The Resonance Paradox (absolute space and motion?)
I describe below a paradox arising from Albert Einsteins Theory of Special Relativity. The paradox is resolved if we assume that either the First Postulate of Special Relativity or the Lorentz Transformation for length contraction are incorrect. In either case Special Relativity Theory, although it has remarkable power, seems to be logically inconsistent. I could develop an argument to that effect elsewhere, but that is not my purpose here. It is better to build on a new theory that may well be nearer to the truth than to attempt to pull down an elegant and beautiful thought structure created by genius. I should state at the outset that the best i can hope to achieve personally, through science and philosophy, is to build a thought structure in my mind that explains everything of stuff and the stuff of everything with the least number of mysteries left over. To this end I have recently begun a study of the Wave Structure of Matter Theory, developed by Milo Wolff and others, which promises to be the simplest description of all observable phenomena. If this theory is correct then it may be possible to relate the absolute motion of matter to absolute space. My method will have two main strands: the development of a geometric and mechanical analogy of the theory (to enable a mental visualization of the wave structures) and the use of thought experiments.
Space and the Wave Structure of Matter
If space is infinite it has no boundary. If it has no boundary it cannot have a center. A center is only a kind of geometric point, so it seems unlikely to me that there is any such thing as “a geometric point in space”. When imagining an entity without boundary or center or point the concept of motion seems meaningless, for if it moves, no mark exists to show that movement. If space is infinite it cannot be in motion, for to be in motion requires a movement to another space. In my minds eye i try to move it but i cannot, it is wedged in by more of itself in all directions. It neither has space to move into or anything else to push against to produce that movement. Neither can it recede and leave nothing in its place. If space goes on forever it cant go anywhere that it isn’t already at. It has nowhere else to go. According to Wave Structure of Matter (WSM) theory, whilst space is at absolute rest in the above sense, it does support waves that give rise to all observable phenomena. All motion is therefore referred back to space. A study of the Resonance Paradox in terms of WSM may furnish the answer to the question “How can i detect motion with respect to absolute space?”
The Resonance Paradox
An experiment is performed somewhere deep in space where two rocket-ships float, docked together.
On board rocket-ship 1, a team of experimental physicists construct the following apparatus: A 1 meter steel rule is fixed at one end so that it lies lengthwise along the axis of the hull. If the free end of the rule is deflected and then released it will posses a simple harmonic motion of a certain frequency. I have described a spring steel pendulum. A second spring steel pendulum is similarly mounted but at right angles to the first. The apparatus is nicely set up so that the two pendulums oscillate with the same frequency when deflected and released together. The frequency of each pendulum will be determined by the mass and length of the steel rule. To make sure that the pendulums are oscillating in unison our physicists add a refinement. The positive terminal of a battery is connected to the fixed end of one pendulum and the negative terminal is connected to the fixed end of the other pendulum. Two electrical brushes are arranged so that they contact the free ends of each pendulum when they are at mid point in their trajectories ( when each possesses maximum kinetic energy and minimum potential energy). A light bulb is connected to the two brushes. It will be seen that the light bulb will flash in sympathy with the simple harmonic motion of the two pendulums only when they are oscillating in unison.
One of the physicists is now elected to remain on board rocket ship 1 with the apparatus and the rest of the team board rocket ship 2. They undock and the intrepid scientist on rocket ship 1 fires up his motor, accelerates to half the speed of light and then cuts his motor. His ship is now in uniform motion with respect to ship 2 at half the speed of light along the axis of one of the pendulums. He sets the two pendulums in motion. Back on rocket ship 2 the scientists turn a powerful telescope towards the light bulb on the remote ship.
What will they see?
Statement 1
According to Special Relativity Theory the experimenter riding along in Rocket Ship 1 will obtain the same result as he did when the apparatus was first set up: The pendulums will oscillate in unison and the light will flash.
Statement 2
According to Special Relativity Theory the observers that remain behind must apply the Lorentz Transformation. They will get a different result. Due to relativistic length contraction the pendulum with its axis along the direction of motion will be shorter than the pendulum at right angles to the line of motion and will therefore have a shorter period of oscillation. The pendulums will not oscillate in unison and the light will not flash.
Both statements cannot be correct so Special Relativity Theory has generated a seemingly unresolvable paradox.
One or other of the statements must be correct. Which?
I will proceed later by assuming each in turn to be correct and investigate the possible implications for each case. Before i do so i would like to preempt some questions about the experimental set up.
The apparatus described in the above thought experiment was chosen for ease of explanation. When analyzed critically we find some refinements are required. If we hold the Lorentz Transformations to be correct then both pendulums will undergo identical mass increase and be subject to identical time dilation. The length contraction will only be experienced by the pendulum in the line of motion. However, as Geoff Haselhurst pointed out "according to special relativity the pendulum at right angles will also be thinner than the other one (which is shorter). How would this affect its frequency of oscillation?"
Good question. It is possible that the restoring force (springiness) of the spring pendulum might be altered by this effect. Springiness is to do with Hooke's Law and Young's Modulus of Elasticity. The thinner pendulum will have a smaller cross sectional area which will (possibly) affect its Young's Modulus of Elasticity and therefore its behavior according to Hooke's Law. I do not know of any investigations into how Hooke's Law or Young's Modulus of Elasticity might be altered under relativistic conditions, however, it seems unlikely that they would alter in exactly the right way to compensate for the shortened pendulum. Nevertheless I can modify the experiment to allow for the possibility of this happening. See drawing below. Each pendulum is now a "rigid" bar with a lead ball on the end. The restoring force is supplied by torsional springs which share a common axis. Any change in the restoring force (springiness) due to relativistic effects would now be common to both pendulums.So...does the light flash or does it not? I invite your comments. I have not reached a conclusion as yet but i do believe that exploring the two possibilities will lead to some interesting philosophical speculation, especially in the case that length contraction is real and detectable. That is a subject for another post.
Space and the Wave Structure of Matter
If space is infinite it has no boundary. If it has no boundary it cannot have a center. A center is only a kind of geometric point, so it seems unlikely to me that there is any such thing as “a geometric point in space”. When imagining an entity without boundary or center or point the concept of motion seems meaningless, for if it moves, no mark exists to show that movement. If space is infinite it cannot be in motion, for to be in motion requires a movement to another space. In my minds eye i try to move it but i cannot, it is wedged in by more of itself in all directions. It neither has space to move into or anything else to push against to produce that movement. Neither can it recede and leave nothing in its place. If space goes on forever it cant go anywhere that it isn’t already at. It has nowhere else to go. According to Wave Structure of Matter (WSM) theory, whilst space is at absolute rest in the above sense, it does support waves that give rise to all observable phenomena. All motion is therefore referred back to space. A study of the Resonance Paradox in terms of WSM may furnish the answer to the question “How can i detect motion with respect to absolute space?”
The Resonance Paradox
An experiment is performed somewhere deep in space where two rocket-ships float, docked together.
On board rocket-ship 1, a team of experimental physicists construct the following apparatus: A 1 meter steel rule is fixed at one end so that it lies lengthwise along the axis of the hull. If the free end of the rule is deflected and then released it will posses a simple harmonic motion of a certain frequency. I have described a spring steel pendulum. A second spring steel pendulum is similarly mounted but at right angles to the first. The apparatus is nicely set up so that the two pendulums oscillate with the same frequency when deflected and released together. The frequency of each pendulum will be determined by the mass and length of the steel rule. To make sure that the pendulums are oscillating in unison our physicists add a refinement. The positive terminal of a battery is connected to the fixed end of one pendulum and the negative terminal is connected to the fixed end of the other pendulum. Two electrical brushes are arranged so that they contact the free ends of each pendulum when they are at mid point in their trajectories ( when each possesses maximum kinetic energy and minimum potential energy). A light bulb is connected to the two brushes. It will be seen that the light bulb will flash in sympathy with the simple harmonic motion of the two pendulums only when they are oscillating in unison.
One of the physicists is now elected to remain on board rocket ship 1 with the apparatus and the rest of the team board rocket ship 2. They undock and the intrepid scientist on rocket ship 1 fires up his motor, accelerates to half the speed of light and then cuts his motor. His ship is now in uniform motion with respect to ship 2 at half the speed of light along the axis of one of the pendulums. He sets the two pendulums in motion. Back on rocket ship 2 the scientists turn a powerful telescope towards the light bulb on the remote ship.
What will they see?
Statement 1
According to Special Relativity Theory the experimenter riding along in Rocket Ship 1 will obtain the same result as he did when the apparatus was first set up: The pendulums will oscillate in unison and the light will flash.
Statement 2
According to Special Relativity Theory the observers that remain behind must apply the Lorentz Transformation. They will get a different result. Due to relativistic length contraction the pendulum with its axis along the direction of motion will be shorter than the pendulum at right angles to the line of motion and will therefore have a shorter period of oscillation. The pendulums will not oscillate in unison and the light will not flash.
Both statements cannot be correct so Special Relativity Theory has generated a seemingly unresolvable paradox.
One or other of the statements must be correct. Which?
I will proceed later by assuming each in turn to be correct and investigate the possible implications for each case. Before i do so i would like to preempt some questions about the experimental set up.
The apparatus described in the above thought experiment was chosen for ease of explanation. When analyzed critically we find some refinements are required. If we hold the Lorentz Transformations to be correct then both pendulums will undergo identical mass increase and be subject to identical time dilation. The length contraction will only be experienced by the pendulum in the line of motion. However, as Geoff Haselhurst pointed out "according to special relativity the pendulum at right angles will also be thinner than the other one (which is shorter). How would this affect its frequency of oscillation?"
Good question. It is possible that the restoring force (springiness) of the spring pendulum might be altered by this effect. Springiness is to do with Hooke's Law and Young's Modulus of Elasticity. The thinner pendulum will have a smaller cross sectional area which will (possibly) affect its Young's Modulus of Elasticity and therefore its behavior according to Hooke's Law. I do not know of any investigations into how Hooke's Law or Young's Modulus of Elasticity might be altered under relativistic conditions, however, it seems unlikely that they would alter in exactly the right way to compensate for the shortened pendulum. Nevertheless I can modify the experiment to allow for the possibility of this happening. See drawing below. Each pendulum is now a "rigid" bar with a lead ball on the end. The restoring force is supplied by torsional springs which share a common axis. Any change in the restoring force (springiness) due to relativistic effects would now be common to both pendulums.So...does the light flash or does it not? I invite your comments. I have not reached a conclusion as yet but i do believe that exploring the two possibilities will lead to some interesting philosophical speculation, especially in the case that length contraction is real and detectable. That is a subject for another post.
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