Two centuries of Fourier theorem: Its successes and enigmatic issues that are holding back the progress of physics!
Prof. Chandrasekhar Roychoudhuri
Department of Physics
University of Connecticut, Storrs, CT
12:00 Noon
Chem. 260
It is just over two hundred years that Joseph Fourier successfully introduced his powerful mathematical theorem in physics. It is one of the most pervasively productive and useful tool of physics and optics because its foundation is based on the superposition of harmonic functions and yet we have never declared it as a principle of physics, perhaps for valid reasons. And, yet there are a good number of situations where we pretend it to be the Principle of Superposition of physics, even though light beams pass through each other unperturbed. This has created epistemological problems of enormous magnitude.
The purpose of this talk is to elucidate the problems while underscoring the roots of successes and the elegance of the theorem, which are not openly discussed. We will make our points by taking six major engineering fields of optics and show in each case why it works and under what restricted conditions by bringing in the relevant physics principles. The fields are (i) optical signal processing (diffraction), (ii) Fourier transform spectrometry (interference), (iii) classical spectrometry of pulsed light, (iv) coherence theory, (v) laser mode locking and (vi) pulse broadening. We underscore that mathematical Fourier frequencies, not being physical frequencies, cannot generate real physical effects on our detectors. Appreciation of this fundamental issue will open up new ways to be innovative in designing many new optical instruments. We underscore the importance of always validating our design platforms by emulating real working (interaction) processes in nature even though the real details may be “invisible” to our instruments. This talk summarizes activities published since 2003 in various places including a biannual SPIE conference series on “The nature of light: What is a photon?” [OPN Oct. Sp.Issue (2003); SPIE Proc.Vol.5866 (2005), Vol.6664 (2007), Vol.OP300 (2009) and CRC Press (2008)]
|