In Hawking’s view physics has been broken up into many partial theories, while the ultimate goal of physicists is to unify them. The two basic theories of 20th-century physics, relativity theory and quantum theory, are based on completely different logical prerequisites and exactly separate: matter is described as particles in relativity theory and as waves in quantum mechanics. Here, based on the identical logical prerequisites, we unify Einstein’s special relativity (SR) and de Broglie’s matter-wave theory (MWT) into the theory of dualistic relativity (DR), taking a significant step toward the unification of relativity and quantum mechanics. From the definition of time, we derive the Lorentz transformation in differential form and establish the theory of DR, which generalizes the wave-particle duality of matter motion, and uniformly derives Einstein’s formula E=mc2, Planck’s equation E=hf, and de Broglie’s relation λ=h/p. From the logical prerequisite completely different from Einstein’s hypothesis of the invariance of light speed and along the logical path completely different from Einstein’s SR, we have deduced the whole theoretical system of Einstein’s SR and de Broglie’s MWT. In the theory of DR, the two great formulae originally separated, Einstein’s formula E=mc2 and Planck’s equation E=hf, become a pair of twin formulae unified in an identical theoretical system.
In Hawking’s view physics has been broken up into many partial theories, while the ultimate goal of physicists is to unify them. The two basic theories of 20th-century physics, relativity theory and quantum theory, are based on completely different logical prerequisites and exactly separate: matter is described as particles in relativity theory and as waves in quantum mechanics. Here, based on the identical logical prerequisites, we unify Einstein’s special relativity (SR) and de Broglie’s matter-wave theory (MWT) into the theory of dualistic relativity (DR), taking a significant step toward the unification of relativity and quantum mechanics. From the definition of time, we derive the Lorentz transformation in differential form and establish the theory of DR, which generalizes the wave-particle duality of matter motion, and uniformly derives Einstein’s formula E=mc2, Planck’s equation E=hf, and de Broglie’s relation λ=h/p. From the logical prerequisite completely different from Einstein’s hypothesis of the invariance of light speed and along the logical path completely different from Einstein’s SR, we have deduced the whole theoretical system of Einstein’s SR and de Broglie’s MWT. In the theory of DR, the two great formulae originally separated, Einstein’s formula E=mc2 and Planck’s equation E=hf, become a pair of twin formulae unified in an identical theoretical system.
A hypothesis is put forward according to which the formulas of Relativity are a consequence of the laws of quantum physics and may be applied only to quantum objects. According to the wave - particle duality quantum bodies are simultaneously the waves and considered in the present research with a use of the wave equation and requirement of its Lorentz‘s invariance. The property of invariance with respect to the Lorentz’s transform is analysed in hyperbolic coordinates in an area of complex numbers. An examination showed that formulas of relativistic kinematics can be obtained based on the condition of equality of the amplitudes and phases of the wave, observed from different inertial frames. There is no need to introduce the concept of a unified entity of space-time, but the return to the idea of aether and matter waves de Broglie occurs. The physical model becomes borrowed partly from quantum field theory. It is assumed that the moving particle binds to a wave of the aether disturbance, and only this wave acts on the other particle like an electromagnetic field pushes an electrical charge. The model of colliding elastic balls becomes inapplicable, but equations of relativity mechanics remain the same, however, with a new interpretation. The mass of a particle in all coordinate systems is constant, in exchange the expressions of energy and momentum alter relative the classical case, include the property of aether – coefficient c of the wave equation, and acquire relativistic forms.
This paper presents a novel theory of wave mechanics derived from a re-examination of the foundations of relativity. By expanding the traditional linear transformation ansatz to include a vector-valued temporal component, we demonstrate that Einstein's postulates, coupled with the principle of single-valued time, are sufficient to predict wave-like, quantizable behavior in particle motion. This approach naturally leads to a Clifford algebra framework and reveals the necessity of a dynamic, higher-dimensional temporal space. We derive Lorentz transformations and demonstrate the origin of the spacetime metric's signature. Furthermore, we obtain relations analogous to De Broglie's and show compatibility with Planck's distribution law. Notably, our theory provides a unified framework for spin-0 and spin-1/2 particles and offers a complete, normalized solution for a particle at rest, resolving a long-standing challenge in quantum mechanics. The inherent coupling of the Einstein Field Equations with the derived wave equation suggests potential implications for cosmology, including alternative explanations for dark matter and MOND. This work establishes a foundation for a new, consistent, and intuitive understanding of the quantum world, with experimentally testable predictions that distinguish it from conventional quantum mechanics.
This paper presents a novel theory of wave mechanics derived from a re-examination of the foundations of relativity. By expanding the traditional linear transformation ansatz to include a vector-valued temporal component, we demonstrate that Einstein's postulates, coupled with the principle of single-valued time, are sufficient to predict wave-like, quantizable behavior in particle motion. This approach naturally leads to a Clifford algebra framework and reveals the necessity of a dynamic, higher-dimensional temporal space. We derive Lorentz transformations and demonstrate the origin of the spacetime metric's signature. Furthermore, we obtain relations analogous to De Broglie's and show compatibility with Planck's distribution law. Notably, our theory provides a unified framework for spin-0 and spin-1/2 particles and offers a complete, normalized solution for a particle at rest, resolving a long-standing challenge in quantum mechanics. The inherent coupling of the Einstein Field Equations with the derived wave equation suggests potential implications for cosmology, including alternative explanations for dark matter and MOND. This work establishes a foundation for a new, consistent, and intuitive understanding of the quantum world, with experimentally testable predictions that distinguish it from conventional quantum mechanics.
This paper presents a novel theory of wave mechanics derived from a re-examination of the foundations of relativity. By expanding the traditional linear transformation ansatz to include a vector-valued temporal component, we demonstrate that Einstein's postulates, coupled with the principle of single-valued time, are sufficient to predict wave-like, quantizable behavior in particle motion. This approach naturally leads to a Clifford algebra framework and reveals the necessity of a dynamic, higher-dimensional temporal space. We derive Lorentz transformations and demonstrate the origin of the spacetime metric's signature. Furthermore, we obtain relations analogous to De Broglie's and show compatibility with Planck's distribution law. Notably, our theory provides a unified framework for spin-0 and spin-1/2 particles and offers a complete, normalized solution for a particle at rest, resolving a long-standing challenge in quantum mechanics. The inherent coupling of the Einstein Field Equations with the derived wave equation suggests potential implications for cosmology, including alternative explanations for dark matter and MOND. This work establishes a foundation for a new, consistent, and intuitive understanding of the quantum world, with experimentally testable predictions that distinguish it from conventional quantum mechanics.
This paper presents a novel theory of wave mechanics derived from a re-examination of the foundations of relativity. By expanding the traditional linear transformation ansatz to include a vector-valued temporal component, we demonstrate that Einstein's postulates, coupled with the principle of single-valued time, are sufficient to predict wave-like, quantizable behavior in particle motion. This approach naturally leads to a Clifford algebra framework and reveals the necessity of a dynamic, higher-dimensional temporal space. We derive Lorentz transformations and demonstrate the origin of the spacetime metric's signature. Furthermore, we obtain relations analogous to De Broglie's and show compatibility with Planck's distribution law. Notably, our theory provides a unified framework for spin-0 and spin-1/2 particles and offers a complete, normalized solution for a particle at rest, resolving a long-standing challenge in quantum mechanics. The inherent coupling of the Einstein Field Equations with the derived wave equation suggests potential implications for cosmology, including alternative explanations for dark matter and MOND. This work establishes a foundation for a new, consistent, and intuitive understanding of the quantum world, with experimentally testable predictions that distinguish it from conventional quantum mechanics.
This paper presents a novel theory of wave mechanics derived from a re-examination of the foundations of relativity. By expanding the traditional linear transformation ansatz to include a vector-valued temporal component, we demonstrate that Einstein's postulates, coupled with the principle of single-valued time, are sufficient to predict wave-like, quantizable behavior in particle motion. This approach naturally leads to a Clifford algebra framework and reveals the necessity of a dynamic, higher-dimensional temporal space. We derive Lorentz transformations and demonstrate the origin of the spacetime metric's signature. Furthermore, we obtain relations analogous to De Broglie's and show compatibility with Planck's distribution law. Notably, our theory provides a unified framework for spin-0 and spin-1/2 particles and offers a complete, normalized solution for a particle at rest, resolving a long-standing challenge in quantum mechanics. The inherent coupling of the Einstein Field Equations with the derived wave equation suggests potential implications for cosmology, including alternative explanations for dark matter and MOND. This work establishes a foundation for a new, consistent, and intuitive understanding of the quantum world, with experimentally testable predictions that distinguish it from conventional quantum mechanics.