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I have a question which is kind of philosophical, since I am from a non-mathematical background.
Background- As I decipher from Schrodinger equation, small particles have discrete energy or quanta. And if we try to pin point their location at any given time, we can only determine a probabilistic position. I deduce that these particles are kind of independent of space-time, and that their space-time fabric at any given point will be probabilistic. In other words, there is no equation to define space-time fabric for small particles. Coming to Einstein's theory of general relativity which says that gravity results for changes in space-time fabric, and has a definitive equation for space-fabric.
Einstein has based his equations assuming a definite and continuous space.
Can you extend/ re-derive einstein's equation of general theory of relativity assuming a probabilistic space-time?
Analogy- Galaxies are moving away from each other. At any given point of time, position of a galaxy in only probabilistic, through we can determine position with a very high probability in this case.
Please can you provide your answer at firstname.lastname@example.org too