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Since you are approaching it all from the math side, one of the most interesting things to me at the moment might also be very interesting to you possibly, if you'd not already learned of it. It's very intriguing that 500 pages of algebra that QFT can lead to in order to calculate an outcome can it turns out be reduced into a single term, and how that's actually geometry...., so that one can approach it from the other side, without having to do all that algebra at all (suggesting it might be that QFT is just a step towards something more insightful)(....The problem with Bohmian mechanics is the concept of time.
Quantum field theories originated when physicists were able to combine special relativity where time is relative with quantum mechanics.
Bohmian mechanics relies on absolute time and Lorentzian relativity requiring the existence of an ether which was ruled out by the Michelson- Morley experiment.
On the subject of particles it was in classical physics where the point particle was introduced, where the mass and charge of a particle was concentrated into an infinitesimally small volume.
It made the mathematics considerably more simple.
For example the inverse square law for the gravitational force F between two objects is based on the equation F= Gm₁m₂/r² where m₁, m₂ are their point masses and F is a function of the distance variable r.
A more realistic equation is to consider the mass of the objects not their point masses expressed in terms of density ρ and volume v where m = ρv where the equation becomes F = Gρ₁v₁ρ₂v₂/r².
Problems arise for irregular sized objects where the volume v is not easily defined mathematically.
Ironically while point masses makes Newtonian gravity easier to handle, gravity messes up QFT which also assumes point masses.
A quantum theory of gravity is possible where particles are not point sized such as in String theory
It's so interesting to me about how it is a geometric thing.
A Jewel at the Heart of Quantum Physics | Quanta Magazine
Physicists have discovered a jewel-shaped geometric object that challenges the notion that space and time are fundamental constituents of nature.
www.quantamagazine.org
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