Dear Hollis Williams ,

Here is the unification of the Einstein equations with the photon energy (quantum):

Preprint ENERGIA FOTÓN, APROXIMACIÓN GRAVEDAD UNIVERSAL DE NEWTON Y L...

There is still much to unify the 2 theories, but it is a beginning, look in the DISCUSSION how certain quantum oddities fit

I do not know what trends are currently dominating in QM, I can only suggest my own "trend". See my article `Subquantum Leapfrog`

https://vixra.org/abs/1801.0379

I am not sure that I understand what is asked. Let me answer to the question which appeared in the title. Such a question implies a type of personal

view.

As we know all physically-relevant problems of QM (bound states, scattering etc) are non-exactly-solvable, meaning a solution can not be presented in terms of elementary functions and their combinations. How to write approximate solutions

which guarantee a given accuracy in ALL (or many) characteristics of the physics phenomenon we study? Such an approach may lead to a new insights. Molecular physics seems the best field to study...

Not only quantum physics requires refreshing, also cosmology requires repair.

Take a look at Preprint Representing basic physical fields by quaternionic fields

Dear Hollis Williams ,

You're right, but I don't translate it because already with the first part:

Preprint ALL SPECIAL RELATIVITY EQUATIONS OBTAINED USING GALILEAN TRA...

I learned that publishing preprints is useless, no matter what you discover, no matter all the proofs (reproducible by anyone through math) that you add, it will be useless. There is too much noise.

The only possible way for my theory to be accepted is to get a patent and build something material that does not exist, applying that theory (maybe in the field of semiconductors, superconductors, etc). That is why my line of research changed towards quantum, that untranslated preprint was only a step to understand it better and like I had it, well... I published it.

I suspect that the reason you struggle with quantum mechanics is because of quantum foundations, which are the most interesting and intractable problems in quantum mechanics. You can read an overview here.

http://www.cs.ox.ac.uk/people/bob.coecke/RanchinMres.pdf

Here is an overview of the difficulties in devising a theory of quantum gravity.

https://arxiv.org/pdf/0907.4238.pdf

The most successful attempt at quantum gravity is superstring theory. Here is a good introduction.

https://arxiv.org/pdf/hep-ex/0008017.pdf

If you have further questions, you can email me at [email protected]

QM by itself can be technically challenging on its own, mixing it with GR is a mistake, no matter what some famous claim. Stay away from the

loudmouths.

Just make sure you can handle QM by itself, widly applied in Solid State Physics problems or Chemistry.

The General Relativity is not science to follow, period. stay out of it.

It is been over 100 years many good scientists stocked in it, and didn't gain anything, even Mr. Einstein could explain his own GR theory.

Quantum mechanics does not exist, but quantum physics exist.

Article How the Quantum Universe Works

Article Hydrogen's Journey in the Universe

regards

@Ayaz Mohmood Dar,

I can only give you this advice: start from

quantum mechanics as a `mathematical theory being applicable to a

certain physical domain' (analogous to `classical rigid body

theory' , being applicable to the macroscopic behaviour of billiard

balls on a billiard table). Forget about the idea that we should

aspire at finding the `theory of everything'. As far as quantum

mechanics is concerned: do not forget that human observers are not

able to see objects like atoms and electrons, but at best see the

pointers of their measuring instruments (or even just the `graphs

produced by their printers after the measurement results have been

processed by their computers').

Physical reality plays with several kinds of spaces that appear to be derivable from a very basic concept of space. Mathematicians and physicists call this basic concept a vector space or linear space. linear combinations of vectors and scalars can reach every location point in the vector space. Vectors have a length, a start location, and a direction. Vectors are independent when the map of one vector onto the other reduces to a point. The number of mutually independent vectors that have unit length determines the dimension of the vector space. Many number systems are vector spaces that provide arithmetic rules, which relate the locations in the vector space. The real numbers occupy a one-dimensional vector space. The complex numbers can be constituted from two real numbers and their vector space is two-dimensional. Two complex numbers constitute a quaternion and quaternions form a four-dimensional vector space. Octonions cover an eight-dimensional vector space. These number systems exist in many versions that distinguish in the way that Cartesian and polar coordinate systems sequence their members. These coordinate systems determine the geometric symmetry of the version of the number system. Functions can map number systems onto themselves by locally changing the inter distance of the originally equidistant Cartesian location marks. In the vector spaces of the number systems always one of the dimensions is occupied by real scalars. The other dimensions are occupied by spatial vectors. The arithmetic rules for the real scalars and the spatial vectors differ.

At the turn of the nineteenth century to the twentieth century David Hilbert and some other scientists discovered that a kind of vector space exists that can archive sets of numbers. John von Neumann, the assistant of David Hilbert suggested the name Hilbert space for this type of vector space. The Hilbert pace differs from the most basic vector space in the fact that for every pair of vectors the Hilbert space provides an inner product that uses a selected version of a number system to specify its value. Soon it became known that Hilbert spaces can only cope with members of a number system that forms an associative division ring. This reduces the choice to versions of the real numbers, the complex numbers, and the quaternions. Operators map Hilbert spaces onto themselves. Some of the vectors are mapped onto themselves. In that case, the inner product can deliver the scaling number. This number is called eigenvalue and the corresponding vector is called eigenvector. The eigenvalues of an operator combine in the eigenspace of the operator. The selected version of the number system represents the eigenspace of a dedicated operator that we call the reference operator. This eigenspace forms the private parameter space of the Hilbert space. A category of operators exists that share the eigenvectors of the reference operator and replace the original eigenvalue by the target value of a selected function. Thus, the private parameter space acts as the root geometry of the Hilbert space that provides the Hilbert space with a geometric center and a geometric symmetry. Operators of separable Hilbert spaces have countable eigenspaces.

Later in the twentieth-century, ways were discovered to define non-separable Hilbert spaces for which some of the operators have eigenspaces that are not countable. These eigenspaces form continuous manifolds.

Each infinite-dimensional separable Hilbert space owns a unique non-separable companion Hilbert space that embeds its separable partner.

Hilbert spaces are vector spaces that support an inner product for every vector pair. Another characteristic is that Hilbert spaces are complete. No more conditions distinguish the Hilbert space from its more basic predecessor, the most primitive vector space. This fact enables a very significant extension of the structure of the Hilbert space. We can define a new concept, which is a system of Hilbert spaces that all share the same underlying vector space. We call this new concept a Hilbert repository. Most of the participating Hilbert spaces are quaternionic separable Hilbert spaces. One of these separable Hilbert spaces has infinite dimensions and therefore it owns a unique non-separable companion. Together with its companion, it forms the background platform of the Hilbert repository. They deliver the background parameter space and the background symmetry of the Hilbert repository. All other Hilbert spaces float with their geometric center over the background parameter space. The extension goes together with significant restrictions. Only certain types of quaternionic separable Hilbert spaces can become members of the Hilbert repository. The axes of their Cartesian coordinate systems must be parallel to the axes of the background Cartesian coordinate system. This enables mathematical methods to compare the difference in the geometric symmetry between the floating platforms and the background platform. The Hilbert repository exploits this possibility to place sources or sinks at the geometrical centers of the floating platforms that represent symmetry-related charges and raise corresponding symmetry-related fields. If no geometric symmetry difference exists, then the value of the charge equals zero.

The type-restriction results in the fact that only a shortlist of symmetry-related charges are possible. The Standard Model that shows the measured characteristics of particles, contains a similar shortlist. In the Standard Model, the charges are called electric charges. This is a promising result.

This suggests that the floating platforms in the Hilbert repository represent elementary particles.

Something is still missing. It is not clear how these elementary particles interact with the fields that are archived in the background platform. Also, the Hilbert repository does not yet explain the stochastic behavior of elementary particles.

If every floating platform contains a private footprint operator, whose eigenspace is filled with an ongoing hopping path of a point-like object, then it is possible to find the way that the elementary particles interact with the field that embeds them. If the ongoing hopping path recurrently regenerates a coherent hop landing location swarm and a stable location density distribution describes this swarm, then the square of the modulus of what physicists call the wavefunction of the particle equals this location density distribution. This is possible if the eigenspace of the footprint operator was filled by a stochastic process that owns a characteristic function. A combination of a Poisson process and a binomial process, where the binomial process is delivered by a spatial point spread function can do the job. The characteristic function is the Fourier transform of the point spread function and the point spread function equals the mentioned location density distribution. The ongoing embedding process that embeds the hop landing location into the embedding field mimics the activity of the stochastic process. The footprint operator archives the ongoing hopping path as a string of quaternionic eigenvalues that each contain a timestamp and a three-dimensional hopping location. After sequencing the timestamps the eigenspace of the footprint operator tells the life story of the elementary particle. The ongoing embedding is monitored by a time window that scans over the full Hilbert repository. The range of the scanning time covers the range of archived timestamps.

The fact that at its birth, every floating platform contains a filled eigenspace of its footprint operator is still an unsolved aspect of the Hilbert repository.

Preprint Representing basic physical fields by quaternionic fields

In

Preprint NOTION OF PROBABILITY AMPLITUDE EMERGING FROM THE DYNAMICS O...

it is shown how a smooth motion of a particle having a dipole-like fluctuating charge distribution gives rise to the notions of 'probability density' and 'probability amplitude'. These notions emerge from an approximation procedure which is based on a particular time-slicing procedure applied to small time intervals, somewhat similar to what is done in Feynman's path integral approach to quantum mechanics. This allows a new thorough understanding of the physical meaning of the 'wave function' of quantum mechanics, and thereby suggests some modifications and a non-axiomatic setup of a new realistic quantum mechanics such that the theoretical concepts of this theory are almost completely induced by theoretical concepts of classical field theory.

A really hot topic in QM is that of indefinite causal ordering in lab processes. I learned about that while writing a paper on p-adic QFT (in which there is no natural notion of light cone, hence no natural notion of causality, so you have to look for a proper replacement, see https://arxiv.org/abs/1805.08613 if you are interested, the full paper appeared in Reviews in Mathematical Physics). There are several groups actively working in that area of causal orderings in QM, see, for instance:

Article Quantum Metrology with Indefinite Causal Order

Preprint Ergotropy from indefinite causal orders

Article Causal orders, quantum circuits and spacetime: distinguishin...

Preprint Experiments on quantum causality

and references therein...

Ayaz Mohmood Dar

Dear Ayaz

You may be interested by this related analysis:

Michaud, A. (2020) Gravitation, Quantum Mechanics and the Least Action Electromagnetic Equilibrium States. In: Amenosis Lopez, editor. Prime Archives in Space Research. Hyderabad, India: Vide Leaf. 2020

https://videleaf.com/gravitation-quantum-mechanics-and-the-least-action-electromagnetic-equilibrium-states/

Best Regards, André

Ayaz Mohmood Dar For a viewpoint on quantum mechanics please give a look to this recent note:

Preprint The Quantum Captivity of Physics

The Schrodinger equation has no proof, and is remarkably similar to many other very close versions.

So there are explorations in say indefinite metric QM, Pseudo Hermitian Hamiltonians, the study of symmetries to garantee certain properties, Sturm Liouville version, and so on. For example orthogonalization could take place with respect to some weight function or matrix.

For example conservation of matter can be proved not only in Schrodinger, but other versions as well. One is hard pressed to say which feature of Schrodinger leads to success.