| Topic: |
Science > Physics |
| User: |
"Eckard Blumschein" |
| Date: |
30 Apr 2007 01:15:38 AM |
| Object: |
No common complex domain/space |
This question of mine was called overly vague and speculative by
Igor Khavkine <ikhavki@uwo.ca> Canada
Obviously, he understood some consequences although I wrote 'common
complex domain/space?'.
Most frequently, time domain is considered the original domain from
which Fourier transform leads into a complex frequency domain.
Alternatively it is also possible to perform FT of an original function
of frequency into a complex time domain. Original functions of reality
are always real and unilateral. Each of the two complex counterparts
exhibits Hermitean symmetry. In order to benefit from complex calculus,
one may choose either complex frequency domain or complex time domain.
While the original quantity is physically correct, the conjugate one in
complex domain must be unphysical in that, it is apparently symmetrical
and complex. This avoidable dilemma due to complexity has often been
overlooked. Of course, the uncertainty relation between the two
conjugate variables of a Fourier transform pair attracts more attention
since there is no remedy for it.
My related question refers to operators on a Hilbert space. They may be
complex in general. Recall that rewriting f(x) like a complex function
F(ix) is just a shorthand for the decision to replace e.g. 2 cos(x)dx
just by exp(ix)dx and omit exp(-ix)dx. Getting rid of the imaginary part
is one of two essential steps back to reality. 80 years ago, complex
functions of negative and positive frequency were considered unphysical
and therefore avoided which might have led to the assumption of a real
Hamiltonian, too. Who did deal with the question whether a particular
observable quantity belongs to either a real or a complex Hermitean
operator in Hilbert space? I merely found that Weyl worried about
possibly illusory symmetries.
Eckard Blumschein
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| User: "Eckard Blumschein" |
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| Title: Re: No common complex domain/space |
30 Apr 2007 10:09:24 AM |
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You may get a few more details from IEEE:
ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=4069377&arnumber=4069448&coun
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| User: "Eckard Blumschein" |
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| Title: Re: No common complex domain/space |
02 May 2007 02:43:51 AM |
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On 4/30/2007 5:09 PM, Eckard Blumschein wrote:
You may get a few more details from IEEE:
ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=4069377&arnumber=4069448&coun
IEEE Workshop on Signal Propagation on Interconnects, May 2006, pages
173-176. Abstract, full text PDF 3173 KB.
Digital Object Identifier 10.1109/SPI.2006.289213
also available via
http://iesk.et.uni-magdeburg.de/~blumsche/M283.html
Is there anything we cannot agree on?
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| User: "Eckard Blumschein" |
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| Title: Re: No common complex domain/space |
03 May 2007 05:44:25 AM |
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Past and future are at least so different as are water (past) and air
(future) in a picture by Wheeler:
http://www.bigear.org/vol1no4/wheeler.htm
So far, physics leargely ignores this distinction.
A. Einstein even wrote: "For us believing physicists, the division into
past, present and future has merely the meaning of an albeit obstinate
illusion." No matter that he wrote it in a letter of condolence.
Such thinking hinders physics.
Given you consider this a matter of taste, philosophy, or speculation,
then you should at least accept or try to refute some related strongly
substantiated suspicion of mine. I found out that physicists did not
properly take into account the most trivial basics of complex Fourier
transform. They just learned to get rid of the imaginary part but they
mistook the apparent symmetry. While differential equations are
undoubtedly time-symmetrical, reality is one-sided. Future influences do
not already exist and will never exist in advance.
On 5/2/2007 9:43 AM, Eckard Blumschein wrote:
On 4/30/2007 5:09 PM, Eckard Blumschein wrote:
You may get a few more details from IEEE:
ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=4069377&arnumber=4069448&coun
IEEE Workshop on Signal Propagation on Interconnects, May 2006, pages
173-176. Abstract, full text PDF 3173 KB.
Digital Object Identifier 10.1109/SPI.2006.289213
also available via
http://iesk.et.uni-magdeburg.de/~blumsche/M283.html
Is there anything we cannot agree on?
.
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