Special and General Theory of Relativity - Rentoria.pptx

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1. Special and General Theory of Relativity

2. explain how the special theory of relativity resolved the conflicts between Newtonian mechanics and Maxwell’s electromagnetic theory; and explain the consequences of the postulates of general relativity. 1 At the end of the lesson, you should be able to: 2

3. In 1865, James Clerk Maxwell theorized that electromagnetic field moves through space at a fixed speed. He wrote set of four equations that describe all the laws of electricity and magnetism. Upon evaluating Maxwell’s equation for the speed of light, c is equal to 2.99792458✕10​ 8 m/s. This showed that the speed of electromagnetic waves is universal. The Special Theory of Relativity

4. In 1905, Albert Einstein published his theory of special relativity to explain how motions can be compared in different inertial frames. He referred to motions between two objects as relative. The Special Theory of Relativity Albert Einstein

5. The following are the postulates of the special theory of relativity. The physical laws have the same mathematical form for all frames of reference moving at a constant velocity with respect to each other. This is also known as the principle of relativity. This suggests that there is no correct frame of reference and the laws of physics can be applied to all reference frames involved. The Special Theory of Relativity

6. The following are the postulates of the special theory of relativity. The speed of light in a vacuum is independent of the motion of its source and of the observer. The speed of light is essentially constant where c is equal 3✕10 8 m/s. The Special Theory of Relativity

7. The theory is useful only under “special” cases where motion is uniform. It is not applicable to accelerated and change-in-curvature motions. The Special Theory of Relativity

8. Space “contracts” and the time “dilates” as a consequence of relativity. The amount of length contraction and time dilation is given by the Lorentz factor , named after Hendrik Lorentz who had been exploring transformation equations. The Special Theory of Relativity Hendrik Lorentz

9. A person who is initially stationary tends to observe a slower “clock” than a person travelling at a speed of light. It is only significant when one of the objects involved travel at relativistic speed , or speed near the speed of light. This observation is referred as time dilation . A classic example of time dilation is the twin paradox. Time Dilation

10. Time Dilation Twin paradox

11. Time dilation has been established to be equal to where Δ​t is the relative time or the time observed in the other reference frame, Δ​t is the proper time of the time in observer’s own frame of reference, v is the velocity of two frames, and c is the speed of light. The denominator is equivalent to the Lorentz factor. Time Dilation

12. Suppose the traveller travelled the space at 95% the speed of light. How much time did his twin observed on Earth if upon returning, the traveller measured the journey time to be 10 years based on his clock?

13. Step 1 : Identify what is required to find in the problem. You are asked to calculate for relative time (​Δ​t) observed by the traveller’s twin on Earth. Suppose the traveller travelled the space at 95% the speed of light. How much time did his twin observed on Earth if upon returning, the traveller measured the journey time to be 10 years based on his clock?

14. Step 2 : Identify the given in the problem. The proper time and the speed of the traveller as measured by the percentage of the speed of light are given. Suppose the traveller travelled the space at 95% the speed of light. How much time did his twin observed on Earth if upon returning, the traveller measured the journey time to be 10 years based on his clock?

15. Step 3 : Write the working equation. Suppose the traveller travelled the space at 95% the speed of light. How much time did his twin observed on Earth if upon returning, the traveller measured the journey time to be 10 years based on his clock?

16. Step 4 : Substitute the given values. Suppose the traveller travelled the space at 95% the speed of light. How much time did his twin observed on Earth if upon returning, the traveller measured the journey time to be 10 years based on his clock?

17. Step 5 : Find the answer. The twin left on Earth aged 32 years, compared to the traveller that aged only 10 years. Suppose the traveller travelled the space at 95% the speed of light. How much time did his twin observed on Earth if upon returning, the traveller measured the journey time to be 10 years based on his clock?

18. The length of an object seems to contract when travelling at relativistic speeds, according to equation: where L is the relative length or the length measured by another observer, L is the proper length or the length measured by the observer on the original reference frame, v is the relative velocity of the two frames; and c is the speed of light. Length Contraction

19. A rocket is observed by a person on Earth. What is the length of the rocket as observed by the astronaut inside it if the observer on Earth sees that the rocket is 5.5 m long and it zooms in a speed of 95% that of the speed of light?

20. Step 1 : Identify what is required to find in the problem. You are asked to calculate for proper length (L) of the rocket as observed by the astronaut inside it. A rocket is observed by a person on Earth. What is the length of the rocket as observed by the astronaut inside it if the observer on Earth sees that the rocket is 5.5 m long and it zooms in a speed of 95% that of the speed of light?

21. Step 2 : Identify the given in the problem. The relative length and the speed of the traveller as measured by the percentage of the speed of light are given. A rocket is observed by a person on Earth. What is the length of the rocket as observed by the astronaut inside it if the observer on Earth sees that the rocket is 5.5 m long and it zooms in a speed of 95% that of the speed of light?

22. Step 3 : Write the working equation. A rocket is observed by a person on Earth. What is the length of the rocket as observed by the astronaut inside it if the observer on Earth sees that the rocket is 5.5 m long and it zooms in a speed of 95% that of the speed of light?

23. Step 4 : Substitute the given values. A rocket is observed by a person on Earth. What is the length of the rocket as observed by the astronaut inside it if the observer on Earth sees that the rocket is 5.5 m long and it zooms in a speed of 95% that of the speed of light?

24. Step 5 : Find the answer. This suggests that even though the rocket ship is 17.6 m, it appears to be “contracted” and smaller for an observer seeing it at relativistic speeds. A rocket is observed by a person on Earth. What is the length of the rocket as observed by the astronaut inside it if the observer on Earth sees that the rocket is 5.5 m long and it zooms in a speed of 95% that of the speed of light?

25. It is the extension of the special relativity. It includes the effects of accelerating objects and their mass on space-time. It explains the concept of gravity. The General Theory of Relativity

26. It is based on two postulates: The principle of equivalence states that the effects of gravity and the effects of acceleration are the same. Gravity is not a force but a consequence of the curvature of space-time, caused by the uneven distribution of mass/energy. The General Theory of Relativity

27. Mercury did not follow a precise elliptical orbit but rather a slowly shifting path. The curvature of space-time explained by general relativity accounted for the 43 seconds of arc shift in the orbit of Mercury. The General Theory of Relativity Perihelion shift of Mercury

28. General relativity also states that light can be bent by massive objects such as a star (e.g., Sun). The General Theory of Relativity Gravitational bending of light

29. In 1919, Arthur Eddington confirmed Einstein’s prediction that light is bent by gravity. During a solar eclipse, light from distant stars that passed very near the sun can be observed. Eddington observed that the stars shifted position, consistent with Einstein’s prediction. The General Theory of Relativity

30. It also predicted the existence of bodies massive enough to pull light and keep it from escaping. Black holes are formed when supermassive stars collapse upon itself, forming a body with a very strong gravitational pull. The General Theory of Relativity Image of a black hole at the center of galaxy M87

31. In 1905, Einstein published his theory of special relativity to explain how motions can be compared in different inertial frames. The principle of relativity states that the physical laws have the same mathematical form for all frames of reference moving at a constant velocity with respect to each other. 1 2 The speed of light in a vacuum is independent of the motion of its source and observer. 3

32. The consequences of the special theory of relativity include time dilation and length contraction. The general theory of relativity is the extension of the special relativity. It includes the effects of accelerating objects and their mass on space-time. 4 5 The principle of equivalence states that the effects of gravity and the effects of acceleration are the same. 6

33. Gravity is not a force but a consequence of the curvature of space-time, caused by the uneven distribution of mass/energy. 7

34. Identify the term or terms described in each item below. He is a great scientist who pioneered relativity and modern physics. It is the principle which states that all physical laws are correct in all frames of reference. It is the theory of relativity that applies only to objects that move in uniform motion. It is the factor that is incorporated in calculating time dilation and length contraction. It is the value of the speed of light in vacuum expressed in m/s.

35. What is time dilation and length contraction? Explain these phenomena as consequences of the theory of special relativity.