![]() (This line of reasoning turns out to be faulty, by the way, but it's a mistake that pays off in the end.) R μν − (½ R − Λ) g μν =Įinstein assumed that the universe was static and unchanging. The cosmological constant was invented as a way to hold back gravity so that a static universe wouldn't collapse. R μν − ½ Rg μνĮinstein's odd choice of sign might make more sense if you factor out the metric tensor on the left side of the equation. Or maybe gravity is the curvature of space-time caused by mass-energy on top of the curvature of space-time itself. Maybe gravity is the curvature of space-time caused by the mass-energy of stuff within it plus the energy of space itself. The cosmological constant is a quantity used in general relativity to describe some properties of space-time. Space-time is more than just a set of values for identifying events. They will be derived with minimal to no proof, however. Some of these simpler equations are appropriate to the level of this book, which means you can learn how to do some general relativity. Statement of the awesome: These equations can be broken down into simpler equations by those with a lot of skill.Statement of the obvious: Solving these equations turns out to be hard.In reverse adjective order these equations are differential because they deal with rates of change (rates of differing), partial because there are multiple variables involved (multiple parts), nonlinear because some of the operations are repeated (a rate of change of a rate of change), and coupled because they cannot be solved separately (every equation has at least one feature found in another). What looks like one equation is actually a set of ten coupled nonlinear partial differential equations. That's right, I used the plural form - equations. The Einstein field equations… R μν − ½ Rg μν = Gravity isn't a force, it's the curvature of space-time caused by the presence of mass-energy. Objects trace out world lines that are geodesics (paths of least action in curved space-time) unless acted upon by a net external force - a new version of the law of inertia.Mass-energy curves space-time - a new version of Hooke's law.The local effects of gravity are the same as those of being in an accelerating reference frame. Accelerated motion in the absence of a gravitational field (apparent weight) is indistinguishable from unaccelerated motion in the presence of a gravitational field (true weight).The absence of a gravitational field (true weightlessness) is indistinguishable from free fall acceleration in a gravitational field (apparent weightlessness).I will not define time, space, place and motion, as being well known to all. Discussion an introduction of sorts for a disorganized section
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