- Classical physics as the geometry of space-times regarded as 4-surfaces in certain 8-dimensional space-time. This generalizes and modifies Einstein's vision. Note that in quantum context the plural "space-times" indeed makes sense.
- Quantum physics as infinite-dimensional geometry of the world of classical worlds=space-time surfaces. This vision generalizes further the vision of Einstein. One of the paradoxes of the sociology of post-modern physics is that M-theorists refuse to realize the enormous unifying power of infinite-dimensional geometry.
- Physics as number theory vision involves several ideas bigger than life.
- p-Adic physics as physics of cognition and intentionality and fusion of real physics and physics of cognition to single super physics by fusing real numbers and p-adic number fields to a larger structure. p-Adic numbers can be applied also to real physics and leads to a plethora of quantitative predictions. It became already decade ago clear that p-adic numbers provide a royal road to the understanding of elementary particle masses. The idea is somewhat tricky: just the requirement that physical system allows p-adic cognitive representations poses unexpectedly strong constraints on the properties of the system, in this case to the values of elementary particle masses. Knowing this I become very sad when I see colleagues to continue the fruitless and more and more bizarre looking M-theory Odysseia. They are now quite seriously suggesting that we must accept that physical theories will never be able to predict anything concrete. They simply cannot imagine the possibility that M theory might be wrong or even worse, not-even-wrong! For the critical discussions about the state of M-theory see the blog Not-Even Wrong of Peter Woit.
- Space-time surfaces as hyper-quaternionic surfaces of 8-dimensional octonionic space-time is an idea which has started to flourish during last months: for details see TGD as a Generalized Number Theory II: Quaternions, Octonions, and their Hyper Counterparts. TGD can be formulated in two dual manners. First corresponds to M^4xCP_2 picture and the second, number theoretical formulation, can be seen as a string model in 8-dimensional Minkowski space M^8 of hyper-octonions. I refer to the possibility to formulate the theory either in M^8 or M^4xCP_2 as "number theoretical compactification". Of course no (spontaneous) compactification occurs. If I would be forced to introduce this monstrously ugly super-stringy notion into TGD, I would be ready to hang myself. What is so beautiful that the classical notion of complex analytic function generalizes to the level of hyper-octonions and physics at this primordial number-theoretical level looks ridiculously simple. WZW action for the automorphism group G_2 of octonions and Dirac action for octonionic 2-spinors satisfying Weyl conditions with solutions given by hyper-octonion analytic functions. In the quantization the real Laurent coefficients of spinor field and G_2 valued field are replaced by mutually commuting Hermitian operators representing observables coding for quantum states so that also quantum measurement theory and quantum-classical correspondence pop up in the number theoretical framework. Here I cannot resist revealing one more fascinating fact: G_2 is a unique exception among simple Lie groups in that the ratio of long roots to short ones is sqrt(3): do not hesitate to tell this also to your friends;-)! The number three pops up again and again in TGD, for instance, the existence of so called trialities corresponds to the existence of classical number fields. I have told at my homepage about my great experiences during which I had the vision about number three as the fundamental number of mathematics and physics and also precognition about the "theory of infinite magnitudes", that is the theory of infinite primes about which I am going to say something after two paragraphs. Perhaps the most beautiful aspect is that m+n-particle vertices correspond to a local multiplication of hyper-octonionic spinors coding for m incoming resp. n outgoing states and the inner product of these products in accordance with the view that generalized Feynman diagrams represent computation like processes developed in Equivalence of Loop Diagrams with Tree Diagrams and Cancellation of Infinities in Quantum TGD I have not taken strings seriously but I must admit the amazing possibility that all information about both classical physics (space-time dynamics) and quantum physics as predicted by TGD might be coded by these number theoretical strings, which are however quite different from the strings of super-string models. The corresponding string diagrams generalize so called braid diagrams to Feynman diagrams a la TGD and also provide a physical realization of topological quantum computation at the level of fundamental physics.
- The notion of infinite primes was inspired by TGD inspired theory of consciousness and is now an organic part of quantum TGD.
- Infinite primes are in one-one correspondence with the states of repeatedly second quantized arithmetic quantum field theory and can be identified as representations of physical states. Infinite primes can in turn be represented as 4-dimensional space-time surfaces. The conjecture that these surfaces solve the field equations of TGD is equivalent with the conjecture that hyper-octonionic spinor fields code for space-time surfaces as hyper-quaternionic surfaces by defining what I call Kähler calibration.
- Infinite primes force also to generalize the notion of ordinary number: each real number corresponds to an infinite number of different variants, which are equivalent as real numbers but p-adically/cognitively non-equivalent so that space-time points becomes an infinitely structured an complex algebraic hologram able to represent in its structure even entire physical universe! This is Brahman=Atman mathematically. Leibniz realized this when he talked about monads but was forgotten for five centuries.
- A further bundle of ideas relates to TGD inspired theory of consciousness. There are two books about this: TGD Inspired Theory of Consciousness and Genes, Memes, Qualia and Semitrance.
- The starting point is a real problem as always. Now it is the paradox created by the non-determinism of quantum jump contra determinism of Schrödinger equation. TGD leads to a solution of the paradox and at the same time emerges a notion of free will and volition consistent with physics. There is no attempt to explain free will and consciousness as as illusions (whatever that might mean!). They are still stubbornly trying to do this, these stubborn neuroscientists!
- A new view about the relationship between experienced, subjective time and the geometric time of physicist emerges. The outcome is a revolutionary modification of the notions of both time and energy.
- The new view about time gives the conceptual tools needed to make scientific statements about what might happen for consciousness after biological death and TGD inspired consciousness has grown into two books covering basic phenomena of consciousness from brain functions to paranormal.
- The possibility of negative energies and signals propagating backwards in geometric time and reflected back by time reflection has several implications. Communications with geometric past (long term memories!) and in principle even with civilizations of geometric future become possible. Intentions might be realized by control signals sent backwards in time. Instantaneous remote sensing by negative energy signals becomes possible, etc...
- p-Adic mathematics leads to and identification of genuine information measures based on Shannon entropy and the replacement of ordinary real norm with p-adic norm and applicable as measures of conscious information. The idea about rationals and algebraic numbers as islands of order in the sea of chaos represented by generic real numbers finds a direct counterpart at the level of physical correlates of conscious experience.
Friday, February 11, 2005
It occurred to me that I could try to summarize the great ideas behind TGD. There are many of them and I cannot summarize them in single page. My dream is to communicate some holistic vision about what I have become conscious of and therefore I start just by listing the great ideas that come to my mind just now and continue later by giving details. These ideas are also summarized in the chapter Overview about the Evolution of Quantum TGD of TGD.