Thomas Dent
May5-04, 03:54 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 wondering if anyone had read the paper by the above authors on\nthe effect of proliferating vacua on the cosmological constant\n(hep-th/0311152). The basic idea is that when you have a potential\nwith two or more minima separated by a barrier, the ground state\nwavefunction has significant amplitude in all minima and has a lower\nenergy than states localized in either minimum separately. Under\ncertain conditions this effect (lowering of the global ground state\nenergy relative to localized ground states) can be well-approximated\nby using WKB tunneling amplitude.\n\nThe authors make an extremely rough estimate of what this would do to\na very large number of metastable vacua in a "string landscape". (Not\nall states need be connected by nonzero tunneling amplitudes.) Quantum\nmechanically, the ground state is a superposition of very many local\nminima. They plug in some numbers and turn out to require that in\norder to cancel a typical vacuum energy density of order m_susy^2\nm_Pl^2, where m_susy is about 1 TeV, each vacuum should be capable of\ntunneling to about 10^32 others (out of a total number of 10^90).\n\nSo we live in a superposition of a very large number of "vacua", near\nthe ground state of the complete potential - so far as it can be\nthought of as an effective potential. And it\'s here that my head\nstarts to hurt somewhat. The authors specify that all the vacua that\ncontribute to the result should have the same number of families,\nlow-energy gauge group, softly-broken supersymmetry, etc. (putting\nthis down to "superselection sets of properties") and go on to hope\nthat one can derive some results in particle physics from such a\nvastly-superposed Universe. Wouldn\'t we already have noticed if we\nlived in a superposition of vacua corresponding to different values of\nthe fine structure constant, for example? In contrast to the\n"monovacuists", who hold out (in principle) the hope of unambiguous\npredictions, this view of a single superposed ground state seems to\npresent radical problems of principle for experiment. What is an\nelectron in such a superposed ground state?\n\nThere seem to be two possibilities: first, that most of or all the\nvacua contributing to the superposition have virtually the same values\nof observables. So we can take the electron to be a superposition of\nvery similar entities in each vacuum. This hardly seems credible,\nsince we are talking about 10^32 *distinct* and *different* vacua. Or\nthere is really a statistical distribution of values - even for\nquantities we thought could be measurable with arbitrary precision.\nMaybe this would explain the anomalous 5 sigma effects that are always\ncropping up!!\n\nNow I\'m guessing by this time you will have decided that this idea\nlooks nothing like our universe. So then the question is, why *isn\'t*\nour universe a superposition of a large number of vacua? After all,\nthe authors seem to have shown (under certain assumptions) that the\ntunneling amplitude in the early Universe was large enough for\nsignificant mixing to occur.\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 wondering if anyone had read the paper by the above authors on
the effect of proliferating vacua on the cosmological constant
(http://www.arxiv.org/abs/hep-th/0311152). The basic idea is that when you have a potential
with two or more minima separated by a barrier, the ground state
wavefunction has significant amplitude in all minima and has a lower
energy than states localized in either minimum separately. Under
certain conditions this effect (lowering of the global ground state
energy relative to localized ground states) can be well-approximated
by using WKB tunneling amplitude.
The authors make an extremely rough estimate of what this would do to
a very large number of metastable vacua in a "string landscape". (Not
all states need be connected by nonzero tunneling amplitudes.) Quantum
mechanically, the ground state is a superposition of very many local
minima. They plug in some numbers and turn out to require that in
order to cancel a typical vacuum energy density of order m_{susy}^2m_{Pl}^2, where m_{susy} is about 1 TeV, each vacuum should be capable of
tunneling to about 10^32 others (out of a total number of 10^90).
So we live in a superposition of a very large number of "vacua", near
the ground state of the complete potential - so far as it can be
thought of as an effective potential. And it's here that my head
starts to hurt somewhat. The authors specify that all the vacua that
contribute to the result should have the same number of families,
low-energy gauge group, softly-broken supersymmetry, etc. (putting
this down to "superselection sets of properties") and go on to hope
that one can derive some results in particle physics from such a
vastly-superposed Universe. Wouldn't we already have noticed if we
lived in a superposition of vacua corresponding to different values of
the fine structure constant, for example? In contrast to the
"monovacuists", who hold out (in principle) the hope of unambiguous
predictions, this view of a single superposed ground state seems to
present radical problems of principle for experiment. What is an
electron in such a superposed ground state?
There seem to be two possibilities: first, that most of or all the
vacua contributing to the superposition have virtually the same values
of observables. So we can take the electron to be a superposition of
very similar entities in each vacuum. This hardly seems credible,
since we are talking about 10^32 *distinct* and *different* vacua. Or
there is really a statistical distribution of values - even for
quantities we thought could be measurable with arbitrary precision.
Maybe this would explain the anomalous 5 \sigma effects that are always
cropping up!!
Now I'm guessing by this time you will have decided that this idea
looks nothing like our universe. So then the question is, why *isn't*
our universe a superposition of a large number of vacua? After all,
the authors seem to have shown (under certain assumptions) that the
tunneling amplitude in the early Universe was large enough for
significant mixing to occur.
the effect of proliferating vacua on the cosmological constant
(http://www.arxiv.org/abs/hep-th/0311152). The basic idea is that when you have a potential
with two or more minima separated by a barrier, the ground state
wavefunction has significant amplitude in all minima and has a lower
energy than states localized in either minimum separately. Under
certain conditions this effect (lowering of the global ground state
energy relative to localized ground states) can be well-approximated
by using WKB tunneling amplitude.
The authors make an extremely rough estimate of what this would do to
a very large number of metastable vacua in a "string landscape". (Not
all states need be connected by nonzero tunneling amplitudes.) Quantum
mechanically, the ground state is a superposition of very many local
minima. They plug in some numbers and turn out to require that in
order to cancel a typical vacuum energy density of order m_{susy}^2m_{Pl}^2, where m_{susy} is about 1 TeV, each vacuum should be capable of
tunneling to about 10^32 others (out of a total number of 10^90).
So we live in a superposition of a very large number of "vacua", near
the ground state of the complete potential - so far as it can be
thought of as an effective potential. And it's here that my head
starts to hurt somewhat. The authors specify that all the vacua that
contribute to the result should have the same number of families,
low-energy gauge group, softly-broken supersymmetry, etc. (putting
this down to "superselection sets of properties") and go on to hope
that one can derive some results in particle physics from such a
vastly-superposed Universe. Wouldn't we already have noticed if we
lived in a superposition of vacua corresponding to different values of
the fine structure constant, for example? In contrast to the
"monovacuists", who hold out (in principle) the hope of unambiguous
predictions, this view of a single superposed ground state seems to
present radical problems of principle for experiment. What is an
electron in such a superposed ground state?
There seem to be two possibilities: first, that most of or all the
vacua contributing to the superposition have virtually the same values
of observables. So we can take the electron to be a superposition of
very similar entities in each vacuum. This hardly seems credible,
since we are talking about 10^32 *distinct* and *different* vacua. Or
there is really a statistical distribution of values - even for
quantities we thought could be measurable with arbitrary precision.
Maybe this would explain the anomalous 5 \sigma effects that are always
cropping up!!
Now I'm guessing by this time you will have decided that this idea
looks nothing like our universe. So then the question is, why *isn't*
our universe a superposition of a large number of vacua? After all,
the authors seem to have shown (under certain assumptions) that the
tunneling amplitude in the early Universe was large enough for
significant mixing to occur.