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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. Albert Einstein ...

  3. 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 inaccurate. It's a good place to start though, as it's easierto describe than Einstein's theory. Suppose you have two objects, say the Sun and the Earth, with masses and respectively. Write for the distance between the two objects. Then Newton’s law says that the gravitational force between them is where is a fixed number, known as Newton's constant. The formula makes intuitive sense: it tells us that gravity gets weaker over long distances (the larger the smaller ) and that the gravitational for...

    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 electrostatic force between them. But this can't be true. Einstein's special theory of relativity,proposed ten years before the general theory in 1905, says thatnothing in the Universe can travel faster than light — not even the"signal" that communicates that two objects have moved apart and theforce should become weaker.

    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 probably familiar withfrom school. A charged particle gives rise to an electric field, which is"felt" by another particle (which has its own electric field). Oneparticle will move in response to the other's electric field — that's whatwe call a force. When one particle is quickly moved away from the other, then thiscauses ripples in the first particle's electric field. The ripples travel through space, atthe speed of light, and eventually affect the other particle. In fact, theparticle that is moved a...

    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 heavier object will be diverted by thatdent. Rather than carrying on moving along a straight line, it will startorbiting the heavier object. Or, if it is sufficiently slow, willcrash into it. (It took Einstein many years of struggle to arrive athis theory — see thisarticleto find out more.) Another lesson ofEinstein's theory is that space and time can warp into each other —they are inextricable linked and time, too, can be distorted by massiveobjects. This is why we talk, not just about the curvature...

    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 and pressure are distributed throughout the Universe. It is what became of the term in Newton’s equation, but it is much more complicated. All of these things are needed to figure out how space and time bend. goes by the technical term energy-momentum tensor. The constant that appears on the right-hand side of the equation is again Newton’s constant and is the speed of light. What about the Greek letters and that appear as subscripts? To understand what they mean, first notice that spacetime has f...

    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 matter moving in the 1-direction of space. The motion causes time and the 1-direction of space to mix and warp into each other — that effect is described by the left-hand side of the equation. (The analogue goes for an equation with and equal to 2 or 3.) If the equation only has 1s, 2s or 3s, for example then it relates only to space. The term on the right-hand side now measures the pressurethat matter causes in the corresponding direction of space. The left-hand side tells you how that matter ca...

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

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

    Mar 30, 2017 · Einstein's Theory of Special Relativity History. Before Einstein, astronomers (for the most part) understood the universe in terms of three laws of motion... Famous equation. Einstein's work led to some startling results, which today still seem counterintuitive at first glance... Special 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. Special Relativity Formulas › high-school › physics

    Some Special Relativity Formulas 1 Introduction The purpose of this handout is simple: to give you power in using special relativity! Even though you may not, at this stage, understand exactly where all of these formulas come from, you can certainly understand what they mean and have fun with them.

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  7. General Relativity - » Department of Mathematics › aretakis › General Relativity

    General Relativity is the classical theory that describes the evolution of systems under the e ect of gravity. Its history goes back to 1915 when Einstein postulated that the laws of gravity can be expressed as a system of equations, the so-called Einstein equations. In order to formulate his theory, Einstein had to reinterpret fundamental concepts of

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

    May 28, 2021 · 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.

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