The Landscape and The Matrix [Archive]

Lubos Motl

Apr19-04, 02:53 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>On Mon, 12 Apr 2004, Moshe Rozali wrote:\n\n> Ok, good, we are getting to the point. In the probabilistic view we\n> are in some unlikely vacuum, specified by some set of parameters {y}\n> you decide somehow are not explainable, and the rest of physics {x}...\n\nHi Moshe, I still sympathize with your approach.\n\nLet me propose the following analogy between the Landscape and the Matrix\n(the movie). I hope that this analogy will make it clear why I consider\nthe landscape anthropic approach misguided.\n\nOne can use the laws of the Standard Model to prove - under controllable\nconditions - the existence of a state in the Hilbert space that describes\na large computerized machine with artifacts of human brains attached to\nit. The computer is running a program that gives the brains feelings of\nthe real world, following some physical laws. In fact, we are not too far\nfrom constructing such a system.\n\nActually there is more than one way to construct this Matrix. Most details\nin the machine don\'t matter, and therefore there are at least 10^{10^{26}}\nways to construct the Matrix, i.e. that many microstates in the Hilbert\nspace, and all of them work. Note that the number of realizations of the\nMatrix is much bigger than any proposed number of the flux vacua.\n\nTherefore, most physicists should focus on this "generic" Universe - they\nshould study the idea that we live in the Matrix.\n\nOK, I think that the pattern is now clear. Obviously, I was just joking.\nBut the point is that I think that this approach through The Matrix is\nvery similar to the anthropic type of arguments.\n\nImagine that we want to show that the idea that we live in the Matrix is\nnot a terribly convincing scientific conjecture. What arguments can we\ngive that it is not convincing? Well, The Matrix is a hugely fine-tuned\nstate, there are still many more states that do *not* look like the\nMatrix, and we intuitively feel that it cannot be created "out of\nnothing". Someone had to design it and construct it - it really does not\nmatter whether we call this creator God or anything else. Such an event of\nCreation is unlikely, and the number of observations that we can explain\nfrom this starting point minus the number of assumptions that we must make\nis smaller than in other theories, and therefore this type of Matrix\ntheory (i.e. that we live in the Matrix) is not too convincing\nscientifically.\n\nActually, I think that the same arguments can be applied against the\nanthropic reasoning because the landscape and the Matrix are analogous.\nThe vacua with a complicated structure of hidden dimensions, convoluted\nconfigurations of fluxes, and so on, are simply contrived and artificial\nmuch like the Matrix, and I think it is reasonable to say that it is\nunlikely that something like that is created from the scratch, in any sort\nof cosmic evolution that seems scientific, especially if it is possible\nto have life in much more "canonical" and simpler Universes.\n\nFor example, if there are e^{3000} vacua of the type XYZ, then in the\ncosmological setup we must treat them as microstates, and these vacua\ncarry the entropy S=3000, and according to the holographic bounds, the\nUniverse that contains such a vacuum can never have surface area smaller\nthan A = 4G.S = 1200 Planck areas because it must remember "which" vacuum\nis inside. This is a pretty large bubble, and it is unlikely that such a\nperturbation will be created from "nothing" or from a generic "previous\nUniverse", much like it is unlikely that the Matrix is suddenly\nconstructed. Although I don\'t know the exact rules how such probabilities\nare calculated, I think that the commonsense is sufficient to see that the\nrepresentatives of huge (i.e. contrived) classes will be disfavored, and\nthe fact that there is a large number of vacua of the type XYZ should\nalways be a reason *not* to study them too much.\n\nIf someone knows about a well-defined difference between the Matrix and\nthe Landscape, I would love to hear about it.\n\nAll the best\nLubos\n_____________________________________ _________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\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>On Mon, 12 Apr 2004, Moshe Rozali wrote:

> Ok, good, we are getting to the point. In the probabilistic view we
> are in some unlikely vacuum, specified by some set of parameters {y}
> you decide somehow are not explainable, and the rest of physics {x}...

Hi Moshe, I still sympathize with your approach.

Let me propose the following analogy between the Landscape and the Matrix
(the movie). I hope that this analogy will make it clear why I consider
the landscape anthropic approach misguided.

One can use the laws of the Standard Model to prove - under controllable
conditions - the existence of a state in the Hilbert space that describes
a large computerized machine with artifacts of human brains attached to
it. The computer is running a program that gives the brains feelings of
the real world, following some physical laws. In fact, we are not too far
from constructing such a system.

Actually there is more than one way to construct this Matrix. Most details
in the machine don't matter, and therefore there are at least 10^{10^{26}}
ways to construct the Matrix, i.e. that many microstates in the Hilbert
space, and all of them work. Note that the number of realizations of the
Matrix is much bigger than any proposed number of the flux vacua.

Therefore, most physicists should focus on this "generic" Universe - they
should study the idea that we live in the Matrix.

OK, I think that the pattern is now clear. Obviously, I was just joking.
But the point is that I think that this approach through The Matrix is
very similar to the anthropic type of arguments.

Imagine that we want to show that the idea that we live in the Matrix is
not a terribly convincing scientific conjecture. What arguments can we
give that it is not convincing? Well, The Matrix is a hugely fine-tuned
state, there are still many more states that do *not* look like the
Matrix, and we intuitively feel that it cannot be created "out of
nothing". Someone had to design it and construct it - it really does not
matter whether we call this creator God or anything else. Such an event of
Creation is unlikely, and the number of observations that we can explain
from this starting point minus the number of assumptions that we must make
is smaller than in other theories, and therefore this type of Matrix
theory (i.e. that we live in the Matrix) is not too convincing
scientifically.

Actually, I think that the same arguments can be applied against the
anthropic reasoning because the landscape and the Matrix are analogous.
The vacua with a complicated structure of hidden dimensions, convoluted
configurations of fluxes, and so on, are simply contrived and artificial
much like the Matrix, and I think it is reasonable to say that it is
unlikely that something like that is created from the scratch, in any sort
of cosmic evolution that seems scientific, especially if it is possible
to have life in much more "canonical" and simpler Universes.

For example, if there are e^{3000} vacua of the type XYZ, then in the
cosmological setup we must treat them as microstates, and these vacua
carry the entropy S=3000, and according to the holographic bounds, the
Universe that contains such a vacuum can never have surface area smaller
than A = 4G.S = 1200 Planck areas because it must remember "which" vacuum
is inside. This is a pretty large bubble, and it is unlikely that such a
perturbation will be created from "nothing" or from a generic "previous
Universe", much like it is unlikely that the Matrix is suddenly
constructed. Although I don't know the exact rules how such probabilities
are calculated, I think that the commonsense is sufficient to see that the
representatives of huge (i.e. contrived) classes will be disfavored, and
the fact that there is a large number of vacua of the type XYZ should
always be a reason *not* to study them too much.

If someone knows about a well-defined difference between the Matrix and
the Landscape, I would love to hear about it.

All the best
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Moshe Rozali

Apr19-04, 08:40 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>Oh, Lubos, this is all wasted on me, I don\'t watch this sort of\nmovies, tried once but found it too painful (ask Arvind, it was his\nfault). I also don\'t have an "approach", just confused in general. I\nwas trying to see if the "principle" (whether you find it useful or\nnot) can be phrased in a self-consistent and scientific way, and I am\nalmost convinced now (some doubt lingers though, but it will have to\nwait for another time)\n\nOne comment though about your message, before I go back to work (have\nto finish up a few things before the next holiday takes me by surprise\nagain), the fact that flux vacua are "contrived" I view as a good\nthing. It is probably a good sign when things get dirty, I\'ll take\nthat over spherical cows... as for the other parts of your message,\nmaybe you are right, I wouldn\'t know...\n\n\nbest regards,\n\nMoshe\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>Oh, Lubos, this is all wasted on me, I don't watch this sort of
movies, tried once but found it too painful (ask Arvind, it was his
fault). I also don't have an "approach", just confused in general. I
was trying to see if the "principle" (whether you find it useful or
not) can be phrased in a self-consistent and scientific way, and I am
almost convinced now (some doubt lingers though, but it will have to
wait for another time)

One comment though about your message, before I go back to work (have
to finish up a few things before the next holiday takes me by surprise
again), the fact that flux vacua are "contrived" I view as a good
thing. It is probably a good sign when things get dirty, I'll take
that over spherical cows... as for the other parts of your message,
maybe you are right, I wouldn't know...

best regards,

Moshe

Urs Schreiber

Apr19-04, 09:11 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>On Mon, 19 Apr 2004, Lubos Motl wrote:\n\n> ...Therefore, most physicists should focus on this "generic" Universe -\nthey\n> should study the idea that we live in the Matrix.\n>\n> <snip>\n> Imagine that we want to show that the idea that we live in the Matrix is\n> not a terribly convincing scientific conjecture. What arguments can we\n> give that it is not convincing? Well, The Matrix is a hugely fine-tuned\n> state, there are still many more states that do *not* look like the\n> Matrix, and we intuitively feel that it cannot be created "out of\n> nothing".\n\nYour first point is the only relevant one. The Matrix is not generic. This\nis the counter to the argument in the previously quoted paragraph.\n\n> Actually, I think that the same arguments can be applied against the\n> anthropic reasoning because the landscape and the Matrix are analogous.\n> The vacua with a complicated structure of hidden dimensions, convoluted\n> configurations of fluxes, and so on, are simply contrived and artificial\n> much like the Matrix, and I think it is reasonable to say that it is\n> unlikely that something like that is created from the scratch, in any sort\n> of cosmic evolution that seems scientific, especially if it is possible\n> to have life in much more "canonical" and simpler Universes.\n>\nYour point seems to be that we should not consider finely tuned states\nthat are not representative of the generic solution. This is obviously\ncorrect. But why do you feel that the generic vacuum is not of the form\n"CY plus fluxes"? This is a really broad class of solutions.\n\nBesides, suppose we do find a new larger class of solutions tomorrow.\nSurely this only aggravates the whole problem with the landscape? The\nresurgence of anthropic arguments seems inevitable.\n\nIt doesn\'t really matter if these vacua are "simpler", whatever that\nmeans. There may be some cosmological argument that picks out a\nparticular vacuum, that would be great, but I think it\'s highly unlikely.\n\n> For example, if there are e^{3000} vacua of the type XYZ, then in the\n> cosmological setup we must treat them as microstates, and these vacua\n> carry the entropy S=3000, and according to the holographic bounds, the\n> Universe that contains such a vacuum can never have surface area smaller\n> than A = 4G.S = 1200 Planck areas because it must remember "which" vacuum\n> is inside.\n\nNow this I don\'t understand at all. Why do you restrict to type XYZ? I\nwould have thought that if this makes any sense, all vacua of string\ntheory should be microstates of any universe. Also, do you think vacua\nwith different CCs should be thought of as microstates of one universe?\n\nRegards,\n\nArvind.\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>On Mon, 19 Apr 2004, Lubos Motl wrote:

> ...Therefore, most physicists should focus on this "generic" Universe -
they
> should study the idea that we live in the Matrix.
>
> <snip>
> Imagine that we want to show that the idea that we live in the Matrix is
> not a terribly convincing scientific conjecture. What arguments can we
> give that it is not convincing? Well, The Matrix is a hugely fine-tuned
> state, there are still many more states that do *not* look like the
> Matrix, and we intuitively feel that it cannot be created "out of
> nothing".

Your first point is the only relevant one. The Matrix is not generic. This
is the counter to the argument in the previously quoted paragraph.

> Actually, I think that the same arguments can be applied against the
> anthropic reasoning because the landscape and the Matrix are analogous.
> The vacua with a complicated structure of hidden dimensions, convoluted
> configurations of fluxes, and so on, are simply contrived and artificial
> much like the Matrix, and I think it is reasonable to say that it is
> unlikely that something like that is created from the scratch, in any sort
> of cosmic evolution that seems scientific, especially if it is possible
> to have life in much more "canonical" and simpler Universes.
>
Your point seems to be that we should not consider finely tuned states
that are not representative of the generic solution. This is obviously
correct. But why do you feel that the generic vacuum is not of the form
"CY plus fluxes"? This is a really broad class of solutions.

Besides, suppose we do find a new larger class of solutions tomorrow.
Surely this only aggravates the whole problem with the landscape? The
resurgence of anthropic arguments seems inevitable.

It doesn't really matter if these vacua are "simpler", whatever that
means. There may be some cosmological argument that picks out a
particular vacuum, that would be great, but I think it's highly unlikely.

> For example, if there are e^{3000} vacua of the type XYZ, then in the
> cosmological setup we must treat them as microstates, and these vacua
> carry the entropy S=3000, and according to the holographic bounds, the
> Universe that contains such a vacuum can never have surface area smaller
> than A = 4G.S = 1200 Planck areas because it must remember "which" vacuum
> is inside.

Now this I don't understand at all. Why do you restrict to type XYZ? I
would have thought that if this makes any sense, all vacua of string
theory should be microstates of any universe. Also, do you think vacua
with different CCs should be thought of as microstates of one universe?

Regards,

Arvind.

Lubos Motl

Apr20-04, 12:40 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>On Mon, 19 Apr 2004, Arvind Rajaraman (signed as Urs Schreiber) wrote:\n\n> Your point seems to be that we should not consider finely tuned states\n> that are not representative of the generic solution. This is obviously\n> correct. But why do you feel that the generic vacuum is not of the form\n> "CY plus fluxes"?\n\nDon\'t you think that instead of asking me to prove that something is not\ngeneric, the physicists who propose that something *is* generic should\nexplain and prove their claim - and especially why this claim is\nphysically relevant? These models might be generic in the sense that a\ngeneric paper in 2003 that discusses the embedding of the real world in\nstring theory focuses on the flux vacua. Otherwise if we talk about the\n"real" genericity, I don\'t even know what this statement means.\n\nWhat is the measure that decides whether something is generic or not? If\nit is the sort of measure "one configuration of fluxes and shape of the\n\'hidden\' dimensions, regardless of the configuration of the \'large\'\ndimensions - one vote", then I don\'t think that such a notion of\ngenericity (and any consequence of such a notion) is worth a serious\ndiscussion because it is a randomly chosen and dynamically unjustifiable\nmeasure that is unlikely to have any trustable physical consequences.\n\nAny cosmological selection mechanism or any calculation of the measure\nmust involve the early history of the Universe where the difference\nbetween the "hidden" and "large" dimensions went away, and therefore a\n"bureaucratic" measure based on a completely different treatment of the\nlarge and the hidden dimensions is guaranteed to be wrong.\n\n> This is a really broad class of solutions.\n\nSo is the Matrix.\n\n> Besides, suppose we do find a new larger class of solutions tomorrow.\n> Surely this only aggravates the whole problem with the landscape? The\n> resurgence of anthropic arguments seems inevitable.\n\nWell, I really don\'t think that the purpose of science is to look for ever\nlarger classes of increasingly contrived solutions, and I don\'t care too\nmuch which class has the biggest "population". These increasingly\nhuman-engineered solutions just don\'t seem interesting for scientifical\npurposes. The purpose of science is, on the contrary, to look for special\n(and robust) enough collections of ideas or equations so that they can\nexplain something and reduce the number of independent assumptions about\nthe reality. The scientists have always had a lot of ways how to construct\nhuge numbers of models (for example, by saying that every feature of the\nworld must look exactly the way it does - how it was created by God -,\notherwise the Universe would not work), but the models that came with an\nunnecessarily large number of assumptions, parameters and/or structures\nhave, at least so far, always been proved irrelevant and inferior to other\ntheories that we treat seriously today. In other words, the anthropic\noption was *always* there, and it *never* led to anything correct.\n\n> It doesn\'t really matter if these vacua are "simpler", whatever that\n> means.\n\nDo you really believe that it does not matter? In my opinion it is the\nnumber one thing that matters in science if one decides which theory among\nthe theories more or less capable to describe reality is better and/or\ncloser to the truth. The simpler model with a smaller number of parameters\nand assumptions is always preferred, and the models with many parameters\ni.e. the models from these "huge classes" must never become the ultimate\nexplanation that we are satisfied with. I think that this is a totally\nfundamental rule of looking for the truth in theoretical physics. This\nrule was important before people decided that the theory of everything\narises from string theory (recall which explanations of the\nMorley-Michelson experiments would have to be adopted if special\nrelativity were not found), and it must also be true even if we look for\nthe right explanation within the framework of string theory.\n\n> There may be some cosmological argument that picks out a particular\n> vacuum, that would be great, but I think it\'s highly unlikely.\n\nLet me give you an example how the Big Bang could give us a more realistic\nmeasure than the naive measure that leads many people to these strange and\nnot-quite-reasonably sounding anthropic conclusions. Imagine that a Planck\ntime after the Big Bang, in some "foamy" regime, the Universe is in a\nthermal-like ensemble of all conceivable early Universes. By definition,\nthe theory of everything is nonsingular, and therefore this generalized\ntemperature (or imagine some sort of chemical potential for the fluxes and\nother parameters) is NOT infinite. Let\'s simplify and call this\ntemperature right after the Big Bang "Planck temperature". It is of order\none, and it gives an exponential Boltzmann supression of the states with\ntoo high energy (or flux).\n\nFor example, a state with the total number of fluxes - the counterpart of\nthe energy - equal to 4000 will have a supression exp(-4000). If the\nensemble is well-defined and convergent, this supression goes to zero\nfaster than the number of states with comparable fluxes goes to infinity,\nand therefore these increasingly complicated vacua are increasingly\nunlikely and irrelevant for the statistical purposes. (Incidentally, do\nyou believe that the number of the vacua similar to flux vacua is finite?\nIs there some evidence?) The truly generic state according to this more\nrealistic description will be a relatively simple state. Well, it can be a\nlittle more complicated, but it is certainly not true that the more\ncomplicated ("generic" according to the naive measure, i.e. coming from a\nvery large family) state you choose, the more it will contribute to the\nensemble. On the contrary.\n\n> > For example, if there are e^{3000} vacua of the type XYZ, then in the\n> > cosmological setup we must treat them as microstates, and these vacua\n> > carry the entropy S=3000, and according to the holographic bounds, the\n> > Universe that contains such a vacuum can never have surface area smaller\n> > than A = 4G.S = 1200 Planck areas because it must remember "which" vacuum\n> > is inside.\n>\n> Now this I don\'t understand at all. Why do you restrict to type XYZ?\n\nBecause I wanted to calculate the lower bound. In reality, one does not\nneed to restrict to the class XYZ, and the entropy - and therefore the\nsize of the bubble - is even much bigger, and it is even less likely that\nyou will end up in one of these artificially engineered vacua.\n\n> I would have thought that if this makes any sense, all vacua of string\n> theory should be microstates of any universe. Also, do you think vacua\n> with different CCs should be thought of as microstates of one\n> universe?\n\nDefinitely if you consider any ensemble right after the Big Bang because\nsome relatively small differences in the CC did not matter when the\nUniverse was Planckian. Is there some reason to have doubts that these\nflux vacua must be treated as macroscopically indistinguishable\nmicrostates right after the Big Bang (which is the only moment when such\nquestions matter)?\n\nCheers,\nLubos\n______________________ __________________________________________________ ______\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\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>On Mon, 19 Apr 2004, Arvind Rajaraman (signed as Urs Schreiber) wrote:

> Your point seems to be that we should not consider finely tuned states
> that are not representative of the generic solution. This is obviously
> correct. But why do you feel that the generic vacuum is not of the form
> "CY plus fluxes"?

Don't you think that instead of asking me to prove that something is not
generic, the physicists who propose that something *is* generic should
explain and prove their claim - and especially why this claim is
physically relevant? These models might be generic in the sense that a
generic paper in 2003 that discusses the embedding of the real world in
string theory focuses on the flux vacua. Otherwise if we talk about the
"real" genericity, I don't even know what this statement means.

What is the measure that decides whether something is generic or not? If
it is the sort of measure "one configuration of fluxes and shape of the
'hidden' dimensions, regardless of the configuration of the 'large'
dimensions - one vote", then I don't think that such a notion of
genericity (and any consequence of such a notion) is worth a serious
discussion because it is a randomly chosen and dynamically unjustifiable
measure that is unlikely to have any trustable physical consequences.

Any cosmological selection mechanism or any calculation of the measure
must involve the early history of the Universe where the difference
between the "hidden" and "large" dimensions went away, and therefore a
"bureaucratic" measure based on a completely different treatment of the
large and the hidden dimensions is guaranteed to be wrong.

> This is a really broad class of solutions.

So is the Matrix.

> Besides, suppose we do find a new larger class of solutions tomorrow.
> Surely this only aggravates the whole problem with the landscape? The
> resurgence of anthropic arguments seems inevitable.

Well, I really don't think that the purpose of science is to look for ever
larger classes of increasingly contrived solutions, and I don't care too
much which class has the biggest "population". These increasingly
human-engineered solutions just don't seem interesting for scientifical
purposes. The purpose of science is, on the contrary, to look for special
(and robust) enough collections of ideas or equations so that they can
explain something and reduce the number of independent assumptions about
the reality. The scientists have always had a lot of ways how to construct
huge numbers of models (for example, by saying that every feature of the
world must look exactly the way it does - how it was created by God -,
otherwise the Universe would not work), but the models that came with an
unnecessarily large number of assumptions, parameters and/or structures
have, at least so far, always been proved irrelevant and inferior to other
theories that we treat seriously today. In other words, the anthropic
option was *always* there, and it *never* led to anything correct.

> It doesn't really matter if these vacua are "simpler", whatever that
> means.

Do you really believe that it does not matter? In my opinion it is the
number one thing that matters in science if one decides which theory among
the theories more or less capable to describe reality is better and/or
closer to the truth. The simpler model with a smaller number of parameters
and assumptions is always preferred, and the models with many parameters
i.e. the models from these "huge classes" must never become the ultimate
explanation that we are satisfied with. I think that this is a totally
fundamental rule of looking for the truth in theoretical physics. This
rule was important before people decided that the theory of everything
arises from string theory (recall which explanations of the
Morley-Michelson experiments would have to be adopted if special
relativity were not found), and it must also be true even if we look for
the right explanation within the framework of string theory.

> There may be some cosmological argument that picks out a particular
> vacuum, that would be great, but I think it's highly unlikely.

Let me give you an example how the Big Bang could give us a more realistic
measure than the naive measure that leads many people to these strange and
not-quite-reasonably sounding anthropic conclusions. Imagine that a Planck
time after the Big Bang, in some "foamy" regime, the Universe is in a
thermal-like ensemble of all conceivable early Universes. By definition,
the theory of everything is nonsingular, and therefore this generalized
temperature (or imagine some sort of chemical potential for the fluxes and
other parameters) is NOT infinite. Let's simplify and call this
temperature right after the Big Bang "Planck temperature". It is of order
one, and it gives an exponential Boltzmann supression of the states with
too high energy (or flux).

For example, a state with the total number of fluxes - the counterpart of
the energy - equal to 4000 will have a supression \exp(-4000). If the
ensemble is well-defined and convergent, this supression goes to zero
faster than the number of states with comparable fluxes goes to infinity,
and therefore these increasingly complicated vacua are increasingly
unlikely and irrelevant for the statistical purposes. (Incidentally, do
you believe that the number of the vacua similar to flux vacua is finite?
Is there some evidence?) The truly generic state according to this more
realistic description will be a relatively simple state. Well, it can be a
little more complicated, but it is certainly not true that the more
complicated ("generic" according to the naive measure, i.e. coming from a
very large family) state you choose, the more it will contribute to the
ensemble. On the contrary.

> > For example, if there are e^{3000} vacua of the type XYZ, then in the
> > cosmological setup we must treat them as microstates, and these vacua
> > carry the entropy S=3000, and according to the holographic bounds, the
> > Universe that contains such a vacuum can never have surface area smaller
> > than A = 4G.S = 1200 Planck areas because it must remember "which" vacuum
> > is inside.
>
> Now this I don't understand at all. Why do you restrict to type XYZ?

Because I wanted to calculate the lower bound. In reality, one does not
need to restrict to the class XYZ, and the entropy - and therefore the
size of the bubble - is even much bigger, and it is even less likely that
you will end up in one of these artificially engineered vacua.

> I would have thought that if this makes any sense, all vacua of string
> theory should be microstates of any universe. Also, do you think vacua
> with different CCs should be thought of as microstates of one
> universe?

Definitely if you consider any ensemble right after the Big Bang because
some relatively small differences in the CC did not matter when the
Universe was Planckian. Is there some reason to have doubts that these
flux vacua must be treated as macroscopically indistinguishable
microstates right after the Big Bang (which is the only moment when such
questions matter)?

Cheers,
Lubos
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