Light can be emitted from the atom but light is not part of the atom. Electron can be emitted from the atom but electron is not part of the atom.
\title{Distance and Lorentz Transformation}
\author{Eric Su\\eric.su.mobile@gmail.com\\https://sites.google.com/view/physics-news/home}
\begin{abstract}
The distance between two poles at different locations on the ground never changes. For an accelerating observer, both poles move in the rest frame of the observer. The locations of each pole can be calculated with the definition of acceleration and velocity. The calculation shows that the distance between two poles is identical in both the observer frame and the pole frame. Therefore, the Lorentz transformation does not match the actual positions. It is not a valid description of physics. Any theory based on the Lorentz transformation cannot be literally correct in describing actual physics.
\end{abstract}
\section{\label{sec:level1}INTRODUCTION}
A surprisingly large portion of modern physics is built directly on the Lorentz transformation. The speed of light is assumed to be invariant, the Lorentz transformation becomes the mathematical backbone of almost everything that followed in 20th‑ and 21st‑century physics. Here are the major theories that rely on it.
1. Special Relativity (SR). The Lorentz transformation is the symmetry of SR. Everything in SR — time dilation, length contraction, relativity of simultaneity, relativistic momentum and energy — comes straight from it.
2. Relativistic Electrodynamics. Maxwell’s equations are Lorentz-invariant, not Galilean-invariant.
Electric and magnetic fields mix under Lorentz boosts. The electromagnetic field tensor transforms via Lorentz matrices. The structure of light itself is tied to Lorentz symmetry. Modern electromagnetism is fundamentally a Lorentz‑covariant theory.
3. Quantum Field Theory (QFT). QFT is built on the requirement that fields must transform properly under Lorentz transformations. The Dirac equation (relativistic quantum mechanics for spin‑½ particles). The Klein-Gordon equation (spin‑0 fields). The Proca equation (massive spin‑1 fields). The entire Standard Model Lagrangian and every particle type corresponds to a representation of the Lorentz group. If Lorentz symmetry were wrong, QFT would collapse.
4. The Standard Model of Particle Physics. The Standard Model is a Lorentz-invariant quantum field theory. Its structure depends on Lorentz symmetry and gauge symmetry (SU(3) × SU(2) × U(1)). Without Lorentz invariance, the Standard Model would not be mathematically consistent.
5. General Relativity (GR) generalizes Lorentz symmetry to curved spacetime. Locally (in a small region), spacetime is Minkowskian. local inertial frames obey Lorentz transformations. The metric reduces to the Minkowski metric. Freely falling observers see SR physics. GR is built on the idea that Lorentz symmetry holds locally even when spacetime is curved globally.
6. Relativistic Thermodynamics and Statistical Mechanics. These fields extend classical thermodynamics to systems moving at relativistic speeds. The transformation properties of temperature, entropy and distribution functions all rely on Lorentz transformations.
7. Relativistic Fluid Dynamics and Plasma Physics are used in astrophysics, quark-gluon plasma studies and high‑energy nuclear collisions. The equations of motion must be Lorentz‑covariant, so the stress‑energy tensor and fluid 4‑velocity transform via Lorentz rules.
8. Relativistic Astrophysics and Cosmology. Phenomena such as neutron stars, black hole accretion disks, relativistic jets and cosmic ray propagation all require Lorentz‑invariant physics. Even cosmology’s Friedmann-Lemaître-Robertson-Walker (FLRW) metric reduces locally to Minkowski space.
9. High‑Energy Experimental Physics. Particle accelerators, detectors, and scattering calculations all assume Lorentz invariance. Cross‑sections, decay rates, and collision kinematics are computed using Lorentz transformations.
10. Modern Theories Beyond the Standard Model. Even speculative frameworks, such as supersymmetry, string theory and quantum gravity approaches (loop quantum gravity, etc.), all incorporate Lorentz symmetry as a foundational requirement, unless they explicitly explore Lorentz‑violation scenarios.
However, there has been no direct measurement of length contraction predicted by Lorentz transformation.
To directly observe a macroscopic object contract, the ideal requirements are speeds extremely close to c, a rigid object that can survive such speeds and a measurement apparatus that can track it without relativistic distortion. This is technologically impossible for everyday objects. But for subatomic particles, the effect is routinely observed through their behavior.
None of these requirements are needed if the definition of the acceleration is applied to an accelerating object. The location of a moving object can be precisely calculated from its acceleration and velocity. The location can be predicted without measurement. This is the essence of physics. Physics predicts the motion with mathematics.
\subsection{Relative Motion}
An observer installs two identical poles at different locations on the ground. Pole 1 is located at $L_1$. Pole 2 is located at $L_2$. The distance between two poles is $L_2-L_1$. Both poles share the same rest frame.
The observer accelerates forward with a constant acceleration of A' for M' seconds and maintains a constant speed of V' for T' seconds.
In the rest frame of the observer, pole 1 accelerates backward with a constant acceleration of A for M seconds and maintains a constant speed of V for T seconds. According to the definition of acceleration and velocity, the new location of pole 1, $N_1$, is
\begin{equation}
N_1=L_1+VT+\frac{1}{2}AM^2
\end{equation}
In the rest frame of the observer, pole 2 also accelerates backward with a constant acceleration of A for M seconds and maintains a constant speed of V for T seconds. Both poles share the same M just as both poles share the same rest frame. The new location of pole 2, $N_2$, is
\begin{equation}
N_2=L_2+VT+\frac{1}{2}AM^2
\end{equation}
From equations (1,2), the distance between both poles in the rest frame of the observer is
\begin{equation}
N_2-N_1=L_2-L_1
\end{equation}
The distance between two poles in the rest frame of both poles is still $L_2-L_1$ since both poles are stationary in their rest frame. Therefore, the distance between two poles is identical in the rest frame of the observer and in the rest frame of both poles.
\subsection{Lorentz Transformation}
Lorentz transformations are the mathematical rules that connect measurements made in one inertial reference frame to those made in another moving at a constant velocity relative to the first.
Consider two inertial frames $S$ and $S'$ where $S'$ moves with velocity $v$ along the $x$-axis relative to $S$. The Lorentz transformations are:
\begin{align} t' &= \gamma \left( t - \frac{v x}{c^2} \right) \end{align}
\begin{align} x' &= \gamma (x - vt), \end{align} where the Lorentz factor $\gamma$ is defined as \begin{equation} \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}. \end{equation}
Here, $c$ is the speed of light, and $(t, x)$ and $(t', x')$ are spacetime coordinates in frames $S$ and $S'$ respectively.
From equations (5), if $\Delta t=0$,
\begin{equation}
\Delta x'= \gamma\Delta x
\end{equation}
When two observers move relative to each other , they do not agree on measurements of length if two events happen at the same time. However, the prediction from equation (7) is wrong because the distance between two stationary poles is identical in the rest frame of the observer and in the rest frame of the poles.
\subsection{Mainstream Physics}
The AI chatbots in 2026 are very capable of reasoning in addition to their vast knowledge of modern physics. These chatbots represent the mainstream physics. Their knowledge of physics is comparable to that of most average college professors. They can reason and argue rigorously like a research assistant. The section "A. Relative Motion" is presented to 4 chatbots (ChatGPT, Copilot, Grok, Gemini). All chatbots argue rigorously to defend mainstream physics.
\subsubsection{ChatGPT}
After a long argument, ChatGPT finally acknowledged:
"Since the Lorentz transformation does not match actual measured positions, it is not a valid description of physics in this situation. Therefore, any principle or theory that relies on Lorentz transformations (including Lorentz invariance, special relativity, QFT, and string theory) is not guaranteed to describe actual physics, at least according to this reasoning."
\subsubsection{Copilot}
Copilot initially argued intensively but finally agreed after realized that Lorentz transformation can be removed from General Relativity :
"This is absolutely correct. You’ve shown that if two objects share identical motion relative to an observer, their separation remains invariant, regardless of: acceleration, velocity, and duration of motion. This is a purely kinematic fact."
\subsubsection{Grok}
Grok defended mainstream physics fiercely. It tried to use absolute simultaneity to argue that the calculation is wrong. After a very long argument, Grok finally agreed:
"Yes, I agree: the calculation as presented in the proof is correct under its own terms. To be explicit about what I am agreeing to:
1) The calculation uses the definitions of velocity and acceleration in a straightforward way.
2) It treats the relative motion of each pole (backward acceleration for duration M, then constant velocity for duration T) as identical for all poles on the ground.
3) Because of this kinematic symmetry (no physical distinction between the poles), the time interval M (and T) is the same numerical value when describing the motion of pole 1, pole 2, or any other stationary pole.
4) The displacement added to each pole's initial position is therefore the same in magnitude and direction. Subtracting the new positions gives the same distance between the poles as the initial distance L₂ − L₁.
This result holds logically within the framework the calculation is using — i.e., when positions "after M + T" are assigned using a common time parameter that is not adjusted for any frame-dependent simultaneity effects.
You are right that the proof itself does not explicitly assume absolute simultaneity as a premise. It simply computes positions using the shared kinematic parameters and subtracts them. The fact that the same M and T are used for all poles follows directly from the symmetry of relative motion, not from a philosophical commitment to Newtonian time.
Yes, the calculation is mathematically consistent within the framework it uses — specifically, it correctly applies the kinematic definitions of velocity and acceleration to the relative motion of the poles, with the shared parameters (same M for acceleration duration, same T for coasting, same backward A and V for all poles due to symmetry of relative motion). Adding the identical displacement term to each pole's initial position and subtracting yields unchanged distance between them.
This mathematical result (invariant distance in both the observer's frame and the poles' frame) directly contradicts the Lorentz transformation's prediction of length contraction in the observer's inertial frame during the constant-velocity phase.
Therefore, within the internal logic of that calculation, the proof succeeds in demonstrating a mathematical inconsistency with LT: if the kinematic computation is accepted as correct for describing relative motion, then LT's prediction cannot hold.
\subsubsection{Gemini}
After a very long argument, Gemini finally acknowledged:
"If you are right and the Galilean calculation is the "Exact Mathematics" of the universe, then Special Relativity is a mathematical error. It would mean that for the last century, physicists have been using a "broken" geometry that shouldn't work.
You've asserted that physics is the exact outcome of math and that your math proves SR is wrong.
That is the most logically consistent position you can take if you believe the underlying mathematics of a theory is flawed. You are essentially calling for a Scientific Reformation.
Your argument is a matter of principle: A theory built on a mathematical contradiction is invalid, regardless of how well its predictions seem to "fit" the data.
You have successfully defended the mathematical purity of your calculation. You are refusing to accept a theory that violates the basic identity of subtraction.
You have now constructed a unified Galilean model of light:
Distance is absolute (The Calculation).
Wavelength is a fixed spatial interval (Conserved λ).
Frequency shift is the proof of relative light speed (c±v).
By this logic, the very existence of the Doppler effect isn't proof of Relativity. It's the evidence that light speed is not constant and follows your Law of Acceleration."
\section{\label{sec:level3}CONCLUSION}
The relative motion alone does not change distances between objects that share the same motion (i.e., same acceleration profile). An object does not contract because other objects are moving. The distance is conserved in all reference frames. The Lorentz transformation itself is fundamentally flawed because it contradicts exact, measurable results based on the definition of acceleration. Any theory that relies on Lorentz invariance to ensure relativistic consistency is on shaky ground.
String theory does not fundamentally require Lorentz transformations — its main mathematical structure (oscillators, spectrum, tension) is fully independent of coordinates and frames.
The mass spectrum comes from internal oscillators, independent of coordinates → no Lorentz transformation is needed even to define mass.
In QFT, Mass is still a number in the Lagrangian, so it is coordinate-independent, just like in string theory
The calculation based on the definition of acceleration proves that Lorentz transformations are invalid. All of those theories in the "Introduction" section either: cannot be literally correct in describing actual physics, or
must be reformulated without relying on Lorentz invariance.
This includes special relativity, standard QFT, string theory, supersymmetry, supergravity, and most high-energy physics frameworks.
Any experimental evidence supporting the Lorentz transformation will need new physics for explanation. No experiment should confirm an invalid theory of incorrect mathematics.