A. Questions related to time, entropy, causality, and T violation
A1. Arrow of time (e.g. entropy's arrow of time): Why does time have a direction?
Understanding of the arrow of time requires a new ontology. I have talked a lot about zero energy ontology (ZEO) which also solves the basic problem of quantum measurement theory and allows free will without conflict with the deterministic laws of physics such as field equations: in TGD dynamics of space-time surfaces and modified Dirac equation.
ZEO allows to distinguish between geometric time and experienced time and to understand their correlation. One could speak about quantum arrow inducing thermodynamical arrow of time and arrow of psychological time. Thermodynamical arrow basically reduces to a generation of entanglement entropy accompanied by entanglement negentropy associated with p-adic degrees of freedom assignable to cognition. Cognitive evolution as a "positive" aspect of the arrow of time.
That there is only single arrow of time is only a belief. There are many examples, where this is not the case: the spontaneous build up of molecules from their their building bricks and phase conjugate laser beams for which second law holds true in reverse time direction.
ZEO predicts both arrows of time and in living system the arrow of time at control level (magnetic body carrying dark matter in TGD sense) can change. TGD based view about memory and motor actions relies on this. Re-incarnation in very general sense is one quite radical prediction.
A2. Questions about entropy
Why did the universe have such low entropy in the past, and time correlates with the universal (but not local) increase in entropy, from the past and to the future, according to the second law of thermodynamics.
In TGD cosmology radiation dominated era is preceded by a period during which normal space-time with 4-D M4 projection did not exist. Space-time surfaces were cosmic strings with 2-D M4 projection. A phase transition occurred. The cosmic strings are unstable against developing 4-D M4 projection. The projection started to increase and produced flux tubes and the magnetic and volume energy of flux tubes decayed to ordinary particles (possibly dark in TGD sense). This is TGD counterpart of inflation. This process still continues and especially interesting are phase transitions reducing length scale dependent cosmological constant.
In primordial phase particles were absent and their contribution to entropy was not present. This might explain why the entropy was low. How much entropy did string degrees of freedom carry? If this contribution was small then one can argue that the very early Universe had low entropy. The fact that the amount of string energy per volume went to zero like cosmic time a suggests that also the entropy per unit volume went to zero.
A3. Questions about causality
Are there exceptions to the principle of causality? Is there a single possible past? Is the present moment physically distinct from the past and future, or is it merely an emergent property of consciousness? What links the quantum arrow of time to the thermodynamic arrow?
There are two causations: causality of field equations which is not violate and causality of free will associated with state
function reduction in ZEO. The two causalities are consistent since act of free will does not affect single time evolution but replaces superposition of deterministic time evolutions with a new one. "Now" is associated with experienced time, not with geometric time With respect to geometric time states are superpositions of classical time evolutions- preferred extremals - inside causal diamond defining what one might call perceptive field of self.
A4. Questions about CP and T violation
Why are CP violations observed in certain weak force decays, but not elsewhere? Are CP violations somehow a product of the Second Law of Thermodynamics, or are they a separate arrow of time?
The violation of T symmetry implied by CP violation must be distinguished from the generation of arrow of time and I would not speak about this as quantum arrow. T violation means that the for conscious entities with opposite arrows of time is slightly different already at the geometric level- dynamics of space-time surfaces in TGD. The analog of Kahler action in M4 degrees of freedom forced by twistor lift of TGD implies this. CP/T violation induces also matter antimatter asymmetry, which is not a small effect at all. Twistor lift of TGD predicts small CP breaking and the mechanism generating matter antimatter asymmetry. The decay of cosmic string to ordinary matter produces slightly more matter than antimatter outside strings and after annihilation only matter remains.
B. Interpretation of quantum mechanics
How does the quantum description of reality, which includes elements such as the superposition of states and wavefunction collapse or quantum decoherence, give rise to the reality we perceive?
Another way of stating this question regards the measurement problem: What constitutes a "measurement" which apparently causes the wave function to collapse into a definite state? Unlike classical physical processes, some quantum mechanical processes (such as quantum teleportation arising from quantum entanglement) cannot be simultaneously "local", "causal", and "real", but it is not obvious which of these properties must be sacrificed, or if an attempt to describe quantum mechanical processes in these senses is a category error such that a proper understanding of quantum mechanics would render the question meaningless.
Answer: No "interpretation" of QM is needed in ZEO. What is new that quantum measurement theory extends to a theory of consciousness describing also observer as "self" and as part of physical system rather than outsider. State function reduction is completely universal process rather than something performed only by human observer.
We perceive the world as classical because the very feature of state function reduction as a basic building of conscious experience makes the world classical in degrees of freedom about which it give information. Quantum measurement is always an answer to a question and state function reduction selects one option.
State function reduction in the sense of ZEO involves two new elements.
- The poorly undestood weak measurements assumes also in standard QM corresponds to "small" state function (SSR) essentially as time localization (measurement of clock time): the time evolution of self is sequence of SSRs. The members of state pairs defining zero energy state that are associated at active, shifting boundary of CD changes and gives rise to sensory input and all induced by it. The members of state pairs at passive boundary does not change and this corresponds to generalize Zeno effect. The states remain unentangled and give rise to permanent part of self.
- "Big" reduction (BSR) corresponds to ordinary state function reduction and changes the arrow of time for self. At elementary particle level the duration of single lifetime for self is very short. At our level situation is different. The larger the size scale of quantum system, the longer the duration of life cycle. Many-sheeted space-time and hierarchy of CDs is required to understand self hierarchy geometrically.
Space-time locality in TGD is replaced with locality in the world of classical worlds (WCW). There is no spooky action. Entangled states have flux tubes connecting them as correlates of entanglement: they form single space-time surface essentially, single point of WCW. Apart from state fuction reduction quantum TGD is purely classical: WCW spinor fields obey formally single particle Dirac equation and there is no second quantization at this level.
- In ZEO the quantum universe is re-created in every SR and this occurs in all scales corresponding scale hierarchy of CDs. The is no unique past and geometric past is also re-created to some degree.
C.1 Is there a theory which explains the values of all fundamental physical constants?
Answer: In TGD there the fundamental constants are CP2 size scale which is not coupling parameter but provides universal unit of length. Kaehler couplings strength analogous to critical temperature is fundamental dimensionless constant. Its values are fixed as analogs of critical temperature. Quantum criticality determines the values of all coupling parameters. Basically the coupling constants should be expressible in terms number theoretical information. For instance, the value of effective Planck constant heff=nh0 would correspond to the dimension of extension of rationals characterizing adele. I have made a concrete proposal for the discrete coupling constant evolution.
C2. Is there a theory which explains why the gauge groups of the standard model are as they are
Answer: GUT approach is given up in TGD as too naive and "too easy". It leads to proton instability, predicts desert, and is untestable and l there is not a single piece of evidence for a larger gauge group.
To me the correct question is "Why standard model gauge group is so special and how it emerges". There are 3 manners for this in TGD.
- The construction of WCW geometry requires maximal isometry group since WCW is infinite-D. Already in the case of loops spaces this is required. Hence one expects that TGD is highly unique from the condition that it exists.
- CP2 codes for the standard model symmetries.
- M4 and CP2 are also the only 4-D spaces having twistor space with Kahler structure so that in TGD M4xCP2 is completely unique.
- M4 and CP2 are also number theoretically unique. SU(3) as isometry group is also automorphism group of octonions. In M8-H duality at the octonionic M8 level provides purely algebraic description of space-time surfaces. Algebraic equations instead of partial differential equations for space-time surface as in M4xCP2.
M8-H duality maps quaternionic algebraic surfaces in octonionic M8 to preferred extremals in H. Dynamics at M8 level states that space-time surfaces are associative and thus quaternionic and therefore 4-D. 2-D string world sheets and 1-D strings appear also as complex (commutative) and real surfaces.
1+3 signature is completely unique in TGD framework. For 4-D space surfaces light-like 3-surfaces identified as boundaries between Euclidian and Minkowski regions of space-time surface have extended KAc-Moody symmetry since light-like 3-surface is metrically 2-D. In other dimensions one does not obtain this. Also the light-cone boundary of M4 (boundaries of CD) are light-like and this gives rise to infinite-D maximal isometry group of WCW as consisting of symplectic transformations.
C4. Questions about dimensionless physical constants
At the present time, the values of the dimensionless physical constants cannot be calculated; they are determined only by physical measurement. What is the minimum number of dimensionless physical constants from which all other dimensionless physical constants can be derived? Are dimensional physical constants necessary at all?
Answer: Basic dimensionless coupling constant in TGD is Kaehler coupling strength analogous to critical temperature. Its possible values are determined by quatum criticality condition but I cannot really calculated yet. Other dimensionless coupling strengths are derived from this. I have proposed general scenario for the evolution of Kaehler coupling constant having length scale dependent cosmological constant as evolution parameter.
CP2 length R is the only dimensional parameter. It is not coupling constant, however. It defines universal unit for length measurement and p-adic length scales are derived units. Note that in string models dimensional coupling has no geometric interpretation. Cosmological constant is generated in twistor lift dynamically and is scale dependent. In short scales approaching CP2 length it is very large but in long scales very small since it decreases like the inverse of p-adic length scale squared. Cosmological constant replaces cuffoff length in discrete coupling constant evolution.
CP2 length takes the role of Planck length and is about 103.5 times longer. Newton' constant is identified as G= R2/ℏ1. ℏ1 =n1ℏ. This assumes that the n= ℏeff/ℏ0 decomposes to n= n1× n2 meaning that space-time surface corresponds to n1-fold covering of M4 (n1 valuedness of CP2 coordinates) and n2-fold covering over CP2 n2 copies of n1 valued regions which could look like n1 flux tubes in parallel. G is predicted to have spectrum and its measurements indeed give values, which differ "too much". I wrote about this a blog posting and article: see this.
C5. Do "fundamental physical constants" vary over time?
Answer: In TGD fundamental constants do not vary over time. They vary as a function of the scale of the space-time surface. p-Adic length scales are fundamental and the hierarchy of Planck constants assigns a scale hierarchy to each p-adic scale as its multiples n= heff/h0.
D. Questions about particles
Are any of the fundamental particles in the standard model of particle physics actually composite particles too tightly bound to observe as such at current experimental energies? Are there fundamental particles that have not yet been observed, and, if so, which ones are they and what are their properties? Are there unobserved fundamental forces?
Answer: Many-sheeted space-time is crucial element. This is completely new as compated to GUTS and allows to avoid the fine tuning problems and understand particle mass scales number theoretically. For instance, electron corresponds to Mersenne prime M127 which is the smallest Mersenne not completely super-astrophysical: therefore electron is the lightest stable elementary particle.
In TGD all particles - also bosons - are bound states of fundamental fermions that correspond to spinor fields of H=M4xCP2. They have electroweak quantum numbers and spin of ordinary elementary fermions. Color is not spinlike quantum number but CP2 partial wave and baryon and lepton number correpond to different H-chiralities.
p-Adic fractality of TGD Universe predicts entire scaled variants of hadronic and electroweak physics and the are pieces of evidence for M89 hadron physics for which hadrons would have mass scale 512 times that of ordinary hadron physics: two handfull of ordinary mesons appear as bumps with predicted mass. These findings have been forgotten since they do not fit to SUSY predictions. Lubos Motl has been enthusiastic about them as SUSY Higges but has suffered disappoint every time! My role in the game has been took particle data tables and identify the meson!
TGD predicts only standard model forces but there could be scaled up versions of them.
E. Questions about physical information
E1. Are there physical phenomena, such as wave function collapse or black holes, which irrevocably destroy information about their prior states?
TGD State function is definitely real process. The self is a system hopping around in Platonia - state space formed by WCW spinor modes defining fermionic Fock states depending on space-time surface - and learning about it by coding information as memories to its quantum state. Adelic physics makes this concrete by providing entanglement negentropies as a measure for conscious information and by predicting evolution as increase of dimension of extension of rationals identied as =heff/h0.
How is quantum information stored as a state of a quantum system? Does state function reduction destroy information? Depends on what kind of information one is talking about. State function reduction answers question and therefore produces conscious information: observer knows the state of the system. On the other hand, when performed for ensemble it generates entropy but this is loss of information about ensemble.
E2. How is quantum information stored as a state of a quantum system?
Conscious information has negentropic entanglement assignable to p-adic degrees of freedom describing cognition as a correlate. It is measured by p-adic negentropy which is just the analog of Shannon entropy with logarithms of propabilities replaced with logarithms of their p-adic norms. The unavoidable increase of dimenaion of algebraic extension of rationals means increase of maximal negentropy and therefore evolution. The difference for the sum of p-adic entanglement negentropies and real entanglement entropy tends to grow and is zero for rational number based physics at the lowest level of evolutionary hierarchy. This also explains why evolution tends to produce entropy.
G. Questions about fine-tuned Universe
The values of the fundamental physical constants are in a narrow range necessary to support carbon-based life. Is this because there exist other universes with different constants, or are our universe’s constants the result of chance, or some other factor or process?
Answer: In TGD the Universe fine-tunes itself: evolution is the manifestation of this process. In adelic physics predicts the dimension n of extension of rationals is bound to increase in statistical sense since there is infinite number of extensions larger than given value n and only finite number them with smaller dimension. The increase of n=heff/h0 implies increase of scale of quantum coherence and algebraic complexity increases cognitive resources and the maximal entanglement negentropy increases.
In ZEO state functions replace the superposition of space-time surfaces with a new one so that this process became possible.
H. Questions about quantum field theory
H1. Is it possible to construct, in the mathematically rigorous framework of algebraic QFT, a theory in 4-dimensional spacetime that includes interactions and does not resort to perturbative methods?
Answer: I do not believe that QFT is enough. Pointlike particles must be replaced with extended particles and the replacement with 3-surfaces means unification of the notions of particle and 3-space.
In TGD framework number theoretical universality more or less forces the conclusion that loop corrections must vanish since scattering amplitudes must be rational functions of momenta. Therefore scattering amplitudes must reduce to sums over finite number of terms. For twistor lift this implies that scattering amplitudes are sums over resonances: string models emerged from dual resonance models assuming this. Discrete mass spectrum is implied and would be due to the gravitational biding.
Coupling constant evolution discretizes and coupling constants are analogous to critical temperatures. TGD can be indeed regarded as a square root of thermodynamics.
H2. Given an arbitrary compact gauge group, does a non-trivial quantum Yang-Mills theory with a finite mass gap exist?
This problem is also listed as one of the Millennium Prize Problems in mathematics.
Answer: I would not have added this to a list of millenium problems. First of all, I do not believe that gauge theory can be more than effective description in long length scales. There is a simple argument for thow standard model emerges from the many-sheeted space-time of TGD.
YM theory suggests continuum mass spectrum contrary to experimental facts. The understanding of mass requires a scale and YM theories have no scale. Scales emerges by the replacement of point-like particle with extended objects so that YM theories are very probably not enough to explain mass gap. In TGD this object is 3-D. The notions of particle and space are unified. p-Adic length scale hypothesis allows to understand the emergence of scales quantitatively. This indeed leads to p-adic mass calculations which are very successful. This however requires bringing cognition to the realm of described phenomena.
In TGD variant of twistor approach masslessness in 4-D sense is replaced with masslessness in 8-D sense. Since particle massless in 8-D sense can be massive in 4-D sense this allows to overcome the basic problems of gauge theories - also twistor Grassmann approach - related to mass gap. But this requires space-time as 4-surface and particles are small space-times.