Conservation of Momentum
The total momentum of an isolated system is invariant in each inertial reference frame. However, this conservation can not hold under Lorentz transformation from the center-of-mass frame to another inertial reference frame[59,33].
The total momentum is transformed into a function of the relative motion between the original reference frame and the final reference frame. Total momentum is no longer conserved under Lorentz transformation.
The papers[11-18] below verify the violation of conservation of momentum by Lorentz transformation.
The paper [59] vefiies that mass is independent of velocity.
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59. The total momentum of an isolated system is invariant if the system is subject to a conservative force. An isolated system of two identical objects subject to the gravitational force presents a rigorous proof that the mass of the object is independent of the direction of its motion.
In an inertial reference frame moving in the transverse direction to the direction of gravitational force, the law of conservation of momentum requires the mass of an object to be independent of its speed.
53. The charged particle beam in accelerator such as LHC at CERN is subject to Lorentz force until beam collision or extraction. The magnetic force in the transverse direction keeps the beam in a curved path. The gravitational force in the downward direction puts the particle of the beam into projectile motion.
Conservation of momentum is expected in the longitudinal direction for all forces are in the transverse direction. However, a rigorous examination proves the discrepancy. The representation of energy and momentum can not uphold the law of conservation of momentum.
33. An isolated physical system of elastic collision between two identical objects is chosen to verify the conservation of momentum in two inertial reference frames. In the first reference frame, the center of mass (COM) is stationary. In the second reference frame, the center of mass moves at a constant velocity. By applying Lorentz transformation to the velocities of both objects, total momentum before and during the collision in the second reference frame can be compared. The comparison shows that conservation of momentum fails to hold when both objects move together at the same velocity.
18. A stellar system of two identical stars in orbital motion is chosen to manifest a physics law, conservation of momentum, in Special Relativity. Both stars move around each other in a non-circular orbit. The single gravitational force between two stars demands that total momentum of this stellar system remains constant in any inertial reference frame in which the center of mass moves at a constant velocity. The calculation of total momentum in two different inertial reference frames shows that the momentum expression from Special Relativity violates conservation of momentum.
17. A physical system of a mechanical spring is chosen to manifest a physics law, conservation of momentum, in Special Relativity. Two identical objects are attached to the ends of this mechanical spring. The single force between two identical objects demands that total momentum of this physical system remains constant in any inertial reference frame in which the center of mass moves at a constant velocity. The calculation of total momentum in two different inertial reference frames shows that the momentum expression from Special Relativity violates conservation of momentum.
16. In the history of physics, momentum has been represented by two expressions. One from Issac Newton, the other from Special Relativity. Both expressions are expected to describe a physical system that demands conservation of momentum. By examining the gravitational force between two identical particles in two different inertial reference frames, the momentum expression from Issac Newton is found to obey conservation of momentum while the momentum expression from Special Relativity is found to violate conservation of momentum.
15. In the history of physics, kinetic energy has been represented by two expressions. One from Issac Newton, the other from Special Relativity. Both expressions are expected to describe a physical system that demands conservation of momentum. By examining the expression of momentum in a projectile motion, the kinetic energy from Issac Newton is found to obey conservation of momentum while the kinetic energy from Special Relativity is found to violate conservation of momentum.
14. An isolated physical system of gravitational force between two identical particles is chosen to manifest the physics law, conservation of momentum, in a random inertial reference frame under Lorentz Transformation. In this random reference frame, the center of mass moves at a constant velocity. By applying Lorentz transformation to the velocities of both particles, total momentum in this random inertial reference frame can be calculated and is expected to remain constant as gravitational force accelerate both particles toward each other. The calculation shows that conservation of momentum fails to hold under Lorentz Transformation.
13. An isolated physical system of elastic collision between two identical charged particles is chosen to manifest the physics law, conservation of momentum, in a random inertial reference frame under Lorentz Transformation. In this random reference frame, the center of mass moves at a constant velocity. By applying Lorentz transformation to the velocities of both particles, total momentum during the collision in this random inertial reference frame can be calculated and is expected to remain constant. The calculation shows that conservation of momentum fails to hold under Lorentz Transformation.
12. An isolated physical system of elastic collision between two identical objects is chosen to manifest the physics law, conservation of momentum, in two inertial reference frames. In the first reference frame, the center of mass (COM) is stationary. In the second reference frame, the center of mass moves at a constant velocity. By applying Lorentz transformation to the velocities of both objects, total momentum before and during the collision in the second reference frame can be compared. The comparison shows that conservation of momentum fails to hold when both objects move together at the same velocity.
11. An isolated physical system of inelastic collision between two identical objects is chosen to manifest the physics law, conservation of momentum, in two inertial reference frames. In the first reference frame, the center of mass (COM) is stationary. In the second reference frame, one object is at rest before collision. By applying Lorentz transformation to the velocities of both objects, total momentum before and after the collision in the second reference frame can be compared. The comparison shows that conservation of momentum fails to hold when both objects move together at the same velocity.