But why does quantum mechanics assume that there is an absolute size that can not be compare to others.

The reason is that to observe the size of something we must interact with it.  However, we cannot do that without changing it.  For example one cannot observe a book in a totally dark room.  Yet turning a light on allows one to see and compare it to other books because some of the photons emanating from it will be absorbed and some will bounce off.  However, the absorbed photons will cause it to heat up and change.

In Classical mechanics is it important that act of observing a system does change it.  This is because one of its basic assumptions is that the characteristics of a system are caused by earlier events and if one knows their history one can predict their future to any degree of accuracy.   However, if the act of observing a system makes a noticeable change in it one can not predict its future with complete accuracy because that act is not reflected in its history. Therefore their must exist something relative smaller than what is being observed so that it will not make a noticeable change in the characteristics of a system when used to make a measurement.

This is why Classical mechanics assumes that when making an observation it is always possible to find something small enough so that can interact with a system without making a noticeable  change in the system being observed.      

Yet as mentioned earlier Quantum Theory is fundamentally different from classical mechanics in that it assumes that everything is quantized and that its smallest possible unit is defined by Planck’s constant or 6.62606957×10^−34.   How we arrive at that number is unimportant to this discussion however what is important is that it defines the degree by which we can determine smallness because there can be absolutely no disturbance, or anything else relatively smaller than it.

Dirac one of founders of modern quantum mechanics defined why this is so important in determining size when he said.

“(Quantun Mechanics assumes) There is a limit to the fineness of our powers of observation and the smallest of the accompanying disturbance, a limit that is inherent in the nature of things and can never be surpassed by improve technique or increased skill on the part of the observer.

In other words if there is an absolute limit to the smallness of a disturbance associated with a measurement as quantum theory suggests then there is also an absolute limit to the smallness of a entity that can be measured without creating a noticeable difference in its future.

Earlier it was mentioned that Classical mechanics requires the interaction of an observer with a system being measured must be small enough so that does not make a noticeable difference in its future.  Therefore, it assumes that one can always make the size of an observing system small relative to the one being observed.

However, the quantum mechanical assumption that there is an absolute limit to the smallest of a disturbance means that also is a limit to the “size” of a system that can be measure without making a noticeable difference in its future.  In other words there is a limit to the “smallness” of an our ability to make a measurement and therefore an absolute limit to “smallness”.

This is how one can justified saying one of the fundamental difference between quantum and classical Newtonian physics is size.

Later Jeff

Copyright Jeffrey O’Callaghan 2012

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