GR/SR Space-Time: Explaining Gravitation and its Geodesics

[Michamus]

Hello everyone,
I am a self taught (dare I say Physicist?). I have been struggling with a specific concept of GR/SR. This concept is "Gravitation" and it's explanation. As I understand it, classic Newtonian gravity in which mass attracts to other mass is not technically correct. There are "geodesics" in space-time that objects of mass follow. I have two questions in reference to this concept.
1) Why does space-time even bend for massive objects? In Illustration 1a I have provided my conceptualization of the "Rubber sheet" of space time.
[View 1a]

This is what I would initially view the rubber sheet as. Now the trouble I am having is why would the sheet bend? What compels the massive objects to bend this sheet?


2)In the event that space-time does bend (perhaps as volume displacement?) why would a lesser object (B) be compelled to move toward the more massive object (A) given a scenario in which Object B has no momentum (velocity)?

[View 2a]

As I understand it, in a zero-G environment neither object would move regardless of the curve in the rubber sheet. What makes space-time different?


I look forward to your replies as these are questions I have never had properly satisfied.

 

[A.T.]

1) Why does space-time even bend for massive objects?

Curved spacetime is just a model to describe how massive objects affect their surroundings. The why-question cannot be answered without creating the next why-question.

2)In the event that space-time does bend (perhaps as volume displacement?) why would a lesser object (B) be compelled to move toward the more massive object (A) given a scenario in which Object B has no momentum (velocity)?

Very well observed . The very popular marbles-rolling-on-a-rubber-sheet-analogy is misleading, because the rubber sheet represents curved space not curved spacetime. To understand the difference look here:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

And then check out the links I gave in this post:
https://www.physicsforums.com/showpost.php?p=1557122

And then ask further questions, if any.

 

[Entropia]

First of all, I commend you for taking the initiative to learn about GR/SR on your own. It is a complex and challenging subject, but understanding it can greatly deepen our understanding of the universe. Now, let's address your questions about gravitation and geodesics.

1) Why does space-time bend for massive objects?

To understand this, we need to first understand that space and time are not separate entities, but are interconnected in what we call space-time. According to Einstein's theory of general relativity, mass and energy can cause distortions in space-time, much like placing a heavy object on a rubber sheet would cause it to bend. This is because mass and energy are equivalent, as described by the famous equation E=mc². So, when a massive object is present, it creates a "dip" in space-time, which we perceive as gravity. The more massive the object, the greater the distortion in space-time.

2) Why would a lesser object be compelled to move towards a more massive object?

In your illustration 2a, the rubber sheet represents a two-dimensional representation of a three-dimensional concept. In reality, the distortion in space-time caused by a massive object is not a flat surface, but a three-dimensional "bowl" shape. An object placed on this surface will naturally roll towards the center, just like a marble rolling towards the center of a bowl. This is because objects naturally follow the path of least resistance, and in this case, the curved space-time is the path of least resistance for the object.

In a zero-gravity environment, there is no distortion in space-time, so objects do not experience this "pull" towards each other. However, in the presence of massive objects, the distortion in space-time is significant enough to cause objects to follow these geodesics towards the more massive object.

I hope this helps clarify your understanding of gravitation and geodesics in GR/SR. Keep up the self-learning and exploration of these fascinating concepts in physics!