LIGO not LEGO: Sound & Light

http://en.wikipedia.org/wiki/LIGO

The artifice underlying Einstein’s STR is the mathematical construct that the two reference frames are represented by different equations, or laws of motion; but from within a reference frame an observer cannot distinguish whether he or she is in motion or at rest, based on mathematical observations from within the reference frame.  An outside observer can make the distinction.

For sound waves, my thought experiment shows that these formulas are the same and are not the simplest form of the laws of motion.  The unassailable wall between reference frames has been breeched by my pace car experiment.  For light waves, it may be just a matter of time for this light wave from beneath its black pall; that a reference frame may regarded as at rest, when in actuality it is in motion.  But mathematical laws for bodies at rest were indistinguishable from bodies in motion  by the principles of relativity, and the construct of reference frames.  Now this dreamstate has been intruded upon by the presentation of my thought experiment.

For a sound source in motion, my thought experiment  shows the breakdown of the artifice of the principles of relativity.  The equation of motion laws have been  assailed. They no longer take their simplest form in either reference frame; neither the one regarded as at rest, nor the one regarded as in motion.  However, or a light source in motion, the artifice stands impregnable.  The Null Result of the MM experiment provides a sturdy defense.  The motion of the light source is cloaked in invisibility, hiding behind the bending of the space-time continuum; whatever that may be, mathematics or reality, mathematics is not reality.  Thus for light, can this wall of separation ever be scaled? I do not know.

In Livingston, Louisiana and Hanford, Washington, USA the Laser Interferometer Gravitational-Wave Observatory (LIGO) conducts experiments to detect gravitational waves; these waves were predicted by Einstein in his General Theory of Relativity.  They have not detected any as yet.  So I have come up with an alternative use of the facilities while they are waiting to catch a Gravitational Wave.

The facility is a multi-kilometer sized Michelson-Morley interferometer intended to measure interference from two light beams reflected by mirrors along two long enclosed arms, or corridors, perpendicular to each other.  My thought experiment will require only the single arm parallel to the earth‘s motion in its orbital path around the sun.

Instead of a light emitter at the intersection of the two arms, there is a sound cannon at this axis or origin point.  At the end of this arm is a sound sensor that activates a light emitter.  Since the air molecules are pretty much motionless in this enclosed corridor, they will follow the course of the motion of the corridor.  This is a consideration that will have an effect on the form of the law of motion of the sound pulse through the still air.  The air and corridor are motionless relative to each other in the reference frame attached to the earth.

Thus the sound cannon and the sound sensor/light emitter configuration form a tandem that are at rest relative to one another but are on the earth as it hurtles through the Cosmos at the velocity, v; a velocity, a motion, as seen by an observer at rest not on the Earth.  Essentially the roles of the light and sound have been reversed in this thought experiment.  The light receiver and a clock are moving towards the light source, creating a scenario that is similar to the pace car thought experiment.

The sound source and the light source are moving in tandem relative to Space (Aether?).  Since the experiment takes place in a closed corridor, sound will adhere to the principle of relativity as regards the air molecules;  but light has only Einstein’s accounting for this scenario of motion, since he accepts that light waves can travel where there is no medium.

This leads to a very similar scenario that involves sound waves (which violate Galilean invariance), which could be solved with a simple mechanical application.  Whereas, light solves the situation by means of the complicated application of the STR (Lorentz transformation, length contraction, and time dilation, etc.) involving the alteration of space.

As compared with sound, light, in the STR, does not adhere to this violation the same way.  With no mathematical or scientific justification, other than that the equations work.  All that is solid melts into air, as space and/or the Aether remain unexplained mysteries.

So if a similar scenario to the sound configuration/pace car is set up for light, the time for light to make its return flight will be according to Einstein t = L / c. It is only my speculation that a precise clock could be made to measure a time minutely different from t = L / c, such as t = L / (v + c).  But Einstein says this difference is impossible to access. By some transmutation of space, or the Aether, due to the velocity of the object, it cannot be measured.  His definition of Space and Reality does not allow it. because his definition of reality imagines it is not there.

A precise enough clock already exists that could measure this time difference over this long distance, between the earth in motion (velocity) to that of the earth at rest. Maybe this thought experiment would be successful.  But the null result of the MM experiment to detect the Aether wind,  and STR time dilation and length contraction denies the possibility of detecting this time difference.  The time will follow the usual law of Newton and thus be different in two reference frames moving with a constant velocity relative to each.  The Lorentz transformation and time dilation are to account for this conceptual difference.

If she starts her precise clock at the moment that she fires the sound cannon then the time for the sound pulse to travel L, is t = L / c (because the air molecules though motionless within the sealed corridor, they are moving at the same velocity of the earth).  The time for the returning light pulse , would be however, according to classical mechanics, L / (c + v) which would account for the forward motion of the earth and light receiver (through the Aether wind of MM) meeting the light pulse traveling in the opposite direction, by algebra..

If the earth were at rest, then the total time for this experiment would be T = [L/c] + [L/c]  combining the time for the sound to travel down the corridor, and the time for light to travel back along the corridor. And thus this is the total time put forward by the principle of relativity and STR.

For a wave (sound or light) violating Galilean invariance this is L / (c + v).  If a train of the same length as the LIGO observatory were traveling across the flat featureless landscape, then the sound waves traveling back towards the caboose would travel a shorter distance than L because of the train’s forward motion. On a windless day, this is because the motion of the train is disconnected from the stationary air (medium).  But in the long narrow laboratory of LIGO, there is no medium for the light to interact with, that can even remotely unmask or explain the Earth’s motion.  So, we are left only with mysteries, shadows, and suspicions.

According to classic mechanics, and the MM experiment, the total time would be T = [L/c] + [L/(c+v)]   This is a small but measurable difference according to the construction of my thought experiment.   But according to STR, time dilation and length contraction this difference vanishes.  What should arise from the motion of the earth, disappears into space-time.  Einstein’s STR attributes and conforms the difference in times due to an alteration in the fabric of space; not an alteration directly linked to, or coming out of the Earth’s velocity.

Currently there is research being done in the area of Quantum Theories which predicts that at the subatomic level, there is a violation of Lorentz invariance by electromagnetic waves.  This may provide fertile ground for the possibility of conducting some form of this thought experiment.

Pace Car 1 : Sound & Light

Theatre of Her Mind

A scene is acted out in the theatre of her mind as kilometer post after kilometer post silently count the length of her journey.  It is the principle of relativity that struts and storms across the stage.  According to which, all laws of motion take their simplest form within a single inertial reference frame when that reference frame is attached to a body.  In any other reference frame considered attached to a moving observer then there is defined a Galilean transformation which defines a mathematical relationship between the object and the observer with one or the other moving, or at rest; while the other is considered moving, or at rest. These two relative reference frames are the foundation of the Newtonian description of motion of physical objects.

She pictures herself and a compatriot traveling down a long level straight section of turnpike, on a windless day. She imagines that if she paces her friend’s auto, adjudging that she is neither gaining ground, nor losing ground, she can safely assume that both autos are traveling at the same velocity; remaining at a constant distance, L, apart as the pair rolls down the highway.  With this conclusion in mind, she can regard that the pair of autos have formed a tandem, which is open to the mathematics that was presented before.  Amidst the soybean fields along the turnpike, a football field is parallel and aligned with the roadway.  So she notices, that when he is at one goal line, she is at the other goal line, thus establishing L, their distance apart (there are many methods for establishing L)..

In the reference frame attached to the autos, the vehicles are at rest relative to one another.  Another observer is seated on a wooden bench, motionless, at rest, in a roadside rest area. In his reference frame, he sees the tandem traveling down the turnpike at the velocity, v. From his viewing position he factors in the addition of velocities that occurs in the auto reference frame.

If a projectile were launched (as from a front or rear mounted machine gun a la James Bond, addition of velocities by transfer of momentum, applies to each bullet) from either auto to the other, then the addition of velocities would be hidden and unobservable by either driver.  So if she sends her light signal to the forward auto, then he fires a single bullet back towards her auto.  The bullets velocity, as she sees it is, v = d / t with addition of velocities masking transfer of momentum.

Tokio Drift in Japan

From within the reference frame attached to the rest area, however, the observer would include this in his calculations, by the Galilean transformation.  From his vantage point, he observes that L, is the distance between the tandem autos; and during the same universal Newtonian time, t, that the pair is traveling at the velocity, v.

Then her imaginings shifts scenes.  For sound, along with no change to their vehicle speeds, the sound pulse acts as a projectile through the still air, but different.  It is in the nature of sound waves (and light waves) to violate Galilean invariance; in that the velocity of the source or receiver does not under normal measuring conditions, have an impact on the wave speed.

Thus in still air, the equation of motion would include, by algebra, the velocity of her vehicle L = ct + vt. (her vehicle has the velocity, v and the speed of sound is, c and each begins its movement at the ends of L).   This formula factors in the aspect that the auto moves forward through the still air, while at the same time, the sound pulse continues to travel at the same speed.  The auto meets the sound pulse somewhere within the distance, L.  The auto travels forward the distance vt, with v as the velocity of her auto; while at the same time the sound pulse travels rearward, the distance ct, with c as the speed of sound through the windless air. This all takes place during the same Newtonian universal time, t.

This is identical in form to the Galilean transformation as used by the rest area observer.  She has made a quantum leap across reference frames; working completely from within the reference frame attached to her vehicle.  The air (medium is motionless) resides in the rest area reference frame; it is disconnected from the autos reference frame.  However, it is somehow interacting and mixing within the two reference frames; it is interwoven in a mathematical way that is different from the rules of engagement, but forward by the principle of relativity.

Danica Patrick

So, she imagines, if she sends the light signal from her headlights forward to her compatriot’s auto and begins her clock at the same moment, then, disregarding his reaction time, he could fire a single imaginary bullet from his imaginary gun back towards her auto.  When the bullet pierces her front radiator she stops her clock.  The time she measures for the bullets airtime to arrive at her auto would be the simple Newtonian law of motion, t = L / c.  The bullet slows down or speeds up depending on the guns direction of motion, so as to appear to arrive in the same time as if it were at rest.

However, for a sound pulse this would not be the case.  The time would be t = L / (c + v) after algebraic rearrangement.  This is different from the simplest form of the Newtonian equation of motion; it can be solved for the velocity, v, the velocity of her automobile.  This is not absolute motion, nor strictly a limited relative motion, but is some kind of intermediary motion.  Peeling back and revealing a previously unobservable layer of reality.

She has found a means to determine her own velocity not just relative to her friend’s auto, which is in motion relative to the roadway, but at rest relative to her; but also she has found her velocity relative to the observer at rest.  If suddenly, by some alien magicks they find themselves on a featureless landscape, plunged into an eerie darkness, but at the same distance apart; in the dark the Newtonian or Galilean principle of relativity method, does not visually work. But, by a sonic phenomena combined with the light method I have described here, she could still find the velocity of her auto.