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The Equivalence Principle, Its Flaws and Their Consequences

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The Equivalence Principle, Its Flaws and Their Consequences Clive Tickner BSC, BA. [email protected] THE EQUIVALENCE PRINCIPLE, ITS FLAWS AND THEIR CONSEQUENCES. Abstract Einstein maintained that gravity, being the ‘force’ that we ex peri ence holding us down on planet E arth, is equivalent to the ‘pseudo force’ provided by acceleration in a non - gravitational field. By examining the impact of the difference between red and blue - shift frequencies transmitted in both travelling and Earthb ound spacecraft I reveal crucial flaws in this conviction. In providing several flawed examples, which claim to verify this established principle, I discuss their errors and examine the consequent theories concerning light, time, mass and space that have a risen under the 'Equivalence' umbrella. In this illustrated essay I also suggest alternative experiments and analytical conclusions in the hope that, in a subject not impervious to criticism, there might be further enlightening debate. Keywords The strong equivalence principle, the weak equivalence principle, gravitational red - shift, cosmological red - shift, blue - shift, Pound - Rebka, Minkowski, Time Dilation, Sagnac Effect, Atmospheric Refraction, Astronomical Refraction, Terrestrial Refraction, Turbulence. Einstein, Einstein's elevator. Presentation Throughout this essay I will be inserting established axioms against which many of my points may be judged . 1 I am taking an axiom as being a well documented and recognized piece of evidence that is fully accepte d by standard physics as an incontrovertible fact . CONTENTS Abstract Keywords Presentation PART 1 THE PRINCIPLE of EQUIVALENCE EXAMPLE showing the initial weakness of the Principle of Equivalence PART 2 EINSEIN / MINKOWSKI's ELEVATOR; 1. 1) http://ww w.dummies.com/how - to/content/einsteins - general - relativity - theory 2) from abyss.uoregon.edu/. 3) www.tat.physic.uni - tuebingden.de; 4) www.muonray.blogspot.com. 5) www.newtonphysics.on.ca. 6) www.pitt.edu also uses a similar example to 'prove' the Equiva lence Principle. 7) http://slideplayer.com/slide/4846233/ 8) uk.pinterest.com/kamcheukwai/images/ 9) www.abyss.uoregon.edu and others PART 3 LIGHT's FREQUENCY RED SHIFT, BLUE SHIFT and the GRAVITATIONAL ATTRACTION of LIGHT GRAVITATIONAL RED - SHIFT COSMOLOGI CAL RED - SHIFT 2 THE POUND - REBKA EXPERIMENT PART 4 THE CONCEPT OF SPACETIME PART 5 EINSTEIN / MINKOWSKI's ELEVATOR; 2 THE REPRESENTATION OF SPACETIME PART 6 THE CONFLICTING ISSUES OF TIME DILATION; 1, the THEORIES 1) GRAVITATIONAL TIME DILATION CONFUSING CO NCLUSIONS SIDEREAL TIME 2) RELATIVISTIC TIME DILATION EINSTEIN's TRAIN and PYTHAGORAS THE PULSE ALTERNATIVE PENROSE'S ANDROMEDA ARMADA LIGHTNING STRIKES a TRAIN DIVERGENT CLOCKS CONFUSING CONCLUSIONS CURVED and FLAT SPACE PART 7 THE CONFLICTING ISSUES OF TIME DILATION; the EXPERIMENTS 1) Gravity Probe A 2) Hafele and Keating 3) The National Physical Laboratory 4) University of Maryland 5) Accelerating Muons CONFUSING CONCLUSIONS atomic clocks. 3 PART 8 THE ALTERNATIVES The Sagnac Effect The principle. GPS an d the Sagnac Effect Atmospheric refraction Astronomical refraction Terrestrial refraction Turbulence PART 9 THE EQUIVALENCE PRINCIPLE, SPACETIME and LIGHT the physics and conflicts PA RT 10 SUMMARY ACKNOWLEDGEMENTS 4 PART 1 THE PRINCIPLE of EQUIVALENCE Einstein maintained that gravity, being the ‘force’ that we experience holding us down on planet earth, is equivalent to the ‘pseudo force’ provided by acceleration in a non - g ravitational field. Originally Einstein posited his Weak Equivalence Principle: that being that Gravitationa l and inertial masses are equal, subsequently elaborating this into the Strong Equivalence Principle: that being; There is no observable distinction between the local effects of gravity and acceleration. Below I discuss the flaws in the simplicity of these statements. For example, the above claims would identify the experience of a space ship ’s crew, whilst accelerating under the rocket’s own propulsi on , and being free from other gravitational forces , as being equivalent to the ‘pull’ of the Earth's gravity. The Equivalence Principle equates gravitational and inertial mass, claiming that there is no difference between a uniform, static, gravitational f ield and the ‘G’ forces associated with an inertial (accelerating) object, and this theory became a fundamental contribution to General Relativity If this is even close to being the case then it would seem necessary, however, to be more accurate and to com pare Earth’s gravity with, specifically an acceleration of 1g only. The directional vector of gravity’s ‘acceleration’ is upwards from the planet’s centre. The space ship ' s vector of acceleration is always against the mass ejected by its engines, but, clea rly we need to equate those forces as being 1g in both cases. When an object falls towards Earth it falls at an accelerating velocity of 9 .8 meters per second, per second, therefore we accept that this is the speed we attribute to a ‘1g’ force. Below, in o rder to explore the correctness of Einstein's claim I attribute this same figure to an accelerating space craft. EXAMPLE showing the initial weakness of the Principle of Equivalence. The g force in a rocket is the thrust per unit mass. To gain 1g horizont ally requires travelling at 9.8m/s ² In other words, an acceleration of 1g is accepted as being a continuing increase in an object’s velocity of approximately 22mph per second. 5 Let us consider a rocket which is 500 feet long, nose to tail. Our rocket is in a geostationary position, at a height of 22,236 miles above the equator, travelling in a circular orbit, in the same direction as the Earth, and is therefore appearing motionless. A single pulse of light is created by a transmitter in the tail, every se cond, to be received by a recorder in the nose. Light travels at 1 nanosecond per foot, so the pulse must take 500 nanoseconds to travel from tail to nose. The rocket then begins an immediate acceleration of 1g, and then continues to increase its speed by approximately 22 mph every second, consequently maintaining the 1g pseudo force. Now, an object in ‘free fall’ inside the rocket would behave as it would on Earth, it would ‘fall’ in the opposite direction to that of the rocket’s travel. But this is not s ufficient to prove the exact correlation between a 1g acceleration and the 1g force on Earth. Considering our rocket, then, after one second, at 1g, it will be travelling at 22.369 mph (32.807 feet per second) This means that the pulse sent at the moment the rocket began immediately to accelerate, now has, in that first second of the rocket’s travel, to traverse an extra 32.807 feet to reach the recorder. At 1 nanosecond per foot of travel, the new distance for the pulse’s journey has to be the initial 500 feet length of rocket, plus the 32.807’ additional distance the recorder has inevitably moved forward, away from the source; this total now being 532.807 feet, and the time taken to cross this new distance, therefore, is 532.807 nanoseconds. The light pul se has no mass, it is unaffected by the acceleration of the craft, and independent from the speed of the craft. Once emitted the pulse is completely autonomous, free of the vehicle and of the medium in which it is travelling. There is no friction that woul d affect its path and the pulse cannot be ‘dragged’ along just because it is travelling in a craft which itself is in forward motion. After 2 seconds the rocket will be accelerating through 44.738 mph (65.615 fps). At this specific moment a second light pu lse is emitted at the tail source. Whilst this pulse is travelling towards the recorder, the craft is still accelerating forward, taking the nose recorder further from the actual point in space where it was when the pulse was transmitted. Again the pulse h as to traverse a longer distance, that being the initial 500 feet plus the 65.615 feet that the craft has travelled during that next second. The time for the second pulse to travel from source to recorder is therefore 565.615 nanoseconds. This follows that ; After 3 seconds the rocket will be travelling at 67.108 mph (98.425 fps) increasing the pulse’s distance to travel from tail to nose to 598.425 feet, timed at 598.425 nanoseconds. 6 After 4 seconds the rocket will be travelling at 87.240 mph (127.952 fps) increasing the pulse’s distance to travel from tail to nose to 627.952 feet, timed at 627.952 nanoseconds. Avoidable information ; After 5 seconds the rocket will be travelling at 109.609 mph (160.759 fps) increasing the pulse’s distance to travel from tail to nose to 660.759 feet, timed at 660.759 nanoseconds. After 6 seconds the rocket will be travelling at 131.97 mph (195.556 fps) increasing the pulse’s distance to travel from tail to nose to 695.556 feet, timed at 695.556 nanoseconds. After 7 seconds the rocket will be travelling at 154.34 mph (226.365 fps) increasing the pulse’s distance to travel from tail to nose to 726.365 feet, timed at 726.365 nanoseconds. After 20 seconds the rocket will be travelling at 438 mph (642.40 fps) increasing the pulse’s distance to travel from tail to nose to 1,142.40 feet, timed at 1,142.40 nanoseconds. After 30 seconds the rocket will be travelling at 657 mph (963.60 fps) increasing the pulse’s distance to travel from tail to nose to 1,463.60 feet, timed at 1,463.60 nan oseconds. After 60 seconds the rocket will be travelling at 1,320 mph (1,936 fps) increasing the pulse’s distance to travel from tail to nose to 2,436 feet, timed at 2,436 nanoseconds.
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