Cosmic Adventure 5.3 Frames in Motion in Relativity

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FRAMES IN MOTION

Cosmic Adventure 5.3


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.


𝑥′ = 𝑥′′ + 𝑣𝑡𝑥′′ = 𝑥′ − 𝑣𝑡

The classical equations for two systems’ positions related to each other. 𝑂′′ ison the move at velocity 𝑣.

𝑠 = 𝑣𝑡 𝑥′′

𝑥′

𝑂′ 𝑃𝑂′′


𝑠 = 𝑣𝑡

0’

𝑥′

P

System 1 Primed (‘)

𝑥′′

0’’ P

System 2 Primed (‘’)

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 𝑣 which becomes their relative speed.


System x:

𝑥′ = 𝑥 − 𝑣𝑡

𝑦′ = 𝑦

𝑧′ = 𝑧

𝑡′ = 𝑡

System x’:

𝑥 = 𝑥′ + 𝑣𝑡

𝑦 = 𝑦′

𝑧 = 𝑧′

𝑡 = 𝑡′

The trouble with these equations is that the speed of light is not

considered.

No Light Involved


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:

𝛾 =1

1 −𝑣2

𝑐2

𝛾 =1

1 −𝑣2

𝑐2


𝑥′′ =𝑥′ − 𝑣𝑡

1 −𝑣2

𝑐2

𝑡′′ =𝑡′ − 𝑣𝑥′/𝑐2

1 −𝑣2

𝑐2

𝑥′ =𝑥′′ + 𝑣𝑡

1 −𝑣2

𝑐2

𝑡′ =𝑡′′ + 𝑣𝑥′′/𝑐2

1 −𝑣2

𝑐2

This Lorentz factor is the crucial element in most of equations and operations of my theory. It is mysterious and powerful.


𝑠 = 𝑣𝑡

0’

𝑥′

P

System 1 Primed (‘)

𝑥′′

0’’ P

System 2 Primed (‘’)

Two Static Reference Systems

For example, in calculating the Lorentz factor when the relative velocity is one-hundredth of that of light:

𝑣 =𝑐

100= 0.01𝑐


Examples of Valuating 𝜸 at Low Velocity

For low velocity such as

𝑣 = 0.01𝑐:

1 −𝑣2

𝑐2→ 1 −

0.012𝑐2

𝑐2

= 1 − 0.001 = 0.995

= 0.9975

𝑥′′ =𝑥′ − 0.9975𝑡

0.9975

𝑡′′ =𝑡′ − 0.9975𝑥′/𝑐2

0.9975

Since 0.9975 is close to unity, there is not much change to the equations.


Example of 𝜸 at High Velocity

For high velocity such as

𝑣 = 0.9𝑐:

1 −𝑣2

𝑐2→ 1 −

0.92𝑐2

𝑐2

= 1 − 0.81 = 0.19

= 0.4359

𝑥′′ =𝑥′ − 0.4359𝑡

0.4359

𝑡′′ =𝑡′ − 0.4359𝑥′/𝑐2

0.4359

Since 0.4359 is comparatively small, it is able to impart significant changes to the equations.


So the effects of Relativity will become noticeable at very high speed – at least somewhere close to that of light.


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.


OBJECTS IN MOTION IN VISONICS

To be continued on

Cosmic Adventure 5.4

Cosmic Adventure 5.3 Frames in Motion in Relativity

Science

Transcript of Cosmic Adventure 5.3 Frames in Motion in Relativity