Orthodox quantum mechanics

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According to Leibniz’s indiscernible principle, two numerically distinct  objects can’t share all their properties in common. It is Heisenberg’s uncertainty principle in disguise. It again reminds us that science is nothing but  ‘natural philosophy in a new package’.

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Fundamentally ‘identical’ things in the same state of motion are numerically distinct  objects having all their intrinsic properties in common and even spatio-temporal location cannot distinguish them. According to quantum mechanics, they are in ‘entangled states’.

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“Things are identical if the name of one can be substituted for that of the other without loss of truth.”

-Church

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“By an aggregate we are to understand any collection into a whole of definite and separate

objects of our intuition or of our thought.”

-Cantor

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Leibniz’s principle of indiscernibles  is actually the noncontextuality within quantum mechanics. Physicists still wonder whether it is a logical principle, or merely an empirical principle.
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Each subsystem of the universe can be unique (enough to initiate nonlocal interactions) in term of their relations to the rest of the universe because space and time are just relational and dynamic properties.

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Cosmological general relativity deals with background independent but  spatially compact space-time.

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The laws of physics are independent of any ideal element or fixed, non-dynamical structures.

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Everything that influences the
evolution of a subsystem of the universe is itself a part of the universe.

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Anything that influences the universe is bound to evolve in response to those influences.

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The doped material is an extrinsic impurity into an intrinsic semiconductor to modulate its electrical, optical and structural properties.

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Helium atoms in a beaker of superfluid helium or electrons in a doped semiconductor are single systems (ensembles) with a large number of subsystems(identical particles moving in the same external potential).

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Inter-ensemble, non-local interactions happen between beakers of superfluid helium atoms. Even if there are no copies of that beaker in the universe, there are greater than 10^20 ensembles of  sub-systems due to the imposition of the inter-ensemble interaction between the identical particles.

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“Macroscopic” quantum systems  constitute an ensemble of microscopic systems all by themselves.

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It might not be  coincidental that quantum interactions between distant subsystems require a preferred simultaneity and  general relativity requires preferred foliations/branchings.

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The absolute notions of similar or not can be replaced by degrees
of similarity for non-local interaction between identical subsystems.

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Though degrees of similarity for non-local interaction are unwelcome  in a fundamental theory, any theory of subsystems is bound to be approximate. This is a sort of  cosmological dilemma.

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Leibniz’s Principle of sufficient reason boils down to “why is the universe like X rather than Y has a reason
sufficient to explain why.” The belief  eliminates arbitrary choices from fundamental laws and initial conditions of physics.

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The number of similar subsystems indicates quantum potential.

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Microscopic systems are predictable  only statistically because they belong to ensembles of similar systems interacting non-locally with
each other, just by virtue of their similarities(maintenance of Heisenberg’s uncertainty).

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Macroscopic systems are unique and interact locally.

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Systems which have no causally indistinguishable copies in the universe behave classically, because for such systems there is no confusion possible and no quantum potential. Energy distinguishes copies. Lower energy implies higher variety.

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Ensembles are called ‘quantum states’.

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Only nonlocal interactions between members of  ensembles give rise to quantum phenomena.

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All the  information about a subsystem is contained in its
view of the rest of the universe, through its causal links or other rela-
tions to other subsystems. This is main logic behind quantum mechanics.

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Quantum mechanics is a description of subsystems of the universe.

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A quantum state is an ensemble of similar systems present in the universe at a given time.

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Quantum mechanics is ultimately based on the speculation that our universe is a sort of system  maximizing the distinctiveness of each subsystem.

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Quantum mechanics is ultimately based on the principle of maximal
variety.

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A system with a particular quantum state takes on an ensemble of similar  subsystems of the universe.

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What we call ‘quantum mechanics’ is actually the story of an imaginary ( officially ‘postulated’) interaction increasing identical subsystems’  distinctiveness, by extremizing the variety.

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