Lecture 14: Einstein & The Expanding Universe

Transcription

1 Lecture 14: Einstein & The Expanding Universe As with all course material (including homework, exams), these lecture notes are not be reproduced, redistributed, or sold in any form.

2 From Lecture 13: Hubble showed that more distant galaxies appear to be moving away from us more quickly. Straight line given by this equation: Today s value: 70

3 The theoretical backbone of an Expanding Universe

4 Special Relativity Einstein s Assumptions: 1) The laws of physics take the same form in all uniformly moving reference frames. 2) In any uniformly moving reference frame, the velocity of light c is the same, whether emitted by a body at rest or a body in uniform motion.

5 Time Dilation Moving clocks seem to run slowly when viewed by people who are not moving with the clocks. Moving train. Bulb & mirror. Light takes time to bounce back from the mirror h v This is not an artifact of the clocks, time itself does not tick by at the same rate. It looks to a stationary observer that time ticks by more slowly on moving rockets than it does to a person riding along on the rocket! h Non-moving observer: the distance the light travels is longer, and therefore it must take longer for light to complete its path. This result is because the speed of light is not affected by the speed of the train!

6 Time Dilation Moving clocks seem to run slowly when viewed by people who are not moving with the clocks. Moving with train: Measures 2 seconds. This is not an artifact of the clocks, time itself does not tick by at the same rate. It looks to a stationary observer that time ticks by more slowly on moving rockets than it does to a person riding along on the rocket! Watching the train: Measures 2.5 sec.

7 Time Dilation Moving clocks seem to run slowly when viewed by people who are not moving with the clocks. Moving with train: Measures 2 seconds. This is not an artifact of the clocks, time itself does not tick by at the same rate. It looks to a stationary observer that time ticks by more slowly on moving rockets than it does to a person riding along on the rocket! Watching the train: Measures 2.5 sec.

8 Length Contraction 10% speed of light 87% speed of light Lengths of moving objects are contracted when viewed by stationary observers. 99% speed of light

9 Length Contraction 10% speed of light 87% speed of light Lengths of moving objects are contracted when viewed by stationary observers. 99% speed of light

10 Impact Newton forgive me. - Einstein Planck After his work on relativity was published, Einstein expected sharp opposition, criticism, at least something but the first response from the scientific community was frosty silence. The first response was from the famous Professor, Max Planck Planck is the one who explained blackbody radiation & won Nobel prize for it. Planck realized immediately the importance of the work, and gave talks on it. From 1906 on, visitors would come to Bern to see Einstein & talk science. Einstein s reputation in science circles grew starting ~1908. Became an associate professor in 1911, and in 1912 he was invited back to the Swiss Federal Institute of Technology, now as a full professor.

11 Impact Newton forgive me. - Einstein Relativity demanded a new way of thinking. The Laws of Newton and his successors were only valid for speeds much much smaller than that of light. No longer a need for the Aether medium of light.

12 Aside: Is dilation real? Experimental Verification Time dilation was first observed in 1941 by studying cosmic rays, highenergy particles that stream to the surface of the earth from space. Specifically, muons are particles that disintegrate spontaneously after an average lifetime of about 2x10-6 seconds. It is clear that in its short lifetime a muon cannot, even at the speed of light, travel more than 600 m. Muons are created as cosmic rays, at the top of the atmosphere, some 10 km up. We can detect them down here on earth. How can that be? From the muon's point of view (i.e. from their frame of reference) they only live about 2x10-6 s. However from our point of view they live considerably longer, indeed long enough to reach the surface of the earth. In 1971, atomic clocks were flown on jet planes around the world and time dilations were measured as predicted: about 10-4 seconds.

13 Moving beyond Special Relativity While others were still thinking about the implications of special relativity, Einstein was already moving forward. Einstein realized that he would also have to modify Newton s gravity in order for it to sync it with Special Relativity: Then there occurred to me the happiest thought of my life: The gravitational field has only a relative existence Because for an observer falling freely from the roof of a house there exists at least in his immediate surroundings no gravitational field.

14 Moving beyond Special Relativity to General Relativity 1907: The Equivalence Principle: gravity and acceleration are equivalent. It occurred to Einstein that if a man were falling from the roof of his house and tried to let anything drop, it would only move alongside him, thus indicating the equivalence of acceleration and gravity. 1911: Einstein realized that the bending of light in a gravitational field, which he knew in 1907 was a consequence of the equivalence principle, could be checked with astronomical observations.

15 Towards his greatest work, General Relativity I have just completed the most splendid work of my life... to his son Hans Albert, : Hunting for The Theory. Einstein began to search for particular equations ones that would extend relativity to objects moving in an arbitrary way with respect to one another. The search was arduous with entire years spent in blind alleys. Einstein had to master more elaborate mathematical techniques than he had ever expected to need... Planck: As an older friend I must advise you against it for in the first place you will not succeed, and even if you succeed no one will believe you. 1915: Success!! Albert Einstein completes his Theory of General Relativity gravity curved space

16 General Relativity Einstein s equations: Matter tells space how to curve and space tells matter how to move No need for Force of Gravity! All motion is along straight lines in curved space-time.

17 1915: General theory of relativity Gravity curves space Predictions: 1. Starlight will bend around the sun 2. Mercury's orbit will precess at a different rate than predicted by Newton.

18 Testing Relativity Einstein published a paper calling on astronomers to test two predictions of his theory: Light from a distant star should bend if it crosses close to the gravitational field of the Sun. This should be measurable during a solar eclipse. Solar spectral lines should redshift relative to spectral lines produced on Earth's surface because of the gravitational field.

19 1919: The bending of starlight Starlight passing near the sun should be slightly deflected by gravity. This deflection could be measured when the Sun's own light was blocked during an eclipse. Einstein predicted a specific amount of deflection Arthur Eddington leads a solar eclipse expedition which detected gravitational deflection of light by the Sun Announcement of the eclipse results caused a sensation. This proved Einstein s prediction, lending validity to his theory of General Relativity. Einstein received world fame.

20 Bending of starlight When asked what he would do if the measurements of bending starlight at the 1919 eclipse contradicted his general theory of relativity, Einstein said, "Then I would feel sorry for the good Lord. The theory is correct." New York Times on November 10, 1919.

21 Einstein s Gravity & the Expanding Universe Space-time is dynamic. Expansion is allowed, even expected.

22 Relativity and the Expanding Universe Friedmann Einstein, your equations give rise to an expanding Universe. Einstein Friedmann introduced idea in 1922, before Hubble

23 Relativity and the Expanding Universe Friedmann Einstein, your equations give rise to an expanding Universe. Einstein Friedmann introduced idea in 1922, before Hubble I will change my equations to keep the Universe static.

24 Relativity and the Expanding Universe Friedmann Einstein, your equations give rise to an expanding Universe. Einstein Friedmann introduced idea in 1922, before Hubble I will change my equations to keep the Universe static. Λ

25 Relativity and the Expanding Universe Friedmann Einstein, your equations give rise to an expanding Universe. Einstein Friedmann introduced idea in 1922, before Hubble I will change my equations to keep the Universe static. Λ Einstein proposes the cosmological constant which acts against gravity in order to keep the Universe static.

26 The person who put together Einstein s relativity with the observed redshifts of galaxies was a little-known Belgian priest and mathematician: Georges Lemaître. In 1927, after hearing about Slipher s redshifts, he wrote a paper that connected the observed redshifts with the expanding Universe of general relativity. He put it in an obscure journal and nobody noticed. Unlike Hubble, Lemaitre knew what the redshifts meant. Einstein: Your calculations are correct, but your physics is abominable. [He later changed his mind ] Lemaitre later proposed that the Universe might have begun as an infinitely small pinpoint a primordial atom (1946) - [i.e. the Big Bang].

27 The person who put together Einstein s relativity with redshifts of galaxies was a little-known Belgian priest and mathematician: Georges Lemaître.

28 The person who put together Einstein s relativity with redshifts of galaxies was a little-known Belgian priest and mathematician: Georges Lemaître. Galaxies are rushing away from us does this imply that we are somehow located at the center of the Universe? No.

29 Expanding Universe.

30 Expanding Universe.

31 Expanding Universe.

32 Expanding Universe.

33 Expanding Universe.

34 Expanding Universe.

35 Expanding Universe.

36 Expanding Universe.

37 Expanding Universe.

38 Expanding Universe.

39 Expanding Universe.

40 Expanding Universe. Looks the same from everywhere

41 The Cosmological Principle When viewed on sufficiently large scales, the properties of the Universe are the same for all observers....or the Universe looks the same whoever and wherever you are. This implies that the Universe is homogenous and isotropic on large scales (i.e. over large distances).

42 Class dismissed til Monday. No Discussion Sections on Thursday, May 11th