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      • The General Theory of Relativity can actually be described using a very simple equation: R = GE (although Einstein 's own formulation of his field equations are much more complex).
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  2. Einstein’s Relativity Explained in 4 Simple Steps › science › article

    May 16, 2017 · Einstein’s Relativity Explained in 4 Simple Steps. The revolutionary physicist used his imagination rather than fancy math to come up with his most famous and elegant equation.

  3. Einstein's Theory of Special Relativity | Space › 36273-theory-special-relativity

    Mar 30, 2017 · One of the most famous equations in mathematics comes from special relativity. The equation — E = mc2 — means "energy equals mass times the speed of light squared." It shows that energy (E) and...

  4. What is general relativity? | › content › what-general-relativity
    • Start with Newton
    • Different Force, Same Formula
    • The Problem with Newton
    • Why We Need Fields
    • Gravity and Spacetime
    • The Equation
    • Not Just One Equation
    • About This Article

    The general theory of relativity describes the force ofgravity. Einstein wasn't the first to come up with such a theory —back in 1686 Isaac Newton formulated his famous inverse square law ofgravitation. Newton's law works perfectly well on small-ish scales: we can use it to calculate how fast an objectdropped off a tall building will hurtle to the ground and even to sendpeople to the Moon. But whendistances and speeds are very large, or very massive objects are involved, Newton's lawbecomes i...

    There is another formula which looks very similar, but describes adifferent force. In 1785 the French physicist Charles-Augustinde Coulomb came up with an equation to capture the electrostatic force that acts between two charged particles with charges and :Here stands for the distance between the two particles and is a constant which determines the strength of electromagnetism. (It has the fancy name permittivity of free space.)

    Newton's and Coulomb's formulas are nice and neat, but there is aproblem. Going back to Newton's law, suppose you took the Earth andthe Sun and very quickly moved them further apart. This would make theforce acting between them weaker, but, according to the formula, theweakening of the force would happen straight away, the instant you move thetwo bodies apart. The same goes for Coulomb's law: moving the chargedparticles apart very quickly would result in an immediate weakening ofthe electrost...

    This is one reason why the classical idea of a force needs replacing in modern physics. Instead, we need to think in terms of something — newobjects — that transmit the force between one object and another. This was the great contribution of the British scientist MichaelFaraday to theoretical physics. Faraday realised that spread throughoutthe Universe there are objects we today call fields, whichare involved in transmitting a force. Examplesare the electric and magnetic fields you are probab...

    So what about gravity? Just as with electromagnetism there needs tobe a field giving rise to what we perceive as the gravitational forceacting between two bodies. Einstein's great insight was that this field is made of something we already know about: space and time. Imagine a heavy body, like the Sun, sitting in space. Einsteinrealised that space isn't just a passive by-stander, but responds tothe heavy object by bending. Another body, like the Earth, movinginto the dent created by the heavi...

    The general theory of relativity is captured by a deceptively simple-looking equation: Essentially the equation tells us how a given amount of mass and energy warps spacetime. The left-hand side of the equation, describes the curvature of spacetime whose effect we perceive as the gravitational force. It’s the analogue of the term on the left-hand side of Newton’s equation. The term on right-hand side of the equation describes everything there is to know about the way mass, energy, momentum an...

    In Einstein’s equation the Greek letters and are labels, which can each take on the values 0, 1, 2 or 3. So really, the equation above conceals a whole collection of equations corresponding to the possible combinations of values the and can take: and so on. The value of 0 corresponds to time and the values 1,2 and 3 to the three dimensions of space. The equation therefore relates to time and the 1-direction of space. The term on the right-hand side describes the momentum (speed and mass) of m...

    David Tong is a theoretical physicist at the Universiy of Cambridge. He works on quantum theory and general relativity.

  5. List of relativistic equations - Wikipedia › wiki › List_of_relativistic_equations

    To derive the equations of special relativity, one must start with two postulates: The laws of physics are invariant under transformations between inertial frames. In other words, the laws of physics... The speed of light in a perfect classical vacuum ( c 0 {\displaystyle c_ {0}} ) is measured to be ...

  6. E = mc² | Equation, Explanation, & Proof | Britannica › science › E-mc2-equation

    E = mc 2, equation in German-born physicist Albert Einstein’s theory of special relativity that expresses the fact that mass and energy are the same physical entity and can be changed into each other. In the equation, the increased relativistic mass (m) of a body times the speed of light squared (c 2) is equal to the kinetic energy (E) of that body.

  7. General Theory of Relativity - Special and General Relativity ... › topics_relativity
    • Introduction
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    As we have seen, matter does not simply pull on other matter across empty space, as Newton had imagined. Rather matter distorts space-time and it is this distorted space-time that in turn affects other matter. Objects (including planets, like the Earth, for instance) fly freely under their own inertia through warped space-time, following curved paths because this is the shortest possible path (or geodesic) in warped space-time. This, in a nutshell, then, is the General Theory of Relativity, and its central premise is that the curvature of space-time is directly determined by the distribution of matter and energy contained within it. What complicates things, however, is that the distribution of matter and energy is in turn governed by the curvature of space, leading to a feedback loop and a lot of very complex mathematics. Thus, the presence of mass/energy determines the geometry of space, and the geometry of space determines the motion of mass/energy. In practice, in our everyday world, Newtons Law of Universal Gravitation is a perfectly good approximation. The curving of light was never actually predicted by Newton but, in combination with the idea from special relativity that all forms of energy (including light) have an effective mass, then it seems logical that, as light passes a massive body like the Sun, it too will feel the tug of gravity and be bent slightly from its course. Curiously, however, Einsteins theory predicts that the path of light will be bent by twice as much as does Newtons theory, due to a kind of positive feedback. The English astronomer Arthur Eddington confirmed Einsteins predictions of the deflection of light from other stars by the Suns gravity using measurements taken in West Africa during an eclipse of the Sun in 1919, after which the General Theory of Relativity was generally accepted in the scientific community. The General Theory of Relativity can actually be described using a very simple equation: R = GE (although Einstein's own formulation of his field equations are much more complex). Unfortunately, the variables in this simple equation are far from simple: R is a complicated mathematical object made up of 16 separate numbers in a matrix or \\"tensor\\" that describes the distortion of space-time; G is the gravitational constant; and E is another complicated number, also represented by a tensor, representing the energy of the object (or more accurately the 4-dimensional \\"energy momentum density\\"). Given that, though, what the equation says is simple enough: that what gravity really is is not a force but a distortion of space and time, and that the geometry of space and time depends not just on velocity (as the Special Theory of Relativity had indicated) but on the energy of an object. This makes sense when we consider that Newton had already shown that gravity depends on mass, and that Einstein's Special Theory of Relativity had shown that mass is equivalent to energy.

    The theory has been proven remarkably accurate and robust in many different tests over the last century. The slightly elliptical orbit of planets is also explained by the theory but, even more remarkably, it also explains with great accuracy the fact that the elliptical orbits of planets are not exact repetitions but actually shift slightly with each revolution, tracing out a kind of rosette-like pattern. For instance, it correctly predicts the so-called precession of the perihelion of Mercury (that the planet Mercury traces out a complete rosette only once every 3 million years), something which Newtons Law of Universal Gravitation is not sophisticated enough to cope with.

    Gravity Probe B was launched into Earth orbit in 2004, specifically to test the space-time-bending effects predicted by General Relativity using ultra-sensitive gyroscopes. The final analysis of the results in 2011 confirms the predicted effects quite closely, with a tiny 0.28% margin of error for geodetic effects and a larger 19% margin of error for the much less pronounced frame-dragging effect.

    The theory has also provided endless fodder for the science fiction industry, predicting the existence of sci-fi staples like black holes, wormholes, time travel, parallel universes, etc. Just as an example, the notionally faster-than-light warp speeds of Star Trek are based firmly on relativity: if the space-time behind a starship were in some way greatly expanded, and the space-time in front of it simultaneously contracted, the starship would find itself suddenly much closer to its destination, without the local space-time around the starship being affected in any relativistic way. Unfortunately, however, such a trick would require the harvesting of vast amounts of energy, way in excess of anything imaginable today.

  8. Einstein field equations - Wikipedia › wiki › Einstein_field_equations

    These equations, together with the geodesic equation, which dictates how freely falling matter moves through spacetime, form the core of the mathematical formulation of general relativity. The EFE is a tensor equation relating a set of symmetric 4 × 4 tensors. Each tensor has 10 independent components.

  9. Einstein’s theory of special relativity describes what happens as things near the speed of light. Here are some important special-relativity equations that deal with time dilation, length contraction, and more.

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