Frank Hellmann
Apr23-04, 03:24 PM
<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>I was always of the opinion that decoherence/MW based interpretations\nstill needed ad hoc implementation of propabilities, but it occured to\nme while rephrasing this in a recent QM thread that one could write a\nsupperposition differently:\n\ninstead of:\na/b|1> + c/b|2> with a,b,c natural numbers and normalization a+c=b we\ncould forget about normalization and instead call this:\n\na|1> + c|0> and then write this as |1> + |1> + |1> + ... + |0> + |0> +\n....\n\nWhich would create different branches. Now if we further assume c\nhidden variables against which the interactions that lead towards the\nmacroscopic system are unaware, while they in detail still exist, this\nwould lead to all the branches we need to have a proper propability in\nMW.\n\nNow this local variables would have to be very delicately balanced\nbetween not significantly influencing the |pointer state> while still\nbeing significant enough to eliminate the off diagonal elements of our\ndensity matrix, but we\'ve got a lot of hidden complexity between us\nand the atoms we are talking about...\n\nAlso of course the mathematics of the entire system would be changed\nquite dramatically by working with rationals insteaqd of reals.... I\nthink though our final split in different hidden variables could be in\na normal Hilbert space again since the states |1,1>, |1,2>,... make\ntheir own branch and don\'t care about their prefactor.\nI think it would effectively mean an algebraization of QM, all\nprobabilities would be rational instead of real.\n\nHas anybody ever studied such a possibilitie of getting a consistent\nMW interpretation by "smearing out" the ad hoc possibilities over the\nentire theory?\n\n\n---\nFrank Hellmann\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>I was always of the opinion that decoherence/MW based interpretations
still needed ad hoc implementation of propabilities, but it occured to
me while rephrasing this in a recent QM thread that one could write a
supperposition differently:
instead of:
a/b|1> + c/b|2> with a,b,c natural numbers and normalization a+c=b we
could forget about normalization and instead call this:
a|1> + c|0> and then write this as |1> + |1> + |1> + ... + |0> + |0> +
....
Which would create different branches. Now if we further assume c
hidden variables against which the interactions that lead towards the
macroscopic system are unaware, while they in detail still exist, this
would lead to all the branches we need to have a proper propability in
MW.
Now this local variables would have to be very delicately balanced
between not significantly influencing the |pointer state> while still
being significant enough to eliminate the off diagonal elements of our
density matrix, but we've got a lot of hidden complexity between us
and the atoms we are talking about...
Also of course the mathematics of the entire system would be changed
quite dramatically by working with rationals insteaqd of reals.... I
think though our final split in different hidden variables could be in
a normal Hilbert space again since the states |1,1>, |1,2>,... make
their own branch and don't care about their prefactor.
I think it would effectively mean an algebraization of QM, all
probabilities would be rational instead of real.
Has anybody ever studied such a possibilitie of getting a consistent
MW interpretation by "smearing out" the ad hoc possibilities over the
entire theory?
---
Frank Hellmann
still needed ad hoc implementation of propabilities, but it occured to
me while rephrasing this in a recent QM thread that one could write a
supperposition differently:
instead of:
a/b|1> + c/b|2> with a,b,c natural numbers and normalization a+c=b we
could forget about normalization and instead call this:
a|1> + c|0> and then write this as |1> + |1> + |1> + ... + |0> + |0> +
....
Which would create different branches. Now if we further assume c
hidden variables against which the interactions that lead towards the
macroscopic system are unaware, while they in detail still exist, this
would lead to all the branches we need to have a proper propability in
MW.
Now this local variables would have to be very delicately balanced
between not significantly influencing the |pointer state> while still
being significant enough to eliminate the off diagonal elements of our
density matrix, but we've got a lot of hidden complexity between us
and the atoms we are talking about...
Also of course the mathematics of the entire system would be changed
quite dramatically by working with rationals insteaqd of reals.... I
think though our final split in different hidden variables could be in
a normal Hilbert space again since the states |1,1>, |1,2>,... make
their own branch and don't care about their prefactor.
I think it would effectively mean an algebraization of QM, all
probabilities would be rational instead of real.
Has anybody ever studied such a possibilitie of getting a consistent
MW interpretation by "smearing out" the ad hoc possibilities over the
entire theory?
---
Frank Hellmann