Presentation on theme: "General Relativity and The Expanding Universe"— Presentation transcript:
1General Relativity and The Expanding Universe Michael Marshall & Michael Szopiak“Matter tells space how to curve. Space tells matter how to move.” – American physicist John Wheeler
2Special Theory of Relativity General Theory of Relativity 2 Postulates (Einstein, 1905):The form of the laws of physics is the same in all inertial reference framesThe speed of light has the same constant value for all inertial observersGeneral Theory of RelativityEquivalence Principle (Einstein, 1907):In a small region of space-time (locally), it is not possible to distinguish operationally between a frame ‘at rest’ in a uniform gravitational field and a frame uniformly accelerated through empty space
3Consequences of the Equivalence Principle Inertial Mass = Gravitational MassLight is affected (‘bent’) by gravitational fields
4Inertial Reference Frames Performed locally, no experiment inside the free-falling elevator could distinguish it from an inertial frame.Since gravitational andaccelerated frames areequivalent, we cannotdetermine an absolute inertialframe.
5Mach’s Influence on General Relativity It was supposed that Mach’s concept (of an inertial frame determined with a reference to the fixed stars) was incorporated into General Relativity – but these showed otherwise.De Sitter’s (Empty, Expanding) Gödel’s (Absolute Rotation)
6Experimental TestsEinstein’s theory of general relativity and the equivalence principle are tested with three well known experimentsBending of light rays by a gravitational fieldGravitational red shift of LightAdvance of the perihelion of Mercury
7Bending of Light Rays by a Gravitational FieldMass equivalence principle“The form of each physical law is the same in all locally inertial frames.” (Harris 45)Therefore, if light bends in an accelerating frame, any experiment should conclude that light bends in a gravitationally equivalent frame
9Bending of Light RaysThe mass equivalent principle provides another reason for thinking light would bend in a gravitational fieldE = mc2 can be rearranged to m = E/c2Therefore, light (which carries energy) has an effective ‘mass’ in a gravitational field
11The Experiment Travel to Russia and South America Observe solar eclipseCalculate apparent position of star at point 2 and the actual position of the star at point 1
12Einstein’s Prediction In a 1911 paper, he postulated the bending of the starlight to be about 0.83” (seconds of arc) for the given exampleEinstein recognizes theoretical problemRevised prediction of 1.7” before any experiment was performedActual data from 1919 confirms Einstein’s prediction of 1.7”
13An Elegant Theory“Now I am fully satisfied, and I no longer doubt the correctness of the whole system, whether the observation of the eclipse succeeds or not ... The sense of the thing is too convincing.” (Einstein, 1914)“When I was giving expression to my joy that the results coincided with his calculations, he said quite unmoved, ‘But I knew that the theory was correct’, and when I asked, what if there had been no confirmation of his prediction, he countered, ‘Then I would have been sorry for the dear Lord – the theory is correct.’” (Einstein’s student, 1919)
14Interesting Questions What if the expedition had gotten the initial results of 1.7” before Einstein adjusted his numbers?How do you think this would have affected the scientific community’s view of general relativity?How does the concept of falsifiability connect to this experiment if the expedition calculated 1.7” before Einstein adjusted his prediction?Even if Einstein were to correct his error, would his theory have the same strength?Should it have the same strength?
15Gravitational Redshift The Doppler Effect (Revisited)
16Gravitational Redshift The Doppler Effect (Revisited)
17Gravitational Redshift The Doppler Effect (Revisited) Real-World Example: Global Positioning System (GPS)
18Advance of the Perihelion of Mercury Newtonian mechanics fails to properly predict orbital paths for high gravitational fieldsMercury provides the perfect example(Exaggerated picture)
19Perihelion Precession Over one century, Mercury’s orbit appears to advance 5600” of arc per century5026” of arc are due to wobbling of Earth on axis531” of arc are due to perturbation from planetsNewtonian mechanics cannot explain about 43” of the precession of MercuryGeneral relativity is able to account for the missing 43”
20General Relativity’s Success Three experiments validate general relativityThe elegance with which general relativity explains each of these difficult phenomena gives it strength as a theory
21Review of the Classical Universe Newton believed the universe to beEuclidean (have zero curvature)InfiniteFinite amount of matterThen changed position to uniform distribution of matter throughout an infinite space in order to prevent collapse of the universe (“Fixed Stars”)The stability of the universe was in questionNewton postulated that our universe is stable because of the action of God
22Olbers’ ParadoxHeinrich Olbers, an eighteenth century German astronomer, asks the question:Why is it dark at night?This question seeks to understand what it would mean if the universe is actually infinite in both mass and size.Olbers suggests that the sky should appear as bright as the noonday sun.
23Olbers’ Paradox The sky is not as bright as the noonday sun! Thus, we have a contradiction when we say we have an infinite, static, homogeneous universe and a sky that is not always bright.This paradox lacked a solution for over 100 years, and led many to research a finite universe.
24A Review of Curvature Metric 2 dimensions are easier to conceptualize Then you can generalize to higher dimensionsGeodesics are straight lines in a space
26Friedmann’s Solutions To Einstein’s Field Equations
27Solutions To Einstein’s Field Equations Possible Universes:Solutions To Einstein’s Field Equations
28Lemaître’s Universe: A Big Bang Finite past – expanded from a hot, dense beginningPositive curvaturePositive cosmological constant Λ > ΛE
29Vesto Slipher From 1912 to 1925, Slipher measured spectral lines of light fromdistant galaxiesRed shift!Unique spectral linesGreat majority of galaxies arerecedingDid not appear to be random
30Edwin Hubble American (1889-1953) Had much more accurate ways of telling distanceBy finding independent determinations of distances to distant galaxies, he determined that the recessional velocity of a galaxy is directly proportional to its distance from the Earth
31Hubble Constant Doppler-shift Hubble’s discovery Hubble’s Law Age of the Universe13.7 Billion Years
32Hubble’s Law Space is expanding The universe is not static Each observer perceives himselfas the center of the universeUniverse’s expansion is slowingdown, which implies the universeused to be more compactSupports notion of Big Bang
33Olbers’ Paradox (Revisited) Problem of red shiftingThe light from distant stars would not be in the visible spectrumProblem of Hubble radiusIf recessional velocity is equal to the speed of light, then there are parts of the universe we can never know aboutProblem of the beginningOlbers’ paradox relies on the notion that light has had an infinite amount of time to reach the EarthSince Hubble’s Law supports the Big Bang, then the universe has not existed forever as we know it
34Dark MatterInterestingly, it appears that there is not enough mass for the universe to be expanding like it is. This fact has led to the postulation of dark matter.Dark matter is matter that we do not ordinarily encounter, but its postulated affects can be observed through gravitational lensing
35A Modern Model of the Universe Our Galaxy: Disc-shaped; 100,000 ly wide in diameterCosmic Background Radiation: T = 2.7 KBlack Holes: Strong gravitational field (when a massive body undergoes gravitational collapse) is dense enough so the escape velocity is greater than the speed of lightThe Multiverse: Parallel universes?
36Barrow, John D. The Book of Universes: Exploring the Limits of the Cosmos. New York: W. W. Norton & Company Inc., 2011.Harris, Randy. Modern Physics. 2nd ed. San Francisco: Pearson/Addison Wesley, Print.Kehoe, Robert. “Ch. 4 Relativity.” Phsyics.smu.edu. Southern Methodist Univeristy, May Web. 04 AprNave, Carl Rod. "HyperPhysics." HyperPhysics. Georgia State University, Aug Web. 08 Apr <http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html>.Minute Physics YouTube Videos:Olber’s Paradox:Multiverse:Pictures (from Internet):Works Cited