This is most likely a paradox[1].
We assume that the fundamental reason is that they both treat the boundary conditions BC, the source term S and the thermal conductivity/diffusion k and D as scalar quantities when in fact they are tensors or matrices of second rank having spatial components x, y, z. [2]
for example, S=Sx+Sy+Sz and BC=BCx+BCy+BCz.
1- Spiros Konstantogiannis, Eur J 0f Ph, From the state space of quantum mechanics to position and momentum spaces through a simple relation, September 2020.
2- Abbas, Researchgate, A statistical solution to the Schrödinger equation, IJISRT journal, November 2023.
No, because the statement's wrong. Motion in three dimensions can be consistently described in classical and quantum mechanics. And this isn't anything new.
It would be better to study classical mechanics and quantum mechanics before making statements that aren't, just, wrong, but trivially wrong.
Ismail Abbas Stam Nicolis
No, this is not a paradox.
Equations governing the system are often written in vector or matrix form, where the components are organized in a way that allows for the representation of the three-dimensional nature of the problem. For example, the source term S can be expressed as S = Sx + Sy + Sz, where Sx, Sy, and Sz represent the sources in the x, y, and z directions, respectively. Similarly, the boundary conditions BC can be decomposed into components BCx, BCy, and BCz, representing the boundary conditions in each direction.
This approach allows for a more comprehensive and accurate description of the physical system, accounting for the effects in multiple directions. It is not a paradox but rather a necessary consideration when dealing with three-dimensional problems and representing the relevant quantities as tensors or matrices of second rank.
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