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Galaxy NGC4414 from HST Astronomy 162:
Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30

Lecture 32: Space, Time & Gravity
General Relativity

Readings: Ch 24, section 24-2

Key Ideas

General Relativity:
Modern Theory of Gravitation
Matter tells spacetime how to curve.
Curved spacetime tells matter how to move.

Tests of General Relativity:
Perihelion Precession of Mercury
Bending of Starlight near the Sun

Newtonian Gravity

A mass m is accelerated by another mass M:

Newtonian acceleration derivation

Einstein's Discontents

Einstein had two objections to Newton's formulation of Gravity:
  1. The force law (line 1) implies instantaneous knowledge of the distance, R, but information is only transmitted at the speed of light.

  2. The same mass, m, appears in both the force and acceleration laws (lines 1 & 2), but disappears from the final acceleration (line 3). This seems to be coincidental.

"I frame no hypothesis."

Newton could not explain what gravity was.
  • He asserted that Gravity is an "action at a distance".
  • He had no hypothesis for what "agent" communicates the gravitational force across empty space.
  • People assumed that gravity worked as described by Newton, but didn't seem to worry about why it worked that way...

    The Principle of Equivalence

    The first postulate of Special Relativity states:

    In 1907, Einstein generalized this statement:

    There is no distinction between gravitational and inertial accelerations.

    For example, a person sealed in a closed box (no windows) drops an apple and watches it fall down with an acceleration of 1-g. There are no experiments that can be performed inside the boxes that will distinguish between two possibilities:

    1. They and the box are at rest on the surface of the Earth, and the apple is accelerated downward by the Earth's gravity at 1-g.

    2. They and the box are in free space accelerating upwards at 1-g by constantly burning rocket engines, and the apple appears to accelerate downwards because the floor of the box rises up to meet it.
    Both views of the situation are equivalent and indistinguishable.

    General Relativity

    Gravitation binds matter to matter.

    But how does matter "know" that the other matter is "out there"?

    The Goal: Generalize Relativity


    Enter Geometry

    Newton's laws lead to a geometric description of motion:

    Least Action Principle:

    Use geometry to describe the paths of objects moving through space.

    But,

    Einstein showed:

    Modified the Least Action Principle:

    Need to describe the geometry of spacetime.


    The Shortest Path...

    On a flat surface:

    On a curved surface:


    Geometry the Unifier

    In empty space, spacetime is flat:

    Moving objects follow straight lines.

    Newton would have said:


    Curved Spacetime

    Matter curves the spacetime around it:

    A freely falling object follows a curved path.

    Newton would have said:


    A New Theory of Gravity

    General Relativity may be summarized as follows:
    Matter tells spacetime how to curve.
    Curved spacetime tells matter how to move.

    This replaces the Newtonian idea of a "force" with the curvature of spacetime as the agent of Gravity.

    GR has so far withstood all experimental tests.

    [Note: The summary statement above is due to physicist John Archibald Wheeler, who also coined the term "black hole" in the 1960s].


    The Precessing Orbit of Mercury

    Mercury's orbit major axis precesses slowly by approximatesly 574 arcseconds/century:
    Perihelion Precession of Mercury

    Einstein 1, Newton 0

    Newtonian gravity:

    General Relativity:


    Bending of Starlight

    Light travels on the shortest path through spacetime.

    Prediction:

    Confirmed: during the 1919 Total Solar Eclipse.
    Gravitational bending of starlight schematic Observations from the 1922 Solar Eclipse

    Another manifestation of gravitational bending of light by massive objects is the phenomenon of "strong gravitational lensing". This is seen in some massive clusters of galaxies (and a few individual galaxies) with bright objects (galaxies or quasars) directly behind them. The Hubble Space Telescope has made some spectacular images of such gravitational lenses:

    The huge masses of the galaxy clusters acts like a lumpy lens, distorting the images of more distant galaxies far behind them into luminous arcs. You can see an analogous effect by holding a lens at arm's length and looking at how distant objects are distorted as the lens passes between you and them.

    Whither Newton?

    Newton's laws are approximations of GR.

    Conditions:

    Newton's Laws:

    So we continue to use and teach Newtonian physics, only resorting to the more complex mathematics of General Relativity when a full treatment is required.

    However, Relativity (both Special and General) do have real-world applications. For example, The GPS Navigation System.


    Return to [ Unit 5 Index | Astronomy 162 Main Page ]
    Updated: 2006 February 18
    Copyright Richard W. Pogge, All Rights Reserved.