Tuesday, June 05, 2012

Ontologizing

Sean Carroll in Cosmic Variance had a posting related to the low entropy of the universe at big bang. The posting is motivated by a criticism of Carroll's own views. Carroll believes that the low entropy of the very early universe is a problem and that the notion of multiverse somehow resolves it. Carroll has naive view about evolution of universe: just Hamiltonian and unitary time evolution and that's all. No questions about problems with general coordinate invariance and symmetries.

Carroll has developed a rhetoric Occam's razor argument about simplicity of theory. Even lawyer would admire it. Since multiverse interpretation does not involve wave function "collapse" ("":s are due to Carroll) it is simpler as a theory and we have a good reason to accept it. I have learned that a standard manner to build a simple theory is to throw out those things which are difficult to understand. Biology, neuroscience, and consciousness belong to this unlucky stuff in recent day theoretical physics.

Lubos comments the posting of Carroll. Lubos does not see anything problematic in the low entropy of the very early Universe. Second law forces it by definition. Lubos in his characteristic manner takes the recent thermodynamics as the final word of science and concludes that Carroll and everyone disagreeing with him does not understand thermodynamics and is pseudo-scientist.

Second issue discussed is the notion of multiverse and many worlds interpretation of quantum mechanics. Carroll assumes cosmological multiverse in his argument for the low entropy as well as the closely related anthropic principle needed to make at least some sense of multiverse. Lubos believes in multiverse because he believes on inflation (and M-theory!). Lubos does not believe in many worlds interpretation since he does not believe that Schrödinger amplitudes - or more generally quantum states- are "real". I would justify my disbelief on Everett interpretation by simple fact that the multiverse poetry about splitting quantum states to my best understanding does not have any translation to any existing mathematics. This does not however require giving up the notion of quantum state if one is ready to return to the roots and make questions about the nature of time.

Discussion revolves among many notions and to my opinion a lot of assumptions leading to the recent crisis remain implicit in the discussion. It is amusing to see that most problems relate to uncritical belief of the theoretical paradigms created during last decades and to notions which should be challenged. Thefatal turning point was probably the introduction of GUTs for four decades ago bringing in untestable assumptions (such as extension of gauge group). Inflationary scenario is highly hypothetical scenario leading to the multiverse. A further hypothetical element is standard view about SUSY. And finally the landscape summarizing the outcome of super string models.

In the following I summarize TGD point of view on the issues discussed. I hope that reader has familiarity with TGD.

Challenging the status of QFT


Both Carroll and Lubos take QFT approach as granted when one talks about low energy physics. TGD forces to modify this view dramatically.

  1. The notion of many-sheeted space-time and the reduction of the dynamics of classical fields to the dynamics of preferred extremals of Kähler action (just four field like variables, I could say something about simplicity here!). The notion of many-sheeted space-time allows to circumvent the basic objection stating that one cannot have a linear superposition of various fields independently, not even for single field. The point is that only the effects - classically forces - caused by the fields superpose. Particles can have topological sum contacts to large number of space-time sheets and thus they experience superpositions of corresponding forces. This modifies profoundly the existing view. Even the description of Maxwellian fields created by current distribution can be translated to a many-sheeted description by replacing the sum of nearby and radiation fields with a union distinct space-time sheets.

  2. This means giving up the standard view that some GUT with a huge number of field variables describes the low energy limit of THE theory. This picture is just wrong if TGD is correct and I believe that Occam favors TGD. GUTs are also responsible for the many difficulties in theoretical particle physics and cosmology. Standard SUSY is be replaced with something dramatically simpler and having very different physical interpretation. In this framework it is difficult to imagine that the whole CERN would be trying to identify the point of a very high-dimensional parameter space at which the Universe is believed to be lurking. It is strange that SUSY enthusiasts do not realize that just ending up on this situation tells that something must be wrong. Same applies of course to landscapeologists.

Views about quantum theory is

Also the view what quantum theory is must be modified in TGD framework. The original motivation was simple: the path integral approach simply failed in TGD context.

  1. TGD leads to a generalization of Einstein's geometrization program for classical fields. Entire quantum theory must be geometrized in terms of the Kähler geometry of "world of classical worlds" (WCW). Quantum states are interpreted as classical spinor fields in the "world of classical worlds" (WCW). These geometric generalizations of Schrödinger amplitudes are definitely something very real so that I am forced to disagree with Copenhagen interpretation and Lubos. This also leads to a beautiful geometrizaton of fermionic statistics in terms of Clifford algebra of WCW and to "quantization without quantization". At space-time level one has free induced spinor fields and quantization for these. Bosonic emergence means that all states are obtained by using fermions as building bricks. This is also an enormous simplification and if this picture is correct, the standard QFT limit need not have much sense except as approximate description.

  2. Zero energy ontology (ZEO) in which quantum can be seen as a square root of thermodynamics. Quantum states are characterized by entanglement between positive and negative energy parts of zero energy parts and they form what could be seen as a complex square root of density matrix. In this framework "unitary time evolution generated by Hamiltonian" assumed by Carroll is hopelessly simplistic and simply wrong view about the real physical situation. In the p-adic context the the notion of unitary time evolution generated by Hamiltonian is simply non-sense. Zero energy ontology has powerful implications for the notion of Feynman diagrams which are topologized and geometrized. In particular, finiteness of the amplitudes is manifest since also virtual particles consist of massless on mass shell wormhole throats. There are also intriguing connections to the twistor approach.

  3. TGD based view about quantum jump and state function reduction and extension of physics to a theory of consciousness.The new view about the relationship of experienced time and geometric time however allows to have also the notion of quantum jump without logical contradictions, and one can resolve the basic paradox of quantum measurement theory without giving up the notion of objective reality but replacing it with quantum universe recreated in each quantum jump. Free will and consciousness have place in the theory.

    Understanding the anatomy of quantum jumps in ZEO leads to a new view about U-matrix, M-matrix and S-matrix and the resulting picture is extremely simple. U-matrix relates two state basis prepared with respect to either light-like boundary of CD. Time evolution by quantum jumps means sequences of reduction with respect to these two state basis: time flip-flow might be the proper term. Quantum classical corresponds can be used to argue that at space-time level given system is not able to detect the change of the arrow of imbedding space geometric time in this alternating sequence of state function reductions.

    Negentropy Maximization Principle the fundamental principle of consciousness theory generalizing quantum measurement theory implies second law in a generalized form required by ZEO, new view about time, and new view about entanglement due to the possibility of p-adic physics identified as physics of cognition.

Generalization of thermodynamics

The generalization of thermodynamics implied by TGD means strong deviations from the naive belief of Lubos that there is nothing to add to what Boltzmann gave to us.

  1. This includes the definition of entropy in ZEO as a scale dependent notion. This is very relevant when one wants to speak about entropy in cosmological context: entropy characterizes zero energy state and therefore corresponding CD rather than time=constant snapshot of cosmology.

  2. The distinction between subjective time and geometric time demonstrates that many problems of cosmology related to entropy are pseudo problems. Big Bang is temporal boundary, not a moment of creation: quantum jumps are moments of re-creation and can be localized to any CD anywhere in the imbedding space. One should not assign "before" and "after" to geometric time. Colleagues still refuse to consider seriously the possibility that subjective time and geometric might be different although the debate between Bohr and Einstein revolved around this difference (about which neither of them was aware). Presumably the materialistic dogma is the basic explanation for this short sightedness.

  3. Second law holds true but the reversal of the arrow of geometric time is possible at imbedding space level: phase conjugate laser beams and many self-organization processes in biology would represent natural candidates in this respect.

  4. Genuinely negentropic entanglement stable with respect to Negentropy Maximization Principle (NMP) is possible. Negentropic entanglement is the main characterizer of what it is to be living, and space-time correlates of thermodynamics discussed in earlier posting.

TGD analogs for multiverse and inflation

The notion of many words, multiverse and landscape have analogies in TGD Universe but there is nothing problematic in these concepts.

  1. Many world view corresponds to the identification of WCW spinor fields as quantum superpositions of 3-surfaces allowing by holography an interpretations superposition of 4-surfaces. There is however no need to assume the mysterious repeated splitting of the quantum states.

  2. The huge vacuum degeneracy of Kähler action implying 4-D spin glass degeneracy something analogous to multiverse mathematically but free of interpretational difficulties. The non-quantum fluctuating variables - zero modes - include the induced Kähler field with completely well-defined physical interpretation, and serve as macroscopic classical variables essential in quantum measurement theory.

  3. In M-theory spontaneous compactification is needed to get something which could be called physically sensible theory. This leads to the landscape catastrophe spoiling completely the original idea that the dynamics of strings gives gravitation by bringing in gravitational fields as dynamical quantites at target space level. Imbedding space is not dynamical in TGD Universe. This saves from the landscape. Imbedding space is fixed by standard model quantum numbers and the conjecture is that it imbedding space is unique just from the mathematical existence of WCW and has number theoretic interpretation. Already in loop spaces Kähler geometry is unique and requires maximal Kac-Moody symmetry algebra.

  4. Both Lubos and Carroll believe in inflation in turn leading to multiverse. Inflationary scenario is however highly speculative and plagued by numerous difficulties. The recent findings challenging the notion of galactic halo of dark matter, do not help in this respect and again one must ask is the whole approach wrong in some manner.

    In TGD framework there is no inflation. The critical Robertson-Walker cosmologies are unique apart from their duration and correspond to accelerating expansion due to a negative pressure term. Cosmic string explain acceleration expansion at more microscopic level. Cosmic strings dominate during primordial cosmology. Later they expand and give rise to cosmic magnetic fields. They also decay to ordinary matter and dark matter so that the inflaton field is eliminated as so many other fields. Their magnetic tension is responsible for the negative pressure term in the long length scale description in terms of Robertson Walker cosmology. Their magnetic energy corresponds to dark energy.

9 Comments:

At 7:58 AM, Blogger ThePeSla said...

Matti,

I posted from some philosophy of number theory today- I did mention the initial conditions in relation to entropy. You were an example and I am wondering about systems that are not simply p-adic. Hope you enjoy and maybe let me know more what is beyond and how you got the 19 and so on...

It is the same question as to the irrelevant idea and the razor idea of some multiverse after inflation (which is another absurd theory that is only one minor state or view- lacking both future vision and the wisdom of the Greeks.)

Of course I am not claiming to be a philosopher either- or a singer and musician but I have to discourage groupies and I invariably pick hit songs.

ThePeSla

 
At 11:39 AM, Blogger Ulla said...

A BUDDHABROT, a technique invented by Melinda Green. The point is iterated through the function, z = zˆ2 + c, where z has components in both the real and imaginary planes. If the particle escapes (exits the viewing area with high speed), its path is reiterated, exposing its position onto the image surface with each step. In this fashion, areas of dense particle travel appear bright white. The result is an amazing universe of structure, spirituality, and mathematical intrigue.

http://www.complexification.net/gallery/machines/buddhabrot/buddhabrotPRN.jpg

http://www.superliminal.com/fractals/bbrot/bbrot_rgb_small.jpg
http://www.superliminal.com/fractals/bbrot/bbrot.htm

Reminds me of the chakras or energetic systems. Cool pic.

But getting a Mandelbrot on two perpendicular intersecting planes, while having the transition between them being more interesting than simply spinning or rotating the thing on its axis, is more difficult.

Well, the “standard” hypercomplex number system isn't the only option. There are alternative systems that give multiple imaginary components with slightly different interrelations. There are quaternions (tried them, didn't like them), and there are other potential configurations and a larger overarching system of eight-parameter octonions. The Mandelbrot-based solid at the top of this blog was made with one of those. The internal shape is also slightly reminiscent of a Buddhabrot.

 
At 1:39 AM, Blogger hamed said...

Dear Matti,

i am very tired because of much thinking on TGD in this morning! there is some questions, whenever you have free time please answer.

“Use CP_2 coordinates (with u one of the coordinates) in which first contribution is just CP_2 metric. The M^4 contribution is Delta g_uu= m_kl partial_um^kpartial_um^l
But this contribution vanishes since M^4 projection is light-like so that one has just CP_2 metric. The internal geometry is just CP_2 geometry”
I misunderstood: u is one of the coordinates of CP2? which of the coordinates of Eguchihn-Hanson? then 3 coordinates of CP2 are left so that they are orthogonal to u and M4 coordinates? g_uu = 0 then only the 3 coordinates of CP2 have contribution to induced metric?
At last you noted one has just CP_2 metric, but CP_2 metric is not Euclidean then why you noted this is Euclidean region?
When you point to Euclidean regions, this 3-D space is not subspace of a 4D Minkowski space in contrast to common view of every Euclidean space?

Octonion numbers are 1, i1, i2, .. i7 so that i_k^2=-1.
Hyper-octonion numbers are 1, i*i1, i*i2, .. i*i7 so that i=square root of -1 and is commutative and associative with others? Then it is more convenient to say Hyper-octonion numbers are 1, e1, e2, … e7 so that e_k^2=+1? This form a non-associative algebra.
The hyperquaternion are the same as hyperbolic-quaternion in http://en.wikipedia.org/wiki/Hyperbolic_quaternion ?
What is co-hyper-quaternion? Is this an algebra correspond to hyper-quaternion but it is co-associative?
Space-time-surface is a hyper-quaternionic sub-manifold of hyper-octonionic imbedding space. Similarly what is physical interpretation of a co-hyper-quaternionic submanifold?

 
At 3:13 AM, Anonymous matpitka@luukku.com said...

To Hamed:

Yes, variable u can be taken any coordinate for CP_2. u is any function of CP_2 coordinates. This reflects the generality of the solution.

CP_2 has *Euclidian signature of metric* (I might well use sometimes the shorthand "Euclidian"- sorry for confusion. This shorthand is often used when path integral in Minkowskian signature is transformed by Wick rotation to Euclidian one, say over 4-sphere. Minkowskian signature means signature 1-1-1-1. Euclidian as short hand does not mean flat.

 
At 3:17 AM, Anonymous matpitka@luukku.com said...

To Hamed:


I have used terms hyper-quaternion and -octonion in non-standard sense since I simply was not aware of the existence of this kind objects. I introduced the notion much before Wikipedia!

What I mean is following. I complexify octonions and quaternions by adding this commutative imaginary unit to get 16-D space - not a field. In case of hyperoctonions I restrict the consideration to a subspace spanned by 1, iE1,....iE7. These numbers form a sub-space but not field not algebra.

The conjecture is that preferred extremals could be regarded as hyperquaternionic sub-manifolds of imbedding space regarded as hyperoctonionic plane of complexified octonions locally (tangent space). This means following.

In introduce the representation of imbedding space gamma matrices in terms of hyper-octonion units. This is discussed at http://tgd.wippiespace.com/public_html/tgdnumber/tgdnumber.html#visionb .

These "gamma matrices" are actually not matrices in strict sense since they are not associative. This representation exists in dimension 8.

I require that the induced gamma matrices - that is projections

Gamma_mu =Gamma_k partial_mu h^k

of the hyper-octonionic gamma matrices - form a hyper-quaternionic sub-space at each point of space-time surface. This gives algebraic equations at each point of surface in terms of gradients and octonionic structure constants. Second order partial derivatives disappear. The only motivation for the proposal is number theoretical beauty!!

Co-hyper-quaternionic would mean that same holds true for the gamma matrices spanning the 4-D normal space of space-time surface.

This is just a conjecture that I have not been able to prove wrong, perhaps just because I am so lazy to write things out explicitly.

There is second variant about the notion of hyper-octonionity involving Wick rotation so that one can formulate preferred extremals in terms of octonion -real analytic functions but I will not go to this here.

I would not pay too much attention to these conjectures at this stage. It would be better just to understand the use of the geometric variational principle to deduce field equations and understand the basic extremals. Best attitude on your side would be attempt to kill these conjectures some day!

 
At 5:42 AM, Anonymous matpitka@luukku.com said...

Dear Hamed,

I became again interested in finding preferred extremals of Kahler action which would have 4-D CP_2 and M^4 projections. This would correspond to Maxwell phase that I conjecture long time ago. Deformations of CP_2 type vacuum extremals would correspond also to these extremals. The signature of the induced metric might be also Minkowskian.


I proceed by the following arguments to the ansatz.

a) Effective 3-dimensionality for action (holography) requires that action decomposes to vanishing j^alphaAlpha term + total divergence giving 3-D "boundary" terms. The first term vanishes for

j^alpha=0

Empty space Maxwell equations, something extremely natural. Also for the proposed GRT limit these equations are true.

b) How to obtain empty space Maxwell equations j^alpha=0? Answer is simple: assue self duality or its slight modification:
J=*J holding for CP_2 type vacuum extremals or more general condition

J=k*J, k some constant not far from unity.

c) Field equations reduce with these assumptions to equations differing from minimal surfaces equations only in that metric g is replaced by Maxwellian energy momentum tensor T. Skematically:

Tr (TH^k)=0,

where T is Maxwellian energy momentum tensor and H^k is second fundamental form.


d) It would be nice to have minimal surface equations since they are the non-linear generalization of massless wave equations. This is achieved if one has

T= lambda g.

One would have dynamically generated cosmological constant! This begings to look really interesting since it appeared also at the proposed GRT limit of TGD.


e) Very skematically and forgetting indices and being sloppy with signs, the expression for T reads as

T= JJ -g/4 Tr(JJ)

This should be proportional to metric.

Self duality implies that Tr(JJ) is just the instanton density and does not depend on metrica and is constant.

For CP_2 type vacuum extremals one obtains

T= -g+g=0

Cosmological constant would vanish in this case.


f) Could it happen that for deformations a small value of cosmological constant is generated?

The condition would reduce to

JJ= (Lambda-1)g.

I would guess that Lambda must relate to the value of parameter k appearing in the generalized self-duality condition.

This would generalize the defining condition for Kahler form

JJ=-g (i^2=-1 geometrically)

stating that the square of Kahler form is the negative of metric. The only modification would be that index raising is carried out by using the induced metric containing also M^4 contribution rather than CP_2 metric.

g) Explicitly:

J_{alphamu} J^mu_beta = -g_alphabeta

Cosmological constant would measure the breaking of Kahler structure.

This might serve for you or anyone;-) as a teaser but do not take it as any challenge. This kind of problems can well take decades of sub-conscious thought! The reason is that an over-determined system of equations is in question. Algebraic equations from the analog of self-duality and of J^2=-g plus minimal surface equations. Direct attack does not work in this kind of situation.

 
At 1:28 PM, Blogger ThePeSla said...

Matti, hello again,

http://motls.blogspot.com/2012/06/why-matrix-theory-contains-membranes.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+LuboMotlsReferenceFrame+%28Lubos+Motl%27s+reference+frame%29

I find this a strange article, not to criticize theoreticians I do not know but it seems to me that they are close to some new idea (perhaps if they really try to understand what we do know of dark matter (5 times matter) and accept it more abstractly. Duh, the brane idea and the matrix idea are related says our humble correspondent-

Well, this is a good beginning to which I doubt they would explore to the extent you have- like generalizing Feynman and so on. I see also the idea of building things up as a form of local entanglements- rather primitive ideas for advanced people as if they cannot grasp the idea of matter or gravity by the continuity of dark energy.

On top of this there is a sort of revisionism of who discovers what by those who view us but have no dialog- they do claim discovery and force things into their framework- this may be but part of the case yet where it occurs it can do nothing but impeded progress in theory- as I said otherwise the names are not relevant in the long run.

I find Leo's work lately interesting and we do have the mystery of different mechanisms for black holes in the news lately.
I made a photo of the sun reflected hundreds of times on the rivers surface whorls and flows that sort of matched his picture.

I may work off line awhile. I am up to 2003 in computer skills and studying. I am not comfortable with the standard use of the super and sub scripts of the formulas if we want an expanded math and space of which most are trained in I suppose. Perhaps you can modify this meaningfully.

There is an article also that suggests something, they think sound, exists that is a communication between plants (but are there quantum FM like wave forms after all? What could be the link if not something like the analogy to dark matter? Your take on this in the TGD frame would be welcome. (science daily and new scientist, Ulla I will send links later)

Nevertheless we are making breakthrough progress- I see where your take is original despite the drama of detractors.

ThePeSla with no desire to speed up their education beyond a certain point. Dark matter as with any such vacua has structure and it is at least Euclidean.

 
At 1:44 PM, Blogger ThePeSla said...

http://2.bp.blogspot.com/-mmJt5JmahVU/T9EV83hWlfI/AAAAAAAAH-o/B_P0OXxCaBo/s1600/sunscorion.jpg

Silicon Suns like Leo

http://www.newscientist.com/article/mg21428683.300-plants-may-be-able-to-hear-others.html

http://www.sciencedaily.com/releases/2012/06/120607142254.htm

consider what is the symmetry of thermodynamics involved here, as with Leo's concepts and silicon.

It is interesting if the Higgs can be something between matter and dark matter but it may take more than this hint of a description or method of reasoning or experimental possibilities. Let us call this dark mathematical symmetry breaking- your interest in cosmic strings is justified but is not just a matter of membrane and matrix (hmmm tell Lubos the M or W is for the cloud future scientist saw once on mars that looks like Cassiopia :-) M perhaps for beautiful Minds.

Oh, the photo is from my other local blogspot spheresend.blogspot.com two tubers passed under the bridge as I was taking the photo- life is much more complex than simple space and beautiful though we tattoo our skins and contemplate our pierced navels soaking up the sunlight....

 
At 7:49 PM, Anonymous matpitka@luukku.com said...

To Pesla:

Matrix models were a short burst of fashion relatively long time ago. It did not work and was forgotten. Just for curiosity I looked at the idea and wrote even a blog posting about it when japanese string researchers hyped that they can understand the dimension of space-time in this framework.

I found that matrix approach is full of unjustified assumptions. The argument reducing string theory to a dynamics of point (Schrodinger equation!) is a classical example about where a sloppy thinking can lead. To me it is simply nonsense. Today theoretical physicists do very precise and massive calculations but as a rule their conceptual thinking is unforgivably sloppy. They call this sloppiness "pragmatism".

Lubos's interest is easy to understand: he has himself worked with Matrix model when he still did something concrete with strings and M-theory.

 

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