![]() I can understand that it’s tricky to describe it in words, from a mathematical standpoint, but there should be some way to make the idea more understandable. I think I can see what you’re getting at, but it’s easier for me to imagine ‘space’ as something plastic, with gravity as the metric ‘shear’, acting in it. ![]() And from the perspective of someone living on that surface I do not expect it to be seen either? If I was to draw parallel lines on that paper, before bending it I do not expect them to intersect. That’s not creative prose, I mean that literally.Īnd what do you mean by a curved 2D space?Ī bent paper might be defined as ‘curved’, but only when looked at from a 3D perspective. It’s a little more complicated because the time dimension and the spacial dimensions are fundamentally different, but not as much as you’d think.Īnother, slicker-sounding way to describe gravity is: “Things fall because time points a little bit down”. Literally, it takes the original “flatness” of empty space, and curves it. ![]() This is due entirely to the Earth curving space-time around it. As you run time forward you’ll notice that, even though no force is acting on them (don’t say gravity) and they are traveling in straight lines through space-time, they still move together (fall toward the Earth). I say hovering in place because this means the lines they trace out in space-time are (initially) parallel. Now imagine two people hovering above opposite sides of the Earth. So if you’re sitting still (traveling forward in time), and no one applies a force to you, you’ll continue to sit still (travel forward in time). ![]() If an object is not experiencing any force, then it will travel in a straight line through space. These lines are parallel twice, but also intersect twice. They don’t have the same brightness, but they have the same size.A straight line on a sphere always traces out a "great circle", like the equator. Let us assume that there is a class of objects which have the same true size no matter where it is in the universe, which means they are like standard candles. Depending on how the matter is distributed in the space, there are smaller variations in the curvature. The universe has a certain topology, but locally it can have wrinkles. $$ds^2 = c^2dt^2 - \left \$$ Global Topology of the Universe $$ds^2 = a^2(t)\left ( dr^2 r^2d\theta^2 r^2sin^2\theta d\varphi^2 \right )$$įor space–time, the line element that we obtained in the above equation is modified as − The Metric for flat (Euclidean: there is no parameter for curvature) expanding universe is given as − The model depends on the component of the universe. In the future, when the scale factor becomes 0, everything will come closer. The comoving distance which is the distance between the objects at a present universe, is a constant quantity. If the value of the scale factor becomes 0 during the contraction of universe, it implies the distance between the objects becomes 0, i.e. Step 4 − The following image is the graph for the universe that starts contracting from now. Step 3 − The following image is the graph for the universe which is expanding at a faster rate. The t = 0 indicates that the universe started from that point. Step 2 − The following image is the graph of the universe that is still expanding but at a diminishing rate, which means the graph will start in the past. the value of comoving distance is the distance between the objects. Step 1 − For a static universe, the scale factor is 1, i.e. Let us see how the scale factor changes with time in the following steps. The expansion of the universe is in all the directions. The space is forward for photon in all directions. Suppose a photon is emitted from a distant galaxy. Model for Scale Factor Changing with Time In this chapter, we will understand in detail regarding the Robertson-Walker Metric. Horizon Length at the Surface of Last Scattering. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |