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

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In summary, the conversation discusses the concept of gravitation in the context of general and special relativity. The speaker has two questions: why does space-time bend for massive objects, and why would a lesser object be compelled to move towards a more massive object in a curved space-time scenario. The responder explains that curved space-time is just a model to describe the effects of massive objects and provides additional resources for further understanding.
  • #1
Michamus
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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]
GR-Spacetime-nobend.jpg


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]
GR-Spacetime.jpg

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.
 
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  • #2
Michamus said:
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.

Michamus said:
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 :smile:. 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.
 
  • #3


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!
 

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

1. What is the theory of General Relativity and how does it explain gravitation?

The theory of General Relativity (GR) is a mathematical theory developed by Albert Einstein that describes the force of gravitation as a curvature of space-time. According to GR, massive objects such as planets and stars cause a curvature in the fabric of space-time, which then determines the paths of other objects that move through it. This curvature of space-time is what we experience as the force of gravity.

2. What are geodesics and how do they relate to space-time in General Relativity?

Geodesics are the shortest paths between two points in a curved space-time. In GR, the motion of objects is described by following geodesics through space-time, rather than being influenced by a force. Objects will naturally follow the geodesic paths determined by the curvature of space-time.

3. How does General Relativity explain the bending of light around massive objects?

According to GR, light travels along geodesics in space-time. When passing by a massive object, the light follows the curvature of space-time, causing it to appear bent. This is known as gravitational lensing and is a key piece of evidence for the validity of GR.

4. What are some examples of predictions made by General Relativity that have been confirmed by observations?

One of the most famous predictions of GR is the bending of light around massive objects, which was first confirmed during a solar eclipse in 1919. Another prediction is the gravitational redshift, which has been observed in the light from distant galaxies. GR also predicts the existence of black holes, which have been indirectly observed through their effects on surrounding matter and light.

5. How does General Relativity relate to Special Relativity?

Special Relativity (SR) is a theory developed by Einstein that describes the laws of physics in a universe without gravity. GR is an extension of SR, incorporating the effects of gravity into the equations. GR reduces to SR in the absence of gravity, and both theories have been extensively tested and confirmed by experimental evidence.

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