Cosmology - How the Universe Came to Be. PLATO: Cosmology

Transcription

1 Cosmology - How the Universe Came to Be PLATO: Cosmology 1

2 Implications: PLATO: Cosmology 2

3 Implications: Today s best measurement of the Hubble constant: HHubble = 69.3 km/s per Mpc Universe is about 14 billion years old. PLATO: Cosmology 2

4 Copernican Principle Homogeneity does not imply isotropy Isotropy does not imply homogeneity But: Isotropy everywhere does imply homogeneity: If the universe looks the same in all directions from all places in the universe, it must also be homogeneous. This is an assumption! But supported by evidence The Copernican Principle = Cosmological Principle: The universe is homogeneous and isotropic PLATO: Cosmology 3

5 Cosmology A dynamical model for the entire universe What do we need to include? Expansion Matter and how it is distributed in space (density) Some idea what that space is Gravity PLATO: Cosmology 4

6 Special Relativity Einstein (1905): Three Nobel- Prize worthy publications on unrelated subjects... Brownian motion Photo-electric effect (Nobel prize) On the electrodynamics of moving bodies...

7 The Speed of Light 1887: Michaelson & Morley showed the speed of light is constant

8 Special Relativity Requires only three assumptions: The laws of physics are the same in every uniformly moving frame of reference (if I hit my head, an observer moving relative to me will also see me hitting my head) Space is homogeneous and isotropic (a yardstick at rest is exactly a yard long, regardless of where it is used) The speed of light is constant and the same in every frame of reference (Physical equations are the same in every lab)

9 Radical changes... This implies that space and time are no longer independent. Space and time are interwoven into a fabric, called spacetime. Newton s laws must be altered.

10 Frames A frame is really just an imaginary laboratory attached to some object or observer. A frame can be moving with some fixed velocity Such a frame is called an inertial frame Natural laws are formulated in inertial frames A frame can be accelerated Rotating frames are accelerated

11 Frames Each object has a frame that is attached to it In this frame it is not moving and not rotating That frame is called the rest frame of that object (because it is at rest in that frame).

12 Spacetime... Consider a flash of light Its rays will move outward on a sphere

13 Spacetime... Consider a flash of light Its rays will move outward on a sphere

14 Spacetime... Now add another observer, moving at some velocity (say, half the speed of light) Light flash is emitted when observers pass

15 Spacetime... Now add another observer, moving at some velocity (say, half the speed of light) Light flash is emitted when observers pass

16 Spacetime... Now consider the other observer... Light flash is emitted when observers pass

17 Spacetime... Now consider the other observer... Light flash is emitted when observers pass

18 Spacetime... In this frame, the light arrives at the two outer clocks and the observer arrives at the inner clock at the same time

19 Spacetime... In this frame, the light has already passed the right clock and not yet arrived at the left clock when the inner clock reaches him

20 Bye-bye simultaneity Things that happen simultaneous for one observer are no longer simultaneous for other observers in special relativity

21 Spacetime That means: separation in space between two things can turn into a separation in time Space and time are now coupled to each other 4 dimensional

22 Light always takes shortest path between two points time Light travels on straight lines Light rays light cone The shortest connections between points are called geodesics light cone space

23 Cosmology A dynamical model for the entire universe What do we need to include? Expansion Matter and how it is distributed in space (density) Some idea what that space is Gravity PLATO: Cosmology 20

24 Gravity Special relativity formulated in inertial frames Must find an inertial frame for SR! For electric force, just use a neutral particle to anchor frame to, that will be unaccelerated. But gravity accelerates everything (remember Gallileo?) Special relativity does not hold under gravity

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27 Stationary Elevator with gravity: Ball is accelerated down

28 Outside of an accelerated elevator: Ball at rest

29 Inside of accelerated elevator: ball accelerated down

30 =elevator with gravity!

31 General relativity Einstein s fundamental insight: Equivalence principle Gravity accelerates everything Gravity must be a property of spacetime Gravity and acceleration are indistinguishable (Galileo) Formulate physics in terms of accelerated frames

32 Equivalence principle

33 Elevator at rest

34 Elevator in uniform motion

35 Inside the moving elevator

36 Accelerated elevator from outside

37 Inside the accelerated elevator

38 = In an elevator in a gravitational field

39 Light bending: Gravity bends light Recall: light travels on spacetime geodesics In spacetime with gravity, geodesics are curved Geodesics are the straightest possible lines Gravity curves spacetime

40 In curved space Parallel lines don t stay parallel Triangles don t add up to 180 The straightest possible lines are geodesics The stronger the curvature, the stronger theses effects

41 In curved spacetime The actual length to a destination is changed (try this yourself!) The circumference of a circle is no longer 2πR (try this yourself!) Sometimes, more than one path is the shortest path (try this yourself!)

42 In curved spacetime The actual length to a destination is changed (try this yourself!) The circumference of a circle is no longer 2πR (try this yourself!) Sometimes, more than one path is the shortest path (try this yourself!)

43 Is space curved?

44 Light bending (2): Heavy objects curve spacetime Galaxy clusters are very heavy: 1000 trillion times more massive than the sun They should curve spacetime a lot Light should follow curved path around them

45 Light bending (2): Heavy objects curve spacetime Galaxy clusters are very heavy: 1000 trillion times more massive than the sun They should curve spacetime a lot Light should follow curved path around them

46 Light bending (2): Heavy objects curve spacetime Galaxy clusters are very heavy: 1000 trillion times more massive than the sun They should curve spacetime a lot Light should follow curved path around them

47 Curved Spacetime

48 Curved Spacetime Einstein: Mass curves spacetime Cosmos contains mass Spacetime can be curved by mass Cosmological principle: Curvature is the same everywhere

49 Curved Spacetime We have used 2D to visualize curvature (some examples are easy - spheres, e.g.) We understand surfaces (2D) in the context of volumes (3D) But spacetime is 4D! It would take 8+ dimensions of flat space to visualize curved 4D spacetime We cannot even visualize 4D...