Because it's really, really hard to visualize three-dimensional curvature (let alone four-dimensional space-time curvature). Drakkith's picture isn't bad, but it's still hard to understand what that means (at least to me).Crazyhorse2882 said:
... Here is rough indirect approximation and representation of gravity to a point(). A somewhat similar effect. A few pointers thought. It is important to limit yourself to only what the presentation is trying to convey. 2D appears to give the basic and effective illustration for GR. It is simpler when explained in manifolds. Anyways here is the link.Crazyhorse2882 said:
Cool. Though I think one thing to bear in mind is that setup has quite a lot of friction, so it doesn't produce orbits much at all like real ones. If you could produce the same sort of setup, but with minimal friction, that might change. But I doubt that's possible because anything placed on there will deform the sheet, which uses energy and acts as a source of friction. Gravity doesn't have this issue because you don't lose any energy when you deform space-time (if the deformation causes a reduction in the energy of the object doing the deforming, then that energy is stored in the fabric of space-time and not lost...the energy from deforming the sheet is lost to heat).julcab12 said:
The universe is three-dimensional therefore when gravity is projected onto a two-dimensional analog plane it is for demonstration purposes. Gravity collapses space around the center of gravity in three dimensional space but in a two-dimensional analog plain gravity bends space. Only in flatland does gravity bend space.Crazyhorse2882 said:
Clayjay said:
Gravity certainly is a warping of space as well as space-time.TumblingDice said:
If everyone understood and presented the rubber sheet model the way you do, we wouldn't have a problem with it. Unfortunately, very few do, so practically speaking it is a source of misconception and confusion, and that makes it a problem.Android Neox said:
I don't get what you are asking but it doesn't matter since the celestial orbits are well understood and there's no need for that kind of analogy (if that is in fact what you're striving for).FredKnowsNothing said:
You should read up on it. Google "The Twin Paradox" and really study it. The different paths through spacetime will likely become clear to you after a while.
I agree on the orbit being well understood I was thinking of a way to visualize the forces at play, why the Earth would not crash into the sun, how to think of the feeling on our bodies like the pulling force on your body when in an undertow but how you can overcome that force like the Earth does by moving perpendicular. But let's forget that one.phinds said:
AGAIN, read about and actually study the Twin Paradox. The different paths through space-time fully explain that the twins CANNOT have the same age when they meet back up. It has nothing to do with biological processes slowing down (they don't) it is just what happens because of different paths through spacetime.FredKnowsNothing said:
FredKnowsNothing said:
FredKnowsNothing said:
You are a master of understatement. At last count there were 18,397Drakkith said:
Biology and every other chemistry is all subject to the same clock regardless of speed and gravity.FredKnowsNothing said:
All true but still does not resolve his confusion because he does not understand different space-time paths creating differing amounts of time passage.rootone said:
I have the same issue getting past this “ball on water” depiction of space-time (ST). I would like to see and hear ST depicted as a neutrally buoyant ball (mass) suspended in instead of on water. In that case, and assuming the ball is a perfect sphere and its mass is uniformly distributed, it would displace the same amount of water (ST) at any point around the sphere. How then would the path of that passing mass be effected in terms of bending of ST? I get stuck here, as it seems to me that, in that case, gravity must be an unseen force - a force inconsistent with the two dimensional depictions of bending ST.Crazyhorse2882 said:
Hmmm. I'm not familiar with this depiction and I can't quite picture it from your description. What do you mean by "it would diplace the same amount of water (ST) at any point around the sphere"?MikeGF said:
Not having the math is the barrier. As Roger Bacon said nearly 800 years ago:MikeGF said:
Why would you like this? Why do you think it has any relevance to the actual theory of GR?MikeGF said:
The best way to get past this kind of barrier is to give up the idea that you can come up with any useful visualization or intuitive picture without knowing the math and without having tried to work any problems yourself using the theory. Pop science books, articles, and videos try to peddle the fiction that this can be done, but unfortunately it can't. GR simply does not work like anything in your current intuitions; if you want to understand it intuitively, you need to retrain your intuitions. And that requires going through the laborious process of learning the actual theory, which means learning the math.MikeGF said:
True but. It’s a bit like trying to make sense / feeling about any partial differential equation is telling you. You look at the x’s and the y’s and the z’s and, if you’re lucky, you can appreciate the higher ‘slopes’ involved. Try to draw the surface and you may ‘get it’ yourself but will you get it across to another person? 2D is a common language and that may be your limit for some models. For orbits , 3D on 2D can help but the risk is that the drum skin will be taken literally and a rubber sheet will fail.Chronos said:
About the time this thread was started....PeroK said:
The concept of spacetime was first introduced by Albert Einstein in his theory of General Relativity. In this theory, Einstein proposed that space and time are not separate entities, but rather they are interconnected and should be considered together. In order to visualize this complex concept, it is often represented on a 2-dimensional plane, where time is represented as the vertical axis and space as the horizontal axis. This allows for a simplified representation of the intricate relationship between space and time.
By representing spacetime on a 2-dimensional plane, it becomes easier to visualize and understand the concept of how space and time are interconnected. It allows for a simplified representation of complex mathematical equations and helps scientists and researchers to make predictions about the behavior of objects in the universe.
Yes, there are limitations to representing spacetime on a 2-dimensional plane. This representation is based on the assumption that the universe has only three dimensions (length, width, and height). However, some theories, such as string theory, suggest that there may be more than three dimensions. Additionally, this representation does not take into account the effects of gravity and other forces on the fabric of spacetime.
In the representation of spacetime on a 2-dimensional plane, the curvature is depicted as a bending or warping of the plane itself. This bending is caused by the presence of massive objects, such as planets or stars, which create gravitational fields that affect the fabric of spacetime. The amount of curvature is determined by the mass and energy of the objects present.
Yes, there are other ways to represent spacetime, such as using mathematical equations or diagrams. However, the 2-dimensional plane representation is the most commonly used and widely accepted method, as it allows for a simpler visualization of this complex concept. Other methods may be used to explore specific aspects or theories of spacetime, but the 2-dimensional plane representation remains the most useful and widely applicable.