Another gravitation problem

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In summary, the conversation is about finding the relation between the expressions E^{2}-B^{2} and F_{\mu\nu} F^{\mu\nu} and using it to determine that the first is a scalar. The speaker is confused about how to use the formal definition and notations to understand the relation between the two expressions. They are seeking an explanation for how the definitions and notations work together.
  • #1
noamriemer
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Hello!
I need to find the relation between [tex] E^{2}-B^{2} [/tex] and [tex] F_{\mu\nu} F^{\mu\nu} [/tex]
Actually, I need to use this relation to determine that the first is a scalar.
What I can't understand is how these notations match the formal definition:
If I multiply a matrix by another (same size) I should be receiving another matrix of the same size. Not a scalar...
But if I use the notations I need to use here:
[tex] F_{\mu\nu} F^{\mu\nu}\Rightarrow \Sigma_{i=1}^{3} \Sigma_{j=1}^{3} = F_{00}F^{00}+F_{01}F^{01}+...
[/tex] and that is not the product I expect it to be...
Could someone explain me how these definitions get along?
Thank you!
 
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  • #2
Anybody...? I am lost in here ...
Thanks
 

1. How does the force of gravity affect objects?

The force of gravity is a fundamental force of nature that attracts objects with mass towards each other. It is the force responsible for keeping planets in orbit around stars, and objects on Earth from floating off into space.

2. Can gravity be shielded or blocked?

Gravity cannot be shielded or blocked, as it is a fundamental force of nature that acts between all objects with mass. However, the effects of gravity can be counteracted by other forces, such as the force of thrust from a rocket.

3. How does the strength of gravity change with distance?

The strength of gravity decreases with distance between two objects. This relationship is described by Newton's Law of Universal Gravitation, which states that the force of gravity is inversely proportional to the square of the distance between two objects.

4. What is the difference between mass and weight in regards to gravity?

Mass is a measure of the amount of matter an object contains, while weight is the measure of the force of gravity acting on an object. The more massive an object, the greater its gravitational pull, and therefore, the greater its weight will be.

5. How does gravity vary on different planets?

The strength of gravity varies on different planets depending on their mass and size. The larger and more massive a planet is, the stronger its gravitational pull will be. For example, the force of gravity on Earth is about six times stronger than the force of gravity on the Moon.

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