1. The document describes an experiment measuring the length of a moving object using two synchronized clocks, one stationary and one moving with the object. 2. As the moving clock moves away from the stationary clock at a constant velocity, it emits an image of itself at the starting time to the observer. 3. By the time the image reaches the observer, both clocks have ticked forward in time, but the image remains fixed at the starting time. 4. Comparing the times on the clocks and the distances traveled allows calculating the observed length as contracted from the true rest length by a factor related to the object's velocity.

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Cosmic Adventure 5.10
MEASURING A MOVING LENGTH IN VISONICS

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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

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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

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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]

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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

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The ruler is set into motion instantly into constant speed 𝑣, carrying with
it the clocks A and B.
A B𝑙0𝑠 = 0
𝑣
𝑡0 = 0 𝑡0 = 0 𝑡0 = 0
O
Ruler on the move

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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
𝑙0
𝑠 = 0
𝑣
𝑡0 = 0 𝑡0 = 0 𝑡0 = 0
O

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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
𝑙0
𝑠
𝑣
𝑡𝑖𝑚𝑒 = 0 𝑡𝑖𝑚𝑒 = 0 𝑡𝑖𝑚𝑒 = 0
O
Image of B
𝑡𝑖𝑚𝑒 = 0

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❸
A B
𝑙0
𝑠
𝑣
O
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.

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❹
A B
𝑙0
𝑠
𝑣
𝑇𝑖𝑚𝑒 = 𝑡1
O
𝑇𝑖𝑚𝑒 = 𝑡0
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

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❺
A B
𝑠
𝑣
O
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

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❻
A B
𝑠
𝑣
O
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

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❼
A B
𝑠
𝑣
O
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 𝑠2
because it is the length observed and can be rewritten as 𝑙.
𝑙0
Image of B
Image of A 𝑠2 → 𝑙 = 𝑐∆𝑡

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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
𝑐
𝑙
A B
𝑣
𝑙0
𝑠2 → 𝑙 = 𝑐∆𝑡 𝑠1

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Relationship between the Lengths
Interchanging: 1 +
𝑣
𝑐
𝑙 = 𝑙0
The apparent length 𝑙 thus appears in the
equation as:
𝑙 =
𝑙0
1 +
𝑣
𝑐
Since (1 + 𝑣/𝑐) > 1, 𝑙 is shorter than 𝑙0.

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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 B
𝑣
O
𝑙0
Contracted image of ruler
Real Image
𝑙
𝑙 =
𝑙0
1 +
𝑣
𝑐

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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.

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To be continued in Cosmic Adventure 5.11
VELOCITY IN RELATIVITY & VISONICS