[TowerTalk] Much Smaller Antennas Possible?

[Fuqua, Bill L]

  Yes there is no free lunch. In fact the limits for radio waves and photons are the same as described by Heisenberg's Uncertainty Principle.
The limit has to do with the range of  momentum in the x direction and the width, in the x direction, of the aperture. This determines the
beam with for photons, electrons and other very small particles. Antenna gain is achieved by reducing beam width. 
   In regards to radiation efficiency, if you retain 100 percent efficiency and reduce the antenna's size there is no getting around the 
reduction in bandwidth. 
  You can't have your cake and eat it too. 
One thing that I can't get over is that Heisenberg's Uncertainty Principle is misstated in almost all text books, in regards to the
mathematical representation and the reference to a "Measurement". When I sat down to derive it my self I found the result to be quite
different from the published relationships. After doing some research I found that I came to the came conclusion Heisenberg did in his 
first paper and the same year another physicist applied statistics and the current form came about, however, the lower case sigmas which
represent standard deviation has been replaced by deltas which have a completely different mathematical meaning.   
  I have not seen the actual published paper. Can someone provide it? 
73
Bill wa4lav