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Why TGD?
Hamed kindly reminded me about article “Why TGD?” that I wrote
recently: why not mention it in blog article.
The article is as an attempt to provide a popular summary about TGD, its motivations, and
basic implications. This is of course mission impossible as such since TGD is something at
the top of centuries of evolution which has led from Newton to standard model. This means
that there is a background of highly refined conceptual thinking about Universe so that even
the best computer graphics and animations do not help much. One can still try – at least to
create some inspiring impressions. The artice approaches the challenge by answering the most
frequently asked questions. Why TGD? How TGD could help to solve the problems of recent day
theoretical physics? What are the basic principles of TGD? What are the basic guidelines in
the construction of TGD?
These are examples of this kind of questions which I try to
answer in the article using the only language that I can talk. This language is a dialect
used by elementary particle physicists, quantum field theorists, and other people applying
modern physics. At the level of practice involves technically heavy mathematics but since it
relies on very beautiful and simple basic concepts, one can do with a minimum of formulas,
and reader can always to to Wikipedia if it seems that more details are needed. I hope that
reader could catch the basic idea: technical details are not important, it is principles and
concepts which really matter. And I almost forgot: problems! TGD itself and almost every new
idea in the development of TGD has been inspired by a problem.
Why TGD?
The first question is “Why TGD?”. The attempt to answer this question requires
overall view about the recent state of theoretical physics.
Obviously standard
physics plagued by some problems. These problems are deeply rooted in basic philosophical -
one might even say ideological – assumptions which boil down to -isms like reductionism,
materialism, determinism, and locality.
Thermodynamics, special relativity, and
general relativity involve also postulates, which can be questioned. In thermodynamics
second law in its recent form and the assumption about fixed arrow of thermodynamical time
can be questions since it is hard to understand biological evolution in this framework.
Clearly, the relationship between the geometric time of physics and experienced time is
poorly understood. In general relativity the beautiful symmetries of special relativity are
in principle lost and by Noether's theorem this means also the loss of classical
conservation laws, even the definitions of energy and momentum are in principle lost. In
quantum physics the basic problem is that the non-determinism of quantum measurement theory
is in conflict with the determinism of Schrödinger equation.
Standard model is
believed to summarize the recent understanding of physics. The attempts to extrapolate
physics beyond standard model are based on naive length scale reductionism and have products
Grand Unified Theories (GUTs), supersymmetric gauge theories (SUSYs). The attempts to
include gravitation under same theoretical umbrella with electroweak and strong interactions
has led to super-string models and M-theory. These programs have not been successful, and
the recent dead end culminating in the landscape problem of super string theories and
M-theory could have its origins in the basic ontological assumptions about the nature of
space-time and quantum.
How could TGD help?
The second question is
“Could TGD provide a way out of the dead alley and how?”. The claim is that is the case. The
new view about space-time as 4-D surface in certain fixed 8-D space-time is the starting
point motivated by the energy problem of general relativity and means in certain sense
fusion of the basic ideas of special and general relativities.
This basic idea has
gradually led to several other ideas. Consider only the identification of dark matter as
phases of ordinary matter characterized by non-standard value of Planck constant, extension
of physics by including physics in p-adic number fields and assumed to describe correlates
of cognition and intentionality, and zero energy ontology (ZEO) in which quantum states are
identified as counterparts of physical events. These new elements generalize considerably
the view about space-time and quantum and give good hopes about possibility to understand
living systems and consciousness in the framework of physics.
Two basic visions
about TGD
There are two basic visions about TGD as a mathematical theory. The
first vision is a generalization of Einstein's geometrization program from space-time level
to the level of “world of classical worlds” identified as space of 4-surfaces. There are
good reasons to expect that the mere mathematical existence of this infinite-dimensional
geometry fixes it highly uniquely and therefore also physics. This hope inspired also string
model enthusiasts before the landscape problem forcing to give up hopes about
predictability.
Second vision corresponds to a vision about TGD as a generalized
number theory having three separate threads.
- The inspiration for the first thread came from the need to fuse various p-adic physics
and real physics to single coherent whole in terms of principle that might be called number
theoretical universality. - Second thread was based on the observation that classical number fields (reals, complex
numbers, quaternions, and octonions) have dimensions which correspond to those appearing in
TGD. This led to the vision that basic laws of both classical and quantum physics could
reduce to the requirements of associativity and commutativity. - Third thread emerged from the observation that the notion of prime (and integer,
rational, and algebraic number) can be generalized so that infinite primes are possible. One
ends up to a construction principle allowing to construct infinite hierarchy of infinite
primes using the primes of the previous level as building bricks at new level. Rather
surprisingly, this procedure is structurally identical with a repeated second quantization
of supersymmetric arithmetic quantum field theory for which elementary bosons and fermions
are labelled by primes. Besides free many-particle states also the analogs of bound states
are obtained and this means the situation really fascinating since it raises the hope that
the really hard part of quantum field theories – understanding of bound states – could have
number theoretical solution.
It is not yet clear whether both great visions are needed or whether either of them is in
principle enough. In any case their combination has provided a lot of insights about what
quantum TGD could be.
Guidelines in the construction of TGD
The construction of new physical theory is slow and painful task but leads gradually to an
identification of basic guiding principles helping to make quicker progress. There are many
such guiding principles.
- “Physics is uniquely determined by the existence of WCW” is is a conjecture but
motivates highly interesting questions. For instance: “Why M4×
CP2 a unique choice for the imbedding space?”, “Why space-time dimension must be
4?”, etc… - Number theoretical Universality is a guiding principle in attempts to realize number
theoretical vision, in particular the fusion of real physics and various p-adic physics to
single structure. - The construction of physical theories is nowadays to a high degree guesses about the
symmetries of the theory and deduction of consequences. The very notion of symmetry has been
generalized in this process. Super-conformal symmetries play even more powerful role in TGD
than in super-string models and gigantic symmetries of WCW in fact guarantee its existence. - Quantum classical correspondence is of special importance in TGD. The reason is that
where classical theory is not anymore an approximation but in well-defined sense exact part
of quantum theory.
There are also more technical guidelines.
- Strong form of General Coordinate invariance (GCI) is very strong assumption. Already
GCI leads to the assumption that Kähler function is Kähler action for a preferred
extremal defining the counterpart of Bohr orbit. Even in a form allowing the failure of
strict determinism this assumption is very powerful. Strong form of general coordinate
invariance requires that the light-like 3-surfaces representing partonic orbits and
space-like 3-surfaces at the ends of causal diamonds are physically equivalent. This implies
effective 2-dimensionality: the intersections of these two kinds of 3-surfaces and 4-D
tangent space data at them should code for quantum states. - Quantum criticality states that Universe is analogous to a critical system meaning that
it has maximal structural richness. One could also say that Universe is at the boundary line
between chaos and order. The original motivation was that quantum criticality fixes the
basic coupling constant dictating quantum dynamics essentially uniquely. - The notion of finite measurement resolution has also become an important guide-line.
Usually this notion is regarded as ugly duckling of theoretical physics which must be
tolerated but the mathematics of von Neumann algebras seems to raise its status to that of
beautiful swan. - What I have used to call weak form of electric-magnetic duality is a TGD version of
electric-magnetic duality discovered by Olive and Montonen. It makes it possible to realize
strong form of holography implied actually by strong for of General Coordinate Invariance.
Weak form of electric magnetic duality in turn encourages the conjecture that TGD reduces to
almost topological QFT. This would mean enormous mathematical simplification. - TGD leads to a realization of counterparts of Feynman diagrams at the level of
space-time geometry and topology: I talk about generalized Feynman diagrams. The highly
non-trivial challenge is to give them precise mathematical content. Twistor revolution has
made possible a considerable progress in this respect and led to a vision about twistor
Grassmannian description of stringy variants of Feynman diagrams. In TGD context string like
objects are not something emerging in Planck length scale but already in scales of
elementary particle physics. The irony is that although TGD is not string theory, string
like objects and genuine string world sheets emerge naturally from TGD in all length scales.
Even TGD view about nuclear physics predicts string like objects.
For details see the new article Why TGD.
Source: http://matpitka.blogspot.com/2014/02/hamed-kindly-reminded-me-about-article.html
