HSC Space : Section 4

1. HSC Space: Section 4

3. The Aether(no not the one from Thor) Hypothesis • there was medium throughout all of space through which light travelled • The medium was called the luminiferousaether* (or light carrying aether) or simply aether. * sometimes spelled ether

4. The Aether(no not the one from Thor) Properties of the Aether • The aether either had have the elastic properties of a solid - since only solids could transmit transverse waves. • It had to have low density. • It must be transparent • The aether had to penetrate all matter through which light travelled. • Fill all of space

5. The Aether(no not the one from Thor) If aether existed then the Earth should be moving through it as it orbits the Sun (at the orbital speed of about 30 km s-1). Hence from our point of view, we should experience aether past us. This is known as the ‘aether wind’. At any given point on Earth’s surface, the strength and the direction of the aether wind would vary with time of the day and season.

6. Michelson and Morley An experiment that didn’t work… as expected • A paradigm shift in scientific thinking was precipitated by one of the most famous experiments in science… • The purposeof the Michelson-Morley experiment wasto detect and measure the relative motion of the Earth through the aether • The Michelson-Morley experiment relied upon the interference of two rays of light travelling paths perpendicular to each other

7. Michelson and Morley - Set up Main components: • A monochromatic light source • Monochromatic = single colour i.e. single wavelength • A half-silvered mirror • 2 mirrors (normal ones) • Inferrometer /eye piece

8. Michelson and Morley - Set up

9. Michelson and Morley • The rays of light travelling paths A and B produced an interference pattern, seen by the observer • It was predicted, using proven principles, that if the Earth was moving through the aether, that when the apparatus was rotated about a vertical axis, the interference pattern would change

10. Michelson and Morley A e t h e r • If the device is at rest relative to the ether, a particular interference pattern will be seen by the observer and this pattern will be independent of the orientation of the apparatus • However, if the device is actually passing through the aether... A e t h e r

11. Michelson and Morley … then it was predicted that light requiring different times to travel the two different paths, A and B, would result in a different interference pattern As the velocity relative to the aether changes with the Earth’s motion around the Sun, a different interference pattern would be observed. A e t h e r A e t h e r

12. Michelson and Morley Rotating the apparatus would allow the the aether wind to be detected

13. Michelson and Morley - Results No change! O RLY? • Michelson and Morley could not detect any shift in interference pattern. • They tried: • Changing the position of the interferometer • Performing the experiment at different times of the day and/or the year • Repeating the experiment multiple times (even by different physicists) • No shift in interference pattern was observed!!! This is known as the “Null Result”

14. Michelson and Morley - Results

15. Michelson and Morley - Consequences • The results suggested that aether may not exist after all • There were plenty of physicists who were not convinced and believed that the experiment needed modifying. • Thus many refined versions of this experiment has been conducted over various years (up to 2009). • It is known as the most failed experiment in the world! • These results helped scientists to eventually reject the aether model and accept Einstein’s relativity.

16. Competing theories • The theories • Aether model • Theory of relativity • [Maxwell’s electromagnetic theory] • Although Einstein did not know about the Michelson-Morley experiment until after he’d proposed his theory of relativity, the results of the MM experiment were consistent with the theory of relativity and inconsistent with the aether theory

17. Frames of Reference • A coordinate system used to describe the position, velocity and acceleration of an object is called a frame of reference. • If you are in a room you will use the walls, floor, and ceiling of that room as a frame of reference to judge the motion of objects in the room. • Actually, frames of reference are classified into two types depending upon how they are moving. Those two types are called inertial and non-inertial frames of reference.

18. Inertial Frame of Reference • An inertial frame of reference has a constant velocity. That is, it is moving at a constant speed in a straight line, or it is standing still. • There are several ways to describe an inertial frame. An inertial frame of reference is • one with a constant velocity • non-accelerating • one in which the law of inertia holds • one in which Newton's laws of motion consistent apply • one where there are no fictitious forces

19. Non-Inertial Frame of Reference • A non-inertial frame of reference does not have a constant velocity. It is accelerating. There are several ways to imagine this motion. The frame could be: • Traveling in a straight line, but be speeding up or slowing down • Traveling along a curved path at a steady speed • Traveling along a curved path and also speeding up or slowing down. • A non-inertial frame of reference is • An accelerating frame of reference • One in which the law of inertia does not apply • A frame of reference in which Newton's laws of motion do not apply • One in which fictitious forces arise.

20. Experiment: Frames of Reference

21. Principle of Relativity • Einstein used the Michelson & Morley null result to conclude that: • The physical laws of nature are the same in any inertial frame of reference • The speed of light is constant relative to any observer and to the source • These are Einstein’s First and Second Postulates which form the basis for his Theory of Special Relativity • This theory throws up some pretty weird ideas…

22. Principle of Relativity Einstein developed two theories of relativity! The theory of Special Relativity and the Theory of General Relativity Special relativity deals only with motion in inertial frames of reference - that is, ones that are not accelerating. [Einstein’s Theory of General Relativity - not in this course - deals with accelerated frames of reference and gravity]

23. Einstein’s Thought Experiment Gedanken (Thought) experiments It was impossible to achieve the kinds of speeds necessary to test his ideas (especially while working in the patent office…), so Einstein used Gedanken experiments or Thought experiments. His thought experiment in this case was as follows: Suppose I am sitting in a train that is travelling at the speed of light. If I hold up a mirror in front of me and look into it, will I see my own reflection?

24. Einstein’s Thought Experiment Einstein could only see two possible answers, and both of them had real problems for him. • No, he would not see his reflection. This would be because the train was already going as fast as light can travel. Therefore, the light leaving his face would not be able to reach the mirror in order to return as a reflection. By not being able to see his reflection, he would immediately know that the train was travelling at light speed, without reference to an outside point. This is the violation of the principle of relativity predicted by the aether model. • Yes, he would be able to see his reflection, that is, the principle of relativity is not violated. This means that the light leaving his face travels at the usual speed of light, as measured by him on the train. But this would mean that an observer standing on the ground next to the train should be able to measure the speed of that light as twice the usual speed of light!

25. Einstein’s Thought Experiment He decided therefore that: • The principle of relativity is never violated he would see his reflection in the mirror. • This still posed the problem of the person outside the train seeing light travelling at twice its known speed. • He decided then that the speed of light must have the same value regardless of the motion of the observer.

26. Einstein’s Thought Experiment In other words, the person on the train and the person outside the train will both see the same light travelling at the same velocity. This, in itself, seemed an impossibility until Einstein realised that the key lay in the definition for speed, being distance divided by time. His conclusion, therefore, was that the both people watching the same event (the reflection of the image from the mirror) observe different distances and different time intervals, such that distance divided by time always equals the same number, the speed of light. In other words, the two different observers perceive space (distance) and time differently if c is constant!

27. Principle of Special Relativity • The laws of physics are the same in all frames of reference. In other words, the principle of relativity always holds and cannot be violated by optical experiments. (This implied that the aether does not exist.) 2. The speed of light is independent of the motion of the source. It must be accepted, since it is based on observational evidence. The postulate’s consequences completely change the way we perceive the Universe! The second of these postulates is contrary to our everyday experience At different velocities, distances and times take on different values! Length, mass and time all depend on the motion of the observer!

28. Consequences of Principle of Special Relativity

29. Principal of Special Relativity • When the SystemeInternationale (SI) of units was set up in 1875, the metre was defined to be the distance between two lines scribed on a single bar of platinum-iridium alloy.

30. Principal of Special Relativity • The current definition of the metre is much more precise and accessible than this. It utilises the idea from relativity, that the speed of light has a constant value in every inertial frame of reference. • This speed can be measured very accurately as 299 792 458 m/s. In addition, the accuracy of the definition of one second (9 129 631 770 oscillations of the 133Cs atom) is utilised.

31. Principal of Special Relativity • The definition is as follows: one metre is defined as the length of the path travelled by light in a vacuum during the time interval of 1/299 792 458 of a second.

32. Simultaneity • http://www.youtube.com/watch?v=wteiuxyqtoM • The ‘relativity of simultaneity’ refers to Einstein’s contention that if an observer sees two events to be simultaneous then any other observer, in a different frame of reference, may not judge them to be simultaneous. • In other words, whether you judge two events to be simultaneous depends upon your frame of reference.

33. The Equivalence between Mass and Energy • Mass and energy are inter-convertible - Nuclear fission / fusion - Particle / antiparticle annihilation E = mc2

34. Length Contraction

35. v = 80% c v = 99% c v = 99.9% c Length Contraction v = 10% c A fast-moving plane at different speeds.

36. Length Contraction The Tevatron at Fermilab in Chicago accelerates protons and antiprotons to almost 1000 GeV, or one teraelectron volt (1 TeV). At this speed, they are travelling only 300 kilometres per hour slower than the speed of light, the protons and antiprotons circle the Tevatron in opposite directions. The beams ultimately collide with each other at creating bursts of new particles. Question The speed of light = 299 792 458 m / s • Deduce the speed of the protons in the Tevatron. • If the path length that the protons follow at this speed is 6.44 km relative to a scientist working at the Tevatron, what distance do the protons travel in their frame of reference? v = 299 792 458 - 83.3 = 299 792 374.7 m / s

37. Time Dilation Time passes more slowly in a frame of reference moving relative to an observer. This real effect is called time dilation. Show video

38. Time Dilation – Twin’s Paradox The Set-up Sai and Vg are twins. Sai, an astronaut, leaves on a trip many light years (ly) from the Earth at great speed and returns; Vgdecides to remain safely on Earth. The Problem Vg knows that Sai’s clocks measuring his age must run slow, so he will return younger than he. However, Sai (who also knows about time dilation) claims that Vg is also moving relative to him, and so his clocks must run slow. The Paradox Who, in fact, is younger upon Sai’s return?

39. t x Time Dilation – Twin’s Paradox • Vg’s clock is in an inertial system during the entire trip. But Sai’s clock is not. As long as Sai is traveling at constant speed away from Vg, both of them can argue that the other twin is aging less rapidly. • But when Sai slows down to turn around, he leaves his original inertial system and eventually returns in a completely different inertial system. • Sai’s claim is no longer valid, because he doesn’t remainin the same inertial system. Vg does, however, and Sai ages less than Vg.

40. Mass Dilation • Objects moving relative to the observer increase in mass compared with their masses when at rest relative to the observer. • Calculate the mass of a proton at its maximum speed in the Fermilab Tevatron. Proton rest mass is 1.67262158 × 10-27 kg. v = 299 792 374.7 m / s c = 299 792 458 The mass increases by a factor of 1341 times the rest mass.

41. Relationship between theory and evidence using Einstein • Evidence supporting • Atomic clock on plane and GPS atomic clocks • Particle accelerators - path length from frame of reference of high-speed particle is shorter • Particle accelerators - magnetic fields used to control moving particles have to factor in the increased particle mass due to relativistic effects • Relativity predicted • Time dilation • Length contraction • Mass increase

42. Consequences for Space Travel • See handout

43. End of Section 4