![]() ![]() If you fly through a portion of space that was squished in the direction perpendicular to the direction of your flight, you’d find that space seemed to curve and stretch around you as you flew through the squished section, and then returned to normal afterwards. But why not just call this squishing? The reason is because of what it would be like to fly a space-ship through squished space. The degree of the squishing in a given direction is the degree to which you’ve “curved” that Nerf cube from that direction. When you take it out of the container, however, it resumes its normal shape, due to its elasticity.Ĭurved space, as described in relativity theory, is like Nerf space. A Nerf dinosaur, for example, can be squished into a much smaller container, one which doesn’t fit the shape of the foam, but of the container, such as that of a cube. They even make toys out of this stuff, under the brand name “Nerf.” Nerf toys can be squished in all sorts of ways. The notion of “curved space” is notoriously difficult to describe, but I think the best way to think of it is as “scrunched” or “squished” space. ![]() But mathematicians also realized that they had to come up with a notion of intrinsic curvature in order to speak about, for example, the “curved” spaces described in relativity theory. ![]() For example, when a line curves in this sort of spacetime, the degree of the curvature can be measured, and this is known as its extrinsic curvature. The notion of extension in space and time described above is that used by physicists and mathematicians, and its various permutations can be calculated in various ways. I can therefore say that the stone extends a certain volume, in three dimensions, but if we consider time as fourth dimension, we can say that it extends in four dimensions, as what mathematicians call a hypersolid, or a four dimensional shape that ‘moves’ through spacetime, even when the object ‘sits still.’ Time, similarly, can be measured as distance, for example, by measuring how far the hand of a clock has moved. The distances, along the x, y, and z axes, the ‘three dimensions’ of space, can be used to measure the degree of extension, and from these distances, we could calculate the volume that the stone ‘takes up’ in space. This turns out not to be the case with electricity, which simply gets more intense the more is pushed into the same general location in space. We can displace the stone by pushing it out of the way, and two stones can’t be in exactly the same place, simply because matter displaces other matter. That is, a stone takes up a certain amount of space, and it does so over a period of time. Objects in our everyday experience extend over space and time. Relativity Theory: Curved Space, Intrinsic Curvature, and Intension This post will explain what it might mean to think of spacetime intensively, as well as extensively, and why space and time curve into phenomenon all the time, and not just in the strange examples described in Einsteinian relativity theory or quantum mechanics, but in concrete ways in our everyday lives, and in fact, whenever we think, feel, or experience. But what if space and time could be inside certain phenomenon? In fact, this happens all the time. We normally think of things being inside space and time. ![]()
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