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Multipath and Multiparticle Tests of Complex versus Hypercomplex Quantum Theory.

Ece İpek Saruhan1,2, Joachim von Zanthier2, Marc-Oliver Pleinert2

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Summary
This summary is machine-generated.

This study explores hypercomplex quantum mechanics by developing new experimental tests. These tests probe the fundamental number system of quantum mechanics beyond complex numbers.

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Area of Science:

  • Theoretical Physics
  • Quantum Mechanics
  • Mathematical Physics

Background:

  • Quantum mechanics axioms do not specify the Hilbert space's number system.
  • While typically complex, hypercomplex numbers are theoretically possible, necessitating experimental verification.
  • Current tests, like the Peres test, are limited to specific hypercomplex scenarios (e.g., quaternionic).

Purpose of the Study:

  • To develop a general framework for testing hypercomplex quantum mechanics.
  • To propose novel multipath and multiparticle interference experiments.
  • To provide a direct method for probing the dimensionality of quantum mechanics' number system.

Main Methods:

  • Development of a general matrix formalism for interference tests.
  • Analysis of single-particle interference in a generalized Peres test.
  • Introduction of multipath and multiparticle interference protocols.

Main Results:

  • The proposed matrix formalism provides a rigorous mathematical foundation for interference tests.
  • New experimental tests are introduced that are sensitive to various dimensions of hypercomplex numbers.
  • The experiments offer a direct probe into the underlying number system of quantum mechanics.

Conclusions:

  • Experimental verification of hypercomplex quantum mechanics is feasible.
  • The proposed tests extend beyond current limitations, offering broader applicability.
  • This work paves the way for exploring fundamental aspects of quantum theory's mathematical structure.