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Option H: Relativity H7 General relativity. The equivalence principle H.7.1Explain the difference between the terms gravitational mass and inertial mass. H.7.2Describe and discuss Einstein’s principle of equivalence. - PowerPoint PPT Presentation

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Option H: RelativityH7 General relativityThe equivalence principleH.7.1Explain the difference between the terms gravitational mass and inertial mass.H.7.2Describe and discuss Einsteins principle of equivalence.H.7.3Deduce that the principle of equivalence predicts the bending of light rays in a gravitational field.H.7.4Deduce that the principle of equivalence predicts that time slows down near a massive body.

Option H: RelativityH7 General relativityThe equivalence principleExplain the difference between the terms gravitational mass and inertial mass.Consider an experiment which uses two identical closed rooms: one on Earth and the other in a spaceship accelerating at 9.8 m/s2 in interstellar space (no gravitation).

Option H: RelativityH7 General relativityThe equivalence principleExplain the difference between the terms gravitational mass and inertial mass.Dobson is in the room and cannot see outside. He throws up the ball and analyzes its trajectory.Whether in the spaceship, or on Earth, the trajectories are identical. y = yo + vot - 0.5gt2

Option H: RelativityH7 General relativityThe equivalence principleExplain the difference between the terms gravitational mass and inertial mass.On Earth, the net force is given by F = GMm/r2. In the spacecraft the apparent force is given by F = ma, where a = g.The m in F = ma is called the inertial mass. In this formula, it represents the objects resistance to accelera- tion (AKA inertia).The m in F = GMm/r2 is called the gravitational mass. In this formula it represents the mutual attraction between the mass of Earth M and the object m.Gravitational massInertial mass

Option H: RelativityH7 General relativityThe equivalence principleDescribe and discuss Einsteins principle of equivalence.We have often assumed that the two masses were the same.EXAMPLE: Show that the acceleration of a freely-falling body a distance r from a planet of mass M is given by a = GM/r2.SOLUTION: We use Newtons laws for this:From Newtons law of gravity: F = GMm/r2.From Newtons law of motion: F = ma.Equating the two: ma = GMm/r2 a = GM/r2.gravitational massinertial massFYINote that in the last step we just assumed that the gravitational and inertial masses were the same, and we cancelled them out.

Option H: RelativityH7 General relativityThe equivalence principleDescribe and discuss Einsteins principle of equivalence.When formulating his theory of general relativity, Einstein elevated these observations to a principle of physics:The equivalence principle states that No experiment can be conducted which will determine whether you are in a gravitational field or an accelerating reference frame.The equivalence principle can be stated in other ways: A frame of reference moving at constant velocity (a = 0) far from all masses is indistinguishable from a freely falling frame of reference in a uniform gravitational field.Yet another statement is that Gravitational and inertial effects are indistinguishable.

Option H: RelativityH7 General relativityThe equivalence principleDeduce that the principle of equivalence predicts the bending of light rays in a gravitational field.Consider a single photon of light passing from left to right as Dobson accelerates in the direction shown:Dobson observed a BENDING light beamBecause of the principle of equivalence, he cant tell the difference between an accelerating reference frame and a gravitational field.Thus he may infer that a gravitational field bends light beams!Path of photon

Option H: RelativityH7 General relativityThe equivalence principleDeduce that the principle of equivalence predicts that time slows down near a massive body. Recall the Twin Paradox where we discovered that time dilated only for the twin that accelerated.The equivalence principle then predicts that time dilation will occur in a strong gravitational field, which cannot be distinguished from an acceleration.Aging is slower near a large mass like a black hole!

Option H: RelativityH7 General relativitySpacetimeH.7.5Describe the concept of spacetime.H.7.6State that moving objects follow the shortest path between two points in spacetime.H.7.7Explain gravitational attraction in terms of warping of spacetime by matter.

Option H: RelativityH7 General relativitySpacetimeDescribe the concept of spacetime.In 1908, after Einsteins special theory was published, Hermann Minkowski proposed the concept of spacetime, wherein a fourth dimension of proper time ct was added to the usual three spatial dimensions x, y, and z. Recall from geometry that the distance d from the origin to a point P having coordinates (x, y, z) is given by

FYIIt turns out that the distance to a point varies depending on the frames of reference, because of length contraction and time dilation. I really wouldn't have thought that lazy dog Einstein capable of relativity.

Option H: RelativityH7 General relativitySpacetimeDescribe the concept of spacetime.Minkowski defined an interval I having the form It turns out that the interval I is invariant, meaning the I is the same regardless of the frame of reference even with relativistic effects.Einstein at first was not impressed with Minkowski's idea, calling it "banal" and "a superfluous learnedness." Eventually, Einstein used Minkowskis spacetime view of the geometry of the universe in his general theory of relativity (the relativity of non-inertial reference frames). FYINote that the time dimension is ct instead of c so its dimension is in meters (speed time).

Option H: RelativityH7 General relativitySpacetimeDescribe the concept of spacetime.EXAMPLE: As an example of the difference between a spacetime diagram and a traditional space diagram, contrast the plots of a particle in uniform circular motion in the x-y plane.SOLUTION: In the traditional diagram note that the particle keeps repeating its coordinates. In the spacetime diagram the particle never repeats its coordinates. It will repeat spatial coordinates as regularly as the in the traditional diagram, but it will never repeat its time coordinate. This is more in keeping with how things really are. Think of crossing a busy street- same spatial coordinates, different times!space diagramspacetime diagram(x,y,z,ct1)(x,y,z,ct2)(x,y,z)

Option H: RelativityH7 General relativitySpacetimeState that moving objects follow the shortest path between two points in spacetime.It turns out that in general relativity not only is spacetime invariant, but objects always follow the shortest paths between two points.In other words, objects have a propensity to follow paths through the world in such a way that the I in I2 = x2+y2+z2 (ct)2 is always minimized.FYIThe object simply follows the spacetime curvature without thought.

Option H: RelativityH7 General relativitySpacetimeExplain gravitational attraction in terms of warping of spacetime by matter. Einstein termed the natural paths followed due to the curvature of spacetime world lines.As we learned when we discussed fields, a force like gravity can be either caused by action at a distance (F = GMm/r2) or by the gravitational field (g = GM/r2).The spacetime curvature (field) eliminates the need for a planet to know where the sun is and to constantly exchange coordinate information with it, in order to know which way to orbit.Rather, the planet orbits simply by reacting to the field that is the curvature of spacetime. It follow its local world line without the need to know where the source of curvature comes from.

Option H: RelativityH7 General relativitySpacetimeExplain gravitational attraction in terms of warping of spacetime by matter.According to general relativity, the sun curves the spacetime surrounding it, as shown:

Each planet then moves in response to its local closed world line. The result is orbital motion without action at a distance.

Option H: RelativityH7 General relativitySpacetimeDescribe the concept of spacetime.One axis is ct and one is x:ctxFar from mass the particle will move in a straight line.

Option H: RelativityH7 General relativitySpacetimeDescribe the concept of spacetime.ctxClose to a large mass the particle will move in a curved line, responding to the local curvature of spacetime.

Option H: RelativityH7 General relativitySpacetimeDescribe the concept of spacetime.Close to a large mass like Earth the spacetime in its vicinity will become curved.All particles follow the shortest path in spacetime. T

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