Conceptual Physics – Chapter 4:Linear Motion Essay | …
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Many physical phenomena are not themselves light or matter, but are properties of light or matter or interactions between light and matter. For instance, motion is a property of all light and some matter, but it is not itself light or matter. The pressure that keeps a bicycle tire blown up is an interaction between the air and the tire. Pressure is not a form of matter in and of itself. It is as much a property of the tire as of the air. Analogously, sisterhood and employment are relationships among people but are not people themselves.
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Applying the Mathematical Continuum to Physical Space and Time:Following a lead given by Russell (1929, 182–198), a number ofphilosophers—most notably Grünbaum (1967)—took up thetask of showing how modern mathematics could solve all of Zeno’sparadoxes; their work has thoroughly influenced our discussion of thearguments. What they realized was that a purely mathematical solutionwas not sufficient: the paradoxes not only question abstractmathematics, but also the nature of physical reality. So what theysought was an argument not only that Zeno posed no threat to themathematics of infinity but also that that mathematics correctlydescribes objects, time and space. It would not answer Zeno’sparadoxes if the mathematical framework we invoked was not a gooddescription of actual space, time, and motion! The idea that amathematical law—say Newton’s law of universalgravity—may or may not correctly describe things is familiar,but some aspects of the mathematics of infinity—the nature ofthe continuum, definition of infinite sums and so on—seem sobasic that it may be hard to see at first that they too applycontingently. But surely they do: nothing guarantees apriori that space has the structure of the continuum, oreven that parts of space add up according to Cauchy’sdefinition. (Salmon offers a nice example to help make the point:since alcohol dissolves in water, if you mix the two you end up withless than the sum of their volumes, showing that even ordinaryaddition is not applicable to every kind of system.) Our belief thatthe mathematical theory of infinity describes space and time isjustified to the extent that the laws of physics assume that it does,and to the extent that those laws are themselves confirmed byexperience. While it is true that almost all physical theories assumethat space and time do indeed have the structure of the continuum, itis also the case that quantum theories of gravity likely imply thatthey do not. While no one really knows where this research willultimately lead, it is quite possible that space and time will turnout, at the most fundamental level, to be quite unlike themathematical continuum that we have assumed here.