It is very exciting to read a prominent quantum physics paper that finally really unifies charge and gravity forces...or at least is on a viable path for unification. Tejinder Singh has published a series of papers on his quantum matter gravity (QMG) theory that not only unify gravity and charge, but he also shows many measurements that then validate QMG. Furthermore, the principles of QMG are consistent with my quantum matter action theory (shown below, published in three years ago) as well as with the well known continuous spontaneous localization (CSL) theory...QMG is so, so sweet...

Singh’s quantum matter gravity (QMG) unification of gravity and charge is therefore a very exciting development and is especially so for me since QMG has many of the same puzzle pieces as does my quantum matter action universe puzzle. Although QMG is not quite right yet and has not been thoroughly validated by Science, it will be. Basically, QMG defines aikyon particles as the generic aether of the universe and so QMG builds electrons, protons, neutrons, and all else with either fermion or boson aikyon. An 8-D octanion matrix represents each fermion and boson and has the correct quantum spin symmetry for both charge and gravity. Here is the basic action integral, S, which is proportional to the integral of the gravity trace dynamic mass or velocities of fermions and bosons:

Then QMG uses Connes time, t , and classical Euclidean or atomic time emerges from QMG. As a result, QMG defines a new constant of t = 1.0e17 s or 3.2 Byrs, but in Connes time, not atomic time. Alain Connes proposed t  as thermodynamic time, i.e. entropy or temperature time, as have many others in the past. This is a universe or cosmic time that defines the evolution of the universe and so now cosmic time is different from atomic time.

Another key to QMG is in continuous spontaneous localization, CSL, which is a very well know way to collapse the quantum wavefunction conundrum. So CSL is how the reality of classical gravity relativity emerges from QMG. That is very fun…

The 1e-39th scaling between gravity and charge emerges from the ratio (L_P/L)², and both L and L_P are characteristic lengths that each come from known constants. The Planck length is L_P and QMG length L is L = ћ/(c m), a characteristic length that scales with inverse mass ћ/c * 1/m. Here is the QMG Lagrangian equation of motion:

Dark matter simply emerges as a vector gravity from QMG and does not therefore need a new particle at all. However, there are many pesky singularities with many aspects of QMG, but QMG does manage to dodge the renormalization problem from gravity in quantum field theory.

Octonions are eight dimensional matrices that unify gravity and charge in this hypothetical 8-D space. Instead of atomic time, Singh uses thermodynamic or entropy time, t , which was proposed by Alain Connes and so Singh calls t  Connes time, but many others have proposed entropy as the time arrow as well. Of course, the classical evolution of the universe is what drives thermodynamics and entropy and so Connes time is also equivalent to that universe time as well.

The deep dive of QMG into octonion algebra is quite complex and it is not yet clear if the really simple QMG assumptions really justifies the rabbit hole of octonion complexification. A classical 4-D spacetime emerges from the QMG trace of just half of the 8-D octonion matrix and then quantum spin emerges from the other octonion half. The QMG introduces 4-D aikyons to represent fundamental octonion fermion and boson particles along with QMG length (L), gauge (a ), and fermi matrices (b₁, b₂). Each 4-D fermion has progress variables that scale with QMG L, q_F  and mass from momentum of velocity q̇_F and each 4-D boson is on a path, q_B with mass q̇_B. The dot above the q is a single derivative in Coones time, which is an 8-D velocity and proportional to momentum and therefore mass, and so q̣̈ is the double derivative, which is acceleration.

The next step is to renormalize q_B and q_F into q₁ and q₂ to make things pretty and avoid some ugly math...with an even deeper rabbit hole, so buckle up. The QMG aikyons are now either commutating bosons [q_B, p_F] from which classical gravity relativity emerges or noncommuting fermions {q_F, p_F} as quantum field theory emerges. The QMG paths q₁ and q₂ now have both symmetric and antisymmetric superpositions as well as momenta and all show the classic quantum uncertainty noncommutation: [p, q] = -iћ...and voilá! The Hamiltonian wave equation follows with frequency eigenvalues and so oscillating wavefunctions...oops, QMG still has some convergence issues hiding here and there...and so there are many more papers to write…

The QMG goes down a very deep rabbit hole because multiplying 8-D matrices results in two 64-D matrices with a total of 128 matrix elements. Wow! This will be a lot of papers in the future...

Although QMG has many of the features of quantum gravity, it is not yet completely clear if the complexity of octonion algebra is really necessary. After all, matter action has many of the same features, but only uses 3-D, not 8-D. Matter, action, and quantum phase unite into a very nice quantum universe with a Lagrangian, density matrix, and creation/annihilation operators. The quantum matter action causal set has all of the properties such as a Lagrangian for action. It could be that simply including the Fermi spin matrices in the action integral will provide for spin within just matter and action.

The matter action photon is the basic dipole exchange particle for charge and the universe biphoton is the basic quadrupole exchange particle for gravity. Just like the QMG aikyon, matter action has a pervasive aether particle that makes up the whole universe. Instead of using the dimensionless QMG L_P / L for gravity scaling and QMG Connes time, t , matter action uses the dimensionless universe radius over the Bohr radius, radius R_u / r_B. Thus, instead of an arbitrary QMG L, matter action uses the actual universe radius for its dimensionless scaling. 

Connes or entropy time represents the primary QMG quantum time dimension, t  = 1e17 s or 3.2 Byrs. Matter action universe time is t  = 1.2e-17 s, but comes from the time pulse of the universe size, R_u. Atomic time emerges from both QMG and matter action as the classical time of gravity relativity, and so the second primary dimension of universe time plays a key role in quantum gravity relativity.

The QMG length L is inversely proportional to particle mass and so for hydrogen, L = 2.2e-16 m, which turns out to be too small for CSL hydrogen. Matter action defines the characteristic CSL length as 7.0e-8 m, which is the radius at which hydrogen dipole-induced dipole attraction, which goes as 1/r⁶, equals hydrogen-hydrogen gravity attraction, which goes as 1/r². Thus matter action completely agrees with CSL while QMG L for hydrogen CSL seems to be a billion times too small.

The QMG constants are action as ћ / c and time t  = 1.0e17 s from which length emerges proportional to inverse mass. Matter action constants are action the matter scaled Planck constant as 

ћ_ae = ћ / c² 

with units of [kg s] and aether particle mass m_ae as

with units of kg, which scales as the ratio of gravity and charge and inversely with the hydrogen Bohr time, t_B. A universe cosmic time, T_u = ½ * h_ae / m_ae = 13.4 Byrs, emerges from the transform of the universe pulse length of matter action. However, the inverse Hubble constant determines our current cosmic time as T_a = k / Hubble = 1.2e17 s = 3.4 Byrs with a matter-action luminous distance correction, k. The matter-action luminous correction is not a new constant but simply expresses the acceleration of matter-action light over cosmic time.

Finally, Singh's QMG gives Science a truly significant unification theory. It is very pleasing to finally see this happen, but Science will now fight the coming QMG revolution quite fiercely as well it should...eventually, Science will accept something very similar but much simpler than QMG to finally show unification at long last...