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Lietuvos nacionalinė fizikos konferencija 2019 m. spalio mėn. 3-5 d., Kaune

Combinatorial Interpretations Which Distinguish Observer and Observed

Notes

A Geometrical Concept for Distinguishing Observer and Observed

Main concepts

• Grounds for a definition measurement
• Interpretation of the collapse of the wave function
• Complex possibility vs. real actuality

Statement of problem

The measurement problem, whether and how the wave function collapses, persists as a longstanding challenge for the various interpretations of quantum mechanics.

Conclusions

• Four interpretations: quantum, classical, and two intermediate. Classical is a special "objective" frame where the observer has been removed.

Offer an observation

Observer introduces asymmetry. Observer entangles with one possibility.

Measurement finds the system in a definite state. Thus masurement collapses the wave function. The evolution of the system then continues from that definite state.

Questions

• Why cannot we predict precise results for measurements, but only probabilities?
• How can we establish a correspondence between quantum and classical reality?
• How are the probabilities converted into an actual, sharply well-defined classical outcome?

Idea:

• A particle is, of itself, not an observed, but rather an observer. It observes possibilities - it lives in the world of complex numbers. It only collapses when it comes into contact with a second system.
• The Lie algebras give the ways of having a distinct system (An) or having two systems related (in three possible ways (geometries - choice frameworks): gluing, fusing, and folding). This happens to a Or systems
• Observer does not distinguish a particular state. Rather, observer gets entangled with a particular state. Thus the observer is growing a particular reality. How do different observers avoid contradicting each other? The entire system of an observed can be flipped over.

A federation of observers.

Mintys

Coordinate systems symmetry group is not the alternating group but the subgroup of the hyperoctahedral group. And this subgroup can arise only if we replace each dimension with a bipolar axis. Which is the point of the intermediate structures.

Conclusion: Penrose's trinity "three forms of existence" 1.4, pages 17-21 - physical world, Platonic mathematical world, mental world - theoretical physics, theoretical math, theoretical cognition

The meaning of numbers: complex, real, quaternionic.

Is the system symmetric or not. If it is a subsystem, then it is symmetric, and so there is a degeneracy (dividing by 2). If it is not a subsystem, then it is not symmetric.

Žodynėlis

• Bangos funkcija, bangos lygtis
• Kvantinė mechanika
• Hamiltonianas

References

• Penrose, "Road to Reality"
• Corfield
• Arnold

Skaitiniai

• Wave function collapse
• Quantum decoherence
• The Quantum Theory That Peels Away the Mystery of Measurement
• Measurement problem