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This study experimentally tested hyper-complex quantum theories by examining phase non-commutativity using single photons and metamaterials. Results show phases commute, placing limits on hyper-complex quantum theory predictions.

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Area of Science:

  • Quantum Mechanics
  • Metamaterials
  • Photonics

Background:

  • Standard quantum mechanics utilizes complex numbers for wavefunctions, but theoretical alternatives like hyper-complex numbers exist.
  • Experiments have ruled out real numbers, but the necessity of hyper-complex numbers remains unverified.

Purpose of the Study:

  • To experimentally investigate hyper-complex quantum theories.
  • To probe the non-commutativity of phases as a deviation from standard complex quantum theory.

Main Methods:

  • Single photons were passed through a Sagnac interferometer.
  • A metamaterial with a negative refractive index and a positive phase shifter were integrated into the interferometer.
  • A fishnet metamaterial was engineered for negative refractive index at 780 nm.

Main Results:

  • The phase introduced by the metamaterial was shown to commute with other phases with high precision.
  • Experimental data allowed for the placement of limits on specific predictions of hyper-complex quantum theories.

Conclusions:

  • The experimental results constrain the predictions of hyper-complex quantum theories.
  • Further investigation into the fundamental nature of quantum mechanical descriptions may be warranted.