# Question on Einstein's Equation

• timmy
In summary, the Einstein's field equation relates the space curvature to the energy and momentum of a system, such as a planet. This explains the presence of gravity, as the spacetime is warped around a large mass or energy.
timmy
Sorry this may seem like a stupid question but how is it possible to show by using Einstein's field equation that the geometry around the Earth or any other planets is a chute or basically why the presence of gravity is due to the fact that the spacetime curvature is warped around a large mass/energy ?

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timmy,

Your attached picture doesn't show the Einstein's equations.
Droping the indices, in tensor notations, the Einstein's equations read (click for a link on wiki):

"[URL = 8*pi*T[/INDENT][/URL]
On the right-hand side is the stress-energy tensor that accounts for energy and momentum. Therefore, the Einstein's equation above relates the space curvature (R) to the energy and monentum (T).

Michel

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No need to apologize, this is actually a very valid question and one that has puzzled many people. To understand how Einstein's field equation explains the presence of gravity, we first need to understand the concept of spacetime curvature. According to Einstein's theory of general relativity, mass and energy not only affect the space around them, but also the time. This means that the presence of a large mass or energy can warp the fabric of spacetime, creating a curvature.

Now, the field equation states that this curvature is directly related to the distribution of mass and energy in a given space. In other words, the more mass and energy there is in a particular area, the greater the curvature of spacetime will be. This curvature is what we experience as gravity.

To specifically answer your question about the geometry around the Earth or any other planet, we can look at it in this way: the Earth has a large amount of mass, which means it creates a significant curvature in the fabric of spacetime around it. This curvature then causes objects to be pulled towards the Earth, creating the force we know as gravity.

In summary, Einstein's field equation explains the presence of gravity by showing how the distribution of mass and energy in a given space affects the curvature of spacetime. This curvature is what we experience as gravity, and it can be observed and measured through various experiments and observations. I hope this helps clarify the concept for you.

## 1. What is Einstein's equation and why is it important?

Einstein's equation, also known as the mass-energy equivalence equation, is E=mc². It relates energy (E) and mass (m) to each other, stating that mass and energy are interchangeable. It is important because it revolutionized our understanding of the relationship between matter and energy, and led to the development of nuclear energy and weapons.

## 2. How did Einstein come up with his equation?

Einstein developed his equation through his theory of special relativity, which states that the laws of physics are the same for all observers in uniform motion. He used mathematical equations and thought experiments to explore the relationship between energy and mass, leading to the famous equation E=mc².

## 3. Can you explain the components of the equation in simple terms?

The letter E stands for energy, which can take many forms such as light, heat, and motion. The letter m represents mass, which is a measure of the amount of matter in an object. The exponent 2 (²) is a mathematical operation that means the number is multiplied by itself. So E=mc² means that energy is equal to the mass of an object multiplied by the speed of light squared.

## 4. Is Einstein's equation still relevant today?

Yes, Einstein's equation is still relevant and widely used today in various fields such as nuclear physics, astronomy, and engineering. It has also been confirmed by numerous experiments and is a fundamental concept in our understanding of the universe.

## 5. What implications does Einstein's equation have for our understanding of the universe?

Einstein's equation has several implications for our understanding of the universe. It shows that mass and energy are two forms of the same thing and can be converted into each other. It also explains the relationship between mass and energy in nuclear reactions, such as those that occur in the sun. Additionally, it is a key component of the theory of general relativity, which describes the behavior of space and time in the presence of massive objects.

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