Cosmic Adventure 5.10 Length Contraction on the Move in Visonics

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Cosmic Adventure 5.10

MEASURING A MOVING LENGTH IN VISONICS


Clock moving on the x-axis

The visonic theory of light does not involve coordinate system transformations because it is a direct study of the effects of light on observed objects. So a single system is employed - it involves only an observer and an object moving along a common x-axis. This object is preferably a clock that can made to move with a constant velocity.

0 P


When a clock is on the move, it is carrying out two kinds of motion at the same time.

1. Rectilinear motion along the x-axis, generating the sense of spatial motion.

2. The hand rotates on the clock face, generating the sense of change deemed to be in the time domain. Rectilinear Motion


Observer and Runaway Object

To start with, we have two atomic clocks perfectly and locally synchronized. One is used by the observer and the other works as the runaway object.

Clock A[Observer]

Clock B[Moving object]


At the starting time 𝑡0 = 0, all the clocks decked at O, A, and B are perfectly synchronized and moved into position.

A B𝑙0𝑠

𝑡0 = 0 𝑡0 = 0 𝑡0 = 0

O

Synchronized Clocks


The ruler is set into motion instantly into constant speed 𝑣, carrying with it the clocks A and B.

A B𝑙0𝑠 = 0𝑣

𝑡0 = 0 𝑡0 = 0 𝑡0 = 0

O

Ruler on the move


❶ We first select to start at moment 𝑡0 = 0. Clock O remains stationary with the observer; clock B and C move along with the ruler at speed 𝑣.

A B

𝑙0𝑠 = 0

𝑣

𝑡0 = 0 𝑡0 = 0 𝑡0 = 0

O


❷ At the moment, clock B emits an image towards the observer. This is an image of B with fixed time 𝑡0 = 0. All the real clocks keep on ticking and the ruler keeps on moving.

A B

𝑙0𝑠

𝑣

𝑡𝑖𝑚𝑒 = 0 𝑡𝑖𝑚𝑒 = 0 𝑡𝑖𝑚𝑒 = 0

O

Image of B

𝑡𝑖𝑚𝑒 = 0


❸

A B

𝑙0𝑠

𝑣O

𝑇𝑖𝑚𝑒 = 𝑡0

Image of B

This is now the new situation: i. The image of B is fleeting towards A;ii. The clocks keep on ticking;iii. Clocks A and B are shifting to the right.


❹

A B

𝑙0𝑠

𝑣


O


Image of B

Finally, the image of B reaches end A at time = 𝑡1 as registered by the real clocks. Remembering that the image of B is still registering 𝑡0 because it is an image of clock B at 𝑡0.

𝑇𝑖𝑚𝑒 = 𝑡1𝑇𝑖𝑚𝑒 = 𝑡1


❺

A B

𝑠

𝑣O

When the image of B reaches A at time 𝑡1after covering a distance of 𝑠2 = 𝑐∆𝑡1in duration ∆𝑡, A and B should have moved by 𝑠1 = 𝑣∆𝑡1.

𝑠1= 𝑣𝑡1

𝑠2= 𝑐𝑡1

𝑙0

𝑠1= 𝑣𝑡1


❻

A B

𝑠

𝑣O

𝑠2 = 𝑐𝑡1is the length covered by the image of B so as to reach the end A which is now shifted by 𝑠1 = 𝑣∆𝑡1. So the sum of 𝑠1and 𝑠2 should be equal to 𝑙0.

𝑠1= 𝑣∆𝑡

𝑠2= 𝑐∆𝑡

𝑙0

𝑙0


❼

A B

𝑠

𝑣O

From this point on, the current images of A and B should travel together to the observer. This later trip can be ignored because they reach O at the same time. The item to be noted is 𝑠2because it is the length observed and can be rewritten as 𝑙.

𝑙0

Image of B

Image of A 𝑠2 → 𝑙 = 𝑐∆𝑡


Formulation

Original length is 𝑙0: 𝑙0 = 𝑠1 + 𝑠2= 𝑐∆𝑡 + 𝑣∆𝑡= 𝑐 + 𝑣 ∆𝑡

Since ∆𝑡 = 𝑙/𝑐:

𝑙0 =𝑐 + 𝑣 𝑙

𝑐

= 1 +𝑣

𝑐𝑙

A B

𝑣

𝑙0

𝑠2 → 𝑙 = 𝑐∆𝑡 𝑠1


Relationship between the Lengths

Interchanging: 1 +𝑣

𝑐𝑙 = 𝑙0

The apparent length 𝑙 thus appears in the equation as:

𝑙 =𝑙0

1 +𝑣𝑐

Since (1 + 𝑣/𝑐) > 1, 𝑙 is shorter than 𝑙0.


Obviously, what the observer sees is the image of the real ruler. It is shorter as a result of the combination of the speed of the ruler and the speed of light in carrying the image. If we realize that the image is made up of photons, then it is also physically real, though the timing on it is fixed.

A B𝑣

O

𝑙0

Contracted image of ruler

Real Image

𝑙

𝑙 =𝑙0

1 +𝑣𝑐


Illusion or True Effect?

In visonics, this is the illusion of length shortening. It is the image that is shortened.

In relativity, it is called ‘length contraction’ and it is a real effect.

This is not true because the ruler is keeping its true length all the time.


To be continued in Cosmic Adventure 5.11

VELOCITY IN RELATIVITY & VISONICS

Science

Cosmic Adventure 5.10 Length Contraction on the Move in Visonics