Bending Space-Time, Gravity
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Bending Space and Time, and Gravity
The last article described the straight lines of "special" relativity. It explained                     the 'relativity' of space and time, distances and angles, in terms of flat,                     tilting, two-dimensional surfaces and the two-dimensional creatures inhabiting                     this three-dimensional universe of rising services. Surfaces were "stacked"                     upon each other, across time, as a series of consecutive moments, creating                     stacks of moments in – or rather 'across' – time. This simpler universe was                     used to make the concept of relativity easier to grasp. In our universe,                     instead of stacks of two-dimensional surfaces tilting with respect to each                     other across time, stacks of three-dimensional 'spaces' tilt with respect to                     each other, in a universe with 'four' dimensions, not three.
The important point that the last article should have made upon the reader is that the concept of now – that                     corresponding to an all-inclusive, universal present-moment 'now' – is, and                     this is to use the same term that Einstein himself chose to use, a mere                     "stipulation" that we place upon physical existence: nothing actually                     physically existent. In other words, there is no such thing existent outside of                     our mind, regardless of how convinced our minds might be that a universal,                     present moment corresponds to the entire universe. Put bluntly, spaces tilting                     into the future in one direction for a surface considering itself not moving,                     and tilting into the past in the opposite direction with respect to such a                     surface means there is no such thing nor can there ever be such a thing as a                     universal present-moment. Instead, there are many, as many as there are unique                     motions in the universe. We remember that this explanation was discovered by a                     two-dimensional Einstein, who explained how the speed of light, and                     correspondingly the laws of physics, the speed of light being an indispensable                     element of those laws, never changed with motion. This physicist explained the                     most simple case example, that for ‘uniform’ motion: motion that does not                     change speed or direction.
For this article, we return now to our two dimensional Einstein at the moment (albeit a stipulation that we                     impose upon physical existence, not existing beyond the motions of our                     thoughts) he explained the relativity of space and time, distances and angle                     for uniform motion, which is called special relativity: the relativity of space                     and time, distances and angles for uniform motion.
Special relativity’s tilting of surfaces (as well as that of spaces and lines) would 'seem' to                     explain a great deal about two-dimensional reality, though it would not                     immediately explain one rather significant aspect of it, namely gravity; though                     it would, quite naturally, most unavoidably, and rather obviously, lead straight to its explanation; and thus distinguish                     'special' relativity as a unique and singularly 'special' case of a more                     'generalized' form of relativity's geometry, namely "general relativity",                     which, unlike special relativity's straight-line geometry, is a geometry with curves.  Surprisingly, explaining how the speed of light                      never changes with uniform motion in order to keep the laws of nature (of physics) from ever changing                     (i.e. special relativity), explains also gravity! In other words, even though                     we might hardly imagine how, and perhaps even further hardly imagine that it                     even ‘should’ explain it, the speed of light being constant and physical laws                     correspondingly never changing (a corollary) ultimately leads to a very, very,                     very accurate explanation, in the form of a description, for gravity. And, this explanation (                     this description) is absolutely the best testable explanation that has ever existed. In actual                     fact, every last test that science has ever made confirms relativity’s validity                     for explaining space, time, ‘big’ motion, and, most significantly, gravity,                     making relativity’s truth a cornerstone and fundamental foundation of physical theory.
Just as relativity's explaining gravity by virtue of the speed of light being                     constant might seem a surprising relationship, so is the ease with which this                     relationship can be understood surprising also, because applying special                     relativity’s straight-line geometry of unchanging, uniform motion to                      changing, non-uniform motion, is, surprisingly, perfectly appropriate for doing the same thing for                     the phenomena of gravity. Gravity’s effects are completely indistinguishable                     from non-uniform motion. And this is how.
Giving it any thought, the two-dimensional physicist who discovered the special                     relativity of space and time (their inseparability), with respect to 'uniform'                     motion, motion that does not change speed or direction, could not help but                     notice that not all motion occurred at the same 'uniform' speed and unchanging                     direction, but that a great deal of the motion in their universe, very often,                     occurred in a 'non-uniform' way. That is to say, that motion in their universe                     of surfaces would very often, just as it so very often does also in our                     universe of spaces, change in a 'non-uniform' way, either speed, direction, or                     both. Furthermore, because so much motion in their universe would be                     non-uniform, changing from one speed or direction to another in a (seemingly) continuous                     way, then he or she could only conclude that where surfaces tilt as a result                      of uniform motion, surfaces must also be 'bending' with any motion that was non-uniform. Such a conclusion                     would be inescapable, since bending is really nothing more than just a progressively more and more, or less and less tilted frame (though in actual                     fact it is much more complex), corresponding to progressively changing speeds                     or directions (non-uniformly). Realizing that this bending created the 'equivalent'                     effect as gravity on his or her two-dimensional surface, this physicist who                     discovered the first half of the geometry of their universe would now have                     discovered the other half of the                     geometry of his or her universe. This physicist would have discovered the relativity                     of space and time measures (distances and directions [angles]), subject to the                     effects of non-uniform motion and hence, equivalently,                     to the effects of gravity.  Like                     Einstein, such a physicist would have discovered the 'general' relativity of                     surface-time, describing how surface-time 'bends', relative to two-dimensional gravity and to non-uniform motion.                     Finally, there would exist a description of two-dimensional gravity that worked                     accurately.
Just as the great two-dimensional physicists discovering his or her two-dimensional                     version of 'special' relativity could extend that theory and its straight-line                     geometry, by using this singularly simple geometry as a 'special' case "curve"                     for a broader, more comprehensive geometry, that of two-dimensional 'general'                     relativity, so can we three-dimensional creatures do the same thing; which is                     exactly what the great three-dimensional physicist, Albert Einstein, did, by                     extending the description of special relativity's effects upon uniform motion                     (motion that does not change speed or direction) upon three-dimensional space                     (as opposed to a two-dimensional surface) and time, to non-uniform motion                     (again, motion that does change speed, direction, or both), and 'equivalently',                     to the effects of gravity, since the effects of gravity are absolutely indistinguishable from the effects of inertia.  By imagining special relativity’s                     straight lines as curved lines, we can create a conceptual description of space                     and time together (space-time), and a way to imagine the effects of mass, as                     the force of either inertia or gravity upon it.  In this way, we can logically derive the Theory of General                     Relativity in terms of a concept (namely, bending), just as Albert Einstein did                     (in a formal and more precise way using mathematics, instead of using words as                     we are doing here).
The Theory of General Relativity extends Special Relativity’s principles for 'uniform' motion, applying them to                     the non-uniform motion of acceleration (motion that continuously changes speed,                     direction, or both, corresponding to a 'bent' set of space and time measures                     [distances and angles]) and "turning" (changing direction, corresponding to a                     "skewed" set of space and time measures) to those of gravity, in order to                     describe these effects upon space and time measurements. Gravity, like motion,                     affects both the pace of time, and the length of spatial distances. Its effects                     are the same as those of acceleration and/or turning, compressing space, and                     dilating time, in a way that is non-uniform (and so curved or skewed, instead                     of straight). General Relativity uses the 'equivalence' of the 'inertial'                     effects of non-uniform motion, in a way that is non-uniform (and so, "bent"                     [curved], instead of straight).<
General relativity describes how space and time bend (bending being a                     complexity of tilting), as a consequence of the effects of mass's gravity, and                     likewise, as a consequence of the non-uniform motion of acceleration (the                     former, gravity, being indistinguishable from the latter, acceleration).                     Needless to say, every experiment ever conducted by science repeatedly confirms                     relativity's remarkably accurate description of space, time, 'big' motion, and gravity
Because it works so flawlessly, relativity's accuracy is unquestionably true – it is as                     true as space, time, mass, and energy's gravity are 'true'; as true as the                     speed of light being constant and the laws of nature (physics) not changing as                     a consequence of motion or of anything else are true; as true as the                     conservation of energy and momentum are, as true as the passage of time is,                     while you read these words and think the thoughts that they yield as you do so.                     General relativity is a brilliantly stunning example of natural truth's                     expression and of the marvels that such an expression can accurately reveal                     about nature's phenomena.