Absolute Motion vs. Relative Motion

-The first postulate of Einstein in his Special Theory of Relativity (STR) states:

“There is no experiment that can be performed in an enclosed laboratory that can detect absolute motion.”

-Certainly the idea of absolute motion is out of reach for modern scientists.  There is no way to observe an Aristotle’s grid, or Newton’s fixed stars, or the Michelson-Morley Aether; which are at rest in the Universe, and against which all Celestial motions can be defined.

-This leaves us only able to work with relative motions; that is, we can only define one object’s spatial motion in terms of another object’s spatial position.

-There are a few methods by which relative motion can be ascertained.  An observer in a car traveling down the interstate can use a stopwatch to find the time it takes to travel between two consecutive mile posts, then solve for the cars velocity relative to the road by: t = D / v.

-Or, a car traveling down the highway, whose owner is sweating the transmission fluid leak she had found that morning.  She noticed that every ten seconds a drop fell into the puddle forming beneath her stationary car.  So after traveling a while, she pulls into a rest stop to check the leak; has it increased or decreased, she asks herself.  Then she notices it is now not in a puddle, but there is some distance between the drops.  She does not think the leak has stopped, but that because of her motion at a certain velocity, this has cased the puddle not to form.   She imagines she can determine her car’s velocity relative to the road by measuring the distance between the drops: v = D / t

-As part of his daily commute, a driver on a city expressway determines that at a constant velocity relative to the road, within a preset amount of time, he can travel a certain number of miles: D = vt.

-Each of these scenarios obeys invariance, such that the motion will follow the rule that they take on the most simple form of the equations of motion in that reference frame.  However, by using sound waves, which violate Galilean invariance, a new method emerges that also determines relative motion.  This method comes from the Michelson-Morley experiment to detect the Aether.  I have used sound waves in my previous thought experiment.

-This new method does not take on the simplest form of the equations of motion (velocity, time, or position) in each reference frame.  It is identical in both relative reference frames, the one regarded at rest and the other regarded in motion.  This method can also be used to address the issues of simultaneity and clock synchronization from Einstein’s STR.

-In other words, one reference frame takes the simple form of the law, while the other reference frame has a more complicated form; and vice versa, depending on whose reference frame the event is being viewed from.  Now in my statement, the formulae are identical in both reference frames: whether both are moving; one is moving and one is at rest; or both are at rest.  The following considerations give rise to the transformation equations (neither formula makes any statement about the car's motion relative to the moon):

♦ Not t = L / c; but t₁ = [(L + vt₁) / c] = [L / (c - v)] identical from within each reference frame.                 (t₁ = t₁   key point for later) 

An Echo in the Grand Canyon

-An Echo measured at the Grand Canyon fits the formula t = [2L] / c.  But this is only valid in light of the fact that a thin layer of air molecules (atmosphere / medium) is being dragged by the surface of the Earth (like a dimpled golf  ball) as it hurtles through interstellar space.  If this layer were at rest relative to the Earth, then this would allow a new definition of relativity to emerge based on a new Echo formula:

♦ T = [(L - vt₁) / c] + [(L + vt₂) / c ] = [2Lc] / (c²-v²)

-This Echo formula is the key element of my hypothesis.  It comes from the Michelson-Morley interferometer experiment to detect the Aether.  The source of the wave and the reflection from a distant object are at rest relative to each other; but the tandem they form is in motion relative to the medium.  This is the underlying idea that I am trying to exploit in this hypothesis.

The Original Question that Began My Turbulent Journey into the Aether

My journey into the realm of Relativity (Einstein, Newton, Galileo, et. al.) began with a simple question:
Can the speed of sound, c, be substituted for speed of light, c, in the Michelson-Morley interferometer formula?

That is, T = L /(c-v) + L /(c+v). It turns out that the answer (after my online investigations) is yes. The symbol, c, is applied
to both types of waves. While c as the speed for light is 300,000 km /sec , and c as the speed for sound is approx. 300 m /sec.
Additionally, the violation of Galilean invariance by all waves leads to my use of this formula for an "echo"; not T = [2L] / c .

From this I hope to derive new definitions of absolute motion and simultaneity, with experiments using sound instead of light.
This will be contrary to Einstein's Relativity Postulates. In other words by finding time,T, by means of a single clock, then I can
algebraically rearrange the above mentioned formula to find v, the velocity or the absolute motion of an object.

http://stargazerslounge.com/blog/1308-geryllax-vus-blog/

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Galileo's Ship 1 ~ Dialogue Concerning the Two Chief World Systems

In Galileo Galilei’s book, Dialogue Concerning the Two Chief World Systems, he outlines a thought experiment that is to take place on a typical wooden ship of his time.  This experiment illustrates a principle of projectiles in motion and describes the hidden nature of forces and motion.  It introduces his principle of relativity that has come down to us as Einstein’s postulate of absolute motion from his Special Relativity Theory (STR).

Quotes from the book:

“…Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals…”

“…have the ship proceed with any speed, so long as the motion is uniform and not fluctuating this way and that.  You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still…”

“…This is why you should be below decks; for if this took place in the open air, which would not follow the course of the ship, more or less noticeable differences would be seen in some of the effects noted…”

This is the point where I am trying to drive my shoulder into.  Galileo indicates that if his ship experiment is conducted above decks, then the air would have a negligible effect on the outcome.  I think my thought experiment is trying to turn this minor observable effect into an experimentally measurable phenomenon.

In so doing, I think a new state of motion is defined.  It is not absolute motion, it is not relative motion; but is an intermediary state of motion that crosses the line of unobservable information between reference frames.

It involves the formula from the Michelson-Morley experiment to detect the aether.  By taking apart the component parts of this formula, and combining them with the results of data from experimental measurements, a new perspective of the formula can be obtained. This defines a new state of physical motion.  The speed of sound, c, is so much less than the speed of light, c; I don’t think that there will be any undue influence by Relativistic effects.

Algebra: Meeting & Overtaking

I am mainly using two algebra word problem concepts as the mathematical framework for my hypothesis: meeting and overtaking.  That is, the aft vertical pole is meeting the sound wave - air at rest, the train is moving forward; or the aft vertical pole is overtaking the sound wave - air at rest, the train is moving in reverse.

In the reference frame of the moving flatbed train car, the aft pole, the observer and her clock are either overtaking or meeting the fore pole of the train car, depending on whether the train is moving towards or away from the sound emitter.  But the aft pole and the observer will never reach the fore pole because they are moving in tandem (except in a train wreck!!!).

At the same time, on a windless day, the air molecules (medium) are in another reference frame (along with another observer and the platform), which is at rest relative to the first reference frame.  However this other observer, and the station platform, and this other reference frame are not needed for my calculations.  The idea that this other observer gets a similar result to the observer within the flatbed reference frame is what leads me to believe that I have found a new state of motion.

The arrangement of the experimental apparatus is that, affixed to the aft pole is a light emitter and a sound sensor.  There is also a single clock and a single observer seated at this position.  Affixed to the fore pole, is a light sensor and a sound emitter whose purpose is to send a sound wave back towards the original starting position back at the aft pole.

To set up the algebra word problem, I assign letters to the given knowns and unknowns.  The speed of sound is to be represented by c; the speed of the train is to be represented by v; the length of the flatbed is to be represented by L; and the time elapsed while the experiment is conducted is to be represented by t.  The next step is to find the equation expressing the relationship amongst the constants and variables.

For the equation expressing the meeting aspect of this word problem, I imagine that as the train is moving forward relative to the arrangement of the apparatus, the aft pole will meet the sound wave traveling back toward the pole through the air.  This is somewhere within the distance of the starting positions of the aft pole and sound emitter at the instant when the sound is emitted.

♦ ct = L - vt
♦ ct + vt = L
♦ t = L / (c + v)

To continue, for the equation expressing the overtaking aspect of this word problem, I imagine that as the train is going in reverse relative to the arrangement of the apparatus, the sound wave will overtake the aft pole somewhere beyond the distance that they are originally apart.   Thusly, at the same time the aft pole is moving away from the sound.

♦ ct = L + vt
♦ ct - vt = L
♦ t = L / (c - v)

Either of these two equations can be solved for v (unknown), the velocity of the train.  All the other values (knowns) can be found from the experiment.  Taken together, they are identical to the formula from the Michelson-Morley experiment to detect the aether.  So, if they are added, the resulting formula can also be solved for v:

♦ T = [L / (c + v)] + [L / (c -v)] = [2Lc] / (c²-v²)

Due to the idea that the poles are at rest relative to each other, but moving in tandem relative to the medium, creates the scenario that I can algebraically exploit to create this alternative form of echo.  Since sound waves are different from light waves, both by Einstein and by Galileo, I believe I have found a new interpretation of motion.

Caboose 1: The Solution

Suppose a long train with a caboose travels down a level section of track at a constant velocity, v.  There is an observer in the caboose and an engineer in the engine car.  It is a windless day.  This observer may ask: What is the speed of the train relative to the air, or a nearby platform (both at rest relative to train)?

She has a light source (lantern, maybe) to send a signal to the engine car and engineer. The light signal is effectively instantaneous.  He blows the whistle when he receives the signal (disregard reaction time).  If she starts the clock when she sends the light signal, then she can measure the time, t, for her to hear the returning sound (speed of sound, c) signal.

During the same time that the train is in forward motion, the whistle sound is in rearward motion.  She speculates that she will meet the sound wave somewhere within the distance, D, from the engine to the caboose.  By algebra:

♦ ct = D - vt         (t = t)

Is she correct that she can find the velocity, v, of the train?