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It has been proposed that inertia can be explained as follows: when objects accelerate in one direction, a Rindler horizon forms in the other direction suppressing Unruh radiation on that side and producing a net Unruh radiation pressure that always opposes the acceleration, just like inertia. So far, this model has predicted masses over twice those expected. In this paper, an error in this model is corrected so that its prediction improves to within 29% of the expected Planck mass. It is also shown that inertial mass may be understood qualitatively by applying Carnot’s principle and entropy to Unruh temperatures, so that the work needed for inertia comes from the difference in the Unruh temperatures seen by the accelerated object and the cosmos. This implies that highly-accelerated systems may emit heat in a new way.

A modification of inertia (called MiHsC or quantized inertia) has been proposed that assumes that inertia is caused by Unruh radiation, and that this radiation is made inhomogeneous in space by either Rindler horizons caused by acceleration or the distant Hubble horizon. The former predicts the standard inertial mass, and the latter predicts galaxy rotation without dark matter and cosmic acceleration without dark energy. It is proposed here that this model can be derived in an alternative way by assuming that the sum of mass (M), energy (E) and the information content of horizons (I) is conserved (EMI) so that mass–energy is released in a discrete manner when the area of a Rindler horizon reduces. This model could be tested by looking for the quantization of inertial mass and acceleration at very high accelerations, and may provide an explanation for the cosmological constant problem.

Various attempts have been made to fully explain the mechanism by which a body has inertial mass. Recently, it has been proposed that this mechanism is as follows: when an object accelerates in one direction, a dynamical Rindler event horizon forms in the opposite direction, suppressing Unruh radiation on that side by a Rindler-scale Casimir effect whereas the radiation on the other side is only slightly reduced by a Hubble-scale Casimir effect. This produces a net Unruh radiation pressure force that always opposes the acceleration, just like inertia, although the masses predicted are twice those expected, see Ref. 17. In a later work, an error was corrected so that its prediction improves to within 26% of the Planck mass, see Ref. 10. In this paper, the expression of the inertial mass of a elementary particle is derived from the holographic scenario giving the exact value of the mass of a Planck particle when it is applied to a Planck particle.

In this paper, we raise and discuss the fundamental issue whether the interaction-induced inertia in the Higgs mechanism is the same as the charge of gravity or the gravitational mass. True physical mass has to fulfill the dual role of inertia and the gravitational charge, and should respect the weak equivalence principle. This is not yet addressed in the standard model that does not incorporate gravity. Hence, the Higgs scenario still requires a gravitational completion. Some relevant analogies where interaction-induced inertia is not the same as the gravitational charge are mentioned. Probing this line of thought will provide valuable clues and perhaps a remarkable answer to the place and role of gravity in the standard model of particle physics.

In this paper, we take a closer and new look at the effects of tidal forces on the free fall of a quantum particle inside a spherically symmetric gravitational field. We derive the corresponding Schrödinger equation for the particle by starting from the fully relativistic Klein–Gordon equation in order (i) to briefly discuss the issue of the equivalence principle and (ii) to be able to compare the relativistic terms in the equation to the tidal-force terms. To the second order of the nonrelativistic approximation, the resulting Schrödinger equation is that of a simple harmonic oscillator in the horizontal direction and that of an inverted harmonic oscillator in the vertical direction. Two methods are used for solving the equation in the vertical direction. The first method is based on a fixed boundary condition, and yields a discrete-energy spectrum with a wavefunction that is asymptotic to that of a particle in a linear gravitational field. The second method is based on time-varying boundary conditions and yields a quantized-energy spectrum that is decaying in time. Moving on to a freely-falling reference frame, we derive the corresponding time-dependent energy spectrum. The effects of tidal forces yield an expectation value for the Hamiltonian and a relative change in time of a wavepacket’s width that are mass-independent. The equivalence principle, which we understand here as the empirical equivalence between gravitation and inertia, is discussed based on these various results. For completeness, we briefly discuss the consequences expected to be obtained for a Bose–Einstein condensate or a superfluid in free fall using the nonlinear Gross–Pitaevskii equation.

The Lorentz-group of transformations usually consists of linear transformations of the coordinates, keeping as invariant the norm of the four-vector in (Minkowski) space-time. Besides those linear transformations, one may construct different forms of nonlinear transformations of the coordinates keeping unchanged that respective invariant. In this paper we explore nonlinear transformations of second-order which have a natural interpretation within the framework of Yamaleev's concept of the counterpart of rapidity (co-rapidity). The purpose of developed concept is to show that the formulae for energy and momentum of the relativistic particle become regular near the zero-mass and speed of light states. Furthermore, in a covariant formulation, the co-rapidity is presented as a four-vector which admits an extension of the Lorentz-group of transformations. In this paper we additionally show, that in the same way as the rapidity is related to the electromagnetic field, the co-rapidity is related to the field of strengths, which are given by a four-vector. The corresponding equations of such a field are also constructed.

Using Newton’s second law of motion $\sum \stackrel{\rightharpoonup }{F}=d\stackrel{\rightharpoonup }{p}/dt=m\stackrel{\rightharpoonup }{a}$, the inertial mass m = E_o / c² is derived for a resting electron proposed to be composed of a circling spin-½ charged photon of energy E_o and circling momentum P_o = E_o / c. In this view, the inertia of a particle is not due to “vis inertiae” or an “inertial force” within matter that resists acceleration, as Newton proposed. Rather, the inertial mass of an elementary particle of matter is due to the momentum of a circling photon-like object composing the particle. The particle’s inertial mass is calculated as the time rate of change of the momentum vector of a circling photon-like object composing the particle, divided by the associated centripetal acceleration of the circling photon-like object. A transluminal energy quantum model of the proposed spin-½ charged photon is introduced.