What the significance of Einstein's Field equation been completely understood?
956852
The significance of Einstein's Field equation (EFE) is that it describes how stress-energy causes curvature of spacetime, and that spacetime can be treated together as a 4-dimensional surface or manifold.\n\nEinstein's Field Equation is fairly well understood today, and many solutions have been found. However, EFE being a non-linear differential equations, it is very difficult to obtain an exact solution.\n\nThe components of curvature tensors such as the Einstein tensor have, in geometric units, the dimensions of sectional curvature. So do the components of the stress-energy tensor. Therefore the Einstein field equation is dimensionally consistent in these units.\n\nWhat this means is that the units of distance, time, mass, energy, etc., have all been converted into geometric units. In physics, especially in the general theory of relativity, geometric units constitute a physical unit system in which all physical quantities are identified with geometric quantities such as areas, lengths, dimensionless numbers, path curvatures, or sectional curvatures. In this system, the base physical units are chosen so that the speed of light, c, and the gravitational constant, G, and other relevant physical constants are set to equal one.
160596
The time dilation formula of Einstein only refers to inertial motion. The change in time apply to a wave only.\nIn other case time depends on the gravity field that was shown by Kepler and Newton.\nTime seems to be longer when you are waiting doing nothing .That has to do with boredom.\nIf you were to apply the idea of Einstein as in the case of the twins you would think its real. Well if Einstein was able to go back in time he would still be alive to day!
889821
Actually, solutions to Einstein's field equation indicate that the Universe can be either (1) flat, (2) positively curved (like a sphere)or (3) negatively curved (like a saddle). All three curvatures of spacetime equally satisfies Einstein's equation. Also, I believe the solution indicated that the Universe is finite, but "unbounded".\n\nCurrent data from the WMAP satellite tells us that the curvature of spacetime of our Universe is FLAT.
63532
it is an equation by Albert Einstein showing that energy and mass are interchangeable.\n\nE is energy\nM is mass\nC is the speed of light\n\nthus energy equals the amount of mass multiplied by the speed of light squared.
458495
The theoretical physics equation E = mc2 states a relationship between energy (E), in whatever form, and mass (m). In this formula, c², the square of the speed of light in vacuum, is the conversion factor required to formally convert from units of mass to units of energy, i.e. the energy per unit mass. In unit specific terms, E (Joules) = M (kilograms) · (299792458 m/s) 2.\n\nThis formula, which was discovered by Albert Einstein, proposes that when a body has a mass (measured at rest), it has a certain (a very large) amount of energy associated with this mass. This is opposed to the Newtonian mechanics, in which a massive body at rest has no kinetic energy, and may or may not have other (relatively small) amounts of internal stored energy (such as chemical or thermal energy), in addition to any potential energy it may have from its position in a field of force. That is why a body's mass, in Einstein's theory, is often called the rest energy of the body. The E of the formula can be seen as the total energy of the body, which is proportional to the mass when the body is at rest.\n\nConversely, a single photon travelling in empty space cannot be considered to have an effective mass, m, according to the above equation. The reason is that such a photon cannot be measured in any way to be at "rest" and the formula above applies only to single particles when they are at rest. Photons are generally considered to be "massless," (i.e., they have no rest mass or invariant mass) even though they have varying amounts of energy.\n\n\nENERGY=MASS x Speed square \n\n\nbtw  check out my website \n\nhttp://oldman.netfirms.com/
776617
The Einstein field equations (EFE) describe how stress-energy causes curvature of spacetime (not mass since mass and energy are equivalent) and are usually written in tensor form (using abstract index notation) as\n\nGuv = κ Tuv\n\nwhere Guv is the Einstein tensor, Tuv is the stress-energy tensor and κ is a constant. The tensors Guv and Tuv are both rank 2 symmetric tensors, that is, they can each be thought of as 4×4 matrices, each of which contains 10 independent terms.\n\nThe EFE reduce to Newton's law of gravity in the limiting cases of a weak gravitational field and slow speed relative to the speed of light. In fact, the value of κ in the EFE was determined to be \n\nκ = 8πG/c^4\n\nby making these two approximations, where G is Newton's Gravitational Constant.
61437
That would be Einstein's Special Theory of Relativity.\n\nhttp://science.howstuffworks.com/relativity3.htm
895994
Here's some basic background covering how mathematical models of space and time have evolved since ancient times, from the Pythagorean Rule to Newtonian mechanics, Special Relativity and General Relativity.\nhttp://www.theory.caltech.edu/people/patricia/st101.html\n\nEinstein and Special Relativity give us a mathematical model for spacetime that reflects the observed behavior of Nature in that nothing can go faster than the speed of light. (At least not anything observed in a laboratory or in outer space as of yet.) \n\nIn Einstein's time they were already learning about differential geometry, but Einstein motivated this field of mathematics even more when he came up with an equation relating the curvature tensor of the spacetime distance function to the distribution of matter and energy in spacetime, encoded in a tensor Tuv called the stress-energy tensor. \n This equation is now called the Einstein equation: \nRuv - (1/2) guv R = (8 Pi G/c4) Tuv \n This equation (or actually, set of equations, for there is an equation for every combination of tensor indices u and v) models a lot of phenomena in the Universe that was impossible to describe with mathematics just using Newton's law of gravity. For example, observations of the bending of light by gravity, gravitational radiation emitted by pulsars, new observations of black holes and the observed expansion of the visible Universe can all be modelled rather successfully using this elegant formalism uncovered by Einstein.
1055212
E=mc²\n\nOne of the most famous equations in the world, even to non-physicists, the theoretical physics equation E = mc2 states a relationship between energy (E), in whatever form, and mass (m). In this formula, c², the square of the speed of light in vacuum, is the conversion factor required to formally convert from units of mass to units of energy, i.e. the energy per unit mass. In unit specific terms, E (joules) = M (kilograms) multiplied by (299792458 m/s) 2.\n\nMeanings of the formula\nThis formula, which was discovered by Albert Einstein, proposes that when a body has a mass (measured at rest), it has a certain (very large) amount of energy associated with this mass. This is opposed to the Newtonian mechanics, in which a massive body at rest has no kinetic energy, and may or may not have other (relatively small) amounts of internal stored energy (such as chemical energy or thermal energy), in addition to any potential energy it may have from its position in a field of force. That is why a body's rest mass, in Einstein's theory, is often called the rest energy of the body. The E of the formula can be seen as the total energy of the body, which is proportional to the mass when the body is at rest.\n\nConversely, a single photon travelling in empty space cannot be considered to have an effective mass, m, according to the above equation. The reason is that such a photon cannot be measured in any way to be at "rest" and the formula above applies only to single particles when they are at rest. Photons are generally considered to be "massless," (i.e., they have no rest mass or invariant mass) even though they have varying amounts of energy.\n\nThis formula also gives the quantitative relation of the quantity of mass lost from a resting body or an initially resting system, when energy is removed from it, such as in a chemical or a nuclear reaction where heat and light are removed. Then this E could be seen as the energy released or removed, corresponding with a certain amount of mass m which is lost, and which corresponds with the removed heat or light. In those cases, the energy released and removed is equal in quantity to the mass lost, times the speed of light squared. Similarly, when energy of any kind is added to a resting body, the increase in the resting mass of the body will be the energy added, divided by the speed of light squared
561193
You do have a point. Of course Schrodinger's equation was a brilliant breakthrough but these theories necessarily have a mathematical foundation and sometimes that foundation is not as secure as generally perceived. Mathematics is evolving and some of the stuff coming out is very weird, paradoxes and all, and this ends up affecting the way scientists formulate their theories. Put it this way: most physcists are not expert mathematicians and they are often a step behind with respect to rigor. As far as quantum mechanics is concerned, one has to consider its real and significant successes as a useful theory but with the realization that any developing theory  will necessarily have growing pains and it will need to be adjusted, finetuned and sometimes overhauled in the light of new info. in order to be incorporated in a more general theory of which it is a special case much like classical mechanics had to adjust to both quantum mechanics and the special and general theories of relativity. I think the greatest revision to quantum mechanics and General relativity will occur when the large and the small, and the uncertain and the deterministic, are finally 'married' in a breakthrough theory of quantum gravity. The problem with general relativity is that it is deterministic field theory and it is based on the concept of a space-time 'continuum'. I think the concept of continuum upon which the formalism of general relativity is based, is counter-productive and it needsto be replaced with a quantized 'granular' space-time structure that would allow things to get unified. On a philosophical note, you are right, in a sense, concerning questionable foundational definitions since if you keep asking the question: and what precisely do you mean by that? It doesn't take that many questions before you are reduced to axioms which are based on presumptuous perceptions of the human mind: In otherwords we could be missing a lot.
981582
Check Wikipedia: http://en.wikipedia.org/wiki/Theory_of_relativity
745347
The theory of relativity is being used in Fermi lab, U.S. to "create" either energy or new matter from energy.  Newton's laws only define motion, but they do not explain why some of the mysteries of the solar sytem or the universe occur.  With Einstein's theory, however, these mysteries become clearer.  We understand more why they occur this way and can predict how much energy is being "created" by calculating for how much matter is "lost."  Fermi lab is working to create anti-matter, combine it with matter to create energy, and utilizing the energy into more matter -- it's one of their big projects.  I'm sure they're testing for more than that, but it's the overview of what they are doing.
200022
Friedman Solved Einstein's field equation asuming the abscence of mass and he still came out with a description of energy in the Universe.\nWhat exists in the Univerves is Power in the Structure of Space. Relativity theory calls it space- time.Whether we call it Aether or Time -Space ,Its still the same Animal.\nThe can only be so and only if the Universe has restrains. your question was one of the most interesting ones.
965826
L = 8pi G rho/c^4 is the definition of the cosmo constant L (1/m^2); where c = light speed and rho is the energy density of the known universe in a vacuum.\n\nF = GmM/r^2 is the equation for the attraction force F between two masses m and M, r distance apart.\n\nL was created by Einstein to make his equations come out right.  By that, he meant the universe should be spherical (not flat or saddle shaped).  His original results showed a flat universe, and he just "knew" that was wrong; so on came L to fix the shape problem.\n\nF was the result of experiments by Newton.  Through observation, he found that the attractive force between two bodies was proportional to the inverse square of the distance between them and to the product of the magnitudes of the two masses.  That is, F varies as (~) (mV/r^2).  \n\nWhenever there is a proportionality, as in F ~ mM/r^2, there has to be a constant of proportionality.  In this case Newton called it G; so that F ~ mM/r^2 becomes F = GmM/r^2 when the constant is inserted.\n\nThe G in both equations is the same constant.  But Sir Newton came upon it long before Einstein found it could be used in his equations and the calculation of L.  So there is no way that Newton (1642-1727) could know about Einstein's (1879-1955) use of it much later.
337898
The Poisson equation turns out to be one component of the Einstein equation when appropriate approximations are made.
757200
I don't know what Einstein figured out regarding the meaning of life.  I only know about his physics.  As far as the equation, it relates mass and energy.  If mass is converted to energy (such as in a nuclear bomb) the amount of mass lost (times the speed of light squared) is proportional to the energy released.  Fission (or atomic) bombs ideally convert 1 part in a thousand of the mass to energy, while fusion (or hydrogen) bombs convert about 1%.  These figures are assuming 100% efficiency of the mechanism, which is never the case, and so the actual figures are somewhat lower.  The formula also works the other way.  In some nuclear reactions, mass is gained at the expense of energy.
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These are given by Einstein field equations and are unfortunately not so simple as Newton´s equation.\n\nTake a look here:\nhttp://en.wikipedia.org/wiki/Einstein_equations\n\nor here if you want less math:\nhttp://www.black-holes.org/relativity1.html