The internal structure of self-interacting quantum particle like electron is independent on space-time position. Then at least infinitesimal kinematic space-time shift, rotation or boost lead to the equivalent internal quantum state. This assumption may be treated as internal (quantum) formulation of the inertia principle. Dynamical transformation of quantum setup generally leads to deformation of internal quantum state and measure of this deformation may be used as quantum counterpart of force instead of a macroscopic acceleration. The reason of inertia arises, thereby, as a consequence an internal motion of quantum state and its reaction on dynamical quantum setup deformation. The quantum origin of the inertia has been discussed in this article in the framework of "eigen-dynamics" of self-interacting relativistic extended quantum electron. Namely, a back reaction of spin and charge "fast" degrees of freedom on "slow" driving environment during "virtual measurement" leads to the appearance of state dependent non-Abelian gauge fields in dynamical 4D space-time. Analysis of simplified dynamics has been applied to the energy-momentum behavior in the relation with runaway solutions of previous models of an electron.
The internal structure of self-interacting quantum particle like electron is independent on space-time position. Then at least infinitesimal kinematic space-time shift, rotation or boost lead to the equivalent internal quantum state. This assumption may be treated as internal (quantum) formulation of the inertia principle. Dynamical transformation of quantum setup generally leads to deformation of internal quantum state and measure of this deformation may be used as quantum counterpart of force instead of a macroscopic acceleration. The reason of inertia arises, thereby, as a consequence an internal motion of quantum state and its reaction on dynamical quantum setup deformation. The quantum origin of the inertia has been discussed in this article in the framework of "eigen-dynamics" of self-interacting relativistic extended quantum electron. Namely, a back reaction of spin and charge "fast" degrees of freedom on "slow" driving environment during "virtual measurement" leads to the appearance of state dependent non-Abelian gauge fields in dynamical 4D space-time. Analysis of simplified dynamics has been applied to the energy-momentum behavior in the relation with runaway solutions of previous models of an electron.
The role of the CP(N−1) geometry in the intrinsic unification of the general relativity and QFT
Einstein's program of the unified field theory transformed nowadays to the TOE requiring new primordial elements and relations between them. Definitely, they must be elements of the quantum nature. One of most fundamental quantum elements are pure quantum states. Their basic relations are defined by the geometry of the complex projective Hilbert space. In the framework of such geometry all physical concepts should be formulated and derived in the natural way. Analysis following this logic shows that inertia and inertial forces are originated not in space-time but it the space of quantum states since they are generated by the deformation of quantum states as a reaction on an external interaction or self-interaction. In particular, inertia law generalized by Einstein during development of general relativity (GR) will be expressed in intrinsic quantum terms. It is assumed that quantum formulation of the inertia law should clarify the old problem of inertial mass (dynamical mass generation). The conservation of energy-momentum following form this law has been applied to self-interacting quantum Dirac's electron.
The independence of momentum and velocity in Dirac's theory of the electron may be understood classically as a consequence of the radiation reaction force. In earlier work one of the authors has tried to interpret the whole spin phenomenon on this basis, considering the new degrees of freedom as representatives of the higher time derivatives in the equation of motion of a particle extended in space. A consequent treatment of this question by Bopp on the basis of his linear electrodynamics revealed that this program is possible only for integral spin; also, it seemed to be necessary to ignore the non-conservative part of the radiation reaction force. We show here that without alteration of the new formalism the spin may be introduced as an intrinsic feature of the particles, as in older theories, so that half-integral values are included. The Poisson brackets are derived in full generality without reference to a specific model by extension of an idea of Anderson. It is then shown by a contact transformation first discovered in quantum mechanics that the motion under the (third order) radiation reaction force is contained as a particular integral in the (fourth order) equations of motion, which we have in common with Bopp. This holds exactly in absence of the Lorentz force and suggests a simple scheme for the interpretation in quantum mechanics of the radiation reaction. In order to maintain nearly the particular motion in presence of the Lorentz force, a slight alteration of the Hamiltonian is necessary, which has empirical support from the evaluation of the corresponding wave equation.
We consider a quantum particle as a wave packet in the coordinate space. When the conjugate wave packet in the momentum space is considered, we find that the group velocities of these two wave packets, which describe the particle dynamics, are in agreement with the Hamilton equations only if in the time dependent phases one considers the Lagrangian instead of the Hamiltonian which leads to the conventional Schrodinger equation. We define a relativistic quantum principle asserting that a quantum particle has a finite frequency spectrum, with a cutoff propagation velocity c as a universal constant not depending on the coordinate system, and that any time dependent phase variation is the same in any system of coordinates. From the time dependent phase invariance, the relativistic kinematics is obtained. We consider two types of possible interactions: 1) An interaction with an external field, by a modification of the time dependent phase differential with the terms proportional to the differentials of the space-time coordinates multiplied with the components of this field four-potential, and 2) an interaction by a deformation of the space-time coordinates, due to a gravitational field. From the invariance of the time dependent phase with field components, we obtain a mechanical force of the form of Lorentz’s force, and three Maxwell equations: The Gauss-Maxwell equations for the electric and magnetic fluxes, and the Faraday-Maxwell equation for the electromagnetic induction. When the fourth equation, Ampere-Maxwell, is considered, the interaction field takes the form of the electromagnetic field. For a low propagation velocity of the particle waves, we get a packet of waves with the time dependent phases proportional to the relativistic Hamiltonian, as in Dirac’s famous theory of spin, and a slowly-varying amplitude with a phase proportional to the momentum and this velocity. In the framework of our theory, the spin is obtained as an all quantum effect, without any additional assumption to the quantum theory. When a space-time deformation is considered in the time dependent phase of a quantum particle, from the group velocity we get the particle dynamics according to the general theory of relativity. In this way, the relativistic dynamics, the electromagnetic field, and the spin of a quantum particle are obtained only from the invariance of the time dependent phases of the particle wave functions.
Modern quantum mechanics traditionally treats the internal frequencies of quantum systems as static parameters or time-independent eigenvalues, assuming they can be altered instantaneously without resistance. In this paper, we propose the principle of Quantum Frequency Inertia (QFI), establishing that internal transition and resonance frequencies possess intrinsic inertia and relaxation dynamics when subjected to rapid modulation. By formulating an extended Lagrangian and Hamiltonian framework where frequency acts as an independent dynamical coordinate, we derive the governing equation of motion incorporating an inertial coefficient and a characteristic relaxation time scale. Microscopic analysis confirms that this frequency retardation stems from non-Markovian environmental back-action and finite propagation speeds of mediating interactions. We analyze manifestations of QFI across diverse platforms—including atomic clocks, optical cavities, and superconducting quantum circuits—and outline testable predictions such as frequency response resonance peaks and underdamped transient ringing. This framework redefines frequency as an active dynamical degree of freedom, offering new insights into ultra-fast quantum control and metrological limits.
The problem of the reason of physical motion needs a review in the framework of quantum theory. The Aristotle's mistake, Galileo-Newton progress, Einstein physical geometry established the fundamental role of the spacetime geometry in the motion of fields and bodies. Quantum theory poses a new question about the motion of the quantum states and its reason in the quantum state space. The standard approach of quantum theory uses so-called method of the classical analogy where the action functional contains in the additive manner three terms: matter (free particles) + free fields + interaction term. Such approach leads to the quantum state space as some space of functions defined on the spacetime.I think if one tries to understand the peculiarity of the self-interacting quantum particles together with its ``field shell" then the classical scheme should be replaced. Then the role of the spacetime should be revised: the space of the unlocated pure quantum degrees of freedom and its geometry will play the fundamental role and the local dynamical spacetime arises as representation of the internal quantum motions (inverse representation).
Abstract The new quantum theory, based on the assumption that the dynamical variables do not obey the commutative law of multiplication, has by now been developed sufficiently to form a fairly complete theory of dynamics. One can treat mathematically the problem of any dynamical system composed of a number of particles with instantaneous forces acting between them, provided it is describable by a Hamiltonian function, and one can interpret the mathematics physically by a quite definite general method. On the other hand, hardly anything has been done up to the present on quantum electrodynamics. The questions of the correct treatment of a system in which the forces are propagated with the velocity of light instead of instantaneously, of the production of an electromagnetic field by a moving electron, and of the reaction of this field on the electron have not yet been touched. In addition, there is a serious difficulty in making the theory satisfy all the requirements of the restricted principle of relativity, since a Hamiltonian function can no longer be used. This relativity question is, of course, connected with the previous ones, and it will be impossible to answer any one question completely without at the same time answering them all. However, it appears to be possible to build up a fairly satisfactory theory of the emission of radiation and of the reaction of the radiation field on the emitting system on the basis of a kinematics and dynamics which are not strictly relativistic. This is the main object of the present paper. The theory is noil-relativistic only on account of the time being counted throughout as a c-number, instead of being treated symmetrically with the space co-ordinates. The relativity variation of mass with velocity is taken into account without difficulty. The underlying ideas of the theory are very simple. Consider an atom interacting with a field of radiation, which we may suppose for definiteness to be confined in an enclosure so as to have only a discrete set of degrees of freedom. Resolving the radiation into its Fourier components, we can consider the energy and phase of each of the components to be dynamical variables describing the radiation field. Thus if Er is the energy of a component labelled r and θr is the corresponding phase (defined as the time since the wave was in a standard phase), we can suppose each Er and θr to form a pair of canonically conjugate variables. In the absence of any interaction between the field and the atom, the whole system of field plus atom will be describable by the Hamiltonian H ═ ΣrEr + Ho equal to the total energy, Ho being the Hamiltonian for the atom alone, since the variables Er, θr obviously satisfy their canonical equations of motion Er ═ — ∂H/∂θr ═ 0, θr ═ ∂H/∂Er ═ 1.