Can a space-time curve be mapped
Hello and welcome to a video by Dr. Psi. Our subject today will remain a little abstract, just like the theory of relativity in general. Or do we occasionally move at the speed of light? So what. Now it is about the curvature of space-time. Sure, isn't it. Space-time curvature what's behind it? Well, let's deal with that a little today. Well, first we need to clarify a few terms. The three dimensions of space and time as the fourth dimension are known from classical physics. The length and time measurements should be independent of the reference system. And time is a variable that is independent of the state of motion of the observer. That is why one occasionally writes 3 + 1 here, so a total of four dimensions. If we now take the theory of relativity as a basis and consider the space and time coordinates there as closely balanced, they form a four-dimensional space-time. Yes, sometimes this is also referred to as a space-time continuum. This makes time a coordinate like any other in space. And, as with space in time, perspective changes in the time coordinates can occur. Just think of time dilation and the relativity of simultaneity. Yes, this is how we would have examined a few concepts of spacetime in more detail. And now we come to consider this somewhat abstract curvature of space-time. Let us first consider space-time without the presence of matter and suppress one of the space dimensions and also the time dimension. What then remains are two dimensions. This idea leads to a simple consideration of space-time as a 2D model. You can see such a 2D model here. In the literature, this area that you see here is often compared to a stretchy rubber skin. If a ball is placed on this rubber skin, there is a bump or dent. If we transfer this idea to our spacetime, we can combine this with the statements of the theory of relativity and come to a very important statement, namely gravitation bends space. Yes, with that we have explained the heading, so to speak. The sphere that we see here represents gravity and it curves the space. Yes, what are the consequences? Let's look at that in the next scene. Back to our 2D model, which was a simplification of our four-dimensional space-time without the presence of mass or matter. In this coordinate system, the well-known Euclidean geometry applies, parallels run without an intersection. The sum of the angles in the triangle is, well, you certainly know it, 180 °, correct. And the shortest connection between two points is a straight line. And now mass or matter comes into play. And spacetime is curved. What does this mean for the geometry? Now we can formulate the general theory of relativity, I'll shorten it here, you can often find it in the literature. General relativity is a theory of the geometry of space. And when we consider this geometry of space, we limit ourselves to determining the distance and come to the concept of geodesics, which represent the shortest connection between two points. Well what are geodesics on a curved surface? On the normal surface, flat surface, it is clear. Well, let's take a look at a cone here. And there we have marked a certain point and are wondering how the shortest connection between this rigid point around the tip of the cone and itself runs. Well, if we look at the network, we can find the green line we just made, which we imagine as the shortest connection, but we can also draw a straight line here. You see this red straight line. And when we build the cone again from the network of the cone, you will see this geodesic, which is a somewhat serpentine loop. That would be the shortest connection between the one point and itself. Well, you can also find these geodesics on the surface of the sphere. These are the great circles. And the planes and ships move on such great circles. Now we want to come back to experiments that have something to do with spacetime. Yes, we now come to a consequence of the curvature of space-time, which we already know from the experiments to confirm the general theory of relativity, namely the deflection of light by gravity. We see here in a first picture that an observation angle, let's say alpha, is normally established between two fixed stars. The second picture shows the conditions that can be observed during a solar eclipse under otherwise identical conditions. The star one has now apparently assumed a different position as a result of the deflection of light. The observation angle beta is now apparently larger than alpha. Well, image three shows the observation based on curved spacetime, that is, our 2D model with a dent. And here it can be shown how precisely these masses lead to a distortion of space-time and change the course of the geodesics. And so the geometry of the room is influenced by this. Ultimately, this general consideration of the change in geometry in the range of huge dimensions can explain the whole development of our universe. But that brings us into the realm of cosmology and that is now even more abstract and very far away. And the curvature of space-time alone requires a certain power of imagination. Well, let's summarize briefly. We have clarified a few terms, what spacetime is, what curvature of spacetime means due to the presence of matter, we have dealt with an example, the deflection of light by gravity. Yes, that was it again for today and I hope you understood something and I would be happy if we see each other again soon with a video of Dr. Psi.
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