Comparison of string model and TGD: answer to the question of Harekhrisna Acharaya
Harekhrisna Acharaya asked how TGD compares with string theory. In the following a short answer.
TGD could be also seen as a generalization of string models. Strings replace point-like particles and in TGD 3-surfaces replace them.
A. Symmetries
- In string models 2-D conformal symmetry and related symmetries are in key roles. They have a generalization to TGD. There is generalization of 2-D conformal invariance to space-time level in terms of Hamilton-Jacobi structure. This also implies a generalization of Kac-Moody type symmetries. There are also supersymplectic symmetries generalizing assignable to δ M4+×CP2 and reflecting the generalized symplectic structure for the light-cone M4+ and symplectic structure for CP2. These symmetries act as Noether symmetries in the “world of classical worlds” (WCW).
- In string models 2-D conformal invariance solves field equations for strings. This generalizes to the TGD framework.
- One replaces string world sheets with 4-D surfaces as orbits of 3-D particles replacing strings as particles. The 2-D conformal invariance is replaced with its 4-D generalization. The 2-D complex structure is replaced with its 4-D analog: I call it Hamilton-Jacobi structure. For Minkowski space M4 this means composite of 2-D complex structure and 2-D hypercomplex structure. See this .
- This allows a general solution to the field equations defining space-time in H=M4×CP2 realizing holography as generalized holomorphy. Space-time surfaces are analogous to Bohr orbits. Path integral is replaced with sum over Bohr orbits assignable to given 3-surface.
Space-time surfaces are roots of two generalized holomorphic functions of 1 hypercomplex (light-like) coordinate and 3 complex coordinates of H. Space-time surfaces are minimal surfaces irrespective of action as long as it is expressible in terms of the induced geometry.
B. Uniqueness as a TOE
The hope was that string models would give rise to a unique TOE. In string models branes or spontaneous compactification are needed to obtain 4-D or effectively 4-D space-time. This forced to give up hopes for a unique string theory and the outcome was landscape catastrophe.
- In TGD, space-time surfaces are 4-D and the embedding space is fixed to H=M4×CP2 by standard model symmetries. No compactification is needed and the space-time is 4-D and dynamical at the fundamental level.
The space-time of general relativity emerges at QFT limit when the sheets of many-sheeted space-time are replaced with single region of M4 made slightly curved and carryin gauge potentials sum of those associated with space-time sheets.
- Freed found that loop spaces have a unique geometry from the existence of Riemann connection. The existence of the Kahler geometry of WCW is an equally powerful constraint and also it requires maximal isometries for WCW so that it is analogous to a union of symmetric spaces. The conjecture is that this works only for H=M4×CP2. Physics is unique from its geometric existence.
- The existence of the induced twistor structure allows for the twistor lift replacing space-time surfaces with 6-D surfaces as S2 bundles as twistor spaces for H=M4×CP2 only. Only the twistor spaces of M4 and CP2 have Kaehler structure and this makes possible the twistor lift of TGD.
- Number theoretic vision, something new as compared to string models, leads to M8-H duality as an analog of momentum position duality for point-like particles replaced by 3-surface. Also this duality requires H=M4×CP2. M8-H duality is strongly reminiscent of Langlands duality.
Although M8-H duality is purely number theoretic and corresponds to momentum position duality and does not make H dynamical, it brings to mind the spontaneous compactification of M10 to M4×S .
C. Connection with empiria
String theory was not very successful concerning predictions and the connection with empirical reality. TGD is much more successful: after all it started directly from standard model symmetries.
- TGD predicts so called massless extremals as counterparts of classical massless fields. They are analogous to laser light rays. Superposition for massless modes with the same direction of momentum is possible and propagation is dispersion free.
- TGD predicts geometric counterparts of elementary particles as wormhole contacts, that is space-time regions of Euclidean signature connecting 2 Minkowskian space-time sheets and having roughly the size of CP2 and in good approximation having geometry of CP2. MEs are ideal for precisely targeted communications.
- TGD predicts string-like objects (cosmic strings) as 4-D surfaces. They play a key role in TGD in all scales and represent deviation from general relativity in the sense that they do not have 4-D M4 projection and are not Einsteinian space-times. The primordial cosmology is cosmic string dominated and the thickening of cosmic strings gives rise to quasars and galaxies. Monopole flux tubes are fundamental also in particle, nuclear and even atomic and molecular physics, biology and astrophysics. See for instance this .
- An important deviation of TGD from string models is the notion of field body. The Maxwellian/gauge theoretic view of fields is replaced with the notion of a field body having flux sheets and flux tubes as body parts. Magnetic monopoles flux tubes require no currents to maintain the associated magnetic fields. This explains the existence of magnetic fields in cosmic scales and of huge cosmic structures. Also the stability of the Earth’s magnetic field finds an explanation.
The dark energy of cosmic strings explains the flat velocity spectrum of stars around galacxies and therefore galactic dark matter.
The dimensions of extensions correspond to a hierarchy of effective Planck constants heff=nh0 serving as measure of algebraic complexity and giving rise to a hierarchy of increasing quantum coherence scales. Ordinary particles with heff>h behave like dark matter. The identification is not as galactic dark matter but as dark phases residing at field bodies and controlling ordinary matter (heff serves as a measure for intelligence). They explain the missing baryonic matter. For a summary of earlier postings see Latest progress in TGD.
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.
Source: http://matpitka.blogspot.com/2024/05/comparison-of-string-model-and-tgd.html
Anyone can join.
Anyone can contribute.
Anyone can become informed about their world.
"United We Stand" Click Here To Create Your Personal Citizen Journalist Account Today, Be Sure To Invite Your Friends.
Lion’s Mane Mushroom
Mushrooms are having a moment. One fabulous fungus in particular, lion’s mane, may help improve memory, depression and anxiety symptoms. They are also an excellent source of nutrients that show promise as a therapy for dementia, and other neurodegenerative diseases. If you’re living with anxiety or depression, you may be curious about all the therapy options out there — including the natural ones.Our Lion’s Mane WHOLE MIND Nootropic Blend has been formulated to utilize the potency of Lion’s mane but also include the benefits of four other Highly Beneficial Mushrooms. Synergistically, they work together to Build your health through improving cognitive function and immunity regardless of your age. Our Nootropic not only improves your Cognitive Function and Activates your Immune System, But it benefits growth of Essential Gut Flora, further enhancing your Vitality.
Our Formula includes:
Lion’s Mane Mushrooms which Increase Brain Power through nerve growth, lessen anxiety, reduce depression, and improve concentration. Its an excellent adaptogen, promotes sleep and improves immunity.
Shiitake Mushrooms which Fight cancer cells and infectious disease, boost the immune system, promotes brain function, and serves as a source of B vitamins.
Maitake Mushrooms which regulate blood sugar levels of diabetics, reduce hypertension and boosts the immune system.
Reishi Mushrooms which Fight inflammation, liver disease, fatigue, tumor growth and cancer. They Improve skin disorders and soothes digestive problems, stomach ulcers and leaky gut syndrome.
Chaga Mushrooms which have anti-aging effects, boost immune function, improve stamina and athletic performance, even act as a natural aphrodisiac, fighting diabetes and improving liver function.
Try Our Lion’s Mane WHOLE MIND Nootropic Blend 60 Capsules. Today Be 100% Satisfied Or Receive A Full Money Back Guarantee Order Yours Today By Following This Link.