Yamin Choudhury
The Aga Khan School

June 20, 2010

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[Note: The ideas and opinions expressed in this work are those of the author alone.]

The principle of equivalence was formulated by Einstein on the presumption that from inside a closed compartment there is no way to tell whether the compartment is accelerating in space or is stationary in a gravitational field that would produce the same acceleration in the opposite direction on a free falling mass infthe compartment. Or, in terms of forces, that a spring balance having a mass hanging on it would show the same stretch if the compartment was accelerating upwards or if the compartment was stationary on a planet with its gravity pulling it downwards.

Raising the presumption to the status of a postulate, Einstein concluded that light traveling horizontally across the compartment would bend downward under gravity since accelerating the compartment upward in space would cause the light ray to do so. The flaw or error in the principle is right here at the start.

The thought model used by Einstein uses a ray of light entering the compartment from outside in a horizontal direction (perpendicular to the direction of the gravitational force or to the direction of acceleration) through a tiny hole in the wall of the compartment, say for example through the left wall, (this is already equivalent to looking at outside from inside the compartment!) and moves on to hit the right wall at some point on it. Since the compartment is accelerating upwards and the speed of light though large is finite the right wall would move upwards in that time to some extent. The path of light would have been a straight line sloping downwards if the compartment had been moving up at a constant speed. Since it is accelerating upwards the speed keeps on increasing causing light to continually bend or slope down more and more, relative to the inside of the compartment, until it hits the right wall. So the path traced out would be a downward curve. Einstein concluded light would trace out a similar curve under gravity with the compartment stationary in it since he assumed impossibility of detecting the difference between gravity and pure acceleration.

What Einstein failed to see was that the ray would bend downward not only inside the compartment space as it was traveling across it but also at the very point of entry in the left wall. Whatever the direction of a ray entering through the hole in the wall was would keep on entering with greater and greater downward slope and thereafter would bend further down through the space in the compartment before hitting the right wall. The result would be that the light spot on the right wall would not be stationary! The spot formed on the wall would keep on moving downward and with increasing speed. Whereas, under pure gravity with the compartment stationary in it the spot formed on the wall would be stationary. The principle is in principle wrong! We cannot have equivalence under the conditions. That is why a charged particle sitting stationary inside the compartment would be able to sense pure acceleration by radiating and sense pure gravity only by not radiating.

To save the situation we could try setting up the light source inside the compartment fixed on the left wall so as to fire rays horizontally to the right. In this way we also avoid the error of looking outside. Whatever the upward speed of the compartment is the ray will come out horizontally and travel to hit the right wall at a fixed point on it. Does this save the situation? NO! It still does not produce the equivalence of gravity and acceleration. Let us see why.

Consider the paths of a ray of light and of a Newtonian particle, which we can call the test particle, both traveling horizontally at light speed c from left to the right across the compartment to hit the right wall. Since both take the same time to reach the wall they both fall at the same distance down from the horizontal level on the right wall if the compartment is only accelerating upwards. Instead, if the compartment is stationary and sitting on a planet and is subject to pure gravity only then the paths are different. Light has mass due to its energy given by m = E/c2 (where m is the mass, E is its energy and c is the speed of light) which makes E = pc, where p is its momentum by electromagnetic theory. For the test particle of equivalent mass m energy E = ½pc = ½mc2. Now gravity will cause both the masses to be attracted or pulled downward and make their trajectories curve down. Since, to first order, the time of flight across the compartment will be same, the downward change of momentum will be the same for both light ray and test particle. The change in energies for the two will however be different. The change of energy for the test particle dE will be ½cdp while for the light ray the change dE will be cdp, which is twice that for the test particle. The change of energy is provided by gravitational force doing work on either of them by displacing them down along the direction of force. The only way light can gain twice the energy is by displacing twice the vertical distance! Light will bend by twice the amount of a Newtonian particle. Here we have already deduced the famous correct bending of light by gravity without resorting to warping of space or usage of tensors representing curvatures of space and time continuum. We simply recognized electromagnetic theory as giving the correct dynamics of the light ray. Physicists had for lack of insight used Newtonian dynamics for light in computing the bending of light by the Sun and had gotten the wrong measure in spite of Maxwell having laid down the correct formulae many decades before. When Einstein first formulated his general relativistic formula for the bending using warping of space it was not correct. Thanks to Worl War II his formula could not be tested and found wrong and he had time to correct it. What did he correct? I suspect (I do not know) he simply replaced E = ½mc2 by E = mc2 and as for all the tensor formulations they were redundant for his equations become solvable only when space is "flat" which is another way of saying curvatures of space are not there. The curvatures are just a lot of confusion screening the simple truth: E = pc for pure energy. It is simply that transverse and longitudinal inertias of moving bodies are not equal.

Now light is pure kinetic energy only. And we have seen that for its mass, which we used for measure of gravitational force on it, it has half the inertia of the equivalent test particle when forced transversely to its direction of motion. Special Relativity gives the correct effect of this reduced inertia of kinetic energy in a massive particle along directions perpendicular to its motion. In Special Relativity we have both transverse and longitudinal masses. The reduced inertia transverse to the motion of a particle explain both the precession of perihelion of elliptic orbits of planets and the collapsing of orbiting radius of binary neutron stars. Since the transverse inertia of moving particles is reduced an elliptically orbiting planet bends sharper than the Newtonian equivalent when near the Sun as gravitational potential energy of the planet, which belongs to the gravitational field, converts to kinetic energy of the planet as it nears the Sun increasing its relativistic mass but with less than proportionate increase of transverse inertia. This causes the pull of the Sun on it to bend it towards the Sun more than by Newtonian amount (if we may call it so) making it leave the Sun after going around it by tilting its orbit path towards the Sun side.

In the case of binary stars orbiting each other in a circular manner there is no precession but the bending around the common center is more than as calculated by classical mechanics leading to falling in. It is simply reduced transverse inertia causing the sharper bending. The more they bend in faster they move due to loss of potential energy and faster they fall in. There is no total energy change, hence, there is no ‘gravitational wave’ radiation produced, potential energy keeps on changing to kinetic and the transverse inertia keeps on decreasing relative to the increasing relativistic mass and the rate of bending in keeps increasing to end up in collapse. There is no such thing as gravitational waves.

Light cannot orbit around a mass under its gravity it simply collapses into it since it curves sharper than a Newtonian particle and this gives the correct conditions for black holes: using only Newton's gravity and E = pc.

What happens when light moves along the direction of a force that can act on it, in this case along the direction of gravity? The equation is still the same: dE = cdp. If we rewrite it as dp = dE/c we see that for a given change of momentum, whether increasing or decreasing, light has to move twice the distance in the force field compared to an equivalent Newtonian particle undergoing the same change of momentum. For a Newtonian particle dp = 2dE/c. For a massive particle this amounts to having a larger inertia, relativistically, for a given mass than its corresponding Newtonian particle. This means that a massive particle would accelerate or decelerate less than a corresponding Newtonian particle under the force field. This can explain why the galactic recessional deceleration decreases with increasing speeds! More the kinetic energy greater is the mass but more than proportional is inertia greater. Thus further the galaxies are from Earth slower they are decelerating due to gravitational pullback. There is no need to invent the concept of ‘dark energy’ to explain the decrease of deceleration of galaxies with distance from Earth! It is all in the correct use of E = pc.

If we apply the idea to cosmic ‘big bang’ we have that in the beginning there was light for 10-43 seconds in which time light expanded space to Planck’s length and then there was creation of countless particles. Expanding light would not decelerate but would lose energy at rapid rate under the intense gravity of the huge mass of the light. The loss of kinetic energy of light would become field energy. Such high energy in field results in field particles. As light keeps expanding it keeps losing kinetic energy creating field particles but what is happening is that later particles are created after larger distances moved by light due to decreasing of gravity and subject to lesser retardations being further from the gravitational center of origin and, hence, are faster producing the velocity distribution of particles that probably could explain Hubble's law of recession.

In retrospect we see that Einstein's theory of general relativity has masked the equation E = pc in a cobweb of tensor analysis and garbled a whole of a field of physics for ages. I understand that general relativity makes even the so-called string theory almost untenable. The truth is it has masked a simple equation of electromagnetism and done more harm to physics than help it. Quantum theory of gravity, I believe, would be possible if general theory of relativity were totally ignored. The fact that stable bound system cannot be formed under gravitational forces, since they collapse due to inequality of gravitational mass and inertial mass, is probably the root cause of the problem. Gravitational and inertial masses are equal only when the mass is at rest.