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Geryllax Vu

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  1. I have been struggling to find a clear and concise way to describe the point of the experiment and you have grasped it. I believe that as I have presented it your assumption is correct that an enclosed compartment is measurably different from an open reference frame. I agree that it would be possible to hear two tweets as you say because the air molecules in the moving compartment may slow down or speed up the sound wave depending on the sound wave's direction of travel. But a sound wave traveling through still air will always be c. I agree with your observation that there will be no Doppler effect for the train observer because the source and receiver are moving in the same direction at the same speed so the waves spread out at the source but squeeze together at the receiver thus cancelling each other out and leaving the original frequency. I plan on using this difference for the two observers in the future.
  2. 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.
  3. On a windless day a train of length L travels along a level straight section of track at the constant velocity v. An observer in the caboose has a clock and a light source with which she will send a signal to the engineer at the front of the train. Upon seeing this signal, he will blow the whistle which will send out a sound wave that has the constant velocity c through the still air/medium. At this short distance a light signal is effectively instantaneous so upon sending the light signal she also starts the clock that she has. When the sound wave reaches the caboose observer’s ear she will stop her clock. She should then measure approximately the Newtonian universal time interval t between the departure and arrival events of the sound wave in the train reference frame. The caboose and the engine are at a fixed distance apart. They form a tandem which is moving through the still air at the single velocity v each endpoint maintaining their distance of separation. The sound wave and the caboose begin their journeys at the endpoints of L and will meet at some location in space between the original locations of the endpoints along their adjoining line. The sound wave travels the distance ct rearward towards the caboose and the caboose travels the distance vt forward towards the sound wave during the same interval of time t (distance = speed × time) and adding these two distances should equal L. Thus, all the variable values are available from within the train reference frame: ♦ L = ct + vt ; t = L / (c + v ) This formula (similar to the Michelson-Morley experiment) could be used by both the train observer (in the train reference frame) and an observer that she need not communicate with at rest on the nearby platform (in the platform reference frame). The train observer might assume the train to be in motion and would thus measure with her clock an interval of time that would indicate that the sound wave has travelled at the unchanged velocity c for a lesser or greater distance than when the train is at rest. This is a result of the consideration that the air molecules pass easily through the porous conceptual walls of any reference frame that is not an enclosed compartment. Alternatively, the train moves through a cloud of stationary air molecules that are not carried along by the train reference frame. There will be no addition to or subtraction from the velocity of the sound wave only a change in the distance the sound wave travels. The train observer will then not have to apply the principle of addition of velocities from the Galilean or Lorentz transformation between the two reference frames that are in relative motion. Let, L = 1000 meters; c = 343 meters/second; assume v = 30 meters/second: ♦not, t = L / c, (train, air, and platform at relative rest) = [1000 m] / [343 m/s] = 2.92 s ♦but, t = L / (c + v ), (train in motion through air) = [1000 m] / ([343 m/s] + [30 m/s]) = 2.68 s
  4. I personally don’t believe that empty space is a vacuum, Stub. It has cosmic dust and various cosmic particles in it through which sound can propagate. Additionally, these particles can affect the velocity of any waves, light or sound, propagating through them. So if a light source is submerged in any medium such as air, water, or Bose-Einstein condensate then the waves emitted in any direction will be slowed down by some amount as compared to the speed of light in a vacuum. If the medium is set into motion, then the light wave propagating in one direction will be slowed down according to the Fizeau partial convection formula. In the opposite direction it should be sped up but I will accept the top speed limit of light for now. This I think means that light can’t be used to calibrate space-time diagrams because any light experiments conducted in the presence of a medium will mean that light will have different speeds depending on which direction the light wave propagates relative to the medium, from the source to the receiver. This is similar to sound wave propagation.
  5. I'm still fine-tuning this paper but I think it is essentially correct. This is an excellent link Earl, empty space is not empty. Every vacuum has some stuff in it that alters the velocity of light in a mathematical way, I would agree with that.
  6. acey and andrew s If light propagates in the presence of a moving medium within a reference frame, not in a vacuum, then the velocity of the light will show some mathematical variation according to the Fizeau partial convection formula. I think I mentioned in the post that "not every reference frame is an enclosed compartment." Thus the medium within an enclosed compartment has the velocity of the compartment, but in the open the medium has zero velocity relative to the light beam this results in two different values for the speed of light in the two diffferent types of reference frames. You have to ask to which reference frame does the medium belong? This dependence of the wave speed on the motion of the medium is similar for light and sound.
  7. 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. 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.
  9. 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.
  10. The question I want to ask is: can the following thought experiment detect absolute motion, or will it detect a sort of intermediary motion; which is neither absolute motion, nor absolute rest? This intermediary motion 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. This air/medium is in and amongst two reference frames, one at relative rest, and one in relative motion. 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). The Galilean and Lorentz transformations rely upon the mathematical pretense that one reference frame is regarded as being stationary, although actually it is in motion. So that, a fictional wind must be imagined to simulate reality. Whereas imagining that a moving train is simply, moving, will produce an alternative method for mathematically manipulating reference frames which are in relative motion to one another. The speed of the sound wave does not change, but the distance it travels at a constant velocity does change. This will be outlined in the following thought experiment. A question which may come to mind is, to which reference frame does the air belong? A common reformulation of the classical principle of relativity states that: ♦The velocity of any material object moving through space has different values for two observers moving relative to one another at a constant velocity. (Galilean addition of velocities) This experiment seeks to find if these two velocity values are measurably different, or are actually measurably the same. It will measure the time interval between two mechanical events which occur in the reference frame that is moving with a constant velocity. This time interval is measured by the two observers, one in each reference frame, each possessing one of two distantly separated clocks. It is proposed that each clock should then make approximately identical measurements for the time interval between these two mechanical events. 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 (the velocity of the wave does not change, the distance it travels through the still air changes). 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.
  11. 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.
  12. A young woman and her two wyrd sisters are practicing their mysterious magicks tonight. They will exercise their telekinetic and mathematical skills with the levitation of a massive material object. In their alchemical experiment they will test whether two events that would appear simultaneous in a reference frame that is at rest, would these events still appear simultaneous if the reference frame were in motion? Can she make the invisible, visible? It is a windless night, during the witching hour (air / medium at rest relative to earth). Since her youth, a thousand years in the past, she has known that three is a magick number, so the sisters can begin their session under a beneficial sign. The young woman stands at the centerline of a soccer field with one sister at each endline. This field has the length L meters. Now, beforehand, the thrice wyrd sisters had planned their rite. The young woman’s sisters have agreed to take certain actions in response to her initiations. While in a mystical trance she conjures up two digital stopwatches which hover in the air before her, stacked, so that they are perpendicular to a line that runs from endline to endline. She continues her dark rite by whispering the secret words. Then, the entire green turf (and the reference frame attached to it) lifts itself from the dust, and rises above the ancient high treetops. It begins to fly away at the constant velocity c, straight and level, like a magick carpet, off into the starry night. Then, it turns, and flies similarly back to the stadium. A warlock soccer fan, with his supporters scarf, was observing the sisters rehearse their magicks from his stationary stadium seat in a reference frame attached to the earth (at rest). As the carpet tandem passes once again through the stadium, within view of the warlock she will, with some incantations, make a ball of golden light appear above her head. At this flash of light, her sisters, with their supernatural reflexes, will let out a banshee’s wail upon seeing the nearly instantaneous flash from this light. In the same instant, two disembodied bony fingers waft as smoky wisps awaiting, for at the appearance of the light they will start the timing devices. The warlock sees this flash and begins each of his two hidden clocks. Now their clocks are synchronized, so they will measure the same time intervals between these events in their separate reference frames. As each of her sisters’ wail reaches her, the ball of golden light flashes to green when the first sound wave arrives at her central position, then to red when the second sound wave arrives at her central position, the warlock will witness each arrival flash. The difference in arrival times of each sisters’ sound wave is due to the carpet’s forward motion. If the sound waves had arrived at the same time then that would mean the tandem was not moving through the still air and the light would instead flash to blue. They have made a three-seated tandem (aligned parallel to the direction of motion) so that they maintain the same distances relative to each other, no matter how quickly, or slowly, the tandem moves through space; or possibly not even moving at all. The distance L moves through space, neither increasing nor decreasing. So, each pair of clocks will measure two times, one from the forward sister and one from the rearward sister. The following equation adds these two times for a total time T (both the witch at the center position and the warlock seated nearby do this addition): ♦T = t1 + t2 = [0.5L / (c + v )] + [0.5L / (c – v )] = Lc / (c2 – v2 ) = [L / c ] × (1 – [v2/c2])-1 If the carpet were at rest (v = 0) then this formula would reduce to: ♦ Tr = t3 + t4 = [0.5L / (c + 0)] + [0.5L / (c - 0)] = L / c The zero velocity airy particles allow the porous conceptual walls of the reference frames to pass by without hindrance, so the air molecules velocity will neither increase nor decrease the velocity of the sound wave c travelling through the still air. It will remain constant despite the motion, or lack of motion, of the wailing banshees. The magick carpet will move straight, level, and true at the same time as the sound waves are in flight. The length L of the tandem will neither increase nor decrease. As the carpet moves forward, the distance from one sister to the center will appear to shorten, while the distance from the other sister to the center will appear to lengthen. This equation will account for this by inserting the velocity v. She puts some numbers into the calculator that she has been carrying beneath her pointed witchy hat; L = 100 meters; c = 343 meters / second; assume v = 30 meters /second; Tv = total time measured by each pair of clocks: ♦Tv = t1 + t2 = [Lc ] / (c2 – v2 ) = [100 m × 343 m/s] / [(343m)2 – (30 m/s)2 ] = 0.294 s as compared to the total time measured when the carpet is at rest: ♦Tr = t3 + t4 = L / c = 100 m / 343 m/s = 0.292 s thus, her velocity is: ♦v = √c2 – [(Lc ) / Tv)] = √(343 m/s)2 – [(100 m × 343 m/s) / 0.294 s] = 31.3 m/s Thus, she has made her velocity form from the night’s shadows (detecting her absolute motion relative to the still air/medium) using sound waves. She can make her magick carpet fly, through the night sky. This will contradict Galileo, Newton, and Einstein and their precious principle of relativity, which says that what she has done is impossible.
  13. A young woman stands before a high flat concrete wall on a blustery day. She directly faces it, at a distance of L meters away. The wind sweeps down past the wall at the constant velocity v and blows directly perpendicular from the wall to her face. She feels compelled to shout at the wall in some way, but she takes the stopwatch from her pocket and decides upon the experiment that she shall perform (akin to the Michelson-Morley aether wind experiment). The formula for a sound wave to echo back from a hard reflective surface fixed to the earth, when the air is still (medium at rest) is: ♦ 2L = cT However, I speculate that this is not the formula when there is a wind blowing at the constant velocity v in the direction directly opposite to the sound wave emission source. The velocity of the air molecules (medium) will have a measurable impact on the velocity of the sound wave as it travels from the source to the wall, and then back. Our home planet hurtles through interstellar space at a tremendous speed, 30 km/second, but the atmosphere does not get swept away, off into the cosmos. Fortunately for us, the molecular bonds of attraction and repulsion, and the force of gravity, hold a thin layer of atmosphere snugly against the earth’s surface. Though terrestrial winds may surpass 120 km/hour, most of the air molecules we depend upon to fill our lungs cannot attain enough velocity to escape the earth’s embrace. This balancing of hydrostatic pressure and gravity thus bestows upon us, the breath of life. So the earth makes its yearly orbital journey with a thin layer of atmosphere grasping tenuously to it; tornadoes and hurricanes may blow, but we shall breathe. So, when the air appears still, it is actually moving at the velocity of the earth. It is supposed that we cannot detect this motion by any mechanical experiment in the reference frame of the earth; however, it is worth exploring the scenario when the air molecules are disengaged, such as by a wind, from the rapidly moving surface of the land and sea. She stands, with her mouth and ears at the ready, opposite the high and hard reflective surface, forming a moving tandem with it; that any shout she might make would come back to her some moments later. If she is standing at a reasonable distance from this reflective surface on a windless day, then the first formula applies; but if a wind is blowing as I have described before, then the maths are different. The hydrostatic pressure casts a cloak of invisibility over the motion of the stationary earthbound tandem, and the stationary air molecules trapped near the surface of the earth. The earth, the tandem, the earthbound air molecules, are all traveling through the galaxy at the same velocity v locked together in their motion. That is, when the air is still, but a wind will cleave this triumvirate. Despite the tandem being fixed to the earth’s surface during its daily gyre, there is no Doppler effect upon the sound wave traveling from the girl to the wall because the wave crests are squeezed together near the source (girl), but pulled apart near the receiver (wall) by an equal amount; and vice versa on the reflection’s trip, so she would observe no change in the wavelength or frequency of the wave. In the presence of a wind, the Doppler change in frequency vanishes, but the Doppler wind formula remains present and measurable: ♦ c` = c ± w, where c` is the Dopplerian speed of the sound wave in the presence of the wind. Because of the wind’s speed and direction, the new wave speed is c` = c – w as the sound wave travels away from the emitter (her mouth); but it is c`= c + w when the wave is reflected back towards its original source (her ear). That is, when compared to speed of sound in still air, the wind slows down (subtract from) the sound wave speed as it travels in one direction; but speeds up (adds to) the sound wave speed when it travels in the opposite direction. Thusly, the total trip time interval for the sound wave is: ♦not, T = [2L/c] ♦but, T` = [L / (c + w)] + [L / (c – w)] = [2Lc] / (c2 – w2) = [2L / c] [1 / (1 – [w2/c2]) ♦time = distance / speed. With the pen and pad from her other pocket, she begins to make her calculations. The given variable values for her experiment are: c = speed of sound in still air, 340 meters/second; w = speed of wind, 50 m/s; L = 100 meters. So, in the first echo scenario (no wind): ♦T = [2L] / c; T = [2 × 100m] / [340m/s] = 0.588s And, in the second echo scenario (wind): ♦T ` = [2Lc] / (c2 – w2); T ` = [2 × 100m × 340m/s] / [(340m/s)2] – [(50m/s)2] = 0.601s She makes note of these differing measured time values. This leads her to ponder her two scenarios of air motion: molecules at rest in a stationary reference frame, and molecules passing unencumbered through the porous walls of an apparently stationary reference frame. There is a measureable difference between an enclosed compartment and a reference frame. The “conceptual walls” of the reference frame do not compel the air molecules within it to go at the velocity of the reference frame. These free-spirit airy particles are not possessed by the earthbound reference frame. But it is difficult to say to which reference frame they belong; they belong to no reference frame, and are in all earthly reference frames. This alternative echo formula is only a close approximation. The moving air/medium has been disengaged from the stationary earthbound girl-wall tandem in a mathematically revelatory way. This has profound implications for the motion of any material object, when that motion is investigated by sound waves. At the slow speeds of the wind, the measured time interval does not suffer the Special Relativistic effects of time dilation and length contraction; the gamma factor value is negligible at this speed. Thus, the passage of time is nearly absolute, on the scale of her everyday life behind the wall.
  14. According to Galileo, Newton, and Einstein, the classical 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). A common reformulation of this principle states that: ♦The velocity of any motion has different values for two observers moving relative to each other. The following thought experiment proposes to investigate this principle, that is, to find if these two values are measurably different, or measurably the same. It seeks to find the particular values of the motion of material object as seen by two observers in separate references frames, one moving and the other at rest, relative to one another. It will measure the time interval between two mechanical events occurring in the moving reference frame. This time interval is measured by two observers each possessing one of two distantly separated clocks. This thought experiment will use sound waves to determine a closely approximate measurement for the time interval between these two mechanical events. 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 the mentioned 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. Placing each observer in separate reference frames which are moving relative to one another then by the Galilean transformation (addition of velocities) a material object will manifest as its velocity: ♦ u` = u – v where u` is the velocity of the train in the reference fame attached to the train (this is usually zero); u is the velocity of the train in the reference frame attached to the platform; and v is the velocity of the train reference frame. In the reference frame attached to the train, the train itself has a velocity of zero; and in the reference attached to the platform, it will simply have the velocity of the reference frame attached to the train. The velocity of the train is represented by this formula, as well as the velocity of any material object moving within that train; each velocity is seen by the observer sharing the motion of the train, and the observer at rest on the nearby earthbound platform. The usual method from classical physics for finding the train’s constant velocity v is to measure the time interval that it takes for it to travel between two stationary landmarks a known distance apart (velocity = distance/time). But this method would not work in the darkness of night. If an observer on the train has no access to external landmarks then that observer would have no clues to indicate that the train is in motion. For, any mechanical experiment done when traveling at a constant velocity, such as dropping a ball to the floor, or tossing a ball to a friend in another seat, would proceed as if the train were at rest. That is, these material objects would follow a trajectory through space that does not hint at the train’s motion. The following thought experiment could find the velocity of the train, even at night, without any visible external landmarks on the stationary earth as seen through a window. If the experiment is conducted in the moving reference frame of the train, then the arm of the human ball thrower transfers a certain amount of momentum onto the ball from the train, thus increasing or decreasing the velocity of the ball. The observer sharing the motion of the reference frame attached to the train would not and cannot measure this momentum exchange, but the observer on the platform will notice this change of the velocity and trajectory of the ball. However, a sound wave does not mechanically behave in this manner. The mechanical event of a sound wave emission at some point in space, and then the receipt of that wave at some other point in space, will progress in one of two ways. If the experiment were conducted in a closed compartment then the air molecules/medium would have the velocity of the compartment and the moving air will act to increase or decrease the velocity of the emitted wave. This increase or decrease will depend on the direction of the sound wave relative to the compartment, and the emitter’s state of motion or rest within the compartment. But if the experiment were carried out in the open still air then the air molecules will have a velocity of zero which will allow them to pass freely through the “conceptual walls” of the reference frames. Thus, the air will have no effect on the velocity of the emitted sound wave no matter if the emitter is in motion or at rest. The new method presented by this thought experiment for finding the velocity 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 from the open caboose window, she starts the single clock that she has. The platform observer will also see this nearly instantaneous signal (the velocity of light is too fast to be measured by a normal clock) and he will start his single clock at the same moment. Thus, their mechanically identical clocks will essentially be synchronized. Over this short distance, the light signal that the engineer and the platform observer see is approximately instantaneous so that the time t she measures is essentially the time for the sound wave to travel the length L to reach her ear. When she hears the whistle sound she stops her clock and immediately 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 speed of the sound wave and the speed of the train are so much slower than the speed of light, the Special Relativistic (STR) effects of time dilation and length contraction are negligible, and will thus have little to no impact on the time interval measurement. The gamma factor cannot dilate the time interval enough or contract the length enough to create the illusion of a resting reference frame in the presence of a sound wave event. 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 disengaged from the medium (still air). This should lead to, approximately, identical time interval measurements by the observers in each reference frame. This disengagement mechanically permits the air molecules to freely flow between the reference frames which are moving relative to one another. These air molecules easily pass through the “conceptual walls“ of the reference frames, like the ghostly spirits in a haunted house. 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. As the train engine and the caboose move through space they form a tandem, with each car remaining at a fixed distance apart no matter whether the train is in motion, or at rest. An important premise of this experiment is that the sound wave travels between these two endpoints of the train, or alternatively, along the length L. Each observer takes the length L from the train specifications, it is measured when the train is at rest by the traditional units of measurement. Additionally, each observer knows the accepted speed of sound in still air. So, all the variable values are available to the observer within each reference frame. To reflect the conditions under which the caboose and sound wave will meet somewhere between the endpoints of L then the following equation can be set up: ♦ L = ct + vt Certainly, they have measured the same interval of time t in both reference frames. The STR does not account for any time dilation or length contraction at the slow speeds involved here. The observer in each reference frame retrieves the length L from the train specifications. The speed of sound c is assumed to be constant or the same for both observers. Thusly, the formula can be solved for v the velocity of the train as seen from either reference frame: ♦ L = t(c + v) ♦ v = [L / t] – c A similar argument can be made for the case when the train is moving in the reverse direction, the sound wave is then overtaking the caboose, that is, the sound wave will catch up to the caboose somewhere beyond the caboose’s initial position: ♦ L + vt = ct ♦ L = ct – vt ♦ v = c – [L / t] The departure and arrival events of the sound wave occur at the same places and at the same times (invariance of coincidence) in space, and is mathematically observable in each reference frame. The above expression contradicts the Newtonian and Einsteinian principle of relativity in that although the two reference frames are moving relative to each other, this experiment allows each observer to use one and the same formula to find the velocity of the train as seen from either reference frame. This results in not needing the addition of velocities from the Galilean transformation between references frames when sound waves are used to investigate the motion of material objects. So, I hypothesize that a new form of motion unveils its mysteries, it is neither absolute motion, nor absolute rest. An intermediary motion of material objects can now be defined, as they travel through the space of our everyday realities.
  15. 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.
  16. In the 1632 book entitled Dialogue Concerning the Two Chief World Systems by Galileo Galilei (translated by Stillman Drake), he presented his historically important ship thought experiment: “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 a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin……When you have observed all these things carefully (though doubtless when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, 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 whether the ship was moving or standing still …..The cause of all these correspondences of effects is the fact that the ship’s motion is common to all the things in it, and to the air also. 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 effects noted.” This paper will attempt to make a mathematical statement that expresses the differences in time measurements that would result from conducting this thought experiment in the two scenarios presented by Galileo. Consider two observers aboard a Great Lakes tanker traveling in a straight line on an inland portion of a placid river. The ship proceeds at the constant velocity, v, relative to the nearby riverbank. It is a windless day, so that the air/medium is also at rest relative to the moving tanker. On a line parallel to the ship’s direction of travel one observer sits at the rearward end of a lower cabin of length L, and the other observer sits at the frontward end of the same cabin. These two observers thus form a tandem at the fixed distance L apart which they maintain whether the ship is in motion or at rest. The windows and doors of this cabin below decks are closed, so that the air molecules contained within it share in the motion of the ship. The rearward observer is holding a heavy-duty flashlight and a clock, the forward observer has only a sailor’s whistle. They sit facing each other, then, she begins their thought experiment. She flashes the light towards (horizontally and parallel to the ship’s direction of motion) the other observer, and starts her clock at the same moment. When the other ship observer sees the flash of light he blows his whistle back towards her. When the sound wave of his high-pitched whistle reaches her, she stops her clock. The light signal is effectively instantaneous over this short distance, so the duration of time she will measure is for the sound wave to travel at the constant velocity c along the length L to her ear. I will use the symbol c as the velocity of sound, as it is often given in many scientific reference texts. Although this symbol is more often associated with the speed of light, the symbol represents a shared characteristic of waves in that both wave velocities are independent of the velocity of the source of the wave. All observers will see the wave traveling at the same speed, although the air molecules may alter that speed after the sound wave has begun its flight. The speed of sound c is constant in that the emitter does not alter the velocity of the sound wave as a consequence of the emitter‘s motion. She would then calculate the speed of the sound wave, following a fundamental equation of motion, velocity = distance / time, as: ce = L / te The value, te, is the time measured for the sound wave to reach her ear while she is inside the enclosed compartment. In the enclosed cabin the apparent distance the sound wave travels is equal to L. The air / medium matches the velocity of the ship. Next, the two ship observers clamber up to the broad flat main deck, and take their same positions, oriented similarly on a line parallel to the ship‘s motion. They are also seated the same distance L apart. She begins the same experiment that they performed earlier, but now they are exposed to the stationary outside air with the ship moving through the air molecules at the constant velocity, v. She once again flashes the light signal, and at the same moment starts her clock. He blows his whistle once again when he sees the signal, then she measures the time for the sound wave to reach her ear. Once again, using a fundamental equation of motion, she calculates the speed of the sound wave as: cm = L / tm, The value, tm , is the time measured for the sound wave to reach her ear as she sits on the main deck of the ship. On the main deck, the apparent distance the sound wave travels once again is L. The air / medium is at rest relative to the ship. I make the proposition, following Galileo, that ce does not equal cm due to the differing natures of the locations where these two experiments are to take place. In both cases the ship travels forward to meet the sound wave as the wave makes its rearward flight once it is emitted from the source. The velocity for the air / medium is different for the two cases. She might be led to conclude that she has measured two different values for the speed of sound, c. Actually, however, there is a difference between measuring the time within the enclosed compartment where the air molecules have the velocity, v, of the ship relative to the riverbank; and measuring the time on the main deck where the air molecules have a velocity of zero with respect to the ship and riverbank. In the enclosed cabin case, due to the forward velocity of the air molecules matching the ship‘s velocity, the velocity of the air molecules have slowed the sound wave so that it will cover a shortened distance at a lower speed. The time value measured should as a result be as if the ship were at rest. Alternatively, in the open air main deck case, the distance the sound wave travels is also less than L due to the ship’s forward motion. The stationary air molecules, in contrast, have zero velocity as the ship plows through them at the velocity v. The time value measured should be less than if the ship were at rest. Thus the times should be measurably different for the two cases I have presented here. This difference results from the idea that the air molecules in the enclosed cabin have a velocity that is in the opposite direction of the sound wave, the wave is slowed by the contrary motion of this conceptual wind (akin to a Doppler wind): [c - v] = [L - vt] / t c = [(L - vt) / t] + [v / t] c = [L / t] te = [L / c] The sound wave flight time will appear to the ship observer as though the medium, and the ship, were at rest. In the open still air case, the air molecules do not add or subtract from the velocity of the sound wave. The air molecules have been unlinked from the motion of the ship; they are at rest relative to the velocity of the ship: c = [(L - vt) / t] ct + vt = L tm = [L / (c + v)] In this second case the sound wave velocity is unaffected by the motion of the ship, the ship simply moves toward the emitted sound wave, with the wave speed unaltered by the zero air molecules speed. As a consequence, the ship observer measures a shorter time of travel for the sound wave than if the ship were at rest. Although the two thought experiments take place on a single ship traveling at a single velocity, the sound wave passing through the air molecules along the same distance L manifests two different results. In the cabin below decks the air molecules have the velocity of the ship; they are at rest in the reference frame attached to the ship, but in motion in the reference frame attached to the riverbank. On the main deck, in the open still air, the air molecules have a velocity of zero; they are at rest in the reference frame attached to the riverbank, but are in motion in the reference frame attached to the ship. This, I posit, leads to the different results that would be measured. Thus, mathematical distinctions can arise and be measured in terms of the time for a sound wave to travel through air, a distance L on a moving ship. There is a difference between doing this measurement in an enclosed cabin below decks, as opposed to doing this same measurement on the main deck in the open air. Once the sound wave is in flight, its velocity can be altered by the velocity of the air / medium freely-flowing between reference frames. These alterations can be approximately calculated by this thought experiment.
  17. http://cs.astronomy.com/asy/general_discussion/f/27/t/55764.aspx?page=2#507568 Well, you have inspired a new thought experiment in my brain. Corresponding with you is helping to focus my thoughts. So, one of the main ideas of my hypothesis is that the source and the receiver of the waves, light or sound, are paired in a tandem such that the source and receiver are moving in the same direction, at the same constant velocity, v. I am trying to exploit this “tandemness” to analyze the motion of material objects through space. Say, for instance that two spaceships are traveling through space in a tandem like I mentioned before. They each have the same constant velocity, v, and they are some distance, L, apart. The source is in the rear position and the receiver is in the front position, related to the tandem‘s direction of travel. There is an observer on each spaceship, with various electronic instruments onboard. On a nearby planet there is an observer that can view the two spaceships because they are within the sighting range of his telescope. The planet is at rest relative to the spaceship tandem, but it is orbiting, along with the spaceships, around some galactic “zero point”. This motion should have minimal effect on this experiment (“local” vs. “universal“). I will refer to one spaceship of the tandem as the source, and I will refer to the other spaceship as the receiver. If the source emits a pulse of light towards the receiver, there will be no Doppler effect, it is essentially zero. This is because the distance between the spaceships does not increase or decrease. The light waves are compressed together at the moving source, but are then stretched out, as you mention, at the receiver by an equal amount because each spaceship has the same velocity, v. Thus although the spaceships are in motion, there is no change in the frequency of the light that arrives at the receiver. This would also be the case for sound waves. The spaceships in tandem could not use Doppler to detect or distinguish if they are in motion, or at rest, in space. The spaceship observers would conclude, by a frequency measurement (the number of waves per second will be the same as if the tandem were at rest), that the light pulse has traveled the distance, L, and thus they are at rest. This goes along with the “enclosed compartment” you spoke of. However, the planet observer would view the spaceships flying across the night sky. Thus, he would see the light pulse have to travel by some increased distance, such as L + _ because of the forward velocity of the spaceship tandem. So the spaceship observers could say they were at rest, despite the roar of their warp drive engines. By Einstein, their units of length measurement have contracted, creating, for them, the illusion of being at rest. I feel this illusion is just a physics trick of compressing and stretching waves, a trick that is elevated to a scientific principle (Relativity). The planet observer on the other hand, sees the light pulse travel between the spaceships, as well as their forward motion. All these observers experience different philosophical realities in their own reference frames, which Einstein tries to resolve by Lorentz transformations and bending space-time. I think we should be able to find formulas that better reflect our experience of the universe, and the motion of material objects through space.
  18. http://cs.astronomy.com/asy/general_discussion/f/27/t/55764.aspx?page=2#507568 Thank you Gerry, for creating this thought experiment. It’s kind of like having a puzzle to solve. Trying to see which pieces fit and which don’t. Even though I might answer as though I might know something I could quite possibly be wrong on some points, so please don’t take offense at me or my ignorance. So here goes. Two spaceships are traveling, one behind the other, each at the same constant velocity such that their distances apart remain the same. The rear spaceship sends signals to the spaceship in front. The two spaceships notice no doppler affect in the signals because they are in sync with each other time wise. If they are both traveling through space/time in tandem, at the same speed, then their time dilation is also the same, and so both of their clocks are running at the same speed, and the signal would then be in sync with both. That is how I see it, which I think is in agreement with your statements. “The spaceships in tandem could not use Doppler to detect or distinguish if they are in motion, or at rest, in space.” Yes, they could not use their own signal to determine motion in regards to each other, as there would not be any doppler affect in the signal. “So the spaceship observers could say they were at rest, despite the roar of their warp drive engines.” They could only say that they are at rest “relative to each other,” but this does not mean that they could automatically conclude that they are at complete rest in space/time. To make a determination that they are at rest, or in motion, in regards to other objects in space/time, they would have to take other measurements outside of their frame of reference. “On a nearby planet there is an observer that can view the two spaceships because they are within the sighting range of his telescope. The planet is at rest relative to the spaceship tandem...it is orbiting, along with the spaceships, around some galactic “zero point”. ... However, the planet observer would view the spaceships flying across the night sky. Thus, he would see the light pulse have to travel by some increased distance, such as L + _ because of the forward velocity of the spaceship tandem.” I may be missing some aspect of this thought experiment, but from the above quotes, I am getting a conflicting image in my mind. If the planetary observer is at rest relative to the spaceships, then the spaceships would not be moving across the sky. They would appear fixed. If there is no motion between the planetary observer and the spaceships then he would see no doppler affect, and he would conclude that the spaceships were getting neither farther or closer to him. However let us conclude that the spaceships are in motion compared to the planetary observer. “...the planet observer would view the spaceships flying across the night sky. Thus, he would see the light pulse have to travel by some increased distance, such as L + _ because of the forward velocity of the spaceship tandem.” Yes, he would see a doppler affect in their signals. “The planet observer on the other hand, sees the light pulse travel between the spaceships, as well as their forward motion. All these observers experience different philosophical realities in their own reference frames, which Einstein tries to resolve by Lorentz transformations and bending space-time.” If the observer is in motion in regards to the spaceships, then the observer will see a doppler affect from any signals coming from the spaceships. If the spaceships could measure signals coming from the planet, then they too would see a doppler affect in the signals from the planet. They would each be experiencing different realities because they are in different reference frames. Light is known to travel at the same speed for all frames of reference, so what must change then for these different frames of reference? Time flow must change. How is this manifested between different frames of reference in regards to light? Light waves must show a compression or elongation in regards to different frames of reference. “By Einstein, their units of length measurement have contracted, creating, for them, the illusion of being at rest. I feel this illusion is just a physics trick of compressing and stretching waves, a trick that is elevated to a scientific principle (Relativity).” This length contraction is not measurable to a single frame of reference, just as a slow down in time flow rate is not detectable to a single frame of reference. The doppler affect of light is not measurable to a single frame of reference, which is why the MM experiment did not work. In a single frame of reference, you only have one time flow rate, and everything within that framework will always appear normal to the observer in that frame. The only way to notice differences is to compare your frame of reference with a different one. You can call Relativity a physics trick or an illusion, and you may be right. However the formulas do work, and at particle accelerators these affects do seem to actually happen. I will say that I don’t think everything is quite as relative as they say. In most thought experiments regarding spaceships, the universe itself is pretty much ignored. They don’t look at the stars, galaxies, or the CMB which is everywhere. They pretend that all motion is relative only to other objects. For instance, a spaceship fires it’s rockets and is traveling through the universe. But some say that you could just as easily say that the rocket ship is stationary, and that the universe started moving past the spaceship. I would disagree with that. Why? Stand up and spin around. Did you spin, or did you make the entire universe circle about you? Did you make distant stars travel around you at faster than light? But matter can’t travel at faster than light, so it must have been that it was just you that spun around. Those rocket engines on the spaceship did not move the universe, but only the little ship that owned them. Time dilation therefore cannot also be thrown around with impunity. It affects only objects that are in motion through space/time. Relativity has its limits. I think that finding out what those limits are is what you’re concerned with. Thanks again.
  19. Sorry SAAC for not seeing your comment. I am still working through my ideas an I was surprised by any comment!!! To try to answer your question, the transfer of momentum I am speaking of is like from the throwing arm of the person on the train that I mention in the blog entry, the arm velocity adds to the train velocity; or the air molecules within a moving train car which then adds to or subtracts from the speed of sound when it is emitted from a source fixed to the wall of the train car. So a person on the enclosed train car will travel a shorter distance in a longer time, or a longer distance in a shorter time. The rider on the train will not notice any chage from a measurement taken at rest. But by simply opening the window,so the air/medium is disconnected from the motion of the train car, then the air is at rest while the train moves through it, which makes this experiment put the principle of relativity to the test. The air molecules bumping into each other transfers momentum and carry the sound wave slower or faster in the process. This makes the train car appear to be at rest when the train is obviously in motion. Thnx for you comment. Conservation of momentum is an important part of Einstein theory. A woman named Noether wrote about momentum.
  20. 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.
  21. 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.
  22. http://chandra.si.edu/photo/2003/perseus/ I have recently learned about the concept that sound travels through Space. At Harvard’s Chandra X-Ray Observatory they found that the collapse of a Black Hole causes sound waves that travel through interstellar space. Empty space is not a pure vacuum; it has got stuff in it! There is cosmic dust, high-energy particles and magnetic fields in the so-called vacuum of space; that can be detected as evidence of sound waves across thousands of light years of space by Earth instruments. This is evidence of violent space events, such as the collapse of Black Holes. The frequency of the waves detected translate to a B-flat that registers well below the level of human hearing. It’s more a single constant tone rather than a melodious song; but it is far more than the silence of a vacuum as we had formerly thought. A sonic anemometer, or a Pitot tube for Lord Vader’s Death Star may be on the technological horizon. If there is a medium, then my thought experiment becomes plausible. For that matter, any device that is dependent on airflow measurements will become mechanically useful. ll objects that move through a medium, such as air or water, drags a thin layer of the medium along with it as it moves through the medium. From a planet down to a golf ball, hydrostatic pressure causes this anti-aerodynamical layer of medium to stick to the surface of any object in flight. But when the object is far away from any other large object the influence of this thin layer is minimized (such as two objects moving in tandem through space, but at some distance, L, apart). On a day with no interstellar wind a starcruiser travels through the galaxy at some fraction of the speed of light (it is undoubtedly more than one Mach). There are two devices attached to the outer shell of this one kilometer long spacecraft; at the front-end is a sound emitter and at the backend of the spacecraft is an ultra sensitive microphone. Since the air above the thin hydrostatic pressure layer is disconnected from the spacecraft, then the formulas from my thought experiment can be used as a means of determining the velocity of the spacecraft anywhere in interstellar space.
  23. 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.
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