Revolutions must begin as solutions to profound problems. Nima Arkani emphasizes two key problems of recent day theoretical physics. Nima believes that space-time is doomed and formulates second basic problem as question "Why a macroscopic Universe?".
One can see identify the basic problems in very many manners and I have somewhat different identifications. I would add to the list of really big problems also those of neuroscience, biology, and consciousness. There is also a profound problem in the sociology of science due to the uncritical beliefs in naive length scale reductionism and materialism. To me the tragic story of superstring models is a convincing proof that length scale reductionism is dead and it is time to bring fractality to the fundamental physics.
I will compare Nima's problems to some of my personal problems in the following. Maybe reader is inspired to identify his or her own personal problems;-).
Space-time is Doomed
Nima believes that the notion of space-time is useful but redundant: it is doomed, we must get rid of it.
- One can assign to this idea holography, which is a very nice notion. Holography assumes that physics can be described in terms of lower-dimensional basic entities, which would be 3-D surfaces determining space-time.
- Emergent space-time is a stronger, now fashionable, view, which unfortunately seems unable to avoid circular arguments: one starts from 2-D surfaces to get 3-space but already starting point implicitly assumes 3-space.
- Holography would be even stronger in TGD framework. Adelic physics predicts that 2-D (rather than 3-D data) combined with number theoretical discretization of space-time surface in H=M4× CP2 determines the space-time surface and quantum states in zero energy ontology (ZEO).
Nima would like to replace spacetime with twistors.
- Twistor Grassmann approach has turned out to be extremely powerful and simplifies dramatically the calculations in supersymmetric gauge theories but has its problems: particles should be massless. There is
also the closely related problem of infrared cutoff. String models and TGD suggest the idea that masslessness should be generalized: in TGD all particles would be massless in H=M4× CP2 but massive
in M4. This require generalization of twistor approach.
- Twistors are a notion very tightly rooted to space-time geomery - especially that of M4, and I find it very difficult to get rid of them. Twistor space can be seen a bundle structure with space-time as base space so that twistors become rather ad hoc objects if one forgets the space-time. Second problem is that twistors work nicely only for empty Minkowski space. This leads to problems in the twistorialization of gravity.
Personally also I do believe that something is indeed redundant but that it is not space-time. Rather, I would doom the idea about space-time and classical particles as independent entities. I see classical particles are space-time quanta, pieces of space-time identified as 4-D surface. Also classical fields decompose to spacetime quanta - the notion of field body comes out of this.
The topologically simple Einsteinian space-time would be replaced with topologically extremely complex object in all scales: many-sheeted spacetime as surface in certain 8-D space-time H. H =M4× CP2 is given and extremely simple and explains standard model physics. Also the dynamics of space-time surface is extremely simple locally. Globally the situation is totally different. This view changes entirely our interpretation about what we see: we would see the wild topology of space-time surface as various objects of external world just by our bare eyes!
Important point: this revolutionary reinterpretation is not possible without lifting the symmetries of Special Relativity from space-time to imbedding space H= M4× CP2: Symmetries move the space-time in H rather than point of space-time inside space-time. GRT view about space-time is quite too rigid to allow particle physics. H and entire TGD was motivated by the energy problem of GRT, which to me is a big problem.
What about twistors in TGD? One cannot replace space-time with twistors. At classical level one can however replace space-time surface with its 6-D twistor bundle having space-time as base space. This gives rise to the twistor lift of TGD - possibly only for H=M4× CP2 (!!) - does and leads to very powerful and correct predictions allowing to understand how Planck length and cosmological constant emerge from TGD. The point is that M4 and CP2 are the only 4-D spaces allowing twistor space with Kähler structure. TGD is mathematically completely unique as also physically. The huge Yangian symmetries related to twistor amplitudes discovered by Nima and others generalize in TGD and give in ZEO excellent hopes about the construction of scattering amplitudes as representations of super-symplectic Yangian.
Why macroscopic space-time?
In GRT based cosmology it is difficult to understand why macroscopic space-time rather than only Planck length sized objects should exist. Also I see this as a real problem.
To have all possible scales one would need something scale invariant at the fundamental level. GRT the abstract 4-D space-time cannot give it. In TGD the imbedding space M4× CP2 does so. M4 has infinite size, and one can scale the size of space-time surfaces in M4 up and down. This means in particular that one obtains macroscopic space-time.
A more refined formulation is in terms of zero energy ontology (ZEO).
- In ZEO causal diamonds of form CD× CP2 are key objects. CD is intersection of future and past directed light-cones of M4, Penrose diagram is good illustration. CD represents kind of perceptive field for a conscious entity.
- Twistor lift implies that action determining space-time surface contains volume term (cosmological constant) and all space-time surfaces as preferred extremals of action are minimal surface extremals of so called Kähler action. The action would be infinite for infinitely sized space-time surface.
- CD has however finite size and the action remains finite: hence ZEO is forced by twistor lift. CDs form a fractal scale hierarchy. Cosmological constant Λ obeys discrete coupling constant evolution like all coupling strengths (so that radiative corrections vanish). Λ is inversely proportional to p-adic length scale squared and becomes small in long p-adic scales so that space-time surfaces inside arbitrarily large CDs having finite action become possible. One can have macroscopic space-time. By the way, particle mass scales define one fundamental problem of standard physics and p-adic length scale hypothesis, which I conjecture to follow from adelic physics, would solve this problem.
- In cosmology there is also the problem why background temperature is so exactly constant although the distant regions in very early times have not been able to communicate with each other in order to reach thermodynamical equilibrium. There is also the problem of dark matter and energy. In TGD framework these problems are solved by the hierarchy if Planck constants heff/h=n emerging from adelic physics and implying quantum coherence - in particular gravitational one - on all scales. Entire Universe would be like a living organism in this picture.
For a summary of earlier postings see Latest progress in TGD.