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Special Relativity: Time Dilation and Length Contraction

Special Relativity: Time Dilation and Length Contraction. SPH4U. Einstein’s Postulates. All laws of physics are valid in all inertial (non-accelerated) reference frames. Einstein’s Postulates. Light travels at c = 3.0 x 10 8 m/s relative to all reference frames. Simultaneity.

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Special Relativity: Time Dilation and Length Contraction

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  1. Special Relativity: Time Dilation and Length Contraction SPH4U

  2. Einstein’s Postulates • All laws of physics are valid in all inertial (non-accelerated) reference frames.

  3. Einstein’s Postulates • Light travels at c= 3.0 x 108 m/s relative to all reference frames.

  4. Simultaneity This implies that events that are simultaneous (occurring at the same time) for one observer are not simultaneous for an observer in a different reference frame. C will see the lightning flashes at A and B at the same time. D will see the flash at B happen before the flash at A.

  5. Measurement And that observers in different reference frames measure time and length differently. One observer bounces a laser off a mirror on the ceiling. The other sees the light travelling a longer path in a longer time.

  6. Time Dilation By the Pythagorean Theorem: vt’ ct ct’

  7. Time Dilation By the Pythagorean Theorem: vt’ ct ct’

  8. Time Dilation (for an event that occurs in the non-prime reference frame) vt’ ct ct’

  9. Time Dilation dilation = expansion (for an event that occurs in the non-prime reference frame) vt’ ct ct’

  10. Minutephysics http://www.youtube.com/watch?v=ajhFNcUTJI0

  11. Gamma The factor is often written as g: Note that g is dimensionless (it has no units).

  12. Length Contraction Similarly, it can be shown that lengths parallel to the direction of motion are contracted:

  13. Muons Muons created in the upper atmosphere have a lifetime of 2.2 ms in their reference frame but reach the Earth’s surface because they see the distance to the surface as contracted and/or we see the lifetime as dilated.

  14. Example What is the apparent lifetime of a muon travelling at 0.99c?

  15. Example What is the apparent lifetime of a muon travelling at 0.99c?

  16. Example What is the apparent lifetime of a muon travelling at 0.99c?

  17. More Practice Textbook Questions • p. 573 #2, 3 • p. 576 #6, 7, 8

  18. Recommended: “Old School” Relativity http://www.scivee.tv/node/2415

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