event to after it. We do not need a human observer to make quantum mechanics work. All we need is a point of reference, to separate past from future, to separate what has happened from what may happen, to separate facts from probabilities.

You also get a little provocative challenge at the very end of the article in which the scale of the Planck's time measured by a clock violates SR? Hum?

Like I said, whether you agree with the article or not, it is highly fascinating. :)


1 comment:

Tim Cordova said...

Great blog by the way! Enjoy that you seem to keep up on some of the latest information. Good job.