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De Broglie Equation, λ = h/(mv)
Speed of light, c = f λ
and, c = 3 x 10^{8} m/s
and, h = 6.626 x 10^{-34} J.s
Therefore, the frequency associated with an object would be
Frequency, f = c/λ
or, f = cmv/h
or, f = (4.528 x 10^{41}) (mv)
Therefore, the disturbance level associated with an object would be
Disturbance level, DL = (log f) / (log 2)
or, DL = (3.322) log f
Disturbance Level of the earth
m = 5.972 x 10^{24} kg
v = 3 x 10^{4} m/s
f = 8.112 x 10^{70}
DL (earth) = 235.6
Disturbance Level of the sun
m = 1.989 x 10^{30} kg
v = 2 x 10^{5} m/s
f = 1.801 x 10^{77}
DL (sun) = 256.6
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From Wikipedia,
“Historically, the transformations were the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame.”
The null results from Michelson-Morley’s experiment in 1887 led to the belief that the speed of light is the same in all inertial frames. For example, light is observed to have the same speed, c = 3 x 10^{8}, meters/second, relative to the earth and also to the sun, even when earth is moving at a speed 3 x 10^{4} meters/second relative to the sun.
It is possible to show theoretically that the earth has a speed relative to “aether”, which is the reference frame of no inertia as represented by space. However, this speed is so small that no experiment so far has been able to measure it directly. See Michelson-Morley’s Null Result.
But the actual problem lies in combining the speeds that belong to particles, such as, light particles and the earth, which have a difference in inertia of many orders of magnitude. The vector algebra works only with particles or bodies that have inertia of similar orders of magnitude.
Lorentz transformation was an effort to resolve this anomaly, where velocities could not be simply added or subtracted per vector algebra. The following links provide the derivation of Lorentz transformation.
Reference from Yale University
The derivation of Lorentz transformation is based on the following assumptions.
Based on Michelson-Morley’s experiment, the speed of light of 3 x 10^{8} meters/second was not affected by the velocity of the earth, which is 3 x 10^{4} meters/second relative to the sun. This velocity of the earth is 1/10,000 of the speed of light. The “v/c ratios” of most material bodies in the universe are of the same order. Therefore, this assumption is good for a “v/c ratio” of 1/10,000 or less.
Lorentz transformations may not be valid for “v/c ratios” that are much greater than 1/10,000 and close to 1, as found at the sub-stomic level.
In this cosmos, each body is drifting in space under a balance of forces. These forces depend on the inertia of the body. Therefore, the inertial systems are not exactly alike, and we cannot assume the gamma factor to be the same for them.
However, this assumption is good as long as the difference in inertia among these systems is much less compared to their difference in inertia with light.
Lorentz transformations may not be valid for motion of particles with inertia much less than the inertia of earth and closer to the inertia of light, as is the case with sub-atomic particles.
Lorentz transformations are at the heart of special relativity. Therefore, these limitations apply to special relativity as well.
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“The situation grows more and more serious. Two assumptions have been tried. The first, that moving bodies carry ether along. The fact that the velocity of light does not depend on the motion of the source contradicts this assumption. The second, that there exists one distinguished coordinate system and that moving bodies do not carry the ether but travel through an ever calm ether-sea. If this is so, then the Galilean relativity principle is not valid and the speed of light cannot be the same in every coordinate system. Again we are in contradiction with experiment.”
~ Albert Einstein, Evolution of Physics by Einstein
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The null results from Michelson-Morley’s experiment in 1887 initiated a line of research that eventually led to Einstein’s theory of Special Relativity. The expected difference between the speed of light in the direction of movement through the presumed aether, and the speed at right angles, was found not to exist. The special relativity then ruled out a stationary aether.
Light seems to have both wave and particle characteristics. As a wave, light requires a medium; and as particles, light requires some system of coordination among particles. In either case, light requires some relationship within its background, which is space, even when there is no aether.
There seems to be an assumption that moving bodies travel through space without resistance. We do not see space. We can only see a body moving relative to another body. How do we know that a body is moving relative to space?
We all know about inertia. Newton defined it as follows:
“The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.”
If we postulate that inertia is the resistance of space to a moving body then a lot of observations fall into place.
We may then postulate space to be the background of no inertia in which bodies with inertia are drifting at speeds that depend on their inertia.
The difference between the speeds of light and the earth shall be constant because the difference between their inertia is constant. This explains the null result of Michelson-Morley’s experiment.
One may object to the above by saying, “The earth is orbiting the sun. Therefore, it is constantly accelerating in the radial direction towards the sun, but not in the tangential direction. So, there must be a slight difference in speed relative to light in the two directions.”
We may calculate the order of this difference as follows:
So far there has been no Michelson-Morley or another type of experiment that has the level of accuracy to detect the speed of the earth relative to “aether”, which, in this case, is space.
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Thus, the null result from Michelson-Morley’s experiment is questionable when we consider space to be that elusive aether.
This then also makes the postulates of special relativity questionable when we consider inertia to be the resistance of space to a moving body.
This then limits the validity of the theory of special relativity to the explanation of phenomena where speeds involved are much smaller compared to the speed of light.
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The above is the second “Self-Learning” Diagnostic Test for students in middle school and above
Can you find the illegible numbers represented by the *’s?
The purpose of this diagnostics is to assess the following:
Calculators are very useful. They speed up the ability to calculate. But they should augment and not replace a person’s ability to calculate mentally and on paper with pencil. The person should not get so addicted to calculators that he loses his number sense and the gut feeling when computation go wrong.
This exercise may be timed. If the student can do this exercise rapidly and accurately then his attention and self-learning potential are in good shape. No remedy is needed at this level.
If the student is unable to move beyond patterned thinking then he should review the following documents to learn that different ways of thinking are possible.
This diagnostic helps locate and fill some of the early holes in the understanding of math. Filling of such holes in a subject restores student’s eagerness to learn.
With eagerness comes the ability to self-learn.
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The above is the first “Self-Learning” Diagnostic Test for students in middle school and above
Can you compute the three addition problems above on paper with pencil?
The purpose of this diagnostics is to assess the following:
In this diagnostics, the student
This exercise may be timed. If the student can do this exercise rapidly and accurately then his attention and self-learning potential are in good shape. No remedy is needed at this level.
If the student’s focus and confidence in math needs improvement then he should practice mental addition on a gradient as follows.
It all boils down to knowing the sum of two single-digit numbers. And, for that, there are limited numbers of combinations. The rest is attention and technique.
The techniques for mental addition help develop basic number sense. The student is then able to rapidly add two numbers, while also verifying the sum at the same time. This skill is then carried forward to rest of the basic math operations. This builds up a confidence that is hard to shake.
This exercise develops the fundamental thinking skill on which subsequent math skills are built. It fills an early hole in the understanding of math.
The following document provides basic mental addition techniques and exercises. After learning these techniques, the student may develop his own techniques.
This diagnostic helps locate and fill one of the early holes in the understanding of math. Filling of such holes in a subject restores student’s eagerness to learn.
With eagerness comes the ability to self-learn.
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