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Geryllax Vu

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  2. Geryllax Vu
    -Galilean Invariance, and its violation by waves, is a critical concept to my hypothesis. I plan to exploit this phenomenon as a means to take Einstein’s Relativity beyond the speed of light. If I am successful in coming up with a new definition of absolute motion and simultaneity, time travel may be on the horizon.
    -The idea of invariance involves a graphic (coordinates and axes) relationship between reference frames. These axes and coordinates are used as a mathematical means of representing reality. In any reference frame, waves exhibit their constant velocity nature.
    -However which is more akin to the reality we spend our daily lives in, Einstein’s reality or Galileo’s reality? Both use reference frames and the idea that waves (sound and light) violate invariance; but which is closer to the truth?
    -One day, as I was exploring the Echo formula, 2L = ct , I finally realized that the Earth drags a thin layer of atmosphere on its surface, like a golf ball, along with it as it hurtles through space. This causes the air / medium through which a sound travels to produce an Echo that may reverberate off a distant wall, and then return. While the earth is moving the air / medium is also moving with the same velocity (as well as any solid object affixed to the Earth).
    -This scenario makes the formula 2L = ct always work; this is what I mean by invariance. No matter what reference frame you are in the laws of mechanics will yield the same answer even if the two observers are in different reference frames, witness different velocities and distances, but clock the same times for an object in motion. If I can devise an experiment which disengages the motion of the air from the motion of the object, then a different formula arises for an “Echo”.
    -I pull this new formula for an Echo from the Michelson-Morley experiment and the single arm of the interferometer parallel to the objects motion. It involves the time for a wave traveling in one direction and being reflected back to its original starting point, in essence an echo.
    -The formula for this transmitted wave and reflected wave (sound or light) is the following when the source and receiver (reflective object) are at rest relative to each other, but in motion, as a tandem, relative to the air / medium:
    T = [L / (c-v)] + [L / (c+v)] = L {[1 / (c-v)] + [1 / (c+v)]} = [2Lc] / (c²-v²)
    not t = 2L / c
    -This new application of the M&M formula can be solved algebraically for the velocity, v, the absolute motion of the object.
    http://en.wikipedia....lean_invariance
  3. Geryllax Vu
    -So to continue my thought of disentangling reference frames, I think this is an important step in my hypothesis because it allows a mathematical transformation between the flatbed train car and the air / medium. Either the air molecules are in motion while the flatbed is at rest, or the flatbed is in motion with the air molecules at rest (e.g., on a windless day). But I can choose what type of day and conditions under which I want to conduct the thought experiment, beforehand.
    -In an enclosed train car the observer inside, the air molecules, and the walls are all in the same reference frame. An observer at rest on a nearby station platform is in a different reference frame. What I want to accomplish is a shifting of objects from one reference frame to another, so that I can counterclaim Einstein’s absolute motion postulate. In other words find a way to determine the velocity, v from within the train car’s reference frame.
    -By switching to a flat bed train car I can make this shifting from one reference frame to another. In addition, adding a single clock to the flatbed train I can measure the time that the observer (train in motion, observer and platform at rest) on the platform measures. Thus, sort of mixing reference frames.
    -If the conditions of the flat bed train car experiment are either one of those that I mentioned before, then the formula for total travel time, T, of an echo is:
    :Envy: T = {[L + vt1] / c}+ {[L-vt2] / c} = {L / (c-v)} + {L / (c+v)}
    -As an example, consider a long train consisting of an engine with a whistle, some train cars, and a caboose. It is a windless day. If the whistle is blown at the engine on the moving train, then an observer on the stationary platform up ahead of the train whistle, will hear the sound waves with an altered wavelength and frequency due to the Doppler Effect. The source is in motion while the receiver is at rest.
    -However, an observer in the caboose will not experience this alteration due to Doppler because the caboose is at rest relative to the engine/whistle (the compression and rarefaction of the sound waves occurs out of the view of the observer). The engine and caboose are moving in tandem (except if the train is crashing into something) down the track.
    -By taking just the part of the wave pulse (velocity, c,) going back towards the caboose, on a windless day, with the train car in motion:
    :Envy: t1 = [L - vt1] / c (t1 = t1 , or t2 = t2 ,is a key point)
    -This is the phenomenon I wish to exploit. With a single clock, the observer in the caboose would conjecture that the length/distance that he or she is timing is:
    :Envy: L - vt1, not L
    -This can be solved for the velocity, v (absolute motion of entire train).
    http://en.wikipedia.org/wiki/Frame_of_reference
    http://en.wikipedia.org/wiki/Doppler_effect
  4. Geryllax Vu
    -In the book by Galileo Galilei, Dialogue Concerning the Two Chief World Systems, he outlines a thought experiment that is to take place on a typical wooden ship of his time. This experiment illustrates a principle of projectiles in motion and describes the hidden nature of forces and motion. It introduces his principle of relativity that has come down to us as Einstein’s postulate of absolute motion from his Special Relativity Theory (STR).
    -Quotes from the book:
    "…Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals…"
    "…have the ship proceed with any speed, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still…"
    "…This is why you should be below decks; for if this took place in the open air, which would not follow the course of the ship, more or less noticeable differences would be seen in some of the effects noted…"
    -This is the point that I am trying to drive my shoulder into. Galileo indicates that if his ship experiment is conducted above decks, then the air would have a negligible effect on the outcome. I think my thought experiment is trying to turn this minor observable effect into an experimentally measurable phenomenon.
    -In so doing, I think a new state of motion is defined. It is not absolute motion, it is not relative motion, but is an intermediary state of motion that crosses the line of unobserveable information between reference frames.
    -This involves the formula from the Michelson-Morley experiment seeking to detect the aether. By taking apart the component parts of this formula, and combining them with the results of data from measurements, a new perspective of the formula can be obtained. This defines a new state of physical motion. The speed of sound, c is so much less than the speed of light, c; I don’t think that there will be any undue influence by Relativistic effects.
    http://en.wikipedia....ileo's_ship
  5. Geryllax Vu
    -Suppose a hi-speed train is traveling down a long level section of track at a constant velocity, v. It is a windless day. The engineer at the engine decides to blow the whistle at some particular time. An observer in the caboose, and another observer on the train station platform may feel compelled to ask, what is the speed of the train. Can either or both find the speed of the train based only on the blast (sound) of the train whistle?
    -The observer on the caboose might construct her algebra problem like this; she knows the distance, D, from the whistle to the caboose from the known train specifications. But since she also knows that the train is moving with the constant velocity v, the train must meet the sound pulse from the whistle somewhere within the distance between the caboose and the whistle (the whistle and the caboose are at rest relative to each other, hopefully). So she sets up her algebraic equation as follows:
    :Envy: cst = D - vt
    Where cs, is the speed of sound in air, and both times, t, are equal. Rearranging this equation:
    D = cst + vt
    D = t(cs + v)
    [D /t] = (cs + v)
    [D/t] - cs = v
    -So, she imagines if she sends a very fast signal (such as a light signal - virtually instantaneous) to the whistle, starts a clock by her side when she sends the signal, then measures the time until she hears the whistle blast. She should be able to find the velocity of the train, v, from the above equation.
    -On the other hand, the observer on the platform hears this sound pulse from the whistle at the same time. By starting a clock as he hears the first wave front, and then timing the time difference of the arrival of the second sound wave front, he can find the wavelength of the sound as the train approaches him at that instant:
    :Envy: λf = cst
    But by Doppler, the wavelength in front of the moving sound source also equals:
    :Envy: λf = (cs - v) / ƒ0
    He knows the frequency, ƒ0, of the whistle from the train specifications, so by substitution, he can solve for the velocity of the train, v:
    :Envy: v = cs - [(λf)(ƒ0)]
    -If the two observers measure the same whistle blast simultaneously, then will they find the same value for v, the velocity of the train?
    http://en.wikipedia..../Doppler_effect
  6. Geryllax Vu
    -A common thought experiment by Einstein often used to help explain his concept of sim​ultaneity involves a train car and a nearby station platform. If lightning strikes the fore and aft ends of a moving train car at the same time, then a definition of simultaneity emerges.
    -Having grown up in the American Midwest, thunderstorms are a common occurrence. A story that weathercasters often tell is that when a lightning bolt is observed some distance away, then if the time is counted until the thunder reaches the observer, he or she can tell how far away the lightning strike occurred. So using this principle, I think a new type of simultaneity can be defined.
    -Instead of focusing on the scorch marks left by the lightning strike on the train car, or left on the platform, I will concentrate on the audible thunder clap that occurs at the same time as the lightning strike.
    -At the central location of the train car is a single observer, with a single clock, a single sound receiver, a single light sensor. They are all at rest relative to each other within the single reference frame attached to the moving train car.
    -The light from the lightning reaches the central location (a distance L from either end) effectively instantaneously; and thus by definition simultaneously. The observer starts the clock when the light arrives. The light and sound start at the same time, but the sounds will arrive at the central location some time later, possibly at different times. Then, if it can be determined that the sounds were simultaneous, then this leads to the conclusion that the lightening strikes were simultaneous
    -If she sees that the thunder sound arrives at different times she can assume that either the train car is at rest and the lightning did not strike simultaneously; or the train car is in motion, and the lightning strikes were simultaneous.
    -Now the question becomes more philosophy than physics. She has in her mind that it is a windless day, so the air is not moving (nor the platform). So this leaves the only philosophically viable option available to her is that the train is in motion. She then tries to imagine what mathematical means can she use to determine the value of this velocity. Her friend is waiting on the platform (there is a reference frame at rest attached to it) but she will not consult with him.
    -So she adds together the arrival times from the fore and aft ends, which are L / (c-v) and L / (c+v) in non-relativistic terms for sound (not [L / c] + [L / c], since the speed of sound is much less than the speed of light). This becomes [2Lc] / (c²-v²) which leads to her being able to find the velocity of the train, v.
    -Once having this value she can make the comparison and correction, and make a call to the engineer to verify the magnitude and direction of this velocity. So she has found the velocity of the train, and also whether the lightning strikes were simultaneous, completely from within the reference frame attached to the moving train car.
    http://en.wikipedia....of_simultaneity
  7. Geryllax Vu
    -I am mainly using two algebra word problem concepts as the mathematical framework for my hypothesis: meeting and overtaking. That is, the aft vertical pole is meeting the sound wave - air at rest, the train is moving forward; or the aft vertical pole is overtaking the sound wave - air at rest, the train is moving in reverse.
    -In the reference frame of the moving flatbed train car, the aft pole, the observer and her clock are either overtaking or meeting the fore pole of the train car, depending on whether the train is moving towards or away from the sound emitter. But the aft pole and the observer will never reach the fore pole because they are moving in tandem (except in a train wreck!!!).
    -At the same time, on a windless day, the air molecules (medium) are in another reference frame (along with another observer and the platform), which is at rest relative to the first reference frame. However this other observer, and the station platform, and this other reference frame are not needed for my calculations. The idea that this other observer gets a similar result to the observer within the flatbed reference frame is what leads me to believe that I have found a new state of motion.
    -The arrangement of the experimental apparatus is that, affixed to the aft pole is a light emitter and a sound sensor. There is also a single clock and a single observer seated at this position. Affixed to the fore pole, is a light sensor and a sound emitter whose purpose is to send a sound wave back towards the original starting position back at the aft pole.
    -To set up the algebra word problem, I assign letters to the given knowns and unknowns. The speed of sound is to be represented by c; the speed of the train is to be represented by v; the length of the flatbed is to be represented by L; and the time elapsed while the experiment is conducted is to be represented by t. The next step is to find the equation expressing the relationship amongst the constants and variables.
    -For the equation expressing the meeting aspect of this word problem, I imagine that as the train is moving forward relative to the arrangement of the apparatus, the aft pole will meet the sound wave traveling back toward the pole through the air. This is somewhere within the distance of the starting positions of the aft pole and sound emitter at the instant when the sound is emitted.
    ♦ ct = L - vt
    ♦ ct + vt = L
    ♦ t = L / (c + v)
    -To continue, for the equation expressing the overtaking aspect of this word problem, I imagine that as the train is going in reverse relative to the arrangement of the apparatus, the sound wave will overtake the aft pole somewhere beyond the distance that they are originally apart. Thusly, at the same time the aft pole is moving away from the sound.
    ♦ ct = L + vt
    ♦ ct - vt = L
    ♦ t = L / (c - v)
    -Either of these two equations can be solved for v (unknown), the velocity of the train. All the other values (knowns) can be found from the experiment. Taken together, they are identical to the formula from the Michelson-Morley experiment to detect the aether. So, if they are added, the resulting formula can also be solved for v:
    ♦ T = [L / (c + v)] + [L / (c - v)] = [2Lc] / (c²-v²)
    -Due to the idea that the poles are at rest relative to each other, but moving in tandem relative to the medium, creates the scenario that I can algebraically exploit to create this alternative form of echo. Since sound waves are different from light waves, both by Einstein and by Galileo, I believe I have found a new interpretation of motion.
  8. Geryllax Vu
    -An Echo measured at the Grand Canyon fits the formula t = [2L] / c. But this is only valid in light of the fact that a thin layer of air molecules (atmosphere / medium) is being dragged by the surface of the Earth (like a dimpled golf ball) as it hurtles through interstellar space. If this layer were at rest relative to the Earth, then this would allow a new definition of relativity to emerge based on a new Echo formula:
    ♦ T = [(L - vt1) / c] + [(L + vt2) / c ] = [2Lc] / (c²-v²)
    -This Echo formula is the key element of my hypothesis. It comes from the Michelson-Morley interferometer experiment to detect the Aether. The source of the wave and the reflection from a distant object are at rest relative to each other; but the tandem they form is in motion relative to the medium. This is the underlying idea that I am trying to exploit in this hypothesis.
  9. Geryllax Vu
    -1632, Galileo proposed his thought experiment, called “Galileo’s Ship“:
    “…That is why I said you should be below decks; for if this took place above in the open air, which would not follow the course of the ship, more or less noticeable differences would be seen in some of the noted effects…”
    -This is the point which I wish to drive my shoulder into. Focusing on the air as a medium for the transmission of sound waves, I want to transmutate these noticeable differences into mathematically measurable phenomena.
    -In Galileo’s Ship once again:
    “…have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that, you discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still…”
    -It is this not being able to tell whether the ship is moving, or at rest, which is the critical point. This is the foundation of Galilean invariance, or his principle of relativity. It is reiterated by Newton, and appears in the axioms of Einstein; no experiment can be done to detect absolute motion. The laws of physics are the same from the point of view from a reference frame, or within the reference frame.
    -However, it has already been observed by scientists that sound waves violate this invariance, or relativity. Sound waves seem to cross this wall of separation between two reference frames, one at rest and one in relative motion (at a constant velocity). An observer within the ship cabin, shares the motion of the ship, along with the air molecules. This observer is at rest within the ship’s reference frame. The laws of physics take on their simplest form.
    -An observer on the shore sees the ship observer and air molecules following the translatory motion of the ship as it travels through the water. This shore observer factors this translation into a formula, but realizes that he cannot communicate any of this mathematical information to the ship observer.
    -If the cabin observer moved to the open air of the main deck, I think she would have a different set of experiences than she had had below decks. If a sailor is set to ring a bell at the aft end of the ship, then the sound waves would travel to the fore end of the ship where the ship observer could be positioned. The fore and aft positions are at rest relative to each other; but are moving in tandem relative to the still air. This is a critical point; so she proposes to perform a thought experiment.
    -If she were to send a light signal -- a lantern maybe -- to a sailor at the bell, then this sailor would ring the bell (disregarding reaction times). This light signal would effectively be instantaneous over this short distance, D. If she started her chronometer at this exact same moment, then she would measure the time, t1, for the sound wave to return to her. However, because the ship is in translatory motion, with the air at rest (windless day), then the formula she would use is not t = D / c, as below decks; instead, she would use t1 = (D - vt1) / c in the open still air.
    -This would be identical in form to the shore observer’s mathematics (from the Michelson-Morley experiment to detect the Aether). He would simply factor in the translatory motion of the ship in his calculations. The ship observer can safely assume that, because she knows of the violation of invariance by sound waves, that the time she measures would be associated with the formula that includes the ship’s velocity, v. This unknown can then be solved for.
    -This counterclaims the principles of relativity. A certain kind of motion is revealed; it is somewhere between absolute and relative motion. This intermediary motion spins silken threads between reference frames.
    -It seems counterintuitive that the mere addition of four solid walls and the introduction of very slow sound waves can produce more insight into scientific phenomena than super fast light waves. This may be more Philosophy than Physics; what rides on a narrow gauge rail, is our perception of reality.
    http://en.wikipedia.org/wiki/Galileo's_ship
  10. Geryllax Vu
    A scene is acted out in the theatre of her mind, as kilometer post after kilometer post silently count the length of her journey. It is the principle of relativity that struts and storms across the stage. According to which, all laws of motion take their simplest form within a single inertial reference frame when that reference frame is attached to a body. In any other reference frame considered attached to a moving observer then there is defined a Galilean transformation which defines a mathematical relationship between the object and the observer with one or the other moving, or at rest; while the other is considered moving, or at rest. These two relative reference frames are the foundation of the Newtonian description of motion of physical objects.
    She pictures herself and a compatriot traveling down a long level straight section of turnpike, on a windless day. She imagines that if she paces her friend’s auto, adjudging that she is neither gaining ground, nor losing ground, she can safely assume that both autos are traveling at the same velocity; remaining at a constant distance, L, apart as the pair rolls down the highway. With this conclusion in mind, she can regard that the pair of autos have formed a tandem, which is open to the mathematics that was presented before. Amidst the soybean fields along the turnpike, a football field is parallel and aligned with the roadway. So she notices, that when he is at one goal line, she is at the other goal line, thus establishing L, their distance apart (there are many methods for establishing L)..
    In the reference frame attached to the autos, the vehicles are at rest relative to one another. Another observer is seated on a wooden bench, motionless, at rest, in a roadside rest area. In his reference frame, he sees the tandem traveling down the turnpike at the velocity, v. From his viewing position he factors in the addition of velocities that occurs in the auto reference frame.
    If a projectile were launched (as from a front or rear mounted machine gun a la James Bond, addition of velocities by transfer of momentum, applies to each bullet) from either auto to the other, then the addition of velocities would be hidden and unobservable by either driver. So if she sends her light signal to the forward auto, then he fires a single bullet back towards her auto. The bullets velocity, as she sees it is, v = d / t with addition of velocities masking transfer of momentum.
    From within the reference frame attached to the rest area, however, the observer would include this in his calculations, by the Galilean transformation. From his vantage point, he observes that L, is the distance between the tandem autos; and during the same universal Newtonian time, t, that the pair is traveling at the velocity, v.
    Then her imaginings shifts scenes. For sound, along with no change to their vehicle speeds, the sound pulse acts as a projectile through the still air, but different. It is in the nature of sound waves (and light waves) to violate Galilean invariance; in that the velocity of the source or receiver does not under normal measuring conditions, have an impact on the wave speed.
    Thus in still air, the equation of motion would include, by algebra, the velocity of her vehicle L = ct + vt. (her vehicle has the velocity, v and the speed of sound is, c and each begins its movement at the ends of L). This formula factors in the aspect that the auto moves forward through the still air, while at the same time, the sound pulse continues to travel at the same speed. The auto meets the sound pulse somewhere within the distance, L. The auto travels forward the distance vt, with v as the velocity of her auto; while at the same time the sound pulse travels rearward, the distance ct, with c as the speed of sound through the windless air. This all takes place during the same universal time, t.
    This is identical in form to the Galilean transformation as used by the rest area observer. She has made a quantum leap across reference frames; working completely from within the reference frame attached to her vehicle. The air (medium is motionless) resides in the rest area reference frame; it is disconnected from the autos reference frame. However, it is somehow interacting and mixing within the two reference frames; it is interwoven in a mathematical way that is different from the rules of engagement [but forward by the principle of relativity.
    So, she imagines, if she sends the light signal from her headlights forward to her compatriot’s auto and begins her clock at the same moment, then, disregarding his reaction time, he could fire a single imaginary bullet from his imaginary gun back towards her auto. When the bullet pierces her front radiator she stops her clock. The time she measures for the bullets airtime to arrive at her auto would be the simple Newtonian law of motion, t = L / c.
    However, for a sound pulse this would not be the case. The time would be t = L / (c + v) after algebraic rearrangement. This is different from the simplest form of the Newtonian equation of motion; it can be solved for the velocity, v, the velocity of her automobile. This is not absolute motion, nor strictly a limited relative motion, but is some kind of intermediary motion. Peeling back and revealing a previously unobservable layer of reality. The bullet slows down or speeds up depending on the guns direction of motion, so as to appear to arrive in the same time as if the auto were at rest.
    She has found a means to determine her own velocity not just relative to her friend’s auto, which is in motion relative to the roadway, but at rest relative to her; but also she has found her velocity relative to the observer at rest. If suddenly, by some alien magicks they find themselves on a featureless landscape, plunged into an eerie darkness, but at the same distance apart; in the dark the Newtonian or Galilean principle of relativity method, does not visually work. But, by a sonic phenomena combined with the light method I have described here, she could still find the velocity of her auto.
  11. Geryllax Vu
    http://en.wikipedia.org/wiki/LIGO
    The artifice underlying Einstein’s STR is the mathematical construct that the two reference frames are represented by different equations, or laws of motion; but from within a reference frame an observer cannot distinguish whether he or she is in motion or at rest, based on mathematical observations from within the reference frame. An outside observer can make the distinction.
    For sound waves, my thought experiment shows that these formulas are the same and are not the simplest form of the laws of motion. The unassailable wall between reference frames has been breeched by my pace car experiment. For light waves, it may be just a matter of time for this light wave from beneath its black pall; that a reference frame may regarded as at rest, when in actuality it is in motion. But mathematical laws for bodies at rest were indistinguishable from bodies in motion by the principles of relativity, and the construct of reference frames. Now this dreamstate has been intruded upon by the presentation of my thought experiment.
    For a sound source in motion, my thought experiment shows the breakdown of the artifice of the principles of relativity. The equation of motion laws have been assailed. They no longer take their simplest form in either reference frame; neither the one regarded as at rest, nor the one regarded as in motion. However, or a light source in motion, the artifice stands impregnable. The Null Result of the MM experiment provides a sturdy defense. The motion of the light source is cloaked in invisibility, hiding behind the bending of the space-time continuum; whatever that may be, mathematics or reality, mathematics is not reality. Thus for light, can this wall of separation ever be scaled? I do not know.
    In Livingston, Louisiana and Hanford, Washington, USA the Laser Interferometer Gravitational-Wave Observatory (LIGO) conducts experiments to detect gravitational waves; these waves were predicted by Einstein in his General Theory of Relativity. They have not detected any as yet. So I have come up with an alternative use of the facilities while they are waiting to catch a Gravitational Wave.
    The facility is a multi-kilometer sized Michelson-Morley interferometer intended to measure interference from two light beams reflected by mirrors along two long enclosed arms, or corridors, perpendicular to each other. My thought experiment will require only the single arm parallel to the earth‘s motion in its orbital path around the sun.
    Instead of a light emitter at the intersection of the two arms, there is a sound cannon at this axis or origin point. At the end of this arm is a sound sensor that activates a light emitter. Since the air molecules are pretty much motionless in this enclosed corridor, they will follow the course of the motion of the corridor. This is a consideration that will have an effect on the form of the law of motion of the sound pulse through the still air. The air and corridor are motionless relative to each other in the reference frame attached to the earth.
    Thus the sound cannon and the sound sensor/light emitter configuration form a tandem that are at rest relative to one another but are on the earth as it hurtles through the Cosmos at the velocity, v; a velocity, a motion, as seen by an observer at rest not on the Earth. Essentially the roles of the light and sound have been reversed in this thought experiment. The light receiver and a clock are moving towards the light source, creating a scenario that is similar to the pace car thought experiment.
    The sound source and the light source are moving in tandem relative to Space (Aether?). Since the experiment takes place in a closed corridor, sound will adhere to the principle of relativity as regards the air molecules; but light has only Einstein’s accounting for this scenario of motion, since he accepts that light waves can travel where there is no medium.
    This leads to a very similar scenario that involves sound waves (which violate Galilean invariance), which could be solved with a simple mechanical application. Whereas, light solves the situation by means of the complicated application of the STR (Lorentz transformation, length contraction, and time dilation, etc.) involving the alteration of space.
    As compared with sound, light, in the STR, does not adhere to this violation the same way. With no mathematical or scientific justification, other than that the equations work. All that is solid melts into air, as space and/or the Aether remain unexplained mysteries.
    So if a similar scenario to the sound configuration/pace car is set up for light, the time for light to make its return flight will be according to Einstein t = L / c. It is only my speculation that a precise clock could be made to measure a time minutely different from t = L / c, such as t = L / (v + c). But Einstein says this difference is impossible to access. By some transmutation of space, or the Aether, due to the velocity of the object, it cannot be measured. His definition of Space and Reality does not allow it. because his definition of reality imagines it is not there.
    A precise enough clock already exists that could measure this time difference over this long distance, between the earth in motion (velocity) to that of the earth at rest. Maybe this thought experiment would be successful. But the null result of the MM experiment to detect the Aether wind, and STR time dilation and length contraction denies the possibility of detecting this time difference. The time will follow the usual law of Newton and thus be different in two reference frames moving with a constant velocity relative to each. The Lorentz transformation and time dilation are to account for this conceptual difference.
    If she starts her precise clock at the moment that she fires the sound cannon then the time for the sound pulse to travel L, is t = L / c (because the air molecules though motionless within the sealed corridor, they are moving at the same velocity of the earth). The time for the returning light pulse , would be however, according to classical mechanics, L / (c + v) which would account for the forward motion of the earth and light receiver (through the Aether wind of MM) meeting the light pulse traveling in the opposite direction, by algebra..
    If the earth were at rest, then the total time for this experiment would be T = [L/c] + [L/c] combining the time for the sound to travel down the corridor, and the time for light to travel back along the corridor. And thus this is the total time put forward by the principle of relativity and STR.
    For a wave (sound or light) violating Galilean invariance this is L / (c + v). If a train of the same length as the LIGO observatory were traveling across the flat featureless landscape, then the sound waves traveling back towards the caboose would travel a shorter distance than L because of the train’s forward motion. On a windless day, this is because the motion of the train is disconnected from the stationary air (medium). But in the long narrow laboratory of LIGO, there is no medium for the light to interact with, that can even remotely unmask or explain the Earth’s motion. So, we are left only with mysteries, shadows, and suspicions.
    According to classic mechanics, and the MM experiment, the total time would be T = [L/c] + [L/(c+v)] This is a small but measurable difference according to the construction of my thought experiment. But according to STR, time dilation and length contraction this difference vanishes. What should arise from the motion of the earth, disappears into space-time. Einstein’s STR attributes and conforms the difference in times due to an alteration in the fabric of space; not an alteration directly linked to, or coming out of the Earth’s velocity.
    Currently there is research being done in the area of Quantum Theories which predicts that at the subatomic level, there is a violation of Lorentz invariance by electromagnetic waves. This may provide fertile ground for the possibility of conducting some form of this thought experiment.
  12. Geryllax Vu

    Jupiter's Delays

    By Geryllax Vu,

    The mathematical value of the speed of light, c was first discovered as being very large, but finite, by Danish astronomer Olaf Roemer in 1676. During his astronomical observations of Jupiter and the eclipses of its many moons, he calculated the speed of light to a very close approximation. The light covered across the vast distance to the Earth, L, as the moon ventured in and out of Jupiter‘s shadow, at various points of the yearly seasons as both planets orbited the Sun. He was able to compare the times, t, from several observations of Jupiter’s eclipses to arrive at c.
    In 1879, Scottish physicist James Clerk Maxwell proposed, in a letter to American astronomer David Peck Todd, to extend Roemer’s experiments to find the speed, v, of the Earth-Jupiter tandem as the Solar System celestially circumnavigated through the Aether of deep space. At certain times of its yearly orbit, the Earth is in a very advantageous position to observe the moons, such as Io, of Jupiter pass through its shadow, created by the Sun. When Io emerges from this shadow, or eclipse, this event is observable on the Earth.

    If the E-J tandem were at rest in space/Aether, then the light would experience a delay of t = L / c over and above the time for Io to make a single orbit of Jupiter, from shadow to shadow. This is the difference as determined by comparing the orbit times between two or more eclipses. At various points of the year this delay, L / c, is longer or shorter, because, as speculated by Roemer, the distance, L, between Earth and Jupiter is changing. By some mathematical acrobatics, Roemer was able to isolate c, and solve for its value.
    So Maxwell speculated that there was an unaccounted component due to the Solar System’s (with the Earth and Jupiter in it) velocity through interstellar space. To find this velocity, v, became his goal. By making his astronomical observations when Jupiter takes their least amount of time (shortest, L, or L - vt2) between eclipses of Io, and then waiting until the eclipses take their greatest time (longest, L, or L + vt1) for an orbit, then Maxwell concluded that he could introduce the velocity, v of the Solar System.

    These two formed a tandem in which their distance apart, L, was aligned with the hypothetical motion of the SS through space. From this, Maxwell thought that based on astronomical observations at these opposite extremes, the delays would be different. The light is traveling alternately, with and against the motion of the SS. Then he supposed that he could introduce L / (c + v) and L / (c - v); then add these values (I have chosen to add rather than subtract, [2Lc] / [c² - v²], from Michelson-Morley) to solve for the velocity of the SS (and E-J tandem), v.
    According to Einstein’s STR the delay due to the motion of the planets vanishes in the warping of space-time formulas. But astronomical observations have not made a statement confirming or denying the existence of this small delay which could be due to the velocity of the Solar System.
    http://en.wikipedia.org/wiki/Ole_R%C3%B8mer
    http://ether.wikiext.org/wiki/Maxwell_1879_en
  13. Geryllax Vu
    If the train were to come to a complete stop, then begin to move in reverse for a few kilometers, at a new constant velocity, v, with the caboose leading and the engine following; then this would create a new situation and require a new formula. This new formula could be considered to represent the sound wave overtaking (or catching up to) the caboose; it is a windless day, the air molecules (medium) are at rest. This leads to the following formulas related to meeting and overtaking of the sound wave and the caboose:
    Stare into this image to make the train reverse its motion!!!
    ♦ time = distance / velocity
    ♦ [L - vt2] / c = t2 (meeting)
    ♦ or
    ♦ [L + vt1] / c = t1 (overtaking)
    With meeting or overtaking, the path length or distance, L, will increase or decrease due to the motion or velocity of the object in a certain direction and with a certain magnitude. In the forms as listed above, the motion of the train is going along with or is contrary to the motion of the sound wave. These formulas resemble the MM experimental equations for the reflection of a wave at hard surface:
    ♦ L / (c + v) = t2 (meeting)
    ♦ or
    ♦ L / (c - v) = t1 (overtaking)
    As I have shown before the observer on the train uses the following formula to find the train velocity: L = ct2 + vt2 (meeting), or, L = ct1 - vt1 (overtaking). However, the observer at relative rest in the rest area will also use the same formulas. This emerges as a result of the idea that the displacement along the x-axis in a reference frame (whether the reference frame is regarded as in motion or at rest), may be represented by x2 - x1 = L.
    In a reference frame moving with constant velocity relative to the resting frame, by the Galilean transformation this displacement is represented by (x2 + vt) - (x1 + vt) = x2- x1 = L. Thus the formula L = ct2 + vt2 , or L = ct1 - vt1 applies to the motion of the train from the viewpoint of each reference frame. Each reference frame measures the identical time on a clock, and each observer (one at rest, and one in motion) has a means to find the velocity of the train, v, by the same formula (L = ct ± vt), which is not the simplest form of the law or equation of motion (v = [d /t]).
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