Einstein s theory of relativity
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1 Department of Mathematics, Institute of Origins, December 5, 2008
2 Overview UCL Institute of Origins Origins UCL has established the Institute of Origins to promote world leading research in topics related to the Origins and Evolution of the Universe. Our research themes are: Galaxy Evolution Mathematical Foundations Neutrino physics Planetary Science
3 Overview UCL Institute of Origins Origins UCL has established the Institute of Origins to promote world leading research in topics related to the Origins and Evolution of the Universe. Our research themes are: Galaxy Evolution Mathematical Foundations Neutrino physics Planetary Science
4 Overview UCL Institute of Origins Origins UCL has established the Institute of Origins to promote world leading research in topics related to the Origins and Evolution of the Universe. Our research themes are: Galaxy Evolution Mathematical Foundations Neutrino physics Planetary Science
5 Overview UCL Institute of Origins Origins UCL has established the Institute of Origins to promote world leading research in topics related to the Origins and Evolution of the Universe. Our research themes are: Galaxy Evolution Mathematical Foundations Neutrino physics Planetary Science
6 Overview UCL Institute of Origins Origins UCL has established the Institute of Origins to promote world leading research in topics related to the Origins and Evolution of the Universe. Our research themes are: Galaxy Evolution Mathematical Foundations Neutrino physics Planetary Science
7 Overview Overview Albert Einstein 1905 Einstein s Wonderful Year 1915 General relativity Special relativity the twin problem mass-energy equivalence General relativity matter and curvature black holes and wormholes Cosmology from the big bang to today dark matter, dark energy and all that
8 Overview Overview Albert Einstein 1905 Einstein s Wonderful Year 1915 General relativity Special relativity the twin problem mass-energy equivalence General relativity matter and curvature black holes and wormholes Cosmology from the big bang to today dark matter, dark energy and all that
9 Overview Overview Albert Einstein 1905 Einstein s Wonderful Year 1915 General relativity Special relativity the twin problem mass-energy equivalence General relativity matter and curvature black holes and wormholes Cosmology from the big bang to today dark matter, dark energy and all that
10 Overview Overview Albert Einstein 1905 Einstein s Wonderful Year 1915 General relativity Special relativity the twin problem mass-energy equivalence General relativity matter and curvature black holes and wormholes Cosmology from the big bang to today dark matter, dark energy and all that
11 Overview Overview Albert Einstein 1905 Einstein s Wonderful Year 1915 General relativity Special relativity the twin problem mass-energy equivalence General relativity matter and curvature black holes and wormholes Cosmology from the big bang to today dark matter, dark energy and all that
12 Overview Overview Albert Einstein 1905 Einstein s Wonderful Year 1915 General relativity Special relativity the twin problem mass-energy equivalence General relativity matter and curvature black holes and wormholes Cosmology from the big bang to today dark matter, dark energy and all that
13 Overview Overview Albert Einstein 1905 Einstein s Wonderful Year 1915 General relativity Special relativity the twin problem mass-energy equivalence General relativity matter and curvature black holes and wormholes Cosmology from the big bang to today dark matter, dark energy and all that
14 Overview Overview Albert Einstein 1905 Einstein s Wonderful Year 1915 General relativity Special relativity the twin problem mass-energy equivalence General relativity matter and curvature black holes and wormholes Cosmology from the big bang to today dark matter, dark energy and all that
15 Overview Overview Albert Einstein 1905 Einstein s Wonderful Year 1915 General relativity Special relativity the twin problem mass-energy equivalence General relativity matter and curvature black holes and wormholes Cosmology from the big bang to today dark matter, dark energy and all that
16 Overview Overview Albert Einstein 1905 Einstein s Wonderful Year 1915 General relativity Special relativity the twin problem mass-energy equivalence General relativity matter and curvature black holes and wormholes Cosmology from the big bang to today dark matter, dark energy and all that
17 Overview Overview Albert Einstein 1905 Einstein s Wonderful Year 1915 General relativity Special relativity the twin problem mass-energy equivalence General relativity matter and curvature black holes and wormholes Cosmology from the big bang to today dark matter, dark energy and all that
18 Overview Overview Albert Einstein 1905 Einstein s Wonderful Year 1915 General relativity Special relativity the twin problem mass-energy equivalence General relativity matter and curvature black holes and wormholes Cosmology from the big bang to today dark matter, dark energy and all that
19 Albert Einstein Albert Einstein ( )
20 Albert Einstein 1905 Annus Mirabilis particulate nature of light photoelectric effect Brownian motion confirming atomic theory electrodynamics of moving bodies special relativity mass-energy equivalence E = mc 2
21 Albert Einstein 1905 Annus Mirabilis particulate nature of light photoelectric effect Brownian motion confirming atomic theory electrodynamics of moving bodies special relativity mass-energy equivalence E = mc 2
22 Albert Einstein 1905 Annus Mirabilis particulate nature of light photoelectric effect Brownian motion confirming atomic theory electrodynamics of moving bodies special relativity mass-energy equivalence E = mc 2
23 Albert Einstein 1905 Annus Mirabilis particulate nature of light photoelectric effect Brownian motion confirming atomic theory electrodynamics of moving bodies special relativity mass-energy equivalence E = mc 2
24 Albert Einstein 1915 General relativity for about 10 years Einstein worked on a generalisation of Newtonian gravity Marcel Grossmann and Tullio Levi-Civita influenced Einstein by discussing and introducing him to Riemannian geometry Einstein, Albert (1915), Die Feldgleichungen der Gravitation (The Field Equations of Gravitation), Koniglich Preussische Akademie der Wissenschaften R ab 1 2 Rg ab = 8πT ab
25 Albert Einstein 1915 General relativity for about 10 years Einstein worked on a generalisation of Newtonian gravity Marcel Grossmann and Tullio Levi-Civita influenced Einstein by discussing and introducing him to Riemannian geometry Einstein, Albert (1915), Die Feldgleichungen der Gravitation (The Field Equations of Gravitation), Koniglich Preussische Akademie der Wissenschaften R ab 1 2 Rg ab = 8πT ab
26 Albert Einstein 1915 General relativity for about 10 years Einstein worked on a generalisation of Newtonian gravity Marcel Grossmann and Tullio Levi-Civita influenced Einstein by discussing and introducing him to Riemannian geometry Einstein, Albert (1915), Die Feldgleichungen der Gravitation (The Field Equations of Gravitation), Koniglich Preussische Akademie der Wissenschaften R ab 1 2 Rg ab = 8πT ab
27 Albert Einstein 1915 General relativity for about 10 years Einstein worked on a generalisation of Newtonian gravity Marcel Grossmann and Tullio Levi-Civita influenced Einstein by discussing and introducing him to Riemannian geometry Einstein, Albert (1915), Die Feldgleichungen der Gravitation (The Field Equations of Gravitation), Koniglich Preussische Akademie der Wissenschaften R ab 1 2 Rg ab = 8πT ab
28 Albert Einstein Albert Einstein 1947 Latter years Einstein refuses Quantum Theory subsequently refuses Quantum Field Theory God does not play dice
29 Albert Einstein Albert Einstein 1947 Latter years Einstein refuses Quantum Theory subsequently refuses Quantum Field Theory God does not play dice
30 Albert Einstein Albert Einstein 1947 Latter years Einstein refuses Quantum Theory subsequently refuses Quantum Field Theory God does not play dice
31 Albert Einstein Albert Einstein 1947 Latter years Einstein refuses Quantum Theory subsequently refuses Quantum Field Theory God does not play dice
32 Special relativity Speed of light in vacuum same in all inertial systems
33 Special relativity The twin problem: an apparent paradox
34 Special relativity Time dilation in special relativity Time dilation t t = 1 1 v 2 /c 2 t : time interval as measured by a moving observer v: the observer s velocity; c: denotes the speed of light t: time interval as measured by an observer at rest 1/ -term is often called Lorentz factor
35 Special relativity Time dilation how does it effect us? Time dilation The speed of light is about c meters per second. Let s compare this with the following velocities: speeding car at 100 mph (160 kmh or 44 meter per second) super sonic jet 1000 mph (1600 kmh or 444 meters per second) space shuttle mph (28800 kms or 8000 meter per second)
36 Special relativity Time dilation how does it effect us? Time dilation The speed of light is about c meters per second. Let s compare this with the following velocities: speeding car at 100 mph (160 kmh or 44 meter per second) super sonic jet 1000 mph (1600 kmh or 444 meters per second) space shuttle mph (28800 kms or 8000 meter per second)
37 Special relativity Time dilation how does it effect us? Time dilation The speed of light is about c meters per second. Let s compare this with the following velocities: speeding car at 100 mph (160 kmh or 44 meter per second) super sonic jet 1000 mph (1600 kmh or 444 meters per second) space shuttle mph (28800 kms or 8000 meter per second)
38 Special relativity Time dilation how does it effect us? Time dilation The speed of light is about c meters per second. Let s compare this with the following velocities: speeding car at 100 mph (160 kmh or 44 meter per second) super sonic jet 1000 mph (1600 kmh or 444 meters per second) space shuttle mph (28800 kms or 8000 meter per second)
39 Special relativity Time dilation how does it effect us? Let s have a look at the numbers ( ) t t ( ) t t ( ) t t car jet shuttle = = = Conclusion Special relativity does not effect our everyday life!
40 Special relativity Time dilation how does it effect us? Let s have a look at the numbers ( ) t t ( ) t t ( ) t t car jet shuttle = = = Conclusion Special relativity does not effect our everyday life!
41 Special relativity Time travel what can be done? Into the future The theory of special relativity, in principle, allows travelling into the future. Into the past Travelling into the past does not seem to work, unless time bends into, say, a circle.
42 Special relativity Time travel what can be done? Into the future The theory of special relativity, in principle, allows travelling into the future. Into the past Travelling into the past does not seem to work, unless time bends into, say, a circle.
43 Special relativity Time travel what can be done? Into the future The theory of special relativity, in principle, allows travelling into the future. Into the past Travelling into the past does not seem to work, unless time bends into, say, a circle.
44 Special relativity Mass-energy equivalence when a flashlight emits light, it loses mass when a flower absorbs sunlight, its mass increases when a uranium nucleus splits, the mass of the remnants is less than the original mass. The difference appears as light, heat, and kinetic energy
45 Special relativity Mass-energy equivalence when a flashlight emits light, it loses mass when a flower absorbs sunlight, its mass increases when a uranium nucleus splits, the mass of the remnants is less than the original mass. The difference appears as light, heat, and kinetic energy
46 Special relativity Mass-energy equivalence when a flashlight emits light, it loses mass when a flower absorbs sunlight, its mass increases when a uranium nucleus splits, the mass of the remnants is less than the original mass. The difference appears as light, heat, and kinetic energy
47 Special relativity Nuclear explosion
48 Curved spacetime Matter and the curvature of spacetime General relativity field equations R ab 1 2 Rg ab = 8πT ab properties of spacetime = properties of matter matter tells spacetime how to curve and spacetime tells matter how to move
49 Curved spacetime Matter and the curvature of spacetime General relativity field equations R ab 1 2 Rg ab = 8πT ab properties of spacetime = properties of matter matter tells spacetime how to curve and spacetime tells matter how to move
50 Curved spacetime Matter and the curvature of spacetime General relativity field equations R ab 1 2 Rg ab = 8πT ab properties of spacetime = properties of matter matter tells spacetime how to curve and spacetime tells matter how to move
51 Curved spacetime Matter and the curvature of spacetime General relativity field equations R ab 1 2 Rg ab = 8πT ab properties of spacetime = properties of matter matter tells spacetime how to curve and spacetime tells matter how to move
52 Curved spacetime Matter and the curvature of spacetime General relativity field equations R ab 1 2 Rg ab = 8πT ab properties of spacetime = properties of matter matter tells spacetime how to curve and spacetime tells matter how to move
53 Curved spacetime The motion of a particle in spacetime
54 Curved spacetime Black holes Are black holes black? black holes are such dense object that not even light can escape their gravitation attraction since they also attract other kind of matter, it is typically very hot near a black hole while the black hole indeed absorbs light, its vicinity is bright
55 Curved spacetime Black holes Are black holes black? black holes are such dense object that not even light can escape their gravitation attraction since they also attract other kind of matter, it is typically very hot near a black hole while the black hole indeed absorbs light, its vicinity is bright
56 Curved spacetime Black holes Are black holes black? black holes are such dense object that not even light can escape their gravitation attraction since they also attract other kind of matter, it is typically very hot near a black hole while the black hole indeed absorbs light, its vicinity is bright
57 Curved spacetime Black holes Are black holes black? black holes are such dense object that not even light can escape their gravitation attraction since they also attract other kind of matter, it is typically very hot near a black hole while the black hole indeed absorbs light, its vicinity is bright
58 Curved spacetime Black holes a realistic image Galactic centres A black hole may be observed by tracking the movement of a group of stars that orbit its centre.
59 Curved spacetime Wormholes in general relativity
60 Cosmology Cosmology What does cosmology mean? cosmology (κoσµoλoγια) cosmos and logic κoσµoζ a cosmos is an orderly or harmonious system so cosmology is study of the universe in its totality
61 Cosmology Cosmology What does cosmology mean? cosmology (κoσµoλoγια) cosmos and logic κoσµoζ a cosmos is an orderly or harmonious system so cosmology is study of the universe in its totality
62 Cosmology Cosmology What does cosmology mean? cosmology (κoσµoλoγια) cosmos and logic κoσµoζ a cosmos is an orderly or harmonious system so cosmology is study of the universe in its totality
63 Cosmology Cosmology What does cosmology mean? cosmology (κoσµoλoγια) cosmos and logic κoσµoζ a cosmos is an orderly or harmonious system so cosmology is study of the universe in its totality
64 Cosmology Beyond the big bang
65 Cosmology Afterglow light pattern the cosmic microwave background radiation
66 Cosmology The energy content of our Universe
67 Cosmology Dark matter
68 Cosmology What dark energy is not!
69 Cosmology What dark energy could be the cosmological constant The cosmological field equations of general relativity R ab 1 2 Rg ab + Λg ab = 8πT ab properties of spacetime + a cosmological constant = matter The field equations with cosmological matter R ab 1 2 Rg ab = 8πT ab Λg ab properties of spacetime = matter + cosmological matter
70 Cosmology What dark energy could be the cosmological constant The cosmological field equations of general relativity R ab 1 2 Rg ab + Λg ab = 8πT ab properties of spacetime + a cosmological constant = matter The field equations with cosmological matter R ab 1 2 Rg ab = 8πT ab Λg ab properties of spacetime = matter + cosmological matter
71 Cosmology What dark energy could be the cosmological constant The cosmological field equations of general relativity R ab 1 2 Rg ab + Λg ab = 8πT ab properties of spacetime + a cosmological constant = matter The field equations with cosmological matter R ab 1 2 Rg ab = 8πT ab Λg ab properties of spacetime = matter + cosmological matter
72 Cosmology Possible future of the Universe
73 Summary Summary Special relativity and general relativity are fascinating subject areas. Special relativity is full of paradoxes that can be solved. General relativity is more or less understood. Cosmology is about 96% non-understood.
74 Summary Summary Special relativity and general relativity are fascinating subject areas. Special relativity is full of paradoxes that can be solved. General relativity is more or less understood. Cosmology is about 96% non-understood.
75 Summary Summary Special relativity and general relativity are fascinating subject areas. Special relativity is full of paradoxes that can be solved. General relativity is more or less understood. Cosmology is about 96% non-understood.
76 Summary Summary Special relativity and general relativity are fascinating subject areas. Special relativity is full of paradoxes that can be solved. General relativity is more or less understood. Cosmology is about 96% non-understood.
77 Summary Summary Special relativity and general relativity are fascinating subject areas. Special relativity is full of paradoxes that can be solved. General relativity is more or less understood. Cosmology is about 96% non-understood.
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