If you don't understand quantum mechanics, ask yourself if I'm right, because others don't understand  quantum mechanics  either.

By useless  quantum mechanics  we mean incomplete mathematical spaces of a classical 3D+t variety that are inadequate for generating well-defined definitions and hypotheses as well as time-dependent partial differential equations.

The current classical discrete 3D+t space PDE, in which time is an external controller and not integrated into the 3D geometric space, cannot be integrated digitally.

This space is logically incomplete and misleading in the production of definitions and hypotheses as well as in the resolution itself of time-dependent PDEs including the well known Schrodinger equation. No wonder the resulting definitions/assumptions are  and result in weak or intractable quantum mathematics, leading to all kinds of misunderstandings, from horrible notations to undisciplined length of theorems containing a considerable amount of black magic and ending with a gray nature of the mathematical result obtained.

Below we present some of the most catastrophic inaccurate assumptions/conclusions existing in current quantum mechanics, resulting from the use of the 3D+t manifold space to specify initial conditions, boundary conditions and source/term . We conveniently use the form of a Q/A format for better explanation.

Fortunately, the numerical theory of Cairo techniques and the Laplacian theorem constitute an advanced and exhaustive form of the energy continuity equation and can thus create a new quantum mechanics. This also applies to the case of Schrödinger's famous time-dependent PDE.

To be continued.

Q1-

Boltzmann's formula for the microscopic entropy s = kB Log W, why was it criticized by A. Einstein?

* This is a serious question showing the importance of statistics in proving physical events.

One of the most important and precise formulas in the history of science was published in 1877:

s = kB Log W ...... . . . . . . . . (1)

with s approaching 0 as the temperature T in degrees Kelvin tends towards zero.

This relationship is considered to be Boltzmann's best achievement and is engraved on his grave in Vienna.

It is the only derivation of the agreed definition of macroscopic thermodynamic entropy S which appeared as early as 1850.

In fact, the thermodynamic entropy S was introduced by Clausius, Kelvin and others through the second law of thermodynamics:

S = d Q reversible / T. . . . . (2)

Only then did the macroscopic entropy S have a mathematical basis based on a well-defined molecular system of binary interaction.

A. Einstein objected to its pure statistical derivation followed by Boltzmann and asserted that the proof should be made on both statistical mechanics and Newtonian dynamics, which was clearly absent.!

It's quite astonishing that Einstein missed to approve or improve Boltzmann's pure statistical derivation, .

Formula 1 appears to be one of many prominently subjects where math still lags behind physics.

How do thermodynamic entropy dS = dQ (rev) / T and Boltzmann microscopic entropy S = k log W match?

As early as 1850, there was an agreed definition of thermodynamic or macroscopic entropy as S = dQ reversible / T with S approaching some constant or zero as T approaches zero.

However, a breakthrough came in Boltzmann's equilibrium statistical mechanics known as the relationship or proportionality between macroscopic entropy and probability of microscopic states of gas molecules W (Boltzmann called W number of complexions of state known as S = k log W early in 1877).

It worth mentioning that Boltzmann statistics is equivalent to Newtonian dynamics and laws of motion.

Moreover, relationship 1 is considered the best of Boltzmann achievements and is engraved on his grave in Vienna. Only then, the macroscopic entropy had a mathematical basis based on a well-defined molecular binary collisions.

Surprisingly, though, both definitions 1,2 match.

Einstein raised a finger against Boltzmann's derivation [1] based on probabilistic assumptions without any dynamic laws ?

Finally, this is not to discount from Einstein great achievements who slipped only twice (this one and the specific heat of crystal structure where statistics is a must) during 50 years of theories and research discoveries.

1-I. Abbas, Quora Q/A 2021.

Its not usless, only not always understandable.

Q2,

The source question mentions something like a revolutionary reformulation of the classic Schrödinger PDE that we've never heard of.

Can you explain the proposed reformulation and its superiority over the classic Schrödinger PDE, if any?

**The classic Schrödinger equation,i h dΨ/dt)partial=-h2/2m. Nabla^2 Ψ+ V Ψ . . . . (1)

OR,

H^Ψ = EΨ. . . . . (1*)

reduced form, should be conveniently replaced by its square Ψ^2[1*] to conform to the Laplacian PDE and the Laplacian theorem in general, which makes sense and makes sense.

as,

dU/dt)partial=D.Nabla^2 U +S(x,y,z,t) . . . . . . (2)

where U=ψ^2=ψψ*.

It should be noted that the square of the classic Shrödinger PDE, which is equation 2, must be completed by the basic rule of the source term in vacuum dynamics, namely:

S(x,y,z,t) =Constant * V(x,y,z,t) . . . . (3)

Equations 2,3 versus equation 1 are like a huge jumble going from zero or dwarf capabilities to almost infinite capabilities in classical and quantum physics in addition to applied mathematics.

Here in question number 2 we explain how equation 3 solves for loudness in audio rooms and how it can derive and generate the Boltzmann distribution for the first time in 100 years.

Needless to say, the classic Schrödinger equation cannot solve or even address either of the two problems above.

On the other hand, the proposed square of the classical Schrödinger PDE called statistical Laplacian PDE is capable of [1]:

1-Describe and calculate the numerical solution for sound wave intensity and its reverberation time in audio rooms for the first time in the last 100 years.

Additionally, it predicts and measures the speed of sound waves at the NTP at 330 m s^-1.

2-Describe and calculate the numerical solution for the thermal conduction/diffusion energy density (temperature in degrees Kelvin) when the Dirichlet boundary conditions and the initial conditions vector are arbitrarily specified simultaneously, which has never been carried out previously.

Additionally, it predicts and measures the EMW signal speed in  metals as the light wave speed in vacuum at 3E8 m s^-1.

What validates the assertion: quantum mechanics is useless is inherent to Schrödinger's PDE but not to its square.

1-Useless mathematics - The complex untold story, November 2024.

Schrodinger PDE is a weak and incomplete format for describing quantum particle mechanics.

It is only capable of resolving two body systems.

Assuming that the greatest success of classical Newtonian mechanics was the solution of the Earth-Sun system. Likewise, the greatest success of quantum mechanics, combined with Bohr's postulate E2-E1=hf, was the solution of the electron-proton two-body system.

It is a pity that the mathematical solution of this classical and quantum two-body problem ranks among the greatest achievements of humanity.

Only in chemistry do they have approximate experimental and theoretical results for many quantum particle systems occurring in molecular reactions.

Quantum mechanics as a whole needs a better reformulation.

It is worth mentioning that:

1-The statistical theory of Cairo techniques or any other adequate statistical theory can provide a rigorous solution for the hydrogen atom/particle in a central field without the need for Bohr quantification of the angular momentum mv. 2 Pi r=n h.

2- Max Planck's energy distribution law can be derived from Laplacian's theorem or any other appropriate statistical theorem, without needing Planck's hypothesis of quantifying the energy of quantum oscillators E = n h f.

3-Spontaneous explosions in a vacuum like those recorded in vacuum cleaners, vacuum bombs and the Big Bang are a fact despite the denial of the Schrodinger PDE and its iron guards.

4-The Planck constant itself h = 6.35 E-34 J s can be obtained by other means than by fitting the Planck energy distribution with the Balmer or Lyman spectral series.

etc..

Please take a look at,

Useless Quantum Mechanics – The Complex and Untold Story, ResearchGate, November 2024.