![]() ![]() You could slice the block of cheese into a series of 2D scoop-shaped slices, and Euclid’s axioms would not hold on these slices, so they are not flat. However, it would also be possible to make a curved knife, like a sharp-edged spoon. Now, you can slice the cheese with a knife and get a series of 2D slices, and Euclid’s axioms would hold on each 2D slice, so the slices would be flat too. For all practical purposes the 3D geometry is flat, meaning that Euclid’s axioms hold. So how can we have curved spacetime and yet flat space? It seems that a distinction between space and spacetime is being drawn.Ĭonsider a solid block of cheese. As you pointed out, what we have in the universe is curved spacetime. However, what is perhaps more interesting is to consider what is meant by space. Meaning that the Pythagorean theorem holds, parallel lines don’t intersect, the sum of angles in a triangle are 180 degrees, etc. When they say that space is flat they mean that Euclidean geometry works in space. What do they really mean when it is said that universe (or, space) is flat? I have checked several sources and it hasn't helped me. What do they really mean when it is said that universe (or, space) is flat? As a layman, I always get confused. ![]() Whenever youĬan find three points in space, and join them with laser beams, andįind that the triangle doesn’t have the expected 180 degrees, thatĪnd when no matter where the spacecraft are the angles add up to 180ĭegrees-that is what it means for space to be flat.ĭoes it mean one should conduct such an experiment of creating a triangle using laser beams in an empty space devoid of matter? Since as long as there is matter the General Relativity is going to play its role and light is going bend around and angles will add up to more than 180 degrees. Regardless, this is what it means for space to be curved. Or youĬould distrust math and physics and just go out to space to see for Is a consequence of Einstein’s general theory of relativity. You could do the appropriate calculations and realize that this fact Now each of you can measure the angle between the two beams that go inįact: Those three angles won’t always add up to 180 degrees. You point lasers at one another and form a triangle of beams. Three travels to some place in the near universe. Instead, you and two buddies each have a spaceship, and each of the Spacecraft to fly straight ahead or to turn by 90 degrees to the left. Raises all sort of thorny issues about what exactly it means for a That would not be ideal, though, because it You could think of a spacecraft tracing a triangle or a squareīy traveling in space. To avoid any confusion caused by the Earth, take a trip to outer So here we come to the basic fact of life that I was referring to at The quote below is taken from the following web article How can you separate spacetime and space from each other?! Well, IMHO, the spacetime, space, and universe go hand in hand. But, then, at the same time it is said that space (or, universe) is Euclidean but spacetime is curved. ![]() ![]() I would say that by the phrase "universe is flat" what they really mean is that the space is Euclidean or flat. In simple terms, the universe is made up of matter and space. For example, in the video,, and at many other countless places on internet, they show solid surfaces as if we are supposed to measure the curvature of universe by standing on some solid surface. The universe in itself is not some solid object. It is often said that the universe is flat. They can form a triangle using long ropes and the angles of such a triangle would sum up more than 180 degrees since earth has positive curvature. Since the surface of earth is also almost spherical therefore an experiment can be conducted by three persons who are standing many, many kilometers away from each other. The angles add up to 67+48+73=188 degrees. In the picture below a triangle has been drawn on a spherical shaped object. ![]()
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