Inertia, Momentum and
Reference frames

I have debated what to call this section. All devices here operate by momentum, and all have a reference plane. All devices (except mine) have engineering applications, and some raise physical theory off-the-charts. The aspects of this section are pervasive in science, because "Aspects" (in general) are pervasive in science.

SAGAC9.gif, 21 kB
Rate-Gyros were conceived at the turn of the century by Sagnac (1913) and Michelson (1904) and others. I invented this rotating frame of reference. Born out of Newtonian physics, I have shown a mechanical version to demonstrate the principle in its simplist forms. It has no practical significance.

Conceder two marbles injected into frictionless coils;
BBALLBLU.GIF, 0 kB at the same time;
BBALLBLU.GIF, 0 kB traveling at the same speed;
BBALLBLU.GIF, 0 kB counterrotating to each other.

The coils are attached solidly to a rotating space craft, or to a rotating object such as the earth. The counter rotating marbles will arrive at different times when there is rotation as indicated.

Counter rotating optical beams...
But when laser light is used, traveling in fiber optic cable, or in free space using mirrors, then the measurement usually is made by phase difference. If lasers or masers are placed in the loops - and are used actively in the loops - then frequency splitting gives better resolution and sensitivity with the innate feedback characteristics.
EqnD.gif, 2 kB
Let D = Distance contained in either upper loops or lower loops.
Let C = speed of the particle in the media.
Let v = speed produced by rotation. (speed of the loops)

EqndeltaT.gif, 2 kB
Let N = Number of loops
Let R = Radius of a loop
Let C = speed of the particle in the media.
Let v = speed produced by rotation. (speed of the loops)

Equation is similar to a doppler shift with target in motion:
Totally classical.

EqnDeltaTw.gif, 2 kB
Convert to rotational motion:
Eqnda.gif, 1 kB

In practice, a craft would have three of these gyros; all orthoganal to each other.

EqnDeltaA.gif, 6 kB
Let A = total area of all the loops.

In practice, the loops are used by both beams. Counter rotating beams are in the same "channel". Also separation of loops is kept to an absolute minimum.

When I was in the Air Force we did not use Rate-Gyros; We used "position-gyros". Position-Gyros are conventional spinning wheels. They are "spun-up" and calibrated before launch. They give angular displacement from a calibrated orientation.

Rate-Gyros give the rate of change of angular displacement. A tumbling craft will give a steady value indicating radians per second. Without a good computer, they will not give you the direction that the craft is pointing - only that it is spinning. Rate gyros are wonderful for gaining immediate control of a tumbling craft. No computer, at all, is required. As long as each of the three gyros are mounted at each center of gravity axis - it is "direct-drive" to the thrusters.

A similar device, involving a rotating frame of reference, was located at the SanFransico Academy of Science: A large pendulum. (The large pendulum was the highlight of my 8th grade field trip.) Supported from high above (about 30 ft) was a heavy weight; a magnificent brass-looking ball with a small finger at the base. Very slowly the ball would move back and forth to the edge of a large marked circle on the floor. Around the circle, spaced every 10 minutes apart, were pieces of chalk. Momentum laws would keep the swing straight and true; never changing. But the earth would turn under the swing, causing each piece of chalk to be approached, closer and closer with each swing, untill eventually struck.
EqnSFpendulum.gif, 1 kB
The rate of rotation, as seen by the pendulum, depends on the latitude; being the greatest at the axial north and south poles of the earth(revolution/24hr).
I could be wrong, but if the Golden State Park in SF is at 37 degrees Lat, then the equation should be...(assuming the earth is a sphere, which it is not.)
This is known as the Coriolis effect.

Likewise, optical gyros can easily detect the rotation of the earth, depending on the latitude where they rest. A simple device with no moving parts. And as you can see, from the equation, a higher refractive index will yeld a slower media speed and a greater time difference. Otherwise the basic operation is not effected; and remains "classical".
TELESCOP.JPG, 22 kB Cartoon

Albert A. Michelson (Jewish)
1907 A. A. Michelson defined the length of the meter.

But what about lateral movement? The above two devices can reliably detect the revolving of the earth on its axis. But what about the earth traveling around the sun at 3E4 m/sec? Using the same light apparatus as Sagnac, which undeniably exhibited successful technology.

Sound technology - in every way!
The point can not be overstated:
Good, solid, undeniable, sound technology - in every way!

(Before lasers...
Sodium produces clear and pure lines from an orbital 3p to an orbital 3s.)

D is the distance between mirrors.
C is the speed of light, or speed of medium.
v is the speed of the earth, or apparatus.

EqnTT.gif, 3 kB
EqTT1.gif, 3 kB
Orthoganal path
(Depicted in green.)
"Normal" to direction of motion
"Transverse" to motion
"Lateral", "radial"

Time for a transverse direction...
Time to go out to the side mirror and back to start.

EqnTL.gif, 3 kB
EqnTL1.gif, 2 kB
EqnTL2.gif, 2 kB
Axial inline motion
(Depicted in blue.)
Time in the direction of motion

Concurrent direct path
Time Parallel to direction of motion
Longitudinal axis

Time to go up to the front mirror and back to start.

EqTR3.gif, 4 kB
EqTR4.gif, 3 kB
BANASTAR.gif, 1 kB (the Lorentz factor)
The ratio of these two times.
A profound equation!
ProfoundEquationANAM.gif, 6 kB
With only this ONE equation, it is not clear if there is a
length contraction in the direction of motion;
or, a length expansion normal to the direction of motion;
or, a time dilatation.
or, a time contraction.

Or, all of the above.

EqElipsoid.gif, 2 kB
But you can do all kinds of things with it...
Take a sphere for example...
Combine it with the Lorentz factor.
Choose a direction. Like x.

Sphere passing by at 90% the speed of light.
Left image graphed in rectilinear coordinates.
Red axis (horizontal) is the direction of travel.
Z axis (blue) cut away showing inside. Looks like a silicone implant with symmetry around the x-axis (red)

Perhaps your eyes are telling you that this is an ellipsoid. But I am telling you this is a perfect sphere. Either you should get your eyes checked or you should know where is your reference frame! You see, I am still on the sphere, where my eye balls have squeezed the same amount as the sphere. And my ruler has squeezed around too. You are somewhere else. I don't know where you are. You should come over here and look at the picture again.

Converting to polar coordinates (right hand image)... Sphere passing by at 90% the speed of light.
Ellipsoid equation converted to spherical coordinates, and graphed with a little tighter resolution. Cutaway at -70 degrees azimuth.
EqnsExpansion.gif, 5 kB
Here is another thing that you can do...
...An interesting taylar expansion - relativistic expansion of mass-energy.
Balance.jpg, 5 kB
Biological rate-gyro...
Inside your head you have yet another structure that demonstrates this principle - on a personal level. The structure has three loops orthoganal to each other. The liquid contained in each has momentum properties that stimulate hair sensors. The three loops alow an acrobatic creature to be conscious of turning and motion. A better "feel" for lateral movement (I think) is accomplished with two sensors, nether of which is placed at the center of gravity.

Our intire existence is predicated on a familiar frame of reference. Biology and evolution, have given us an inherently physical reality. This view is so vane.