Asymmetry in time domain by means of Hermitian symmetry?

Eckard Blumschein

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Heaviside\'s function has been widely used as to consider asymmetry of\nthe world with respect to past and future time. The Fourier transform of\na single sided real function of time is said to exhibit Hermitian\nsymmetry. This means its real part is a symmetrical function of\nfrequency while its imaginary part is an antisymmetical one. When\nSchroedinger and Dirac introduced complex representations like wave\nfunction and ket, Schroedinger eventually got real results by\nmultiplying psi and its complex conjugate. Because it is - regardless of\nNoether\'s theorem - definitely impossible to measure any future function\nof time, I imagine that use of a sliding Heaviside function could yield\na more realistic description in time domain while many properties are\npresumably not affected from putative temporal asymmetry.\nI am, however, aware of Arnold Neumaier who declared nonhermitian\nHamiltonians essential with respect to an optical potential and complex\nscaling if I understood him correctly.\nAlso, Weisskopf and Wigner in Z. Physik, v 63, 54, 1939 reportedly\naccounted for spontaneous decay by replacing the real eigenvalues by\ncomplex ones the imaginary part of which is 1/2 the state\'s lifetime.\n\nBeing just qualified in application of FT in EE but interested in a\ndeeper understanding of physics as well, I would appreciate a convincing\nelucidation. So far I wonder why quantum physics seems to describe the\nworld in an anticipatory manner. Furthermore, Feynman\'s simultaneously\nback and forth running time is puzzling me. I rather prefer to imagine\nSchroedinger\'s picture or Heisenberg\'s picture being modified into a\nsuperposition of clockwise and anticlockwise rotating phasors or frames,\nrespectively. Direction of rotation is anyway arbitrarily chosen.\n\nMay I ask who already dealt with partial application of Heaviside\'s\nfunction on Hilbert space outside theory of signal processing, in\nparticular in quantum physics?\n\nEckard Blumschein\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Heaviside's function has been widely used as to consider asymmetry of
the world with respect to past and future time. The Fourier transform of
a single sided real function of time is said to exhibit Hermitian
symmetry. This means its real part is a symmetrical function of
frequency while its imaginary part is an antisymmetical one. When
Schroedinger and Dirac introduced complex representations like wave
function and ket, Schroedinger eventually got real results by
multiplying [itex]\psi[/itex] and its complex conjugate. Because it is - regardless of
Noether's theorem - definitely impossible to measure any future function
of time, I imagine that use of a sliding Heaviside function could yield
a more realistic description in time domain while many properties are
presumably not affected from putative temporal asymmetry.
I am, however, aware of Arnold Neumaier who declared nonhermitian
Hamiltonians essential with respect to an optical potential and complex
scaling if I understood him correctly.
Also, Weisskopf and Wigner in Z. Physik, v 63, 54, 1939 reportedly
accounted for spontaneous decay by replacing the real eigenvalues by
complex ones the imaginary part of which is 1/2 the state's lifetime.

Being just qualified in application of FT in EE but interested in a
deeper understanding of physics as well, I would appreciate a convincing
elucidation. So far I wonder why quantum physics seems to describe the
world in an anticipatory manner. Furthermore, Feynman's simultaneously
back and forth running time is puzzling me. I rather prefer to imagine
Schroedinger's picture or Heisenberg's picture being modified into a
superposition of clockwise and anticlockwise rotating phasors or frames,
respectively. Direction of rotation is anyway arbitrarily chosen.

May I ask who already dealt with partial application of Heaviside's
function on Hilbert space outside theory of signal processing, in
particular in quantum physics?

Eckard Blumschein

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