A singularity in the integration invalidated Albert Einstein's paper, "Erklärung Perihelbewegung des Merkur aus". Einstein made an unnecessary approximation on the geodesic equation to calculate the angle of precession for the orbit of Mercury.

Unknown to Einstein, there is singularity in the integration which produces an infinite number for the angular difference between the aphelion and the perihelion.

There is singularity in the geodesic at the aphelion and the perihelion. The angular difference between the perihelion and the aphelion is infinity.

Karl Schwarzschild's metric, derived from Albert Einstein's theory of gravitation, is not compatible with the orbit of any planet in the solar system. The space-time geometry is not a representation of gravitation.

The polarization in the Triboelectric effect is the evidence that electric dipole can be induced in the polar molecular structure. The electric dipole can also be induced in the presence of high voltage. Examples include liquid wax, distilled water. The force between the electric dipole and the source of high potential is greater than the gravity.

The orbit of Mercury according to NASA's data is different from any geodesic in Schwarzschild manifold.  There are two geodesic constants for Schwarzschild's metric. Both constants can be calculated from NASA's data for Mercury. The calculation shows that there are two singularities in the geodesic at both the aphelion and the perihelion.

Schwarzschild's metric, derived from Albert Einstein's theory of gravitation, is not compatible with the orbit of Mercury. The space-time geometry is not a representation of gravitation.

The triboelectric generator produces voltage with mechanical movement of an insulator between two conductors. The generator is an open circuit as these two conductors are not connected. 

A light bulb can produce light if connected to the triboelectric generator. Therefore, the light bulb works in an open circuit.

The polar material is attracted by the electrostatic force due to the formation of electric dipole within the material. Water stream is attracted to both PVC pipe and balloon because water molecule is polar. Liquid mercury is attracted to the PVC pipe because mercury atom becomes polar.

The electrostatic force is also detected by the electroscope. Therefore, the electric dipole is formed within both the electroscope and the liquid mercury.

The electrostatic effect on the electroscope by the PVC pipe can be achieved by applying voltage to the electroscope with an external power supply. Therefore, voltage is the measurement of electric dipole.

The electroscope can be in parallel connection with a capacitor to measure the voltage of the capacitor. Therefore, the electric dipole is the measurement of voltage.

There is no charge accumulation in the conductive layers of the capacitor.

The experimental evidence is provided by two dissectible capacitors of different shape. Each capacitor is disassembled after being charged. The conductive layers are put in contact with each other and other objects to show that there is no charge in the conductive layers. Each capacitor is re-assembled back to its original shape and discharges as usual. 

The electricity is contained in the dielectric layer of the capacitor.

In the presence of a fluctuating magnetic field, voltage can be generated from an open-ended loop of conducting wire. The loop can be connected to a light bulb to form a closed circuit. If the electric current exists in the circuit,the resistance of the loop has to be identical to the resistance of the bulb. This is not always true.

Therefore, Ohm's law is not applicable to any electric power source such as AC transformer and DC battery.

There is no electric current in the open circuit driven by either direct current or alternating current source. Examples of experimental evidence include Tesla coil, AED and household wiring system.

A monopole antenna is an open circuit. Therefore, the radiation from the antenna is created by the oscillation of the voltage, not by the electric current.

Ohm's law states that the electric current from a DC battery will approach infinity if the battery is connected to a resistor whose resistance approaches zero. This is physically impossible as the electric current can not exceed the maximum current from an electrical source. Ohm's law is incorrect and requires correction.

A multilayer capacitor is constructed with N dielectric layers and N+1 conductive layers. An external DC source is connected to the two outermost conductive layers. Upon measurement, voltage is detected on all inner conductive layers. The voltage difference between any pair of conductive layers is measured with a digital multimeter.

The detection of voltage on inner conductive layers proves that voltage is not the result of charge accumulation but is the polarization of the dielectric layer due to the electric force between the conductive layers.

The exact nature of the electric current is clarified with Faraday's law.

A rectangular loop of conductive wire with one side pushed across magnetic field at constant velocity will produce constant EMF according to Faraday's law, and constant electric current according to Ohm's law.

If the electric current was made of electrons, each electron will be under constant acceleration. The velocity of the electron would not be constant. Consequently, the electric current would not be constant and contradict the constant current produced by the constant motion.

Therefore, the electric current is not a stream of electrons moving backward.

Two identical ions are put into a linear motion under the repulsive electric force between them.

To an observer whose inertial motion is perpendicular to the linear motion of ions, there appears to be magnetic field generated by the ions. However, the magnetic force does not exist because the force is conserved in all inertial reference frames. 

In the synchrotron, the particle beam spreads out due to the repulsive electric force within the beam. There is no magnetic force between the particles to keep the particle beam together. 

The experimental data shows that the magnetic field can not be generated by the moving charge.

Two identical systems of simple harmonic oscillation are placed in the same reference frame. The objects in both systems oscillate with the same velocity at all time. The relative distance between two objects remains constant.

The relative velocity between both objects remains zero. In the rest frame of both objects, the relative distance between two objects is always constant. Therefore,

The displacement in space and the simultaneity between two objects are conserved in any reference frame.

Newton's law and the theory of relativity are applied to the elastic collision between two objects of random mass. The conservation law of energy and momentum is the basic requirement for the collision. 

The calculation of velocity confirms that Newton's law is compatible with the elastic collision but the theory of relativity is not.

An isolated system of simple harmonic oscillation (SHO) is placed in the y-direction and observed in the x-direction in another inertial reference frame. Two competing theories are used to calculate the total energy of SHO.

The calculation proves that the theory of relativity violates conservation of energy while Newton's law is compatible with the conservation law of energy.

The unique property of the side-coupled cavity at Fermilab requires the synchronous particle to travel from one cell to next cell in exactly one cycle of RF oscillation. With velocity in each cell precisely determined, the acceleration can be calculated.

The representation of force can be derived from the conservation law of momentum.

The calculation of both acceleration and force confirms that the electric force in the side-coupled cavity is inversely proportional to both speed and gamma of the particle. The electric force diminishes when the speed of particle reaches the speed of light.

The expression of momentum is derived based on the conservation law of momentum for the particle beam in the particle collider.

With the correct expression of momentum, the expression of energy is derived for the kinetic energy gained from the RF cavity in the synchrotron.

The expression of magnetic force is derived based on the experimental data of the dipole magnet in Alternating Gradient Synchrotron at Brookhaven National Laboratory.

The unique property of the Alvarez Linac requires the synchronous particle to travel from one drift tube to next drift tube in exactly one cycle of RF oscillation. With velocity known, the acceleration can be calculated. With energy known, the force can be calculated.

The calculation of both force and acceleration confirms that Newton's second law may be applicable to the particle  in the Alvarez Linac while the theory of relativity can not be applied to the particle.

Consequently, E is not (gamma)m c^2.

The expression of the momentum is derived from the measured magnet field of dipole magnet of 3 synchrotrons (Booster, AGS, RHIC) at Brookhaven National Laboratory. The expression of energy is then derived from the momentum expression with the integration of the force from RF cavity. The result confirms that $E\neq\gamma m c^2$.

The unique property of the Alvarez Linac is that the synchronous particle will travel from one drift tube to next drift tube in exactly one cycle of RF oscillation.

The calculation of acceleration confirms that Newton's second law may be applicable to the particle  in the Alvarez Linac while the theory of relativity can not be applied to the particle. Consequently, $E\neq\gamma m c^2$.

The energy tensors of the metrics from four vacuum solutions of general relativity are calculated for each metric. The calculation shows that most of the energy tensors and the contra tensors are not zero for vacuum. 

The four metrics are Schwarzschild metric, Reissner–Nordström metric, Kerr metric and Newman metric

  The  contracted Bianchi identities in the Riemannian geometry are not equivalent to the covariant derivatives of energy tensor in Albert Einstein's theory of general relativity.

  Both Kerr metric and Schwarzschild metric show that the energy tensor for vacuum is not always zero.

  The metric contradicts the theory of general relativity by proving that energy momentum tensor is not covariant.

   Space-time geometry started with Henri Poincare's Lorentz transformation. It was adapted by Hermann Minkowski and adopted by Albert Einstein for gravitation. Marcel Grossmann incorporated Ricci tensor into the space-time geometry. David Hilbert used Ricci scalar as Lagrangian to show that the time coordinate is not suitable for the elapsed time. Hermann Weyl also avoided time coordinate for the elapsed time. 

  Eric Su proved that Newton's gravity can be represented by Schwarschild's metric only if the proper time is used for the elapsed time.

  In Kerr's manifold, the null geodesic is not deflected by the gravity. The black hole in Kerr's manifold is not equivalent to the black hole in the universe. The manifold fails to represent the gravitation and the universe. Time is not in the space-time geometry.

  Hermann Weyl derived a metric for a static mass in an isotropic manifold. His metric is not equivalent to Karl Schwarzschild's metric which is the only valid solution to Albert Einstein's field equation for Hermann Minkowski's space-time geometry.

  The main error in Weyl's metric is his equation of motion with three positive roots while there are only two positive roots in Schwarzschild's metric. 

 Another related error is that the perihelion and aphelion can not co-exist in Schwarzschild's metric but there is geodesic for both in Weyl's metric.

In Kerr manifold, all null geodesics except the radial geodesic are confined within a sphere with radius proportional to the mass at the origin. There is no gravitational deflection on light from a remote source. 

The radial geodesic extends from the infinity toward the origin with a constant radial velocity. There is no gravity effect on the radial velocity  of the radial geodesic. There is no event horizon. The radial speed is negative and toward the origin. The null geodesic is circular if it forms a closed path.

The black hole in Kerr manifold is very different from the black hole in the universe.

In Schwarzschild manifold, the radial geodesic extends between the origin and the infinity in a straight path.

Light can travel toward and away from the origin. There is no event horizon. The speed of light increases with the mass at the origin. The null geodesic is circular if the geodesic is a closed path. The origin is excluded from all open geodesics. The open geodesic takes the shape of either a parabola or a spiral. Light from the remote star can not fall into the origin.

The singularity at the origin is mathematics, not physics. There is no black hole in Schwarzschild manifold.

The geodesic in Schwarzschild manifold is different from the orbit of Mercury according to the data from NASA. Schwarzschild metric, based on Albert Einstein's theory of gravitation, is not fully compatible with Newton's gravity.

Consequently, the space-time geometry from Minkowski is not a good representation of gravitation.

Another error in Albert Einstein's paper for Mercury. Einstein included an extra term in an equation to calculate the angle of precession. Unknown to Einstein, the equation contradicts Schwarzschild's equations.

The geodesic of Kerr manifold is not compatible with the data of Mercury from NASA.

For light to be represented by the null geodesic in Kerr manifold, there is no star light passing by the surface of the Sun.

The Schwarzschild metric, based on Albert Einstein's theory of gravitation, is not compatible with Newton's gravity nor the data from NASA.

For null geodesic in Schwarzchild manifold, the angle of deflection from the Sun to the earth is approximately 1.0797 arc second.

The english translation of Albert Einsein's 1911 paper: 

"Uber Den Einflub der Schwerkraft auf die Ausbreitung des Lichtes"

The commonality among the geodesics from (Minkowski, Schwarzschild, Su, Kerr) shows that the metrics are more suitable for the spiral galaxy than the solar system.

An error in Albert Einstein's paper rendered his confirmation of the motion of perihelion for Mercury invalid.

Time is excluded from David Hilbert's metric for Karl Schwarzschild's manifold.

The isotropic symmetry corresponds to the conservation of the length in all reference frames.

Elapsed time is conserved in all reference frames. A property of parity symmetry.

Lagrangian can be validated with Hamiltonian. Unproven lagrangain can be formulated into a valid lagrangian.

Light accelerates and decelerates along Schwarzschild geodesic.

The conservation of standing wave corresponds to the conservation of wavelength and elapsed time.

The mass of an object is independent of its motion.

The inertial force from the non-inertial motion can not be identified with any fundamental force such as electric force and gravity.

The covariance property  of the standing wave verifies that the speed of the microwave depends on the choice of reference frame.

The wavelength of light can be altered only if the rest frame of the wave source becomes different from the rest frame of the transmission medium. There is no transmission medium for light and electromagnetic radiation.

In 1887, Voigt was the first person to propose that light travels at constant speed to all observers. In 1905, Einstein copied Voigt's idea into his theory of relativity. 

Albert Einstein is such a copycat.

    Experimental evidences together with theoretical proofs are presented in a single paper. The evidences confirm that the speed of light and electromagnetic radiation can be accelerated by a moving reflector. 

    For the first time since 1902, both evidences and proofs are available to remove any doubt that the assumption from the theory of relativity is invalid in physics. 

    The experimental evidences include radar speed gun, FG5 gravimeter, and spectral shift in astronomy. The theoretical proofs include double-slit interference, conservation of elapsed time, microwave resonance, and Fizeau's cogwheel experiment.

Representation of energy from relativity violates conservation of momentum.

Electromagnetic duality is a property of Biot-Savart law.

    Multiple corrections are made to Maxwell's equations.

Stokes' theorem can not be applied to the magnetic field vector generated by a constant electric current because the magnetic field is not a differentiable vector.

The definition of acceleration should remain intact. The speed of reflected light should increase to match the observed fringe pattern from the gravimeter.

Gauss's flux theorem  is not applicable to the divergence of the electric field.

The ratio of momentum to mass includes a function in addition to velocity. This function is independent of the speed.

Mass is conserved in all inertial reference frames. The mass of a moving object is independent of its velocity.

Fabry-Perot interferometer in two inertial reference frames proves that the wavelength is conserved in both frames.  However, frequency is not conserved due to the Doppler effect.

Same wavelength but different frequency. The speed of light is different in a different reference frame.

The standing wave in the microwave resonator shows that the wavelength is conserved. Two observers moving at identical speed but in the opposite direction will observe two different speed from the same microwave.

Fizeau interferometer in two inertial reference frames proves that the wavelength is conserved in both frames.  However, frequency is not conserved due to the Doppler effect.

Same wavelength but different frequency. The speed of light is different in a different reference frame.

Sagnac effect on inertial motion provides experimental evidence that the speed of light is different in a different direction.

The observed phase difference corresponds to the difference in elapsed time. With the different elapsed time but the same displacement, two light beams travel at different speeds.

    There is a popular belief in modern astronomy that the wavelength can be changed by the choice of reference frame. This erroneous belief results in the problematic prediction of the radial speed of galaxy.

    Wide Field Camera 3 in Hubble Space Telescope provides an excellent example on how the speed of light can change the spectrum.

    In 2009, NASA has confirmed that the speed of laser depends on the relative motion between the moon and the earth. 

    The speed of light is proved to vary with reference frame. Lorentz transformation is proved to be invalid in physics.

Both blueshift and redshift are equivalent to the shifting frequency of the Doppler effect. The wavelength is conserved in all inertial reference frames.

Dark galaxies have radial velocity greater than the speed of light. In the rest frame of a dark galaxy, the earth moves faster than light. No light can reach the earth.

Both blueshift and redshift are caused by the motion of the diffraction grating in the rest frame of the star. The wavelength can not be altered by such motion.

The double-slit interference shows that the wavelength is conserved in all inertial reference frames.

The isotropy of light is not conserved in all inertial reference frames. The speed of light from a moving light source depends on the direction of light.

The standing wave in a microwave cavity demonstrates that the speed of microwave depends on the rest frame of the observer.

The speed of light in the rest frame of the light detector depends on the motion of the light source.

Conservation of wavelength in reference frame is a direct property of parity symmetry.

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.

The wavelength  is conserved in all reference frames.  The frequency varies by reference frame. Doppler effect shows that the speed of wave is different in different reference frame.

An error in Michelson-Morley exepriment gave rise to the speculation of length contraction . Lorentz transformation was proposed to explain this error which is unknown to both Michelson and Morley, 

Conservation of the elapsed time in all reference frames is a property of parity symmetry.

The reflection by a moving mirror will change the speed of light. An approaching mirror accelerates the light upon reflection.

The application of symmetry to physics leads to conservation law and conserved quantity. For inertial reference frames, the reflection symmetry generates not only conservation but also transformation.

Under reflection symmetry, the elapsed time is conserved in all inertial reference frames.  The displacement in space is also conserved in all inertial reference frames. From the conservation of the elapsed time and the displacement, the coordinate transformation between inertial reference frame is derived. Based on the coordinate transformation, both the time transformation and the velocity transformation are also derived.

The derivation shows that all three transformations are dependent exclusively on the relative motion between inertial reference frames.