Can the great incompatibility between GR and QM be overcome?
This is question I asked myself a long time ago, and In fact, with the use of complex numbers, based on most beautiful equation of mathematics, in 1991, I found a way to deduce all fundamental equations of physics, based in a concept I called a Basic Systemic Unit, based on Euler's relation, that has the most remarkable property to remain the same with those operation that represent change, I mean derivation and integration. One of most important aspect of this treatment, is that due to that metric based on the BSU, in which both totalities of time and space are differentiated by that symbol that Descartes called imaginary, I mean
i=sqr(-1)
which in fact is a symbol to differentiate two different orders of reality or totalities, in this case Time and Space. In that metric of the BSU, the part affected by the symbol "i" has to do with Space and is affected by the Sine that has two solutions
Sine(Theta) = Sine(Theta)
Sine(-Theta) = -Sine(Theta)
while that part not affected by "i", or else Time, is affected by the Cosine function that has just one solution
Cos(Theta) = Cos(Theta)
Cos(-Theta) = Cos(Theta)
This fact is the reason of that great incompatibility between GR and QM, as in GR based on Tensor Analysis, Time is reduced to a Space dimension, so it is symmetric just as Space, and can take both signs, so it is possible to conceive travel to the past or to the future, just as space, in which if we have a point of reference, it is possible to travel in any direction.
The BSU is a system in the complex plane, not a trajectory, whose state must be determined in such a way that we must have relations between both totalities, of Time and Space, or the contrary we will have the Uncertainty Principle.
For those interested in how this great incompatibility between GR and QM that has produced the so called the Crisis of Physics, in my paper
QUANTUM PHYSICS
https://www.researchgate.net/publication/384190006_Quantum_Physics
you can find how to overcome that Crisis as is shown with:
- the pendulum formula
- the Special Relativity with another approach based on the BSU
- that of GR, that has to do with the perihelion of Mercury
- and that Schrödinger's wave equation
Thanks for your attention
Edgar Paternina
retired electrical engineer