This space is positively curved in two dimensions. There's zero curvature, and parallel lines or beams of light through the space or along the space stay parallel forever. In space like this, whether in two or three-dimensions, the angles of a triangle add up to 180 degrees. Here's a two-dimensional space that's familiar and Euclidean. In this view, space can have global curvature. ![]() Think of a bug crawling over a rumbled sheet of paper or rubber. It also can be dynamic and expand or contract. Einstein's view of space, somewhat different. We have to imagine this in the three dimensions of space that we inhabit. Just imagine a bug crawling over a fixed grid of graph paper extending infinitely in all directions. Here's Newton's view of space, rectilinear, rigid, not expanding or contracting. Actually, in my observatory here, the multiple mirror telescope, when a image of a single quasar was seen as multiple images caused by this mirage effect of gravitational lensing. It was predicted in the 1930s and finally observed in the 1970s. This phenomenon is called gravitational lensing or the gravitational deflecting of light. The deflection angle is small, for example, for a galaxy causing the bending of light or for the sun causing the bending of a starlight as in this diagram. This curvature makes an observed bending in the path of light as light follows the curvature of space. Mass and energy both cause space to be curved. But they also apply to large situations of curved spacetime like the universe itself. As we'll see, a close to a black hole is one example. This only applies the Einsteinian theory in general relativity in situations where the gravity is very strong. Far away, the theory of Newton would apply. Objects with lots of mass and energy will curve space and distort time nearby. Mass-energy tells spacetime how to curve while curved spacetime tells mass-energy how to move. The Einsteinian concept is quite different. The Newtonian concept is that mass tells gravity how much force to exert and the force tells the mass how to move. ![]() They are part of a four-dimensional construct called spacetime. Space and time are interchangeable and one can be changed into the other in different situations in the real universe. He links them formally with the equation E equals mc squared. But to Einstein, mass and energy are interchangeable. Space and time are very different things. To Newton, mass and energy are very different things. Making this comparison throws into sharp relief just how dramatic and revolutionary general relativity was. ![]() These two very great scientists had completely different ways of thinking about the nature of gravity in space. Let's compare the worldviews of Einstein and Newton regarding space and time. What came before the Big Bang? Is there anything outside our universe? What is reality? We'll finish by looking at the role of life in the universe and ask whether the earth is the only place with biology on it. At the end, will ask questions that don't necessarily have answers. Finally, we will discuss how modern cosmology has shown us that we live in an ancient universe (14 billion years old), in one galaxy in a universe of hundreds of billions of galaxies. We will then learn about the revolutions in physics in the early 20th century that redefined our ideas of space and time, mass and energy. We'll then examine the revolutions of Copernicus, Galileo, and Newton that redefined our place in the universe. We will start with prehistoric cultures who kept accurate calendars and move through the time of the Greek philosophers who laid down the rudiments of logic and mathematics and the modern scientific method. ![]() We'll look at how humans learned to ask questions about the universe, and even before the invention of modern instruments like the telescope, learned some amazing things about their place in nature. This is an introductory level course about the history and philosophy of astronomy, the oldest science.
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