The real and imaginary parts of the complex can well reflect the contradictions of unity of opposites and transformed into each other. The real part of the complex physical quantity reflects the nonlinear and non-superposition characteristics of the particle, the imaginary part reflects the fluctuation characteristics of material linear and superposition. The real part of the complex energy form the macroscopic Einstein mass energy equation, the imaginary part of the complex energy form Planck energy equation. Bosons and fermions are the same substance in different motion state in time and space. The peak of the matter wave form boson state typical; intersection of matter wave and the space formed fermions typical U (20) superunified group covers four kinds of forces.
The real and imaginary parts of the complex can well reflect the contradictions of unity of opposites and transformed into each other. The real part of the complex physical quantity reflects the nonlinear and non-superposition characteristics of the particle, the imaginary part reflects the fluctuation characteristics of material linear and superposition. The real part of the complex energy form the macroscopic Einstein mass energy equation, the imaginary part of the complex energy form Planck energy equation. Bosons and fermions are the same substance in different motion state in time and space. The peak of the matter wave form boson state typical; intersection of matter wave and the space formed fermions typical U (20) superunified group covers four kinds of forces.
A study was carried out to explain a wave propagation of the relativistic energy that comes in the squared form. What looks physically incompatible concept of wave and particle was combined into a general wave of the complex energy. From the fact that the energy of matter is expressed by the squared form, a wave of the massless and massive energies was presented, which plays a role in the formation of matter wave. This study revealed that the energy is separated into the complex value with a imaginary mass that makes the wave different from the plane wave. The wave propagation is described by plugging the complex energy into the wavefunction, in which a modified mass-energy equivalence from the special relativity was used. From the fact that the energy of matter is consist of a complex value, it is also explained that the space around a rest-mass is a space with a imaginary mass. As a result, a general expression of matter and wave is described by the complex wave including an imaginary mass and a real momentum, by which a reasonable explanation is given for the radiation of mass energy, and explains the role of imaginary mass in the propagation of energy.
The theory of relativity represents fields of force as structural properties of space-time, and a field of force is the arena in which the presence of energy is detectable. Energy manifests itself in the physical world as radiation, and Einstein established its fundamental identity with mass.1 This has since been demonstrated experimentally by the annihilation of elementary particles and their conversion into y-rays and the reverse process of conversion of y-rays into pairs of electrons and positrons ('pair production') as observed by Blackett and Occhialini. It is hardly surprising, therefore, that both matter and energy should appear to us in the same phenomenal forms, as particles and as waves. The universal interconnectedness of things is here again exemplified. Space-time structure, in the form of curvature of differing degrees, appears as field, and field, by what Teilhard would call 'complexification', organizes itself into material particles. The contemporary theory of matter, notwithstanding disputes and controversies still current about the concepts involved, unquestionably represents the atom as a complicated organization of fields of force describable without misrepresentation as an energy complex. This being so, an unbroken continuity between space-time, field, energy and matter is established, as a series of forms or manifestations of the real, each a more complex elaboration of its predecessor in the series. The progression is effected, to borrow again from Teilhard, by a process of self-enfoldment (enroulement sur soi-meme) of the prior form: curvature of space gives field, the structure or complexity of the field (as we are about to find) takes the form of waves (or radiation), further complication of these, by superposition, produces wave-packets or particles, and the intricate organization of particles into a single energy system constitutes the atom.
The equation of motion for a particle moving in complex space is obtained and then solved. The interaction between the real and imaginary components of motion can produce what can be regarded as a wave motion in real space. The formation of interference patterns and polarization of a matter wave can be accounted for by the particle’s motion in complex space. The deterministic particle view of a free particle can then be reconciled with its dual probabilistic wave picture but the formulation is entirely in complex space.
Abstract In the standard quantum–field–theoretic description of unstable particles, exponential decay with width is encoded by promoting the energy (or mass) to a complex quantity . This prescription works extremely well in practice, but its imaginary part has no direct counterpart in the usual real–valued notion of energy, and it raises a natural question: where does the imaginary unit really belong? In this letter we show that the same physics can be reformulated in a complex–time framework in which the rest mass remains real and the decay is absorbed into a complex phase associated with the time direction. For a stable relativistic particle, the proper–time action can be written so that the mass controls the rate of phase rotation along a complex extension of time. For a quasi–stable state with width , the standard replacement is equivalently realized by a complex phase whose real part encodes the mass–controlled oscillation and whose imaginary part encodes the exponential damping. As a concrete example we apply this construction to the Higgs boson, whose mass arises from the Higgs vacuum expectation value while its finite lifetime is generated by interactions. In the complex–time picture these two aspects appear as the real and imaginary components of a single geometric object, providing a unified way to relate mass, width and the arrow of time without complexifying the energy spectrum itself. Running Title Unstable States in Complex Time Key Words unstable quantum states; complex time; complex energy; Higgs boson; vacuum structure
Micro-object is both particle and wave, so the traditional Particle Model (mass point model) is actually not applicable for it. Here to describe its motion, we expand the definition of time and space and pick up the spatial degrees of freedom hidden by particle model. We say that micro-object is like a rolling field-matter-ball, which has four degrees of freedom including one surface curvature degree and three mapping degrees in the three-dimensional phenomenal space. All the degrees are described by four curvature coordinate components, namely “k1, k2, k3, k4”, which form the imaginary part of a complex phase space, respectively. While as to the real part, we use “x1, x2, x3, x4” to describe the micro object’s position in our real space. Consequently, we build a Dual 4-dimensional complex phase space whose imaginary part is 4-dimension k space and real part is 4-dimension x space to describe the micro-object’s motion. Furthermore, we say that wave function can describe the information of a field-matter-ball’s rotation & motion and also matter-wave can spread the information of micro-object’s spatial structure & density distribution. Matter-wave and probability-wave can transform to each other though matter-wave is a physical wave. The non-point property is the foundational source of the probability in Quantum Mechanics.