Physics 103 Fall 2017 NAME: Discussion Session 8 General Relativity Worksheet Ha
ID: 2269166 • Letter: P
Question
Physics 103 Fall 2017 NAME: Discussion Session 8 General Relativity Worksheet Having discussed Einstein's theory of Special Relativity, we now turn our attention (briefly) to Einstein's theory of General Relativity, which includes Special Relativity as a limiting case of no gravity. General Relativity describes gravity as the curvature of space and time (of spacetime). We have already seen how Special Relativity leads to some inter esting effects; space and time blend together, events that are simultaneous for one observer are not simultaneous for another observer, and so on. General Relativity also includes all of these effects, as well as more. For instance, gravity can affect the flow of time as well time slows down for observers in a strong gravitational field. General Relativity also predicts the existence of some very strange phenomena, such as black holes. This worksheet investigates some of the ideas of General Relativity 1 Conceptual Questions 1. What is Einstein's Equivalence Principle? 2. If light is massless, then how can it be affected by gravity? 3. What is the proper time for light in flat spacetime? What about in curved spacetime? 4. In what ways does the gravitational theory of Einstein differ from that of Newton? 5. What is a geodesic, and why is it important in General Relativity? 6. What is the metric? What is special about the Minkowski metric? 7. Freely falling observers travel along geodesics in curved spacetime; from this point of view why might it be correct to say that standing on the ground would constitute an "accelerated" observer? 8. Suppose Bob lives in Denver (the Mile-High City), while his twin sister, Alice, lives in Death Valley (located below sea level). They have both attend their family reunion in Las Vegas. Which twin is older? By a little bit, or a lot? 9. What is the equivalent of a photon for quantum gravity? 10. In the early Universe, immediately after the Big Bang, the Universe underwent infla- tion, which is an exponential, faster than light, expansion of the Universe. If nothing can travel faster than light, how is this possible?Explanation / Answer
1- All particles experience the same acceleration in a gravitational field, irrespective of their masses.Einstein extended this idea to the modern equivalence principle.The Principle of Equivalence: For an observer in free fall in a gravitational field, the results of all local experiments are independent of the magnitude of the gravitational field
2-In general relativity, gravity affects anything with energy. While light doesn't have rest-mass, it still has energy and is thus affected by gravity.
4- Newtonian gravity can be written as spacetime curvature. This is counter to the common statements about the novel thing in GR. The key difference is that Newtonian gravity has extra absolute structures that GR does not have:- absolute time and space, a preferred separation of spacetime into time and spatial parts, absolute simultaneity, and a curved connection that is not the special one derived from a spacetime metric.Newtonian equation is a constraint equation - it does not describe a propagating degree of freedom. No gravitational waves, gravitons etc. No speed of light limit for gravity. All matter has an instantaneous gravitational effect on all other matter. This is different in GR since the field equation is a wave equation which describes the propagation of gravitational disturbances from one point to another at the speed of light.
General Relativity is a local theory (no action at a distance). Einsteinian gravity is the curvature of spacetime and the coupling is between mass-energy and geometry.
5- A geodesic generalizes the notion of a "straight line" to curved spacetime.In other words, a freely moving or falling particle always moves along a geodesic.
6-In general relativity, the metric tensor ( is the fundamental object of study. I The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separating the future and the past.
The Minkowski metric is Euclidean-like except for the difference in sign between the time and space
terms in the line element.
9- graviton