Hyper complex or just complex? The future of quantum mechanics!
Hyper complex or just complex? The future of quantum mechanics!
Erlangen, Deutschland - Am 3. März 2025 beschäftigen sich Physiker der Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), darunter Ece Ipek Saruhan, Prof. Dr. Joachim von Zanthier and Dr. Marc Oliver Pleinert , with the question of whether hyper -complex numbers in quantum mechanics are necessary. This remarkable approach comes into the context of the over 100 -year -old quantum mechanics, which was formulated by sizes such as Heisenberg, Born and Schrödinger, and its mathematical basis, which is traditionally based on complex numbers.
The quantum mechanics were created in response to the inadequate explanations of classic physics for certain phenomena in the 1920s. Schrödinger, who presented the alternative wave mechanics, and other physicists developed the theory to describe the wave properties of particles, and to this day no experiment by the quantum mechanics has contradicted, such as in the literature is reported .
The concept of hyper -complex numbers
Hyper complex numbers are expanding complex numbers by further dimensions and have been a topic in the discussion about quantum mechanics since the 1970s. Asher Peres formulated a test to determine whether the quantum mechanics can be completely described with complex numbers. The test contains the comparison of interference patterns of light rays in different interferometers. Early experiments carried out simplified versions of this test, but brought no clear evidence of the need for the need for hyper -complex numbers.
The current research by the FAU physicists have theoretically further developed the Peres test. This new methodology makes it possible to interpret the recent test results as volumes in a three -dimensional space. If the volume is zero, the enough complex numbers would be obvious; Otherwise, hyper complexes would be required. This extended test structure also allows the examination of several light particles through interferometers with any number of columns.
mathematical basics of quantum mechanics
The mathematical formulation of quantum mechanics, which was developed by John von Neumann in 1932, describes a physical system by three main components: conditions, observables and dynamics. In the Copenhagen interpretation, the condition of a system is represented by a complex state vector as well as HERMITE Operators that represent physically measurable variables. The resulting measurement result corresponds to the self -values of the corresponding observable, such as in the Wikipedia is explained.
A particularly important concept of quantum mechanics is the Heisenberg uncertainty, which says that the location and impulse of a particle cannot be determined at the same time. The solutions of the Schrödinger equation describe the development of the wave function of a system over time and must be normal and steady. Measurements lead directly to the equal value of the corresponding operators, which defines the quantum mechanical properties of a system.
In summary, research on the FAU shows that the clarification of the relationship between complex and hyper -complex numbers plays a central role in further understanding and checking the fundamental aspects of quantum mechanics. While previous measurements indicate that complex numbers are sufficient, the question of the need for hyper -complex numbers remains exciting and open to future experiments and findings.| Details | |
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| Ort | Erlangen, Deutschland |
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