There are papers written to this day, on various solutions to these equations. It’s so complicated in fact, that Einstein was skeptical about being able to solve them. If we wrote down all the 10 equations fully, it would take up more than one page of text. It is actually 10 equations, and is very complicated mathematically.
#Gravity curved space geometry einstein general relativity how to
In return, the left side – the curvature resulting in gravity, tells matter on the right side, how to move.Įssentially, what this equation shows is that matter and energy, results in a curvature of space-time which we perceive as gravity.Īlthough this looks like one somewhat simple equation. The right side is the matter and energy which tells space-time, on the left side, how to curve. So this equation describes what John wheeler said so succinctly about general relativity: “ Space-time tells matter how to move, matter tells space time how to curve” In general relativity, the dimensions are 4, so the vectors are 4 x 1 and tensors are 4 x 4 matrices. A vector is a type of tensor represented by an N x 1 matrix. This can be an array of vectors, scalars, or other tensors represented by an N x N matrix. In the context of these equations think of a tensor as a multidimensional array of mathematical components. This is represented by something called the mass-energy-momentum tensor. The right side of the general relativity equation tells us about mass-energy content.
In other words, gravity does not cause the curvature of space time, it is the curvature of space-time. In general relativity, gravity is not a force within the background of space and time like it is in Newton’s equation, but is a curvature of the space-time background itself. This is the analong of force described by Newton. It has two components that describe the curvature and how distances in the curvature are determined. In Einstein’s equation, we have the analog of force – the curvature of space-time on the left side. In Newton’s equation, we have a force on the left side, created by mass on the right side. For one thing Newton’s gravitational constant is present in both equations If we look at Newton’s equation for gravitation and Einstein’s equation of general relativity. And that I hope this will help you better understand quantum gravity. I am going to try to explain those equations to you intuitively and visually, to give you an idea of what the math is trying to say. And there are still papers being written today on specific solutions to these equations.
However, the mathematics of General relativity is so difficult that even a genius like Einstein, could not easily derive it. In order to understand quantum gravity though, you have to first understand general relativity.
One the biggest pursuits in physics is the attempt to find a better theory, a quantum theory of gravity. Today, a hundred years after Einstein’s publication, we find some holes in Einstein’s theory as well, such as its inability to explain the singularity inside black holes, and the big bang. It was a new paradigm that could explain more things. It solved the riddle of Mercury’s precession, and explained that gravity was not a mysterious force acting at a distance in the background of space and time, but was a result of a bending of the background itself – the curvature of space-time. Newton explained gravity as an innate property of objects – a constant instantaneous force that could act over long distances.Ģ50 years later, in 1916, Einstein changed this paradigm with the publication of the General theory of relativity. Later in 1859, Newton’s laws could not explain the the rate of precesssion of Mercury – the way its elliptical orbit rotates around the sun, and is not fixed. This was the idea that a massive object could exert a force instanteously to another massive object at a distance without ever touching it. This equation explained the movement of planets, and it remains very accurate even today under most circumstances.īut it had a few problems, one of which was the idea of action at a distance, that even Newton has trouble accepting. That force of course was gravity.Īnd he expressed this analytically in a remarkable equation that is still used today. In 1687, Isaac Newton changed the way we humans view the cosmos by connecting a force we experience on earth, with the force that controls the movement of heavenly bodies.
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