We assume that this is true when the statistical matrix mechanics of the so-called Cairo techniques are used to replace PDE and its classical mathematical methods of solution.
Moreover, the statistical transition matrix chains of Cairo techniques are effectively capable of resolving time-dependent phenomena in classical and quantum physics.
Furthermore, the subject of vacuum dynamics can be defined and described with adequate rules considered missing in modern quantum mechanics.
Figure 1 showing how
Cairo statistical techniques can ignore PDE and its classical mathematical methods of solution
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Here is an introductory answer showing a simple schematic diagram, Figure 1 showing how
Cairo statistical techniques can ignore PDE and its classical mathematical solution methods such as the separation of variables method and finite difference method techniques.
Furthermore, it is worth mentioning that statistical transition matrix chains of Cairo techniques have recently been successfully introduced in solving many time-dependent phenomena in classical and quantum physics.
Additionally, the topic of vacuum dynamics has recently been defined and described with adequate rules considered missing in modern quantum mechanics and which will be the subject of the next answer.
To be continued.
Science leaves the era of mathematics and enters the era of matrix mechanics and the turning point is the discovery of numerical statistical theory called Cairo techniques and its transition matrices eligible to solve almost all problems of classical physics and of quantum mechanics.
No more partial differential equations, no more numerical integration, no more FDM techniques. . etc.
Statistical matrix mechanics is capable of solving all of the above problems and additionally predicting unknown universal physical rules.
Note that the Heisenberg matrix and the Dirac matrix are neither physical nor statistical and incomplete.
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