There is no length contraction when object is at rest, but time difference happens.

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THE PERCEPTION
OF A LONG IMAGE
AT REST
Cosmic Adventure 5.9

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Looking at a Ruler in Olden Days
We are looking at a ruler at a distance.
In olden days when light speed is not
considered, we could see the ruler in its
entirety at any time. But now a finite
light speed has to be considered, the
situation is slightly different.

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A B
Continuous chain of emitted images from B
Continuous Emission or Reflection from Ruler
In taking the speed of light into consideration, we must first recognize the
fact that continuous emission from the body of the ruler happens all the
time.
Continuous chain of
emitted images from A

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A B
Images from B
Only simultaneous images become Visual
But in actual observations, only those images which reach the eye
simultaneously will be visually perceivable.
Images from A

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So the sighting of a long object relies only on those images which reach
the eye at the same time (simultaneously) will be investigated. This kind of
simultaneity is denied by the Theory of Relativity.
A B
Concurrent images that form
the whole image of the ruler
Simultaneous Sighting
B
A

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Ruler at Rest
In the case of studying a length which is not moving, we start with a
surveyor looking at a stationary ruler of length 𝑙0 at a distance 𝑠 through
a telescope.
A B
𝑙0
𝑠

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Vison in classical optics
The visual appearance of an
object is determined by the
light from all points on the
objects that arrives
simultaneously at where the
eye is.

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In all scales
It takes place in all scales of
material bodies or
environment, from a microbe
to a galaxy.

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Images of Different Times
To have a visual image of the entire ruler, both images of ends A and B
have to arrive at the observer simultaneously.
A B
BA

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Images of Different Times
This image of B will covered the distance 𝐿0/𝑐 in time 𝑡0.
B
Earlier image of B
B
A
𝑡0 =
𝐿0
𝑐

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Images of Different Times
Then this image of B will travel together with an image of A together to
the Observer.
B
Earlier image of B
Image of A
B
A
𝑡0 =
𝐿0
𝑐

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End B at 𝑡1 + 𝑡2 ago
A B𝑙0
𝑡2 =
𝑙0
𝑐𝑠 = 𝑐𝑡1
End A at 𝑡1 ago
This image of B arrives at the
same time with the image of A
because it was emitted earlier
I can see the
whole image
of the ruler
Historic

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That is how we are looking at a long
object with ends of different history.
End B at
𝑡1 + 𝑡2 ago
End A at
𝑡1 ago
𝑡1 =
𝑠
𝑐
𝑡1 + 𝑡2 =
𝑠
𝑐
+
𝑙0
𝑐

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Ruler at Rest
For a rigid ruler at rest, the observer
does not see any difference in length
because the images are flowing in a
continuous stream. The old images and
new ones are in the same position. There
is only a difference in time between the
images of each end.

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Images of Different Times
If the image of end A takes time 𝑡1 to reach the surveyor, the image of B
has to take a bit longer. This longer time is 𝑡2 which takes light to go from
B to A, that is 𝑡2 = 𝑙0/𝑐.
A B𝑙0
𝑡2 =
𝑙0
𝑐𝑐𝑡1
Earlier image of B
Image of A

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𝑡1 =
𝑠
𝑐
𝑡1 + 𝑡2 =
𝑠
𝑐
+
𝑙0
𝑐
The difference in time is:
𝑡1 + 𝑡2 − 𝑡1 =
𝑠
𝑐
+
𝑙0
𝑐
−
𝑠
𝑐
=
𝒍 𝟎
𝒄
For a ruler at rest, the actual length
experiences no change under visual
observation. There is only time
difference if clocks are present.

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A Ruler in Motion
However for a ruler that is on the move
along the line of sight, the situation is
different, because the position of the
ends are changing all the time.

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MEASURING LENGTH IN MOTION
To be continued on Cosmic Adventure 5.9