The Equivalence Principle in General Relativity


November 2021

Jan Onderco

Abstract

General Relativity Equivalence Principle violates conservation of energy physical law!

The equality between the inertial and gravitational mass leads to the Equivalence principle: as far as physical measurements are concerned, an inertial observer in a uniform gravitational field is equivalent to uniformly accelerated observer in the absence of any gravitational field.[1]

Hall Effect

Hall effects arise from rotational and linear motions of particles. These outcomes are linked to transverse drift of the particle in direction orthogonal to its angular momentum and external force.[2] A rotating relativistic flywheel manifests constantly increasing transverse drift effect on a spaceship accelerating at 1g compared to the same scenario when there is a constant transverse drift effect considering the spaceship is standing on the Earth surface. The thought experiment presented in this paper relies on the conclusion that centroid of a system, the transverse drift, depends upon a choice of observer.[3] There could be only one observer with its reference system where the manifested increase of the transverse drift, being observable even locally, determines the correct value of the transverse drift increase and this experiment detects the motion through the space without any signal from the outside. This is possible because there is a preferred reference frame.

Lamb Shift

This author presents a hypothesis: the Lamb shift of hydrogen electron, related to the fine-structure constant, is an effect influenced by the transverse drift of the electron caused by the Earth speed flying through the space. It follows that a free hydrogen atom ‘falling’ to the closest gravity source in free space gains speed in the preferred inertial reference frame and this leads to the transverse drift increase up-to the point the electron separates from the proton. The cause of this effect is explained by Einstein himself in the original 1905 paper[4] showing how electric forces transform to magnetic forces when the hydrogen atom gains speed in the preferred frame. Magnetic field plus electron lead to the Hall effect transverse drift. This is the most simple and the most probable explanation of hydrogen plasma in the interstellar/intergalactic space.

General Relativity energy crisis

A photon emitted at the top of a rocket standing on the Earth surface towards the bottom of the rocket gains energy.[5] The same happens when the photon, as an energy change/quanta, is ‘trapped’ or ‘stored’ as energy between electron and proton in a hydrogen atom.[5] A hydrogen atom falling from the space towards the Earth transforms its potential energy to kinetic energy in the Earth Center Inertial (ECI) reference frame. The hydrogen electron will keep climbing the energy levels because the ‘trapped’ photon in the hydrogen atom is increasing energy, stretching the imaginary ‘elastic string’ between proton and electron. The electron separation from the proton is inevitable.

Minkowski Metric

The generally accepted conclusion “… the initial Minkowski metric g loses any physical signification, for the benefit of the metric g*=g+h.[6] is a confirmation the vector field governing the electromagnetism is misunderstood in the relativity. The hydrogen atom in the rocket standing on the Earth has a ‘constant’ energy in the preferred frame. The hydrogen atom in the rocket in the uniform acceleration keeps gaining energy in the preferred frame. The Equivalence principle does not hold to be true.

Introduction

The Equivalence principle definition can be ‘inverted’: “In a sufficiently small laboratory, there is no experiment done entirely inside the laboratory which can tell whether the laboratory is in free fall in a gravitational field or in uniform motion in empty space.”[7]

Hall Effect transverse drift

Our understanding of physics proven by many experiments teaches us how charged particles drift in a magnetic field, specifically transverse drift of electrons in the Hall effect as shown in Figure 1. The electrons rotate in the magnetic field and drift orthogonally to the applied electric field.[2] The rotational and linear motions of particles are directly linked to the transverse drift. The conservation of the electron angular momentum is one of the factors causing the Hall effect.

Relativistic Hall Effect

Relativistic Hall Effect
Figure 1: Hall effect transverse drift of electrons in the magnetic field.[8] Left: The magnet is away from the conducting plate. Right: The magnet is near the conducting plate.

Figure 2 displays a relativistic flywheel mechanical model and the deformation that is observed outside of the rest frame. The relativistic Angular Momentum (AM) consists of the angular moment vector and the mass-energy dipole moment.[11] The current understanding of physics teaches us that the energy is frame dependent and therefore the result is ‘expected’. Nevertheless a question arises, how do different inertial observers predict collisions of particles with different centroid positions? Do all inertial observers with different relative velocities agree on physics?

Relativistic Hall Effect
Figure 2: Left: A relativistic flywheel of radius R rotating with angular velocity \omega, \omega R/c=0.7 in the rest frame. Right: Deformations of the wheel shape in the frame moving with velocity vx=0.7c. The dots indicate the positions of the geometric and the energy centroids, R’C and R’E.[12]

Relativistic Hall Effect
Figure 3: Left: A relativistic flywheel of radius R rotating with angular velocity \omega, \omega R/c=0.7 and the deformation in the S” frame moving with velocity vx=0.2c. The dots indicate the positions of the geometric and the energy centroids, R”C and R”E. Right: Deformations of the wheel shape in the S”’ frame moving with velocity vx=0.5c. The dots indicate the positions of the geometric and the energy centroids, R”’C and R”’E.[12]

Energy Crisis in Physics

Our understanding of physics is entering dark times. We have an energy crisis looming.

Richard Feynman’s Chapter 42. Curved Space[5] describes the conservation of energy law. The gravitational force on an object is proportional to its mass M, inertial energy is related to mass by M=E/c2.

An atom has a lowest energy state E0 and higher energy state E1, and will emit light/photon when going from E1 to E0. The atom in state E1 is carried from the floor to height H. Work is done lifting m1=E1/c2 against the gravitational force. The work done is

\frac{E_1}{c^2}gH
(1)


The atom emits a photon back to the floor and the same type of atom in state E0 absorbs the photon. The net amount of work is

\Delta U=\frac{E_1-E_0}{c^2}gH
(2)


What is the energy of the photon Eph absorbed at the floor?

E_{ph}+E_0=E_1+\Delta U
(3)


or

E_{ph}=(E_1-E_0)(1+\frac{gH}{c^2})
(4)


Imagine Earth in the far away intergalactic space. We send Voyager flying away from the Earth. The Voyager’s rocket passes the escape velocity, Voyager separates from the rocket and Voyager is cruising on its own, flying away, no force is acting on Voyager any more. Voyager carries two atoms in E1 state. On day one, one atom emits Eph1 photon at H1 back to Earth. On day two, the second atom emits Eph2 photon at H2. H2 > H1 therefore \Delta U_2>\Delta U_1 based on Equation 2. How did we get more work/energy out of nothing, meaning no force acting on Voyager?

The closer look at the Equation 2 tells us the full story. If Voyager acceleration continues up to 1000km then this is the \Delta U value. There is no more acceleration after H=1000km therefore \Delta U is constant. If \Delta U is constant and H is increasing because Voyager keeps flying away then to keep the Equation 2 true E1-E0 has to decrease. The decrease of Voyager speed in exchange for increase of Voyager potential energy affects the electron in the atom. The electron potential energy within atom decreases because the atom decreases the speed in the preferred frame and the Hall effect transverse drift decreases.

Another example would be a Space Station on an elliptic orbit around the Earth. There is no work done on the Space Station. Photons emitted from the same type of atom from the Space Station perihelion and aphelion will have the same energy when absorbed on the Earth. Different perihelion and aphelion heights H, different Space Station speeds at the emission, nevertheless the same absorbed energy on the Earth.

The Equivalence Principle

The Equivalence Principle states the E1-E0 emission at the Space Station perihelion gives locally the same energy as the local emission at the Space Station aphelion. If this is not the case then we have a local experiment capable to detect the height and the speed without any signal from the outside. If the Equivalence Principle is true then the same type of photons emitted towards the Earth and absorbed on the Earth would have different energy hence creating energy out of nothing, the energy crisis. The Equivalence Principle is proven to be false!

The Equivalence Principle compares isolated systems to open systems and claims they are not distinguishable. A rocket with its fuel standing on the Earth surface is an isolated system if we ignore any heat transfer. The same rocket accelerating in space is burning fuel, the inertial mass is decreasing, an open system. Considering the rocket standing on the Earth surface and one ton cargo hanging from the top of the rocket. The rocket walls have accelerometers mounted on them measuring the acceleration showing the gravitational acceleration, nothing else. The one ton cargo is dropped to the floor and the accelerometers are ‘not going to measure’ any change.

The accelerated rocket in space is burning fuel for the acceleration. The accelerometers provide a feedback loop to control the throttle in order to maintain constant 1g acceleration. The rocket engines thrust has to keep decreasing because the rocket fuel burning decreases the total inertial mass. When one ton cargo is dropped in the space accelerated rocket then the sudden change of the rocket losing one ton of mass will disturb the acceleration control systems and the accelerometers will measure the delta. This is a simple experiment to determine the difference between the systems without any signal from the outside. There are many variations of experiments with rotating flywheel that will detect the difference between the rocket standing on the Earth and the rocket accelerating in space.

Conclusion

The Equivalence Principle violates the conservation of energy law.

References

[1] Éric Gourgoulhon, Special Relativity in General Frames, From Particles to Astrophysics, page 723, ISBN 978-3-642-37275-9, 2013.

[2] Konstantin Y. Bliokh, Franco Nori, Relativistic Hall Effect from arxiv.org

[3] Éric Gourgoulhon, Special Relativity in General Frames, From Particles to Astrophysics, page 329, ISBN 978-3-642-37275-9, 2013.

[4] ON THE ELECTRODYNAMICS OF MOVING BODIES by Albert Einstein, page 13 from ffn.ub.es

[5] Feynman-Leighton-Sands, THE Feynman LECTURES ON PHYSICS, The NEW MILLENNIUM Edition, VOLUME II: MAINLY ELECTROMAGNETISM AND MATTER, page 42-10, ISBN 978-0-465-07998-8, 1964, 2006, 2010.

[6] Éric Gourgoulhon, Special Relativity in General Frames, From Particles to Astrophysics, page 722, ISBN 978-3-642-37275-9, 2013.

[7] The Equivalence Principle from vcu.edu

[8] The image is a video screen capture from wikipedia.org

[9] Éric Gourgoulhon, Special Relativity in General Frames, From Particles to Astrophysics, page 320, ISBN 978-3-642-37275-9, 2013.

[10] ON THE ELECTRODYNAMICS OF MOVING BODIES by Albert Einstein, page 8, 9 from ffn.ub.es

[11] Éric Gourgoulhon, Special Relativity in General Frames, From Particles to Astrophysics, page 387, ISBN 978-3-642-37275-9, 2013.

[12] The plotting software code provided by Konstantin Y. Bliokh. Thank you!