# Objects Falling in General Relativity

• d-richard
In summary, the conversation discusses the concepts of special and general relativity, the curvature of space-time, and the understanding of rotation, velocity, and acceleration without a force. The use of visualizations and analogies is suggested for better understanding, particularly for those with a limited understanding of mathematics. The video provided by the poster is recommended and praised for its helpfulness.
d-richard
Greetings,
I've been learning about special relativity and most of the learning media included a part of general relativity. From that I learned that space-time is curved and orbits are nothing more than an object following a path in 4D. However I do not understand how those objects may rotate, as that requires a centripetal force, which in Newton's case was gravity. Also I do not understand how objects may change their velocity's direction without a force or torque in the case of rotational motion (the objects velocity constantly changes during rotation and its angular velocity increases from 0) I also do not understand how objects fall in straight paths on Earth and accelerate in the absence of a force or what keeps us stuck to the ground. Sorry for being so long and thanks for any answers.
P.S As my maths is pretty basic (linear algebra and Euclidean geometry only) I would appreciate a qualitative, not quantitative answer. However if any points must be shown mathematically, then I won't mind the use of maths. Thanks a lot.

d-richard said:
I also do not understand how objects fall in straight paths on Earth and accelerate in the absence of a force

Check out this animation:

Orbits are more difficult to visualize in this way, because they involve 2 spatial dimensions, which together with time require visualizing a curved 3D manifold. An alternative analogy are light rays in a block of varying optical density:

http://www.nature.com/nphoton/journal/v7/n11/full/nphoton.2013.247.html?WT.ec_id=NPHOTON-201311

Last edited by a moderator:
2 people
I had the same doubt OP had and this video is simply perfect. I want to thank you A.T for sharing it! Really.

cb

thanks, that really clarifies things. Great video

Hello,

Thank you for your question. In general relativity, the concept of gravity is quite different from what we are used to in Newtonian mechanics. In fact, gravity is not considered a force in general relativity, but rather a curvature of space-time caused by the presence of mass or energy. This curvature affects the motion of objects and causes them to follow a curved path, which we perceive as falling or orbiting.

To understand how objects can rotate in general relativity, we need to look at the concept of geodesics. In this theory, objects follow the shortest path in the curved space-time, also known as a geodesic. When an object is rotating, it is still following a geodesic, but this path may appear curved to an outside observer. This is similar to how an object moving in a straight line on a curved surface, such as a sphere, may appear to be moving in a curved path to someone standing on the surface.

As for changing velocity and direction without a force, this is also explained by the concept of geodesics. In general relativity, objects in motion will continue to move in a straight line (following a geodesic) unless acted upon by an external force or if there is a change in the curvature of space-time. This is why objects appear to accelerate when they are falling towards a massive object like the Earth; they are following a curved geodesic due to the Earth's curvature.

I hope this helps to clarify some of your questions about objects falling in general relativity. If you would like to delve deeper into the mathematics behind it, I would recommend studying differential geometry and the equations of general relativity. But for a qualitative understanding, the concept of geodesics and the curvature of space-time should suffice. Keep up the curiosity and keep asking questions!

## 1. How does general relativity explain the motion of objects falling towards a massive body?

In general relativity, the force of gravity is not considered a force in the traditional sense, but rather a curvature of spacetime caused by massive objects. This curvature causes objects to follow the shortest possible path through spacetime, which appears as a straight line to an observer. Therefore, objects fall towards massive bodies because they are following the curvature of spacetime caused by the mass of the object.

## 2. How do objects fall differently in general relativity compared to Newton's theory of gravity?

In Newton's theory of gravity, objects fall towards a massive body due to the force of gravity acting on them. However, in general relativity, objects fall towards a massive body due to the curvature of spacetime caused by the mass of the object. This means that in general relativity, objects will follow a curved path towards the massive body, rather than a straight line as predicted by Newton's theory.

## 3. Can objects fall upwards in general relativity?

According to general relativity, objects will always fall towards a massive body due to the curvature of spacetime caused by the mass of the object. Therefore, objects cannot fall upwards in general relativity.

## 4. How does time dilation affect objects falling in general relativity?

According to the theory of relativity, time is not absolute and can be affected by the presence of massive objects. This means that time will move slower for an object falling towards a massive body compared to an observer further away. This effect, known as time dilation, is a result of the curvature of spacetime caused by the mass of the object.

## 5. Can the gravitational force between two objects be explained by general relativity?

No, general relativity does not explain the gravitational force between two objects. Instead, it explains the motion of objects in the presence of massive bodies. The force of gravity is still a mystery in the context of general relativity and is currently being studied by scientists through the development of theories such as quantum gravity.

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