<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>alistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0412021027.302911e4@posting.google. com>...\n> Igor Khavkine <k_igor_k@lycos.com> wrote in message news:<pan.2004.11.30.20.07.27.943107@lycos.com>... \n> > > This requires that every mass in the universe has a quadrupole moment -\n> > > see my post on sci.physics.research "complex conjugate of wavefunction"\n> > > which is detailed below:\n> >\n> > [...]\n> >\n> > Your hypotheses were well debunked in that original thread. There is no\n> > need to reproduce that discussion here.\n\n> I think the hypothesis was not well debunked in that original thread.\n\nYou assign conceptual meaning to mathematical objects used in the\ndescription of a theory, then you proceed to try and derive observable\nconsequences. I think you have this process backwards. This much has\nalready been said, if not in so many words.\n\n> You merely asked what is an imaginary probability?\n\nI don\'t recall ever asking that. And your original post in this thread\ncontained neither the word "probability" nor "imaginary".\n\n> Since I was saying the wavefunction multiplied by the complex conjugate\n> of the wavefunction represented two particles being in the same place\n> at the same time,which I suggested was an imaginary probability squared\n> i.e a real probablity,the real probability, is all an\n> experimental observation, predicted by a theory using imaginary\n> probabilities, would care about.\n\nThe word "probability" has a well defined mathematical and conceptual\nmeaning. Prefixing it with the word "complex" creates something which\nis well defined neither mathematically nor conceptually. The concept\nyou are referring to is well known and goes by the name of\n"amplitude". It is used extensively in any wave theory including\nquantum mechanics and classical optics. However, as you yourself\nsuggest physical meaning is only assigned to probabilities (real\nnumbers) which are the amplitudes "squared".\n\n> I could argue that off-shell\n> particles are unreasonable but experiment suggests otherwise.\n\nI would agree with you, off-shell particles are unreasonable.\nIronically, my belief exists because of support by experimental data,\nnot in spite of it. What experiment do you think demonstrates the\nexistence of off-shell particles?\n\n> And bear in mind that any complex number is something of\n> a mystery to anybody because the square root of -1\n> is not at all intuitive-it is used in science\n> because it is a useful tool which can make predictions that\n> can be verified by experiment.I don\'t like complex numbers\n> because they are counter-intuitive, but unfortunately they\n> are,somehow,attached to reality.\n\nYou are right complex numbers are a tool. And liking a tool or not has\nlittle to do with actually using it. See my comments about complex\nnumbers in the thread you started on their use in physics. If you want\nto know why complex numbers come up in a particular situation, the\nanswer is simple: it all comes down to factoring polynomials that have\nno real roots. The challenge is to uncover where these polynomials are\nhiding.\n\nIgor\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>alistair@goforit64.fsnet.co.uk (alistair) wrote in message news:<861c1b21.0412021027.302911e4@posting.google.com>...
> Igor Khavkine <k_{igor_k}@lycos.com> wrote in message news:<pan.2004.11.30.20.07.27.943107@lycos.com>...
> > > This requires that every mass in the universe has a quadrupole moment -
> > > see my post on sci.physics.research "complex conjugate of wavefunction"
> > > which is detailed below:
> >
> > [...]
> >
> > Your hypotheses were well debunked in that original thread. There is no
> > need to reproduce that discussion here.
> I think the hypothesis was not well debunked in that original thread.
You assign conceptual meaning to mathematical objects used in the
description of a theory, then you proceed to try and derive observable
consequences. I think you have this process backwards. This much has
already been said, if not in so many words.
> You merely asked what is an imaginary probability?
I don't recall ever asking that. And your original post in this thread
contained neither the word "probability" nor "imaginary".
> Since I was saying the wavefunction multiplied by the complex conjugate
> of the wavefunction represented two particles being in the same place
> at the same time,which I suggested was an imaginary probability squared
> i.e a real probablity,the real probability, is all an
> experimental observation, predicted by a theory using imaginary
> probabilities, would care about.
The word "probability" has a well defined mathematical and conceptual
meaning. Prefixing it with the word "complex" creates something which
is well defined neither mathematically nor conceptually. The concept
you are referring to is well known and goes by the name of
"amplitude". It is used extensively in any wave theory including
quantum mechanics and classical optics. However, as you yourself
suggest physical meaning is only assigned to probabilities (real
numbers) which are the amplitudes "squared".
> I could argue that off-shell
> particles are unreasonable but experiment suggests otherwise.
I would agree with you, off-shell particles are unreasonable.
Ironically, my belief exists because of support by experimental data,
not in spite of it. What experiment do you think demonstrates the
existence of off-shell particles?
> And bear in mind that any complex number is something of
> a mystery to anybody because the square root of -1
> is not at all intuitive-it is used in science
> because it is a useful tool which can make predictions that
> can be verified by experiment.I don't like complex numbers
> because they are counter-intuitive, but unfortunately they
> are,somehow,attached to reality.
You are right complex numbers are a tool. And liking a tool or not has
little to do with actually using it. See my comments about complex
numbers in the thread you started on their use in physics. If you want
to know why complex numbers come up in a particular situation, the
answer is simple: it all comes down to factoring polynomials that have
no real roots. The challenge is to uncover where these polynomials are
hiding.
Igor