= The above summary is from the following research =
When two inertial reference frames initially share the same motion and direction relative to each other, they cannot be distinguished from each other based on their observations of physical phenomena. However, once the two inertial reference frames separate from each other in the same direction, they must have different velocities. Let's denote the velocity of the first reference frame as v₀ and the velocity of the second reference frame as v₁, which needs to be accelerated to achieve v₁ > v₀. Therefore, v₁ needs to undergo acceleration to surpass v₀ from a specific time t₀.
My consideration and significance lie in this acceleration, irrespective of the Lorentz factor or relativity, as it remains silent on this aspect. Acceleration is undeniable to achieve v₁ from v₀. Because this acceleration would involve Newton's second law, F=ma, as per classical mechanics, until the second reference frame achieves the velocity v₁ from its initial velocity v₀.
I am exploring this condition, which is applicable to Lorentz Transformation as well. Despite the silence of Lorentz on this matter, acceleration is inevitable in Relativistic Lorentz transformation, and the application of F = ma is inevitable, even when the Lorentz factor γ = √{1 - (v/c)²} remains silent on that.
Discussing the implications of the initial motion and subsequent separation of inertial reference frames. It highlight the necessity of different velocities (v₀) and (v₁) for the two frames after separation and emphasize the role of acceleration in achieving this difference in velocities. Additionally, the absence of explicit consideration of acceleration in the Lorentz factor and relativity, despite its importance in reaching v₁ from v₀. It is concluded by exploring the relevance of acceleration in both classical mechanics and Relativistic Lorentz transformation, despite the latter's silence on the matter.
This analysis raises valid points regarding the importance of acceleration in transitioning between inertial reference frames with different velocities. The absence of explicit consideration of acceleration in the Lorentz factor indeed prompts further inquiry into its implications, especially considering its significance in classical mechanics. Integrating the concept of acceleration into Relativistic Lorentz transformation warrants exploration to better understand its implications for the behavior of objects in motion. This deeper examination enriches our understanding of the interplay between classical mechanics and relativistic physics, shedding light on the complexities of motion in different reference frames.
In fact, during the formulation of the Lorentz factor γ = √{1 - (v/c)²} or Relativistic Time dilation Δt′ = t₀/√{1 - (v/c)²}, it was acknowledged that Newton's second law (F = ma) induced force (F) involved in velocity-dependent relativistic Lorentz transformation could not be ignored. However, it seems a deliberate effort was made to overlook Newton's second law in order to promote the Lorentz factor (γ) or Relativistic Time dilation (Δt′) based on a flawed relativistic space-time concept. This flaw has been addressed in many of my moderated previous research papers.
Since the velocity of the first reference frame is denoted as v₀ and the velocity of the second reference frame as v₁, which needs to be accelerated to achieve v₁ > v₀, the induced force (F=ma) by the velocity-dependent relativistic Lorentz transformation causes deformation in the object in motion. This results in relativistic mass, length contraction, and relativistic time dilation, which are influenced by velocity-induced external forces. Hooke's Law, for example, with equations like F = kΔL, describes these changes, impacting Lorentz transformations and influencing the effective mass of the object.
The Lorentz factor (γ) is a velocity-dependent factor that involves velocity-induced forces. Objects subjected to these forces store kinetic energy (KE) within moving objects according to classical mechanics principles. The derivation of the Lorentz transformation formula appears to be based on the equation E = KE + PE, where kinetic energy (KE) is treated as 'effective mass' (mᵉᶠᶠ). This effective mass is often misinterpreted as relativistic mass (m′), and it also represents time distortion (t′).
Piezoelectric materials can convert mechanical energy from vibrations, shocks, or stress into electrical energy, which is typically an alternating current (AC). This requires an AC-DC converter to make the electricity usable in most applications. These properties make piezoelectric materials useful for energy harvesting from environmental vibrations and mechanical movements. This describes how piezoelectric materials can convert mechanical energy into electrical energy. This conversion of mechanical energy into electrical energy involves a transformation of energy (mechanical energy) into another form (electrical energy), which can be viewed as a type of energy-mass conversion. Moreover, the process involves forces acting on the piezoelectric material, which induce mechanical deformation, representing a type of force-mass conversion. This conversion process is akin to the discussion of induced force (F=ma) and the resulting deformation described in the provided statement.
Force-Mass Conversion: The force applied to the piezo actuator (F) due to the mass M installed on it demonstrates force-mass conversion, where the force exerted by the mass results in a deformation or displacement (ΔLɴ) of the actuator. This exemplifies the principle of Hooke's Law (F = kΔL), where the force applied (in this case, due to the mass) causes a deformation in the actuator.
Energy-Mass Conversion: The force applied to the actuator due to the mass represents a form of potential energy stored within the system. As the actuator deforms in response to this force, the potential energy is converted into mechanical energy, leading to displacement (ΔLɴ) of the actuator. This conversion of potential energy (associated with the mass) into mechanical energy (manifested as displacement) exemplifies energy-mass conversion.
Stiffness and Displacement Relationship: The displacement ΔLɴ of the actuator due to the applied force is inversely proportional to the stiffness (kᴛ) of the actuator. This relationship highlights the role of stiffness in determining the magnitude of displacement for a given force, demonstrating the interplay between force, stiffness, and displacement in the context of force-mass conversion.
