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Geryllax Vu

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  1. Geryllax Vu
    I introduce a modification to my thought experiment; it will expand the use of the lantern as a light signal by the caboose observer. This modification will pull the platform observer into the midst of the experiment.
    There is once again a train of length, L, moving at a constant velocity, v, along a level straight section of track on a windless day. Also, there is again an operator in the engine car and an observer in the caboose car. The platform observer will now take on a more significant role.
    The air molecules, because it is a windless day, along with the platform and the Earth, are at rest relative to the moving train. There is a reference frame attached to the train and a reference frame attached to the Earth thus creating two coordinates systems moving relative to one another. Since the outside air / medium is disconnected from the motion of the train, the method outlined in this thought experiment makes it possible to calculate the velocity of the train. If the experiment were conducted within a single enclosed car, then the air molecules would follow the motion of the train and it would be impossible to find the velocity of the train by the method I have presented here.
    The thought experiment begins with the caboose observer flashing her light signal to the engine car; at the same moment she begins her clock. The operator blows the train whistle at the moment he receives the light signal. Over this short distance the light signal is effectively instantaneous. She is prepared to measure the time, t, for the sound wave from the whistle to reach her.
    When the she hears the sound wave travel the length of the train, from the engine to the caboose, she flashes her lantern once more, and stops her clock. Now this is where my modification enters the experiment. The platform observer also has a clock and he is able to see the flashes of light from the lantern. So, at the first flash he begins his clock, and at the second flash he stops his clock, thus also measuring the flight time, t, of the sound wave.
    Now the physics question becomes, will both observers measure the same time, t? Since the two observers are moving at a constant rectilinear velocity relative to one another, by the principle of relativity they should find different velocities as viewed from the other’s reference frame. This applies to a material object flying through space, because they are in reference frames moving relative to each other. However, this does not apply to sound waves because of their violation of invariance, a concept known to science.
    Her goal is, once again, to find the velocity of the train entirely from within the reference frame attached to the train. The principle of relativity says this not possible, but she imagines herself to be a clever science girl. She ponders upon the problem and imagines that a sound wave would be a solution to her problem; but may open a Pandora’s Box, of which she knows not the contents. Nonetheless, she proceeds.
    She sets her equations as I have shown before. For the train moving forward, the caboose meets the rearward traveling sound wave within the distance L = ct - vt, with c representing the known speed of sound; the sound wave and the caboose start at the endpoints of L. If the train were to go in reverse, the sound wave from the whistle at the engine would have to overtake the rearward going caboose, so then, a similar type of formula would be applied: L - vt = ct. Both the sound wave and the caboose start at the endpoints of L, with each moving in the same direction. Each of the above formulas can be solved for the velocity of the train, v.
    If her algebra is correct, what are the implications? She has found the velocity of the train, she thinks, but she is also aware that this seems to contradict the principle of relativity. The two observers have measured the same velocity for the train though each is in a reference frame moving relative to the other. The train length, L, is found from the technical specifications. The speed of sound, c, can be found in any science text. Thus the platform observer and the caboose observer can use the same equation, L = ct - vt. If they measure the same time, t, as implied by the formulas, then they will each find the same velocity, v, for the train. If they measure the same time, t, as implied by the formulas, then they will each find the same velocity, v, for the train.
    The caboose and platform observer could also find the velocity, v, of the train by another means. By noting the landmarks immediately opposite to the flashes, relative to the embankment, and by measuring the distance between the landmarks by some device, then v = d / t could be found. But the landmark method cannot be extended to find a definition for simultaneity, or make use of Doppler to find a deeper interpretation of the motion of a material object through space. Even more, only sound waves are a mechanical means that can be done from within the train’s reference frame to find v in as advantageous a way, as by sound waves.
    A scenario that is similar, but not the same, is by throwing a lump of coal rearward (instead of a sound wave) from the steam engine with a strong arm. Neglecting air resistance and gravity, it should fly in a level and straight line. From this thrown material object or any other similar type of mechanical experiment, she cannot find the velocity of the train, while riding upon the train. But by a sound wave, she can perform an experiment that allows her to find the train’s velocity. She has uncovered another of reality’s many paradoxes.

    If the platform observer threw a lump of coal, with the same arm strength as the train operator, to another person on the platform, then the platform observer would measure the same velocity (v = d / t) as the train observer for the velocity of the of lump of coal between the engine and caboose, though the train is moving and the platform is at rest. The outsider, by addition of velocities, measures a different velocity for the lump of coal, but he cannot communicate the illusion of the caboose observer’s measurement to her. He sees the lump of coal on the train travel a shorter distance and thus a shorter time (by Galilean transformation). But she is trapped in her illusions, with no mathematical way to clear the shadows of her blindness. She has no way to find the velocity of the train.
    Until a sound wave is applied to the problem. That sound waves violate invariance is already well-known to physicists. Exploiting the phenomenon that sound waves do not gain any addition of velocity (vx = v'x - v0) from transfer of momentum, then this thought experiment makes it possible to measure the same velocity, distance, and time, across reference frames moving relative to each other. The seemingly paradoxical statements can both be true with a little cleverness. That the principle of relativity reflects reality and does not reflect reality seems an inescapable trap. The observers in two reference frames moving relative to one another can both measure different velocities for an object and the same velocity for that object, namely the velocity of the train.
    An intermediary motion arises from betwixt the reference frames. It is different from the transfer of momentum imposed upon a material object by its initial cause of motion. Whether the object or reference frame is already in motion, or at rest, the law describing the object’s motion will be the same simple law (v = d / t), as viewed from within the reference frame. A sound wave leaps the hedge between reference frames; its velocity is not altered by the state of motion, or by the state of rest of the source. And by lifting the veil from this intermediary motion, she has found the velocity, v, of the train.
  2. Geryllax Vu
    As a material object makes its flight through the air (molecules / medium), it is a substantially different thing from a sound wave traveling through air. The principle of relativity holds the pair in a tension of physics contrariness. A material object making a straight line flight at constant velocity through space (air / medium), is seen to have two different velocities, when viewed by two different observers, in two different frames. One frame is considered as being at rest, and the other frame is considered as being in motion with constant velocity. Transfer of momentum and addition of velocities mask the velocity of the reference frame considered in motion, and the principle of relativity as a scientific concept prevents the detection of this motion.
    The foundational propositions of Einstein’s Special Theory of Relativity (STR): the Lorentz transformation, time dilation, length contraction, etc., are based on a particular interpretation of the nature of the relationship between two inertial reference frames. Given two reference frames moving relatively to each other, the observer within the moving frame is considered at rest, though the reference frame is moving. An observer in another reference frame that is at rest or stationary, views the motion of the first frame. The observer in the first reference frame can not by any mechanical experiment detect his or her own reference frame’s motion.

    By STR, though the train is in motion, it is regarded as being at rest in the reference frame attached to the train. In the frame attached to the platform, the observer can clearly see the train’s motion. Nonetheless, the observer on the train is assumed to be unable to do any mechanical experiment that can detect his or her motion. The transfer of momentum of material objects cloaks any motions that might disclose any strange forces at work; through the addition of velocities, substantial speeds are kept hidden. The property of waves (sound, EM, etc.), to not accept this transfer of momentum from its source, leads to the violation of Galilean invariance. In other words, the wave speed remains fixed across reference frames, regardless of their relative velocity.
    For example, a ball thrown rearward from the engine of the moving train has the velocity of the train subtracted from the ball’s velocity. This maintains the appearance of the same distance of travel, and the same time for the journey; unbeknownst to the observer within the reference frame of the thrown ball. However, a sound wave directed rearward will not have any velocity subtracted, so that the wave will appear to travel a decreased distance, over a decreased duration of time, as the train moves forward. This would hint at a possibly deeper reality. For a material object, the influences of forces are somewhat hidden; for a sound wave they are not, they are just dodged and evaded.
    In this thought experiment, I have shown that it is possible by the properties of sound waves, to lift this veil; to pull aside the curtain from the aforementioned proposition of the STR postulate. That is, it is possible to pass through the wall between reference frames like a subatomic particle; to measure the same velocity value of a sound wave, by observers in separate reference frames that are moving with a constant velocity relative to one another. It may become possible to overcome the static that jams any two-way communications between reference frames.
  3. 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
  4. Geryllax Vu
    -The first postulate of Einstein in his Special Theory of Relativity (STR) states:
    “There is no experiment that can be performed in an enclosed laboratory that can detect absolute motion.”
    -Certainly the idea of absolute motion is out of reach for modern scientists. There is no way to observe an Aristotle’s grid, or Newton’s fixed stars, or the Michelson-Morley Aether; which are at rest in the Universe, and against which all Celestial motions can be defined.
    -This leaves us only able to work with relative motions; that is, we can only define one object’s spatial motion in terms of another object’s spatial position.
    -There are a few methods by which relative motion can be ascertained. An observer in a car traveling down the interstate can use a stopwatch to find the time it takes to travel between two consecutive mile posts, then solve for the cars velocity relative to the road by: t = D / v.
    -Or, a car traveling down the highway, whose owner is sweating the transmission fluid leak she had found that morning. She noticed that every ten seconds a drop fell into the puddle forming beneath her stationary car. So after traveling a while, she pulls into a rest stop to check the leak; has it increased or decreased, she asks herself. Then she notices it is now not in a puddle, but there is some distance between the drops. She does not think the leak has stopped, but that because of her motion at a certain velocity, this has cased the puddle not to form. She imagines she can determine her car’s velocity relative to the road by measuring the distance between the drops: v = D / t
    -As part of his daily commute, a driver on a city expressway determines that at a constant velocity relative to the road, within a preset amount of time, he can travel a certain number of miles: D = vt.
    -Each of these scenarios obeys invariance, such that the motion will follow the rule that they take on the most simple form of the equations of motion in that reference frame. However, by using sound waves, which violate Galilean invariance, a new method emerges that also determines relative motion. This method comes from the Michelson-Morley experiment to detect the Aether. I have used sound waves in my previous thought experiment.
    -This new method does not take on the simplest form of the equations of motion (velocity, time, or position) in each reference frame. It is identical in both relative reference frames, the one regarded at rest and the other regarded in motion. This method can also be used to address the issues of simultaneity and clock synchronization from Einstein’s STR.
    -In other words, one reference frame takes the simple form of the law, while the other reference frame has a more complicated form; and vice versa, depending on whose reference frame the event is being viewed from. Now in my statement, the formulae are identical in both reference frames: whether both are moving; one is moving and one is at rest; or both are at rest. The following considerations give rise to the transformation equations:
    ♦ Not t = L / c; but t1 = [(L + vt1) / c] = [L / (c - v)] identical from within each reference frame. Neither formula makes any statement about the car's motion relative to the moon. (t1 = t1 key point for later)
  5. Geryllax Vu
    According to relativistic mechanics, two events occur simultaneously if the light from each of these two spatially separated events meet at the midpoint of the line adjoining them, at the same time. Additionally if this simultaneity occurs in a reference frame that is considered to be stationary, then the events will not be generally regarded as simultaneous in a reference frame that is moving with a linear constant velocity v relative to the stationary frame. This may be true for light waves, but it will not be true for sound waves, which rely for their propagation on a medium that passes easily through the porous conceptual walls of every inertial reference frame. The open still air will not be contained within the walls of both reference frames, in that the air molecules will be at rest according to the viewpoint of one reference frame, but at the same time in motion according to the viewpoint of the other reference frame. This disengagement of the air molecules from the motion of any moving material object within a reference frame is the primary underlying proposition of this paper.
     
    A thought experiment oft used to explicate simultaneity involves an archetypical Einstein train of length L travelling down a long level straight stretch of track, on a windless night, at the constant velocity, v. The air/medium is at rest relative to the earth and track. An observer, holding two mechanically identical clocks, is seated on the roof of the train at the midpoint between the engine and the caboose. She is at rest in the train reference frame, but she feels the still air rushing past her face at the apparent velocity of w (v = w). A storm threatens, and a number of lightning bolts have struck the ground around the rapidly moving train. She prepares herself.
     
    The engine and caboose are at the endpoints of the train, and they along with the midway point on the line joining them, have formed a tandem moving through space such that they maintain their distances of separation, whether the train is in motion or at rest. After a few moments, two lightning bolts strike, one bolt at the engine end of the train, and the other bolt at the caboose end of the train. These two events occur simultaneously, so that the light generated by the strikes against the metal, at each end, should arrive at the midpoint observer at the same time, in the train reference frame, as is supposed by the Special Theory of Relativity. However, the sound wave that is generated by the lightning strike against the metal at each end of the train will not arrive at the midpoint observer at the same time due to the motion of the train reference frame through the still air. Or conversely, so as to preserve mechanical symmetry for the train observer, an apparent wind must blow through the stationary train reference frame which causes the two travelling sound waves to arrive at the central location at different times. So, the train observer determines to use these light signal to mark the departure events of the two sound waves within the train reference frame. The light wave reaches her nearly instantaneously at this short distance, so she uses these flashes as the signals to start each of the clocks she holds so that they will now tick synchronously.
     
    Disregarding observer reaction times, the ticking clocks will essentially measure the time intervals tx for each sound wave to reach the central point as the train is in motion. The sound waves travel at the same constant velocity c through the still air towards the middle location, but the moving train will shorten the distance of travel for the sound wave coming from the engine; and lengthen the distance of travel for the sound wave coming from the caboose. Thus, the two time intervals will not be equal, the arrival events of the two sound waves at her ears will occur at different times and positions within the train reference frame. So, taking this into account, and that time equals distance divided by velocity, with the distance value from the endpoints to the midpoint mathematically being 0.5L:
     
    ♦t1 = [0.5L – vt1] / c = 0.5L / (c + v)
    ♦t2 = [0.5L + vt2] / c = 0.5L / (c – v)
     
    Since t1 ≠ t2, adding these two times gives,
     
    ♦T = t1 + t2 = 2[0.5Lc] / (c2 – v2)
     
    If the train were to be regarded as stationary while the earth and atmosphere are moving past it at the velocity w so that the air/medium remains at rest relative to the earth, then to maintain symmetry, an apparent wind must be summoned which will blow through the resting train reference frame. This will cause the velocity of one sound wave to be decreased, and the velocity of the other sound wave to be increased:
     
    ♦T = t3 + t4 = [0.5 L / (c + w)] + [0.5 L / (c – w)] = 2[0.5Lc] / (c2 – w2) where t3 ≠ t4.
     
    To restate this, each sound wave will travel the same distance from an endpoint to the midpoint. However, the apparent wind will have a velocity w equal to the train’s velocity v which will slow down the sound wave coming from one direction and speed up the sound wave coming from the opposite direction, thusly the sound waves will not arrive at the midpoint between their departure points at the same time. Since w = v, the result will be equivalent to considering the train to be in motion through the still air.
     
    Both these sets of equations resemble the total time formula from the Michelson-Morley experiment to detect the aether wind. However, neither equation takes the form of the total time that would be measured if the train, air, and earth were all at rest relative to one another:
     
    ♦T = t5 + t6 = 0.5L / c + 0.5L / c = 2[0.5L] / c where t5 = t6.
     
    Thus, adding these two measured time intervals, and then algebraically solving for v, the observer in the train reference frame should be able to find the train's velocity relative to the earth. This value of v represents the direction and magnitude of the train’s velocity since the train should be moving in the direction of the time interval with the lower value. Additionally, this velocity value should be equal to the value found by the classical method of measuring the duration of time to travel between two landmarks, of a known distance apart. But this new method, with slight alteration, can apply the Doppler Effect to the problem of the relative motion of material objects. The Doppler frequency shift formula gives differing values depending on the whether the source is moving towards the receiver, or the receiver is moving towards the source. This experiment can thusly be used to distinguish whether the earth and air is moving relative to a stationary train, or to preserve mechanical symmetry, the train is moving relative to a stationary earth and atmosphere. By this experiment, the use of sound waves will allow an observer within the train reference frame to find the velocity of the train reference frame, in contradiction to the classical principle of relativity. All the results of this thought experiment are based only on information available from within the train reference frame, without needing to utilize the Galilean or Lorentz transformation equations between reference frames. The sound wave can discern relative motion between two reference frames, while the light wave cannot.
  6. Geryllax Vu
    According to the relativistic definition of simultaneity, if two spatially separated events occur such that the light waves generated by these two events arrive at the midpoint of the line adjoining them, at the same time, then these two events are considered simultaneous. However, if these two events occur in still air, then any sound waves that might also be generated may not arrive at this midpoint, at the same time. The events occur at the endpoints of their adjoining line and form a tandem, of length L, where all the discrete points on the line remain at a fixed distance of separation, whether the tandem is in motion, or at rest. If this tandem (material object) is moving at a constant velocity v along a line parallel to the line adjoining them, through still air, then the sound waves generated by the events at the endpoints will not arrive at the midpoint simultaneously. The speed and direction of the tandem relative to the still air may then be mathematically determined using a modified formula from the Michelson-Morley experiment, in which the value of c is switched from the speed of light, to the speed of sound. With the light flash signaling the departure time of the sound wave, and using clocks to measure the arrival time of the sound wave, then the time interval t along with all the other variable values are available from within the tandem reference frame (the air molecules pass freely through the porous conceptual walls of the reference frame). This methodology of using sound waves to investigate the motion of a material object, combined with the Doppler Effect, calls into question the classical principle of relativity by allowing the determination of relative motion completely from within a single reference frame which is stationary or in motion.
  7. Geryllax Vu
    Einstein’s Special Theory of Relativity defines simultaneity as: if two spatially separated events occur such that the light waves generated by these two events arrive at the midpoint of the line adjoining them, at a same time t, then these two events are considered simultaneous.  However, if these two events occur in open still air -- which is disengaged from the motion of a material object through space -- then any sound waves that might also be generated at the light flash events may not arrive at this midpoint, at the same time.  The events occur at the endpoints of their adjoining line and form a tandem, of length L, where all the discrete points on the line tandem (e.g., a high-speed train) are moving at a constant velocity v along a line parallel to the line adjoining the collection of points.  The time and distance intervals measured in the tandem reference frame relative to the still air/earth reference frame may then be mathematically determined using a modified formula from the Michelson-Morley experiment in which the value of c is switched from the speed of light to the speed of sound.   This switch is made plausible by the concept of the velocity constancy of wave phenomena. This methodology of using sound waves to investigate the motion of a material object through air thus calls into question the classical principle of relativity by dispensing with the need for a Galilean or Lorentz transformation between relatively moving reference frames. All needed physical information is available from within a single reference frame whether that frame is stationary or in motion.
     
     
     
     
     
     
    According to Special Relativistic (STR) mechanics, two events occur simultaneously if the light from each of those two spatially separated events meet at the midpoint of the line adjoining them, at the same time t.  Additionally, if this simultaneity occurs in a reference frame that is considered to be stationary then the events will not be generally regarded as simultaneous in a reference frame that is moving with a linear constant velocity v relative to the stationary frame.  This may be true for light waves but it will not be true for sound waves which rely on a medium for their propagation, sound does not propagate in a vacuum.  The velocity of the medium has a measurable effect on the velocity c of propagating sound waves which follows the formulas experimentally observed by Doppler.  The medium’s velocity may be zero or have any other value relative to the source and receiver and as a result the arrival times of the sound waves at the midpoint will be staggered due to the motion of the line tandem reference frame through the still air.
     
    An important but generally disregarded characteristic of this air/medium is that the air molecules pass easily through the porous conceptual walls of any inertial reference frame whose motion is disengaged from the open air. The still air will not be delimited by the walls of any stationary or moving reference frame in the same way as any air molecules contained within an enclosed compartment.  A material object in flight within a reference frame follows a trajectory that is essentially the same as the object’s trajectory within an enclosed compartment; the object’s velocity will only be minimally impacted by any air resistance or wind.   For sound waves however not every reference frame is an enclosed compartment.  In the reference frame attached to the train the air molecules will have the velocity of the train only if they are in an enclosed compartment or sealed train car.   This is because the solid walls of the compartment have imparted a mechanically invisible component of velocity upon the air molecules/medium contained within it.   The non-zero velocity of the air then would increase or decrease the velocity of the sound wave and thus mechanically cloak the compartment’s motion during any experiment conducted within the enclosed compartment.  On the other hand, the open still air outside any train compartment will be at rest relative to the moving train.  This zero air velocity will result in the sound wave propagating at a constant velocity c relative to the train.  Each scenario will consequently manifest a different velocity for any sound waves propagating through a medium within a reference frame based on the velocity of the medium relative to the sound wave.
     
    An objective of any test of simultaneity would be to determine if two events occur at the same time or if one event occurs before or after some other event.   This would require some type of time measurement that could make a temporal distinction between what is earlier and what is later in observable mechanical terms.  A possible means of distinguishing whether the abovementioned events are simultaneous involves utilizing sound waves to mechanically measure time intervals and distance intervals.   So sending a sound wave along the length L parallel to its extension in space and then applying mathematical formulas that will allow the measurement and comparison of time and distance intervals in a way which is not constrained by any single reference frame could be a means to mechanically reflect the physics of simultaneity.
     
    A thought experiment oft used to explicate simultaneity involves an archetypical Einstein train of length L (distance between engine and caboose) travelling down a long level straight stretch of track, on a windless day, at the constant velocity, v.  The air/medium is at rest relative to the earth and track.  Suppose additionally that there is an observer seated on the roof at the midpoint of the train situated so as to see both the engine and the caboose and enjoying the view of the landscape.  At some point in time two lightning bolts strike the cast iron hulk of the train, simultaneously, one at the engine end and one at the caboose end.   At the occurrence of these two light flash events there are also two sound wavefronts generated.  The departure events of the two sound waves are consequently also simultaneous.
     
    The arrival events of the light waves at the midpoint of the train will be simultaneous according to the STR.  However, the arrival events of the sound waves will not be simultaneous due to the forward motion of the train through the stationary air.  The relativistic formulas from STR require the acceptance of the mathematical pretense that if the observer is working from within the train reference frame then that frame is to be considered as being at rest. As a result, the propagating light waves will traverse a particular distance in a particular duration of time without taking into consideration the velocity of the train.  However, the formulas for the propagating sound waves will be different as a consequence of the porous conceptual walls of the train reference frame which will allow the train reference frame to pass easily through the air, or the air to pass easily through the train reference frame.  In the moving train reference frame the still air molecules outside the solid walls of any particular train compartment must be philosophically assigned to either the train reference frame or the earth reference frame or maybe both.  The free passage of the external air molecules through the train reference frame will require a more complicated mathematical approach which takes into account the train and sound wave velocities relative to the still air.  So the propagating sound wave will manifest a behavior mathematically different from the light wave in the train reference frame though they are occupying the same region of space.
     
    The train observer does not necessarily have to actually perform an actual mechanical experiment.  She needs only to do some algebra to determine the mathematical solution that will state the simultaneous or non-simultaneous nature of events in the train reference frame. If she held two mechanically identical clocks at a single location she could find the flight time (Newtonian universal time) for each sound wave to reach the midpoint of the train. She would use the light waves as nearly instantaneous signals to indicate that she should start her clocks; at the lengths and speeds of a typical train this approximation should be valid.  In addition, the effects of the gamma factor from the STR is very minimal at the speeds of a typical train in motion. Thusly, disregarding her reaction times, she could start the clocks simultaneously and the identical clocks would proceed to tick synchronously in an identical manner.  Then by marking the clock readings for the arrival events of each sound wave at the midpoint she could make a decision as to the simultaneity of the sound waves arriving at her ears.  If the light wave arrival events are apparently simultaneous but the sound wave arrivals are not, she might conclude that this may be due to the motion of the train.  Another observer on the nearby platform could do the same if he had two clocks and he would come to a similar conclusion.  In addition, there is not any type of direct communication between the two observers mechanical or otherwise.
     
    The train tandem of cars moves through space with each discrete point at a fixed distance of separation from any other point on the tandem.  Working completely from within the train reference frame and using only information available to her from that reference frame then there are only two reasonable mathematical options to pursue.  For the propagating sound wave she must take into mathematical consideration the state of motion or state of rest of the medium and apply the Doppler wind formulas for the flight time of the sound waves from the endpoints to the midpoint through the still air.  As a prelude, each light wave, one from the engine and one from the caboose, will traverse the distance 0.5L at the constant velocity c.  So, according to the STR the formula that best reflects the flight time (relativistic proper time) of the light wavefront coming from either one of two spatially opposite directions in a stationary reference frame is:
     
    [0.5L] / c = t = [0.5L] / c
     
    In a reference frame that is considered as being at rest then the sound wave will propagate in a mathematically similar way according to the classical kinematics formula time = distance / velocity.  However, if the reference frame is regarded as being in motion at the train’s constant velocity v through the still air/medium, then each sound wave one from the engine and one from the caboose will consequently traverse unequal distances.  One distance will be less than 0.5L and the directly opposite distance will be greater than 0.5L due to the motion of the train.   The sound wave will travel these altered distances at the one constant velocity c.  Since the symbol c is commonly used to represent both the speed of sound and the speed of light in many scientific reference texts then the formulas that best reflect a sound wave coming from a direction parallel to the motion of a reference frame moving with the constant velocity v is:
     
    t1 = [0.5L + vt1] / c = [0.5L] / (c – v)
     
    and from the opposite direction,
     
    t2 = [0.5L – vt2] / c = [0.5L] / (c + v)
     
    These two time intervals are self-evidently different, t1 ≠ t2.  Both the train observer and the platform observer will determine the same value for the length interval L and the constant velocity of the train v by classical methods though they are in motion relative to one another.   A particular classical method might be one in which a material object passes certain landmarks a known distance apart in a certain duration of time.   This second pair of formulas will achieve nearly identical time results when used by either observer in his or her own reference frame.  So this time difference could be used to determine simultaneity or not simultaneity due to the motion of a particular reference frame relative to some other reference frame. Also these two mathematical expressions bear a remarkable resemblance to the formulas that arose from the considerations of the Michelson-Morley experiment to detect the aether wind.  That is, the time formulas that were applied to the light traveling along the interferometer arm that was aligned parallel to the direction of the earth’s orbital motion around the sun as an effort to investigate the earth’s motion through space.  The goals of the Michelson-Morley experiment are very similar to the objectives of the thought experiment presented here.
     
    The first pair of formulas imply that the train is at rest or the reference frame attached to the train acts as an enclosed compartment.  This would follow the Galilean and Lorentz reasoning of considering the reference frame attached to a material object to be at rest, although that object is in motion.  Meanwhile, the second set of formulas include the velocity of the train relative to the earth in a mathematical way that recognizes the conceptual porosity of the walls of a moving reference frame following the reasoning of the Michelson-Morley experiment.  The sound waves are in essence either meeting or overtaking the observer at the central location depending on the direction of motion of the sound waves relative to this central observer.  Deriving the formulas recognizes that the distance between events increases for one direction such that the flight time between events also increases by some factor that includes the train velocity v.  In the directly opposite direction the distance the wave travels decreases such that the time of flight for the wave decreases by a similar factor.  The train reference frame will then appear to not be in motion at least according to any mechanical measurements of sound wave velocity made within an enclosed compartment on the train.  While a sound wave travelling through the external still air can to a great approximation detect the train’s motion from within the train reference frame.
     
    Thus by mechanical hypothesis the time and distance interval values are invariant across the relatively moving reference frames. As a result, the variables can be assumed to be equal in both the train reference frame and the platform reference frame.  Consequently, being able to mathematically determine the relative velocity then permits the finding of the simultaneity of events across reference frames which contradicts the STR since the train reference frame and the platform reference frame can use the same formula to investigate simultaneity.  The STR states that the train observer and the platform observer must use different formulas which include the variable for the speed of light waves.  However, the train observer can compare the differing times of sound waves arriving at her ears such that she can come to a decision about the approximate simultaneity of the lightning strikes by factoring in the motion and velocity of the train.  She might conclude that what has caused the staggered times of the sound wave arrival events is the motion of the train.  She may wonder why this is not true for light.
     
    If the train were regarded as being at rest, for the reference frames to preserve mechanical equivalence between the scenarios of a moving or stationary train then an apparent Dopplerian wind of velocity w must be summoned. The relative velocity v represents either the train moving past a stationary earth and atmosphere or the entire earth and sky are moving past a stationary train.  The air/medium must retain the value of zero relative to the earth in both scenarios and the air must observably move past the stationary train or the train must move past the stationary air at either w or v. So this Doppler wind would appear to slow down the sound wave coming from one direction and speed up the sound wave coming from the opposite direction.  Each sound wave would nonetheless travel along the same full length 0.5L between the endpoints and the midpoint on the train but at apparently different velocities:
     
    t3 = [0.5L] / (c + w)
     
    and from the directly opposite direction,
     
    t4 = [0.5L] / (c – w)
     
    where t3 ≠ t4.  Since w = v, then the pair t3 and t4 is mathematically identical to the pair t1 and t2.  This consequently means that the train observer and the platform observer could use the same formulas for measuring the time intervals between the sound wave arrival events. That is, each reference frame can use the one and the same set of formulas to find the invariant time intervals as viewed from each reference frame.
     
    Neither set of formulas specifically refers to measurements that are available only from the platform observer nor does the train observer need any especial information from the platform reference frame to find an algebraic solution for simultaneity.  This algebraic solution will establish a mathematical relationship between relatively moving reference frames that dispenses with the need for any type of transformation equation.  An observer at rest on a nearby platform would also see the sound wave from the engine end of the train arrive at the central location before the sound wave from the caboose. He could also use the abovementioned formulas with the identical variables to determine the time interval values for the departure and arrival events for each sound wave.  Additionally, both observers would see the sound wave flight durations from each direction as measurably different by the same amounts.  The single constant velocity c for the propagating sound waves will manifest in both reference frames though this velocity will have the appearance of having differing values as viewed by each relatively moving observer.  In these two apparently mechanically different scenarios the reference frame from which the velocity of the train is viewed does not matter.  All the variables are readily accessible from within the train reference frame, she simply has to do the algebra.
     
    CONCLUSION
     
    Typical mechanical experiments involving material objects or sound waves which are conducted in an enclosed compartment will usually not reveal the motion of the compartment relative to that which is outside the compartment. However, an experiment involving sound waves which is conducted outside of an enclosed compartment would expose the sound waves to the open motionless external air.   This would present a description of a type of relative motion between reference frames which does not require either a Galilean or Lorentz transformations.   It would establish a mathematical relationship between reference frames that are in motion relative to one another which allows the observers in each reference frame to use identical formulas for making invariant time, distance, and velocity measurements.  The pretense of a stationary system from the Galilean principle of relativity and the Einstein STR can then be discarded and there would be no need for Galilean or Lorentz addition of velocities with respect to sound waves propagating in open still air.  In addition, there is a lack of formulaic influence from the Lorentz gamma factor because v is so much less than c, where that c represents the speed of light
     
    The abovementioned formulas thusly displace the Galilean and Lorentz transformation equations to become a new form for expressing the mathematical relationship between relatively moving reference frames and in doing so challenge the validity of the classical principle of relativity. Since the observers have used identical formulas though they are in relatively moving reference frames then they will be in agreement as to the time measurements that would distinguish between the simultaneous and the non-simultaneous event scenarios.  This would contest the validity of the STR which states that simultaneity can only be a relative concept; in other words, events are only simultaneous in a reference frame that is at rest, but are not necessarily simultaneous in a relatively moving reference frame.  By these sets of formulas events will appear to be simultaneous when viewed by an observer located in a reference frame that is stationary and at the same time when viewed by an observer located in a reference frame that is in motion.  This does not align with the formal definition of simultaneity as stated in the Special Theory of Relativity which is more strictly associated with propagating light waves.
  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
    -Suppose a long train with a caboose travels down a level section of track at a constant velocity, v. There is an observer in the caboose and an engineer in the engine car. It is a windless day. This observer may ask: What is the speed of the train relative to the air, or a nearby platform (both at rest relative to train)?
    -She has a light source (lantern, maybe) to send a signal to the engine car and engineer. The light signal is effectively instantaneous. He blows the whistle when he receives the signal (disregard reaction time). If she starts the clock when she sends the light signal, then she can measure the time, t, for her to hear the returning sound (speed of sound, c) signal.
    -During the same time that the train is in forward motion, the whistle sound is in rearward motion. She speculates that she will meet the sound wave somewhere within the distance, D, from the engine to the caboose. By algebra:
    ♦ ct = D - vt (t = t)
    -Is she correct that she can find the velocity, v, of the train?
  10. Geryllax Vu
    The principle of relativity as annunciated by Galileo, Newton, Einstein, and others, states that no mechanical experiment can be done in an enclosed room that could detect the absolute motion of the room. There may not be anything such as absolute motion, only statements of relative motion expressed by mathematical formulas; but I hypothesize that the following thought experiment outlines a way of defining an intermediary motion that arises from some Aether, that resides between absolute motion and relative motion. This is in contradiction to any form of Relativity that has been expressed by modern science.
    Suppose a long train with several cars, a caboose, and a locomotive engine, travels down a long level section of track at a constant velocity, v. There is an observer in the caboose and an engineer in the locomotive car. It is a windless day (still air, motionless medium). This observer might ask: can I find the speed of the train relative to the air, or another observer at rest on a nearby platform (both at rest relative to train)?
    She has a light source (a lantern, maybe) to send a signal to the locomotive car and engineer. This light signal is effectively instantaneous over this short distance. He blows the whistle when he receives the signal (disregarding reaction time). If she starts her clock when she sends the light signal, then she can measure the time, t, for her to hear the returning sound signal (speed of sound, c; c is a symbol for sound and light, and represents a constant, no addition of velocities).

    Thus, during the same time that the train is in forward motion, the whistle sound wave is in rearward motion. She speculates that she will meet the sound pulse somewhere within the distance, D, from the engine to the caboose. By algebra, with the opposite endpoints of D as the starting places of the caboose’s motion, and the sound wave’s motion:
    ♦ D = ct + vt (t = t)
    ♦ v = [D / t] - c
    Is she correct in thinking that she can find the velocity, v, of the train based on this total time, t; which she measures on her single clock? She imagines that this thought experiment assails the wall of separation between reference frames; between the reference frame attached to the moving train, and the other reference frame attached to the platform which is considered at rest. She has found a method for determining her speed relative to the earth; based only on information available from within the reference frame attached the train. She is furthermore sharing in the motion of train (she is at rest relative to the train).
    The Newtonian laws of motion do not take their simplest form in either reference frame. Instead, each takes on a form related to the Galilean transformation equations (similar to the Michelson-Morley formulas: L = ct + vt; t = L / [c + v]). That is, in both the moving frame, and the frame at rest, the distance, L, between the two starting points stays the same. Despite the Galilean transformation, the distance, L, will be preserved across reference frames (L = (x2 - vt) - (x1 - vt) = x2 - x1 = L; the vt‘s have cancelled out). The observer at rest in the rest area will note that the caboose is in motion, as well as that the sound wave is in motion. But the times measured in each reference frame will be the same, thus allowing the observer on the caboose to solve for v, the velocity of the train. This contradicts the principle of relativity once again.
  11. 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]).
  12. 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
  13. Geryllax Vu
    Now I switch to a different venue for my thought experiment. It will involve two automobiles traveling down a smooth straight level section of turnpike. Each auto will set their cruise controls at a constant velocity, v, which they have agreed upon beforehand. Each driver has fully operational digital clocks, annoyingly loud horns, and bright halogen lights on board. It is dusk on a clear windless day.
    As the convoy (a lead auto and a following auto) makes its way down the road, the pair are rolling in tandem with each other; neither accelerating, nor decelerating, relative to one another. They can be regarded as at rest relative to one other. However, the air is at rest relative to both autos as they are moving down the road (the air and road are both at rest relative to the autos).
    So to check that they are a safe distance, L, apart (stopping distance at this speed) the driver of the following auto conjures up a test. She makes a hands free cell phone call to the driver in the lead car. When he answers she tells him her plan.
    On a windless day they are rolling down the turnpike in tandem, thus they at rest relative to each other; but at the same time, they are in motion, at the same velocity, relative to the road and air. She proposes to flash her headlights as a signal to her comrade‘s auto. When he sees the light signal, he is to honk his horn. At the same that she flashes her lights, she starts her digital clock. Thusly, the time she measures, since the light signal is effectively instantaneous, will be for the horn sound to return to her:
    The distance they are apart will not be L = ct, but rather L = ct + vt, where v is the velocity of the tandem relative to the road and still air (c is the velocity of sound). They will begin at the distance L apart, then her auto and the sound pulse will meet somewhere within L by algebra. This reflects the forward motion of her vehicle at the same time as the sound wave is traveling rearwards. This accounts for all the variables and determines the distance they are apart.
    The pair travels on further, after checking their safe distance. Now, towards the end of their trip, they have reached the familiar environs near the exit for her town. He speeds up to a new constant velocity, u, to make time without risk of losing her. At this new velocity, he gradually pulls away from her. He will travel on to the next town alone. Then, she imagines a continuance for their little thought experiment.
    As he is gradually separating, she realizes that the source (he) and the receiver (she) are no longer in tandem, now a Doppler effect appears because they are no longer traveling at the same speed. An aspect of Doppler (sound waves through air) is that when the source approaches the receiver, there is a slight mathematical difference than when the receiver approaches the source (introducing a sort of wind in either reference frame).
    So if she makes the measurement of the change in frequency from her friend’s auto horn while he gradually separates from her, then she will find the source sound wave to have apparently changed frequency. She knows the frequency of the horn from when the autos are at rest relative to each other.
    In other words she can determine the frequency of the sound of the auto horn while the autos are rolling in tandem (they are at rest relative to each other but moving at the same velocity relative to the air, so ff = f0 ). She can now discern whether she is in motion relative to the air, earth and his auto (which she thinks could be at rest); or whether the air (wind) , earth and his auto are in motion while she is at rest.
    This can seen by a comparison of the two formulas that fit these two scenarios (the different frequencies can be used to solve for using their different velocities); if the frequency she measures is one value of f then she concludes that she is moving; if the frequency has some other value f, then she concludes she is at rest:
    ♦ f = [ c / (c + vs)] f0
    ♦ f = [(c + vr ) / c] f0
    These formulae are clearly different, just by appearance. Therein, the nature of her motion is revealed. Either she is stationary, with the medium in motion; or she is in motion, with the medium being stationary. She has a mathematical means of determining this.
    She can distinguish, by her thought experiment, whether the autos are in motion with the Earth stationary; or the autos are stationary, with the Earth in motion. This is contrary to the principles of relativity which state that both situations are equivalent, or equally valid descriptions of her motion, thus they are interchangeable in a way. But her thought experiment shows that this is unsound.
    http://en.wikipedia..../Doppler_effect
    http://gerrybharris.blogspot.com/
  15. 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
  16. 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
  17. Geryllax Vu
    The question I want to ask is: can the following thought experiment detect absolute motion, or does a sort of intermediary motion emerge which is neither absolute motion, nor absolute rest? It is like Einstein relative motion, but without using a Galilean or Lorentz transformation between reference frames. It comes about when sound waves are used to investigate the motion of material objects through a stationary or moving medium.
     
    According to Galileo, Newton, and Einstein, the principle of relativity states that no mechanical experiment can be done to detect absolute motion, or motion of a material object relative to an everywhere stationary medium (similar to Michelson-Morley aether). A common reformulation of this principle state that:
     
    ♦The same formula is not used for the constant velocity v of a material object as seen by an observer in a reference frame in which the object is viewed as being at rest; or, as seen by an observer in a reference frame in which the object is viewed as being in motion (Galilean addition of velocities).
     
    On a windless night (air molecules at rest relative to the earth), a train of length L is traveling at the constant velocity v along a flat straight section of train track. There is an observer in the caboose (train reference frame) as well as another observer on the station platform near the track (earth reference frame). They each have identical clocks with which to conduct the following thought experiment. They will attempt to detect absolute motion, or at least test a common reformulation of the classical principle of relativity. That is, to show that two observers can measure the same value for the velocity v of the train using the same formula, without a Galilean transformation, although these two references frames are moving relative to one another.
     
    The observer in the caboose has a light source with which she will send a signal to the engineer at the front of the train. She will lean through an open window to do this. Outside the window, the still air does not have the velocity of the train, thus the air velocity will have either some or no effect on the velocity of the sound wave, but it will yield the same result for both observers. Upon seeing the light signal the engineer will blow the train’s whistle, sending out sound waves which the caboose observer will be able to hear. At the moment she sends the signal she starts the single clock that she has. The platform observer will also see this signal and he will start his single clock at the same moment. Thus, their clocks have essentially been synchronized. The two observers will then be in a position to find the motion of the train (material object) relative to the still air (medium at rest, Michelson-Morley).
     
    Over this short distance the light signal is effectively instantaneous, so that the time t she measures is essentially the time for the sound wave to travel the length L to her ear. When she hears the whistle sound she stops her clock and then once again flashes her light. The platform observer also stops his clock upon seeing this second flash. The time interval between the two light flashes therefore represents the time interval between the departure and arrival events of the sound wave, as seen by the observer in either reference frame. Disregarding reaction times, both observers should measure approximately the same interval of time t. Since the speeds of the sound wave and the train are so much slower than the speed of light, the Special Relativistic effects of time dilation and length contraction are negligible.
     
    As the experiment proceeds, the caboose moves in the forward direction, at the speed of the train, to meet the rearward travelling sound wave, so the sound wave will travel a distance that is less than L, the length of the train measured at rest. The speed of the sound wave is not altered by the speed of the source, but the motion of the material object (train) is disengaged from the medium (still air). This should lead to, approximately, identical time interval measurements by the observer in each reference frame. The air molecules freely flowing between the two reference frames moving relative to one another make this supposition mechanically plausible. The mechanical disengagement of the physical train from the still air permits the easy mathematical passage between reference frames, that is the critical premise that underlies this thought experiment. The airy particles pass easily through the porous conceptual walls of the reference frames, like the ghostly spirits of a haunted house.
     
    The caboose and the train engine are at a fixed distance apart. They have formed a tandem which is moving through the air (medium), both at a single velocity, maintaining this distance of separation. The sound wave and the caboose, having begun their journeys at the endpoints of L, will meet at the same location in space as seen by either reference frame. The caboose will have the constant velocity v, and the sound wave will have the constant velocity c. In the same duration of time t, they will have, taken together, traversed the distance L. That is, the distance the sound wave has travelled rearward ct, added to the distance the caboose has travelled forward vt (distance = speed × time), should equal L. Thus, all the variable values are available to each observer within all the adjacent reference frames. To reflect the conditions of their meeting, somewhere within the length L, the following equation can be set up:
     
    ♦ L = ct + vt
     
    If they have measured the same interval of time in both reference frames, then this formula can be solved for v, the velocity (motion) of the train as seen by either reference frame:
     
    ♦ v = [L / t ] – c
     
    (A similar argument can be made if the train is moving in the reverse direction)
     
    Let, L = 1000 meters; c = 343 meters/second; assume v = 30 meters/second:
     
    ♦not, t = L / c (measured when train is at rest) = [1000 m] / [343 m/s] = 2.92 s
     
    ♦but, t = L / (c +v ), (train in motion) = [1000 m] / ([343 m/s] + [30 m/s]) = 2.68 s
     
    ♦v = [L / t ] – c = [1000 m / 2.68 s] – 343 m/s = 30.1 m/s
     
    This expression contradicts the Galilean, Newtonian, and Einsteinian principle of relativity in that although the two reference frames are moving relative to each other, they can each use one and the same formula to find the velocity of the train as seen from either reference frame. This results in bypassing the need for the addition of velocities from the Galilean transformation between references frames, when sound waves are used to investigate the motion of a material object through still air. Thus, a sort of intermediary motion emerges from the mist amongst the reference frames.
  18. 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
  19. Geryllax Vu
    Under the Special Theory of Relativity, the units of length are to be measured in terms of a triangle formed by a vertically reflected light bean. This gives rise to the effect of length contraction appearing between an observer in motion and an observer at relative rest. The phenomenon of length contraction is however indiscernible for the observer who shares in motion.
    If a sound wave is used to measure the unit of length, the length contraction becomes enshrouded in a mist. The contraction appears only slightly when the sound source is in motion (v << c). So, while measuring a unit of length on a measuring stick across reference frames is impossible for a light beam, it is well within the grasp of a sound wave. An observer in motion will totally agree with an observer at relative rest.
    The formula c = L / t or L = ct, is the simplest form of the Newtonian law, or equation of motion in an inertial reference frame by the principle of relativity. A comparison with the result of my thought experiment yields an unmasking of length contraction. The length of the train car, L, can be found from the known speed of sound waves c, and the time measured on the clock. So that the observer on board the train would anticipate the length can be solved for by using algebra.
    But if the train is in motion, then the time measured will be different. It will be: t = L - vat / c, or L - vt = ct or L = ct + vt (with t = t) due to the forward motion of the train car at the velocity, v. And thus the length, through the air that, the sound wave has traveled, as interpreted by the train observer, will be shorter than the length of the train car if it were at rest.
    The setup of my thought experiment uses a single clock, so that no synchronization is necessary. This has been put forward as a proof for supporting STR. In most examples to illustrate STR it is put forward that the observer at rest has to use two clocks for two events that occur at different locations in space.
    However, in my hypothesis there is only one clock and only one observer within the train reference frame. Thus doing an end run around synchronization; it is not a limitation for my hypothesis. I propose that the answer the train car observer measures is identical to that of an observer on the platform, without any sort of communication going on between the two.
    This shakes the appearance and reality of Relativity. An axiomatic statement that these two observers, one at rest, one in motion, will measure two different times and velocities for the same event, is at the heart of Relativity. But my setup has done precisely that.
    Both the train observer and the platform observer will claim the same, identical formula for the motion of the train car; this is the same formula found by the platform observer by the Galilean transformation. Units of length cannot be measured by light waves, across reference frames, to get a single common value; but it can be measured thusly by sound waves, under easily met conditions.
    https://en.wikipedia.org/wiki/Length_contraction
  20. 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.
  21. Geryllax Vu

    Max Born

    By Geryllax Vu,

    The principle of relativity as annunciated by Galileo, Newton, Einstein and many others states that:
    ♦ There is no mechanical experiment that can be done to detect absolute motion.
    A form of this statement is the first postulate of the STR by Einstein. This principle can be rephrased in many formulations, which I will show are all violated by my proposed thought experiment (statement formulations are from Einstein’s Special Theory of Relativity by Max Born).
    1.) The laws of mechanics have exactly the same expression as when referred to a coordinate system at rest in space.
    2.) According to classical mechanics, the velocity of any motion has different values for two observers moving relative to each other.
    3.) There are an infinite number of systems of reference moving uniformly and rectilinearly with respect to each other, in which all physical laws assume the simplest form (originally derived for absolute space or the stationary Aether).
    4.) The laws of mechanics are invariant with respect to Galilean transformations.

    ♦ My caboose experiment is a mechanical experiment using sound waves passing through air molecules. It does not find the absolute motion but an intermediary motion that arises from somewhere between absolute motion and relative motion.
    According to STR, L will always be L , never allowing any indication of motion by ± vt. The only communication about any motion between reference frames is by the Lorentz and Galilean transformations; behind the Greek mask of time dilation and length contraction of units, a difference is seen from the perspective of the other reference frame.
    1a.) The usual mechanics law that is presumed is the simple form v = [d / t], not t = L ± vt as I have shown by this experiment. And it is t = L ± vt in an infinity of other reference frames moving rectilinearly and uniformly relative to the initial reference frame, considered at rest.
    2a.) Any and all observers, in motion and at rest, measure the same value for the velocity of the train. It is not a different value for different observers
    3a.) There are an infinite number - at rest and in motion - but they do not assume the simplest form of physical laws in each frame. They take on the more complicated form I have shown above. That mimics the MM experiment.
    4a) Physicists have long known that sound waves and light waves violate invariance, and I think I have found an experiment that utilize this scientific knowledge. That is, waves are a fount of mechanical information about Nature. Thus they each violate the principle of relativity, with considerable controversy attached. The Lorentz transformation is an overcoming approach for light waves; and my caboose thought experiment overcomes this invariance for with sound waves.
    The violation of invariance results mostly from the consideration that the wave does not increase or decrease its velocity based on the velocity of the source or receiver; the motion of material objects do pick up a momentum from a force, which as a consequence, masks its true velocity across reference frames. In other words the wave does not pick up momentum from its source, so the wave might appear to go slower or faster; or the path length might seem to shorten or lengthen, depending upon the direction and magnitude of the source’s velocity.
    For sound waves the wave crests grow closer together, or farther apart as the wave travels through the medium, but does not change velocity. For light waves, the STR proposes that alterations in space-time account for the differences arising from the point of view of separate observers in separate reference frames.
    Both observers will say that the wave has the same single velocity in her and his own and the other’s references frame, either v = [L / t] - c, or, v = c - [L / t]; but a material object will have a different velocity as measured by each observer looking at the other‘s reference frame. In addition, each observer will use the same simple formula, v = [d / t], of motion for the same object within his or her own reference frame (moving or at rest), but use the velocity addition from the transformation equations in looking at the other’s reference frame. This, I think is the crux of invariance.
    I think the use of sound waves in this thought experiment violate the principle of relativity and the first postulate of the Special Theory of Relativity. This experiment thus contradicts the assertions of the definitions of motion as expressed by Galileo, Newton, and Einstein.
  22. 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.
  23. Geryllax Vu
    It is a premise of the Galilean principle of relativity that every reference frame behaves mechanically like an enclosed compartment at rest.  As a consequence of this premise it is presumed to be mechanically impossible to discern the motion of any reference frame by observing experiments conducted within that reference frame.  Material objects in flight within an enclosed compartment will manifest a particular velocity that arises from momentum transfer through physical contact with the compartment walls.  Objects in flight outside of the compartment will exhibit essentially the same behavior via contact with the external physical structure of the moving compartment.    However, a sound wave in flight through an enclosed compartment where the air has no wind currents in it will manifest one particular velocity while a sound wave propagating through the still air outside the compartment will manifest some other velocity — in a moving enclosed compartment the contained air’s velocity is the same as the compartment’s velocity and would add to or subtract from the sound wave’s propagation velocity.   There is then a difference in the mechanical behaviors of material objects and sound waves when they are moving through any particular medium based on whether that medium is within or outside of a moving enclosed compartment.  Under certain conditions an observer in a stationary or moving reference frame may not have to apply the principle of addition of velocities from the Galilean or Lorentz transformation equations to the propagating sound wave.  Not every reference frame is an enclosed compartment.

  24. Geryllax Vu
    According to Newton and Einstein, the principle of relativity states that no mechanical experiment can be done to detect absolute motion, or motion of a material object relative to a stationary medium (similar to Michelson-Morley). Common reformulations of this principle state that:
    1) The velocity of a material object takes on the simplest formula, as seen by an observer at rest in a reference frame, no matter whether the reference frame is at rest, or moving with constant velocity, v.
    2) The same formula is not used for the constant velocity, v, of a material object as seen by an observer in a reference frame in which the object is viewed as being at rest; or as seen by an observer in a reference frame in which the object is viewed as being in motion (Galilean addition of velocities).
    On a windless evening at dusk (air molecules at rest relative to the earth), a train of length, L, is traveling at the constant velocity, v, along a flat, straight section of train track. There is an observer in the caboose (train reference frame) as well as another observer on the station platform near the track (earth reference frame). They each have identical clocks with which to conduct the following thought experiment. They will attempt to detect absolute motion, or at least test a common reformulation of the classical principle of relativity. That is, to show that two observers can measure the same value for the velocity, v, of the train using the same formula, without a Galilean transformation, although these two references frames are moving relative to one another. Also, this will not be the simplest form for the velocity of the train:
    ♦ v = [d / t]
    To find the absolute motion of the train (material object) relative to the still air (medium at rest – Michelson-Morley), the observer in the caboose has a light source with which she will send a signal to the engineer at the front of the train. He will then blow the whistle, sending out sound waves which the caboose observer will be able to hear. At the moment she sends the light signal she starts the single clock that she has. The platform observer will also see this signal and he will start his single clock at the same moment.
    Over this short distance the light signal is effectively instantaneous, so that the time, t, she measures is essentially the time for the sound wave to travel the length, L, to her ear. When she hears the whistle sound she stops her clock and then once again flashes her light. The platform observer also stops his clock upon seeing this second flash.
    Disregarding reaction times, both observers should measure the same interval of time, t. Since the sound wave and the speed of the train are so much slower than the speed of light, the relativistic effects of time dilation and length contraction are negligible. The caboose moves forward to meet the rearward travelling sound wave, so the sound wave will travel a distance that is less than, L, the length of the train at rest. The speed of the sound wave does not change, but the motion of the material object (train) is disconnected from the medium (still air). This should lead to, approximately, identical time interval measurements by the observer in each reference frame. The air molecules freely flowing between the reference frames moving relative to one another make this supposition mechanically plausible.
    The sound wave and the caboose begin their journeys at the endpoints of L. The caboose has the constant velocity, v, and the sound wave has the constant velocity, c. To reflect the conditions under which they will meet, then the following equation can be set up:
    ♦ L = ct + vt
    If they have measured the same interval of time in both reference frames, then this formula can be solved for, v, the velocity of the train as seen by each reference frame:
    ♦ v = [L / t] - c
    This is obviously not the simplest formula for the velocity of the train in either reference frame. This expression contradicts the Newtonian and Einsteinian principle of relativity in that although the two reference frames are moving relative to each other they can each use one and the same formula to find the velocity of the train as seen from either reference frame. This results in discarding the need for the addition of velocities from the Galilean transformation between references frames.
  25. 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.
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