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FRAMES IN MOTION
Cosmic Adventure 5.3
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Motion in Special Theory of Relativity
In the Special Theory of Relativity, we deal with two observers, each in his own reference system. The first observer stays in rest while the other is on the move.
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π₯β² = π₯β²β² + π£π‘π₯β²β² = π₯β² β π£π‘
The classical equations for two systemsβ positions related to each other. πβ²β² ison the move at velocity π£.
π = π£π‘ π₯β²β²
π₯β²
πβ² ππβ²β²
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π = π£π‘
0β
π₯β²
P
System 1 Primed (β)
π₯β²β²
0ββ P
System 2 Primed (ββ)
Two Static Reference Systems
We start off with two reference systems A and B which are at the same location together. They are in line with each other, but for clarity, we split them into two.
System B is moving away from the stationary system A at a speed π£ which becomes their relative speed.
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System x:
π₯β² = π₯ β π£π‘
π¦β² = π¦
π§β² = π§
π‘β² = π‘
System xβ:
π₯ = π₯β² + π£π‘
π¦ = π¦β²
π§ = π§β²
π‘ = π‘β²
The trouble with these equations is that the speed of light is not
considered.
No Light Involved
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Lorentz Factor
To change them into a form adaptable to the finite speed of light is by the method of coordinate transformation according to the postulates of Special Relativity.
This is done by introducing the Lorentz factor:
πΎ =1
1 βπ£2
π2
πΎ =1
1 βπ£2
π2
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π₯β²β² =π₯β² β π£π‘
1 βπ£2
π2
π‘β²β² =π‘β² β π£π₯β²/π2
1 βπ£2
π2
π₯β² =π₯β²β² + π£π‘
1 βπ£2
π2
π‘β² =π‘β²β² + π£π₯β²β²/π2
1 βπ£2
π2
This Lorentz factor is the crucial element in most of equations and operations of my theory. It is mysterious and powerful.
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π = π£π‘
0β
π₯β²
P
System 1 Primed (β)
π₯β²β²
0ββ P
System 2 Primed (ββ)
Two Static Reference Systems
For example, in calculating the Lorentz factor when the relative velocity is one-hundredth of that of light:
π£ =π
100= 0.01π
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Examples of Valuating πΈ at Low Velocity
For low velocity such as
π£ = 0.01π:
1 βπ£2
π2β 1 β
0.012π2
π2
= 1 β 0.001 = 0.995
= 0.9975
π₯β²β² =π₯β² β 0.9975π‘
0.9975
π‘β²β² =π‘β² β 0.9975π₯β²/π2
0.9975
Since 0.9975 is close to unity, there is not much change to the equations.
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Example of πΈ at High Velocity
For high velocity such as
π£ = 0.9π:
1 βπ£2
π2β 1 β
0.92π2
π2
= 1 β 0.81 = 0.19
= 0.4359
π₯β²β² =π₯β² β 0.4359π‘
0.4359
π‘β²β² =π‘β² β 0.4359π₯β²/π2
0.4359
Since 0.4359 is comparatively small, it is able to impart significant changes to the equations.
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So the effects of Relativity will become noticeable at very high speed β at least somewhere close to that of light.
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The origin of the equations is not clear and the mathematical operations are not that straight forward either. However the idea sounds good and innovative. So we cannot pass our judgements at this moment until we have the presentation from Angela as well.
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OBJECTS IN MOTION IN VISONICS
To be continued on
Cosmic Adventure 5.4
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