Initial Conditions [1/9] |
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One of the important innovations that created modern science around the year 1500 A.D. was the idea that the laws of the material universe could be understood meaningfully only by expressing physical properties as quantified measurements, that is, in numerical terms and not just in words. | ||
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Initial Conditions [2/9] |
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The use of numerical quantities to describe the physical world is the reason why the laws of physics must ultimately be expressed as mathematical equations, and not simply as ordinary sentences. | ||
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Initial Conditions [3/9] |
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For example, although Newton's laws are expressible in words, in order to apply the laws to study a particular system, it is necessary to employ the laws in their form as mathematical equations. | ||
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Initial Conditions [4/9] |
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Newton's laws are perhaps the most important examples of dynamical laws, which means that they connect the numerical values of measurements at a given time to their values at a later or earlier time. | ||
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Initial Conditions [5/9] |
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The measurements that appear in Newton's laws depend on the particular system being studied, but they typically include the position, speed, and direction of motion of all the objects in the system, as well as the strength and direction of any forces on these objects, at any given time in the history of the system. | ||
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Initial Conditions [6/9] |
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In expressing the measurements appropriate for a given system---whether it be the Solar System, a falling object on earth, or ocean currents---the values of the measurements at a given starting time are called the initial conditions for that system. | ||
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Initial Conditions [7/9] |
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As dynamical laws, Newton's laws are deterministic because they imply that for any given system, the same initial conditions will always produce identically the same outcome. | ||
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Initial Conditions [8/9] |
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The Newtonian model of the universe is often depicted as a billiard game, in which the outcome unfolds mathematically from the initial conditions in predetermined fashion, like a movie that can be run forwards or backwards in time. | ||
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Initial Conditions [9/9] |
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The billiard game is a useful analogy, because on the microscopic level, the motion of molecules can be compared to the collisions of the balls on the billiard table, with the same dynamical laws invoked in both cases. | ||
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