Latest debate about multiverse
George Ellis and Jose Silk have written a nice article titled "Scientific method: Defend the integrity of physics". The article criticizes the situation in theoretical physics, which to my view is due to arrogant "the only game in the town" attitude making communications extremely difficult, and the simple and brutal fact that these theories did not work . String models certainly led to a discovery of very powerful and beautiful mathematics: the Universe according to string theory is however certainly not elegant as Brian Greene claims in his book. It would be surprising if this mathematics would not find applications in future physics.
The article of Ellis and Silk has generated a lot of response. One of the responses is the article by Brian Greene titled "Is String Theory About to Unravel?". There is a a strong smell of hype but Greene admits that the connection with experiment is lacking and feels uneasy with multiverse notion.
Peter Woit reacted first and agreed with Ellis and Silk: I can only agree with most what he said. The article of Ellis and Silk generated also science entertainment: Lubos Motl wrote a really long and really aggressive rant and told that all those who do not not blindly believe that string theory is the only game in the town are complete idiots and should flush themselves dow to the toiled where they undoubtedly belong. I cannot avoid associations with old cartoon Tom and Jerry in which Tom tried to destroy Jerry with all kinds of explosives. My humble opinion is that explosives are not the method to build a better world.
Sabine Hossenfelder wrote a nice article Does the Scientific Method need Revision?.
What one means when one says that string theory does not work?
The basic problem was that string world sheet is not 4-D space-time and together with blind belief in GUT ideology this led to a wrong track which led directly to landscape catastrophe and multiverse nonsense. First the adhoc notion of spontaneous compactification was introduced and space-time was identified as actually 10-dimensional object with 6 small dimensions assigned with Calabi-Yau space. The mathematics of Calabi-Yaus is extremely beautiful and only this can explain why so idiotic idea (from the point of view of physics) was taken seriously. The problem is that there is huge number of Calabi-Yaus. This lead to the landscape catastrophe. But still string theory did not work.
Then branes were introduced and space-time was identified as 3-brane. Also higher and lower-dimensional space-times emerged and one had multiverse in which anything goes and there is no hope about testing anything. This opened all the flood gates and endless variety of brane constructions have emerged. One ended up with the multiverse scenario: physics laws depend on the corner of space-time one happens to live in and this forces the introduction of antropic principle if one wants to say something interesting about the universe. Experimentally there is not a slightest indication about multiverse. Ironically, the real physics seems to be extremely simple!
Why theoreticians fell in the trap?
I think that partially this was made possible by the powerful tools of algebraic geometry and I can understand that technically oriented theoreticians loved the application of these magnificent tools developed by mathematicians. Physics was seen as boring low energy phenomenology left for simplistic minds. There was of course also a lot of face keeping and its perfectly understandable that string model gurus who had got power, money, and fame did not want to leave the drowning ship.
In hindsight the tragedy of string theory was that it contained a lot of good mathematics although the proposed physics became gradually more and more non-sensical as the structures became more and more adhoc and complex. Conformal invariance wherefrom everything started is certainly one of the gems with deep physical content. Unfortunately, conformal invariance as such is 2-D notion and should have been generalized to 4-dimensional case in a non-trivial manner without losing the infinite-dimensional character of conformal group.
Could twistors and TGD help out of dead alley?
This is where TGD enters the stage. TGD generalizes conformal invariance and at the same time explains why space-time must be four-dimensional and why 4-D Minkowski space is so unique. What was good that string models brought a lot of new mathematics to the collective consciousness of physics community. Although Calabi-Yau manifolds are not physics, the methods of algebraic geometry used to construct them are extremely powerful and theoreticians have gained impressive knowhow about algebraic geometry. What is lacking is the proper to which one could apply these methods.
The lack of this kind of powerful tools in TGD framework has been a source of personal frustration for me: I have the physics but I do not have the mathematical tools to express it effectively. It seems that the situation is however changing. Twistor spaces associated with 4-D space-times are 6-D like Calabi-Yaus and that associated with empty Minkowski space is Calabi-Yau.
The really important observation is that there are only two twistor spaces with Kähler structure (possessed also by Calabi-Yaus) and M4 and CP2. This fact fixes TGD completely both mathematically and physically: H=M4 ×CP2 is the only choice. TGD also follows from standard model symmetries as well as from number theoretical arguments involving classical number fields. General twistor space has almost complex or even complex structure but not Käahler structure. In any case, the tools of algebraic geometry apply to them. The motivations of Penrose for introducing twistors was indeed this: to use the methods of algebraic geometry to solve field not usable at the level of Minkowski space. These methods indeed work nicely already in the construction of instanton solutions of Yang-Mills equations and one can solve these equations in the twistor space of M4.
But what is so fantastic in these two very special twistor spaces? I realized this only during last week. One of the great challenges of TGD is to construct the solutions of field equations - extremals - of Kähler action since they define an exact part of quantum TGD (in standard QFT this is not the case). The twistor space inspired conjecture is that one can construct solutions of classical field equations of TGD by constructing - not space-time surfaces but their twistor spaces as 6-D surfaces in the twistor space of M4 ×CP2! The twistor space property would be equivalent with extremal property! All structure would be induced also now. This theory would be also a generalization of Witten's twistor string theory which I proposed years ago but in slightly different form and without realizing the connection with twistor spaces. Later I became skeptic and gave up this idea but it can be found in some blog posting.
The transition from 4-D space-time to 6-D twistor space of course looks at first like an un-necessary complication but it brings in complex numbers: all the magnificient technology from algebraic geometry becomes available and string theorists have developed enormous knowhow about it during years! For instance, all the nice mathematics inspired by Calabi-Yaus such as mirror symmetry and associated constructions could generalize to the category of twistor spaces realized as sub-manoflds. The landscape and multiverse would reduce to the world of space-time surfaces representing generalized Feynman diagrams! Physics from TGD and mathematical knowhow from string models!: I dare claim that this is the only way out from the dead alley.