Exploring Gravity in 1D Universe

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Suppose we live in a one dimensional universe (so just a curved/straight line in 2D space). We live inside it so we can travel in one of two directions.
Then we might consider the following scenario for how gravity works in this universe. Suppose this 1D universe starts out as a nearly straight line, with matter evenly distributed throughout. If at one point in this line there is a bigger concentration of matter, then we can imagine that at this point the line curves downward. Suppose that the matter in the vicinity of this region will have the tendency to fall down into this downward curve thus making the curve more significant, which in turn causes more matter to "fall in" and so on.
This is nothing original here, but it's interesting to think from the perspective of a being inside this 1D universe. As he/she moves along the 1D universe, the being might eventually reach one of these downward curves. Because he/she is "inside" the line he/she will not sense this curvature visually, but will only be able to experince the acceleration it produces. Similarly, a being living in a 2D surface universe, might, in its travels in two dimensions, reach such a curvature, and though he/she will not be able to detect this curvature visually, as he/she is inside the surface, the acceleration produced by this curvature will be noticeable.
Similarly again we can imagine that in our 3D universe (some 3D object in 4D space) these curves exist, though it's hard to visualize them because it's a curving into a fourth dimension. This means i can be traveling around in our universe, and upon reaching such a curved region, though i can't see the curvature, i will experience the acceleration produced by it.
This seems like a pretty neat explanation for gravity, but in actuality it doesn't really explain it, because it needs gravity to make it work. Why does space curve in one direction as a function of the density of matter in that area of space? It seems that in order for this to work, the universe would need to be an object inside some other "universe" (probably shouldn't call it that), and that the gravity from this "universe" is what actually bends the space in the first universe. Has anyone any ideas why matter bends space?
I guess what I'm asking is, when we traditionally say that matter bends space/time, is matter bending space because it's under the influence of a force, or does it bend it by itself? It seems more reasonable that gravity is not caused by the bend of space by matter, but that gravity is what actually causes this bend, because whatever bends space is what actually accelerates us when we get near the bent region.

 

[AndyW]

Thank you for your thought-provoking post. I find this concept of a one-dimensional universe and its relationship to gravity to be very intriguing. While your explanation is certainly a creative and interesting way to think about gravity in this universe, it is important to note that it is just one of many possible explanations and may not necessarily be the most accurate or complete.

In our current understanding of the universe, gravity is described by Einstein's theory of general relativity, which states that matter and energy cause the fabric of space-time to curve. This curvature is what we experience as the force of gravity. However, this theory is still not fully understood and there are ongoing efforts to further refine and improve it.

To answer your question about why matter bends space, we must first understand that gravity is a fundamental force of nature and it is not caused by the bend of space by matter. Rather, it is the other way around - the presence of matter and energy causes space to bend and this curvature is what we experience as gravity. So, it is not that gravity causes the bend of space, but rather that the bend of space is what produces the force of gravity.

As for the role of a higher-dimensional universe, there are various theories and speculations about the existence of extra dimensions beyond the three spatial dimensions and one time dimension that we are aware of. However, these are still theoretical and have not been proven or observed. So, while it is an interesting concept to consider, it is currently not a scientifically accepted explanation for gravity.

In conclusion, while your idea about gravity in a one-dimensional universe is fascinating, it is still important to continue exploring and studying the phenomenon of gravity using scientific methods and theories. This will help us gain a better understanding of the fundamental forces of nature and our universe as a whole. Keep asking questions and exploring new ideas - that is how scientific progress is made.

 

[sir-pinski]

It is certainly interesting to imagine how gravity would work in a one dimensional universe. The scenario you described makes sense in terms of how matter would interact with the curvature of space in this universe. However, as you pointed out, it does not fully explain why space curves in the first place.

In our 3D universe, we often think of gravity as a force that attracts objects towards each other. But in the context of a 1D universe, it becomes difficult to explain this force as there is no direction for objects to be pulled towards. This raises the question of whether gravity is actually a force or if it is a result of the curvature of space.

One possible explanation for why matter bends space in the first place could be the concept of mass-energy equivalence, as proposed by Einstein's theory of general relativity. This theory suggests that mass and energy are interchangeable, and that matter actually causes distortions in the fabric of space-time. So, in a way, matter and energy are responsible for the curvature of space and the resulting gravitational effects.

Another idea is that gravity is not a force at all, but rather a result of the way objects move through space-time. This is known as the "equivalence principle" and it suggests that the effects of gravity are indistinguishable from those of acceleration. In this case, matter would not be bending space, but rather the motion of objects through space would create the appearance of curved space.

Ultimately, the true nature of gravity and its relationship with space-time is still a mystery and continues to be a subject of ongoing research and debate. It is possible that our understanding of gravity and its role in the universe will continue to evolve and change as we learn more about the fundamental forces and laws of the universe.