Cosmic adventure 5.9 Length Contraction at Rest in Visonics
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There is no length contraction when object is at rest, but time difference happens.
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Cosmic adventure 5.9 Length Contraction at Rest in Visonics
- 1. © ABCC Australia 2015 new-physics.com THE PERCEPTION OF A LONG IMAGE AT REST Cosmic Adventure 5.9
- 2. © ABCC Australia 2015 new-physics.com 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.
- 3. © ABCC Australia 2015 new-physics.com 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
- 4. © ABCC Australia 2015 new-physics.com 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
- 5. © ABCC Australia 2015 new-physics.com 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
- 6. © ABCC Australia 2015 new-physics.com 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
- 7. © ABCC Australia 2015 new-physics.com 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.
- 8. © ABCC Australia 2015 new-physics.com In all scales It takes place in all scales of material bodies or environment, from a microbe to a galaxy.
- 9. © ABCC Australia 2015 new-physics.com 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
- 10. © ABCC Australia 2015 new-physics.com 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
- 11. © ABCC Australia 2015 new-physics.com 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
- 12. © ABCC Australia 2015 new-physics.com 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
- 13. © ABCC Australia 2015 new-physics.com 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
- 14. © ABCC Australia 2015 new-physics.com 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.
- 15. © ABCC Australia 2015 new-physics.com 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
- 16. © ABCC Australia 2015 new-physics.com 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.
- 17. © ABCC Australia 2015 new-physics.com 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.
- 18. © ABCC Australia 2015 new-physics.com MEASURING LENGTH IN MOTION To be continued on Cosmic Adventure 5.9