Russian physicists conducted a study that could transform our understanding of time, space, and matter.

The work is published in RENSIT: Radioelectronics. Nanosystems. Information Technologies. The idea of the interrelation between space and time can be traced back to the work of Hermann Minkowski, who proposed the concept of spacetime continuum in 1908. “No one has ever observed,” Minkowski said, “any place except at some moment in time, and no time except at some place.”

Minkowski refers to a point in space corresponding to a given moment in time as a “world point,” and the collection of all world points is briefly termed the “world.” Thus, any body existing in space over a certain period will correspond to a specific curve—a world line. “...The entire world seems to break down into such world lines,” Minkowski continues... “physical laws could find their most perfect expression as a relation between these world lines.”

His work laid the foundation for the theory of relativity, where space and time are viewed as a unified whole. Subsequently, Wolfgang Heisenberg formulated the uncertainty principle, which became the cornerstone of quantum mechanics. However, questions remained about how to extend these concepts into higher dimensions and how they relate to other physical quantities such as mass and interval.

Heisenberg's uncertainty principle is a fundamental principle of quantum mechanics that states it is impossible to simultaneously determine a pair of related variables, such as the position and momentum of a particle, with precision.

In their recent work, Russian scientists proposed introducing additional uncertainty relations connecting mass and interval in an extended model of space. This is a 5-dimensional model of extended space (MRP), where mass is added as the fifth coordinate to the three spatial coordinates and one time coordinate. In this model, the relationship between energy, momentum, and mass turns out to be a special case of the Pythagorean theorem in 5-dimensional space conjugate to coordinate space.

The presented (1+4)D model of extended space is based on the physical hypothesis that mass (rest mass) and its conjugate quantity—action (interval)—are dynamic variables. The values of these variables are determined by the interaction of fields and particles. The extended space model is a direct generalization of Special Relativity (SR).

In SR, the interval and rest mass of particles are invariants, while in MRP they can vary. Based on the assumptions made, extended Maxwell's equations are constructed in MRP, which describe not only electromagnetic interactions but also gravitational effects, and have a structure similar to the relativistic generalization of the Schrödinger equation in field-free space in the form of the Klein-Gordon equation.

“Our research emphasizes the importance of additional dimensions in physics and shows that traditional notions of mass and interval can be significantly expanded. We hope this will lead to new discoveries in quantum mechanics and field theory,” said Evgeny Sedelnikov, Associate Professor of the Department of General Physics at MIPT.

The novelty of the research lies in the expansion of the uncertainty principle to include additional coordinates—interval and mass—previously considered as invariant quantities.

The extended (1+4)D space model was created over 25 years ago, recalls Dmitry Tsipenuk, Associate Professor of the Department of General Physics at MIPT: “In due time, after the release of our next article dedicated to various aspects of our model, I visited Academician V.L. Ginzburg three times and presented our work to him—twice before V.L. Ginzburg received the Nobel Prize and once after. Vitaly Lazarovich listened to me attentively for about an hour each time and always tried to help—he referred me to his colleagues or staff for more detailed study of our articles. Once, when he encountered me at his famous seminar at the IAP, Vitaly Lazarovich approvingly patted me on the shoulder and said, ‘Let’s explore five-dimensional space.’”

If the new approach proves correct, it will lead to a greater geometrization of physics than that achieved in Einstein's theory of relativity. All physics in the extended space model can be understood as applied geometry.