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Mk
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Is gravity a result of the curvature of spacetime, or is it the curvature of spacetime a result of gravity? Or something else? Thank you.
Mk said:Is gravity a result of the curvature of spacetime, or is it the curvature of spacetime a result of gravity? Or something else? Thank you.
Mk said:Is gravity a result of the curvature of spacetime, or is it the curvature of spacetime a result of gravity?
YES U ULESS U FIND A GRAVITY AROUND A REGION U CAN'T BIND THE TIME OVER THERE BECAUSE AS U OBSERVE THE IS TIME LAGING ON MOON COMAPRED TO EARTH BECAUSE THERE IS A GAVITY LESS COMAPRED TO EARTH SO GRAVIT6Y IS THE CURAVATURE OF SPACE TIME AND VICE VERSA CAN'T BE RIGHT THING TO BE PRETCTED I HOPE THIS WOULD SATISFY .vanesch said:Gravity IS the curvature of spacetime.
pervect said:There are 16 components in a 4x4 matrix...
masudr said:Yes but the metric is NOT a 4x4 matrix, it is a 2nd rank antisymmetric tensor. If you write it out in some basis it'll look like a 4x4 matrix, but fundamentally a 2nd rank antisymmetric tensor defined in 4 dimensions has 10 degrees of freedom, and therefore 10 components uniquely determine it.
masudr said:Yes sorry I definitely meant symmetric.
But the stress-energy tensor still has 10 components, not 16. Independent or not. I could easily invent an object that had more components based on the 10 already; still that would not justify saying it had any more than the 10 independent ones.
Approaches, in detail
There are equivalent approaches to visualizing and working with tensors; that the content is actually the same may only become apparent with some familiarity with the material.
* The classical approach
The classical approach views tensors as multidimensional arrays that are n-dimensional generalizations of scalars, 1-dimensional vectors and 2-dimensional matrices. The "components" of the tensor are the indices of the array. This idea can then be further generalized to tensor fields, where the elements of the tensor are functions, or even differentials.
The tensor field theory can roughly be viewed, in this approach, as a further extension of the idea of the Jacobian.
* The modern approach
The modern (component-free) approach views tensors initially as abstract objects, expressing some definite type of multi-linear concept. Their well-known properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an extension of linear algebra to multilinear algebra. This treatment has largely replaced the component-based treatment for advanced study, in the way that the more modern component-free treatment of vectors replaces the traditional component-based treatment after the component-based treatment has been used to provide an elementary motivation for the concept of a vector. You could say that the slogan is 'tensors are elements of some tensor space'.
You can define gravity to suit your assumptions you have about it. But I will address only Einstein's definition/view of gravity. Spacetime curvature is another term for tidal forces and where there is spacetime curvature there is a gravitational field. However the converse need not be true. It is quite possible to have a gravitational field without spacetime curvature. In fact the very first gravitational field that was of concern to Einstein was one which had zero spacetime curvature. That gravitational field is a uniform gravitational field. Hence the Equivalence Principle which statesMk said:Is gravity a result of the curvature of spacetime, or is it the curvature of spacetime a result of gravity? Or something else? Thank you.
A uniformly accelerating frame of reference is identical to a uniform gravitational field.
The cause of the curvature of spacetime is the presence of massive objects, such as planets and stars, which create a gravitational field. This gravitational field causes spacetime to curve around it, resulting in the bending of light and the motion of objects in the vicinity.
The curvature of spacetime affects the motion of objects by influencing the trajectory of their motion. Objects move along curved paths due to the curvature of spacetime caused by the gravitational pull of massive objects. This effect is described by Einstein's theory of general relativity.
Yes, the curvature of spacetime can be observed through various phenomena, such as the bending of light around massive objects, the motion of objects in orbit, and the gravitational lensing effect. These observations provide evidence for the existence of the curvature of spacetime.
According to Einstein's theory of general relativity, the curvature of spacetime does affect time. In areas of strong gravitational fields, time appears to pass slower due to the effect of gravity on the fabric of spacetime. This phenomenon is known as time dilation.
The curvature of spacetime is a fundamental concept in understanding the nature of our universe. It explains how gravity works and provides a framework for understanding the motion of objects in space. It also plays a crucial role in the study of cosmology, as the curvature of spacetime is directly related to the shape, size, and evolution of the universe.