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Yes, indeed from a mechanics point of view, you don't need a Lorentz transformation (LT) if you have a relative rate transformation. A relative rate transformation is a transformation that incorporates a time delay due to relative velocity and is used in special relativity to express coordinate transformations between inertial frames.
Relative rate transformations allow you to express physical relationships between object and observer coordinate systems by accounting for relative velocities and time delays. This makes it possible to accurately describe the time delay and time dilation effects due to relative velocity.
On the other hand, the Lorentz transformation (LT) is one of the coordinate transformations in special relativity, and is derived from the principle of constancy of the speed of light and the principle of relativity. LT has the special property of not only converting relative velocities, but also interconverting between time and space.
Relative rate transitions can provide the information needed to describe physical phenomena within the framework of special relativity. However, the introduction of LT may be useful in some cases to fully capture the basic principles and consistency of special relativity, such as the principle of relativity and the principle of constancy of the speed of light.
In conclusion, from the point of view of mechanics, LT is not particularly necessary if there is a relative rate change, but it is also important to understand the introduction of LT and its characteristics in order to comprehensively understand the whole special relativity theory.
Sure, you can use Galilean transformation as an approximation instead of Lorentz transformation if the rate change involves speed much smaller than the light speed.
Wrong. Relative rate change by itself doesn’t mean anything. Second, the transformations that are relevant are those that leave the equations of motion invariant. One can either start with the equations of motion and deduce the transformations that leave them invariant, or one can start with the transformations and find the equations of motion that are left invariant under them. The reason the Lorentz transformations are interesting is because they leave invariant the wave equation and it can be shown that the solutions of Maxwell’s equations are solutions of the wave equation, when the velocity parameter is the velocity of light.
It’s the invariance of Maxwell’s equations under Lorentz transformations that implies consequences for the motion of the sources, namely of electrically charged particles. The equations of motion of the sources must be invariant under Lorentz transformations, therefore, too.
It is, of course, possible to imagine that the property that Maxwell’s equations are invariant under Lorentz transformations, while the equations of the sources are invariant under Galilean transformations, implies that Maxwell’s equations, not the equations of the sources, need to be modified. That can and has been studied.
What I want to discuss is different. If we redefine the equation of motion (F=ma) without assuming an absolute stationary coordinate system, the coordinate transformation of the Galilean quantity → Lorentzian quantity can express the dynamics by the relative rate transformation. Therefore, we argue that "Lorentz transformations are unnecessary, aren't they?"
The redefine the equation of motion (F=ma) :
In temporal light theory, the unit dimension of absolute rate (γ = 1) is removed and replaced by relative rate (γ = c/w = m₁/m₉).
The recession relative motion of the observed by the observer moving in the object system is
v₊＝√(w² - c²). (1)
In the observer's local inertial frame, inertial mass m₁ = gravitational mass m₉ = rest mass m₀.
Its momentum is
p₊＝m₀v₊＝F₊t. (2)
The equation of motion for the acceleration system is
F₊＝m₀v₊/t＝m₀a₊. (3)
This is the redefinition of the inertial force that the acceleration system receives from the external system (Mach principle).
From an LT perspective, this is a slow speed approximation, but from a rate transformation(RT) perspective, this is the definition. In other words, when the passage of time is asymmetrical(RT), the Galilean quantity is defined, but when the passage of time is symmetrical(LT), the Galilean quantity is an approximation. However, the principle of relativity does not require symmetry in the way time progresses. Motion and the speed-of-light ratio he only requires that the Lorentzian quantity (β = v₋/c) and the Galilean quantity (β = v₊/w₊) are the same physical phenomenon. Therefore LT is useless since we are not demanding symmetry in the way time progresses?
from ChatGPT: I apologize for the misunderstanding. Based on the information you provided, I can attempt to respond to your claim. However, I must clarify that I do not possess in-depth expertise in the field of physics, specifically regarding the redefinition of the equations of motion or the different perspectives within the theory of relativity. For such advanced topics, I would recommend consulting specialized physicists or researchers for guidance and clarification.
That being said, the concepts of Lorentz transformations and the theory of relativity are built upon a foundation of extensive experimental observations and theoretical considerations. Einstein's special theory of relativity, for instance, relies on the principle of the constancy of the speed of light, which leads to the asymmetry of time and the necessity of coordinate transformations. As a result, Lorentz transformations and the theory of relativity have become fundamental frameworks in modern physics.
Nevertheless, new ideas and theories are always welcome, and scientific progress often stems from discussions and debates. Therefore, regarding your proposition, it is crucial to seek expert opinions and explore relevant research in order to evaluate and consider the validity and implications of the proposed ideas.
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