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VISONIC TIME DILATION – OBJECT IN MOTION

Cosmic Adventure 5.8

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Though the situation is different from that of the object at rest, the results are the same due to the constancy of light speed.

Same as Clock at Rest

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𝒄 independent of Source

The speed of light is a constant in the universe. This magnitude is independent of the emitting source or the reflecting object. This property is obvious in the following example.

𝑣 = 100 km/sec

𝑣 = 100,000 km/sec

𝑣 = 0 km/sec

𝑐

𝑐

𝑐

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A B

Real clock A

Actual time Actual time

Clock Image Reading on Leaving Clock B

To start with, we have two clocks that are well synchronized and are placed in the same spot to start with. Both clocks register the same time 𝑡 = 0.

Real clock B

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A B

Image of B

𝑐

Real clock A Real clock B

Actual time Actual timeFixed time

Clock Image Reading on Leaving Clock B

As clock B leaves, it still keep on sending its images back to A. There is an image at every instant and we choose only one of them for demonstration purposes. Here we choose one sent at time = ∆𝑡 1. The clocks are still ticking normally, but the image only shows a fixed time of the moment.

𝑣

𝑥1 = 𝑣∆𝑡 1

∆𝑡 1

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Light Speed Constant

As discussed, no matter how fast clock B will move, the speed of the image emitted will not be affected. It is 𝑐all the time.

So this situation is the same when clock B is stationary in. Both being stationary or moving will have no affect the speed of light.

Speed of image of B

𝑐

Speed of real clock B

𝑣

The speed of clock B does not have any effect on the speed of its light image which is always c

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𝑣

A

Real clock A Real clock B

Situation 1

At time ∆t = 0, both clocks are at the starting position A. Clock A is at rest while clock be is moving at velocity 𝑣.

Distance 𝑥 = 0Time ∆t = 0

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𝑣

A B

Real clock A Real clock B

Situation 2

After time = ∆𝑡1, clock B has travelled to B, covering a distance 𝑥1 = 𝑣∆𝑡1. Both clocks now register the same time, that is, ∆𝑡1.

𝑥1 = 𝑣∆𝑡1

∆𝑡 1

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𝑣

A B

Real clock A Real clock BImage

𝑐

Time of image B Reading ∆𝑡1

Situation 3 Image Emission

At this moment of time = ∆𝑡1, clock B sends an image (registering time ∆𝑡1) towards clock A, while keeps on traveling away from B.

Clock B goes on

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𝑣

A B C

Real clock A Real clock BImage

𝑐

Situation 4

This image takes time ∆𝑡2 to reach A at speed c. At the same time clock B has reached C with BC= ∆𝑥1= 𝑣∆𝑡2. The time is then ∆𝑡3 = ∆𝑡1 + ∆𝑡2

𝑥1 = 𝑣∆𝑡1 = 𝑐∆𝑡2 ∆𝑥1= 𝑣∆𝑡2

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𝑣

A B𝑥1 = 𝑣∆𝑡1 = 𝑐∆𝑡2

Image

C

𝑐

Real clock A Real clock B

Actual time ∆𝑡3= ∆𝑡1 + ∆𝑡2

Apparent time= ∆𝑡1

Situation 5

Actual time ∆𝑡3= ∆𝑡1 + ∆𝑡2

∆𝑥 = 𝑣∆𝑡2= 𝑣∆𝑡1 × 𝑣/𝑐

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𝑣

A BApparent position𝑥1 = 𝑣∆𝑡1 = 𝑐∆𝑡2

Image

C

𝑐

Real clock A Real clock B

Actual time ∆𝑡3= ∆𝑡1 + ∆𝑡2

Apparent time= ∆𝑡1

Final Situation 6

Actual time ∆𝑡3= ∆𝑡1 + ∆𝑡2

∆𝑥 = 𝑣∆𝑡2= 𝑣∆𝑡1 × 𝑣/𝑐

Actual position𝑥3 = 𝑣∆𝑡1 + 𝑣∆𝑡2

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Observation 1 – Actual Position & Time

The actual position of clock B is :

𝑥3 = 𝑥1 + ∆𝑥

= 𝑣∆𝑡1 + 𝑣∆𝑡1𝑣/𝑐

= 1 +𝑣

𝑐𝑣∆𝑡1

= 1 +𝑣

𝑐𝑥1

The actual time of B is (same as A):

∆𝑡3 = ∆𝑡1 + ∆𝑡2

= 1 +𝑣

𝑐∆𝑡1

Real clock A

𝑣

Real clock B

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Observation 2 – Apparent Position & Time

The apparent position of clock B is:

𝑥1 = 𝑣∆𝑡1 = 𝑐∆𝑡2

The clock reading of image B is ∆𝑡1. So the apparent time is:

∆𝑡1Image of Clock B

𝑐

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Ration of the two Times

𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑇𝑖𝑚𝑒

𝐴𝑐𝑡𝑢𝑎𝑙 𝑇𝑖𝑚𝑒

=∆𝑡1

1 +𝑣𝑐

∆𝑡1

=1

1 +𝑣𝑐

𝑐

Apparent [Image] time= ∆𝑡1

Actual [Clock A & B] time

= 1 +𝑣

𝑐∆𝑡1

𝑣

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Light Speed Constancy

This result is the same as the case where the object is at rest. It simply demonstrates the fact the speed of light is not affected by the motion of its sources.

𝑣 = 0 km/sec

𝑐

𝑣 = 1000 km/sec

𝑐

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Different between Relativity & Visonics

This phenomenon exhibits an apparent dilation of time. So it is called ‘time dilation’ in the theory of Special Relativity.

But there is a difference.

In Relativity, it is a real event. Time does slows down and leads to absurd events such as ‘twin paradox’.

In visonics, this is an optical phenomenon, just like looking at clocks on distant stars in classical physics.

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Distance Change

Though there is no difference in the change of time between the object being at rest or in motion, a change in the position of the object is involved. We have to get the change in length to see the difference.

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THE PERCEPTION OF A LONG IMAGE AT REST

To be continued on

Cosmic Adventure 5.9