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  1. 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.

  2. Relativity Tutorial › ~wright › relatvty
    • Galilean Relativity
    • Special Relativity
    • Radar
    • Time Dilation
    • Principle of Equivalence
    • Light Cones in Curved Space-Time

    Relativity can be described using space-time diagrams.Contrary to popularopinion, Einsteindid not invent relativity. Galileopreceded him.Aristotlehad proposed that moving objects (on the Earth) had a naturaltendency to slow down and stop. This is shown in the space-time diagrambelow. But Galilean transformations do not preserve velocity. Thus the statement"The speed limit is 70 mph" does not make sense -- but don't try this in court.According to relativity, this must be re-expressed as "The magnitude ofthe relative velocity between your car and the pavement must be less than70 mph". Relative velocities are OK.

    But 200 years after Newton the theory of electromagnetism was developedinto Maxwell's equations. These equations describe waves with a speedof 1/sqrt(epsilono*muo), where epsilono is the constant describing thestrength of the electrostatic force in a vacuum, and muo is the constantdescribing the strength of the magnetic interaction in a vacuum. This isan absolute velocity -- it is not relative to anything. The value ofthe velocity was very close to the measured speed of light, and whenHertz generated electromagnetic waves (microwaves) in his laboratoryand showed that they could be reflected and refracted just like light,it became clear that light was just an example of electromagneticradiation. Einstein tried to fit the idea of an absolute speed oflight into Newtonian mechanics. He found that the transformationfrom one reference frame to another had to affect the time -- the ideaof sliding a deck of cards had to be abandoned. This led to thetheory of special relativity. In special r...

    The constancy of the speed of light allows the use of radar(RAdio Detection And Ranging)to measure the position and time of events not on an observer'sworldline. All that we need are a clock and the ability to emit anddetect radar pulses.

    Armed with radar, we can determine the time of two events on the worldlineof an observer moving with respect to us. We can then compare the time interval we measure to the time interval measuredby the moving observer. Consider the two observers A and B below. This slow down factor is exactly the slow down calculated above in theether model for a bouncing photon clock moving perpendicular to its bounce axis. The clock moving parallel to the axis slows down by thesame amount under special relativity because of the Lorentz-Fitzgerald contractionof moving objects in the direction of motion. Because the clocks of different observers run at different rates, dependingon their velocities, the time for a given observer is a property of thatobserver and his worldline. This time is called the proper timebecause it is "owned" by a given particle, not because it is the "correct"time. Proper time is invariant when changing reference frames becauseit is the property of a particle, not of the refer...

    Einstein proposed that the effects of gravity (in a small region ofspacetime) are equivalent to the effect of using an accelerated frameof reference without gravity. As as example, consider the famous"Einstein elevator" thought experiment. If an elevator far out in spaceaccelerates upward at 10 meters/second2, it will feel like a downwardacceleration of gravity at 1 g = 10 m/s2. If a clock on the ceiling ofthe elevator emits flashes of light f times per second, an observer onthe floor will see them arriving faster than f times per second becauseof the Doppler shift due to the acceleration of the elevator during thelight transit time. The effect of gravity on clocks was tested to greater precision byVessot etal (1980, PRL, 45, 2081) who launched a hydrogen maser straightup at 8.5 km/sec, and watched its frequency change as it coasted up to10,000 km altitude and then fell back to Earth. The frequency shift dueto gravity was (f'/f -1) = 4*10-10at 10,000 km altitude, and theexperimental...

    Unlike the restricted set of Lorentz transformations allowed inspecial relativity, the moregeneral coordinate transformations of general relativity will changethe slope of the walls of the lightcones. In other words, thespeed of light (dx/dt) will change in the transformed coordinates:dx'/dt' will not equal dx/dt in general. The light cones can tiltor stretch. The figure below shows "lightcones" added to theradius vs angle example given above: Thus the fundamentals of relativity that are important for cosmologyare: 1. The speed of light is a constant independent of the velocity of thesource or the observer. 2. Events that are simultaneous as seen by one observer are generally notsimultaneous as seen by other observers, so there can be no absolute time. 3. Each observer can define his own proper time -- the time measured bya good clock moving along his worldline. 4. Observers can assign times and positions to events not on their worldlinesusing radar observations. 5. Every observer w...

    • Introduction to Relativity
    • Special Theory of Relativity
    • General Theory of Relativity

    Relativity is a theorem, formulated by Albert Einstein, which states that space and time are relative and all the motion must be relative to a frame of reference. It is a notion that states, laws of physics are the same everywhere. This theory is simple but hard to understand. It states: 1. There is no absolute reference frame. One can measure velocity if the object or momentum is only in relation to other objects. 2. The speed of light is constant irrespective of who measures it or how fast the person measuring it, is moving. Albert Einstein’s Theory of Relativity encompasses two theories, namely Special Relativity Theory and General Relativity Theory.

    Einstein first introduced this term in the year 1905. It is a theorem that deals with the structure of space-time. Einstein explained this theory based on two postulates – 1. The laws of physics are the same for all irrespective of the velocity of the observer. 2. The speed of light is always constant regardless of the motion of the light source or the motion of the observer. 1. Relativity of simultaneity – two actions, simultaneous for one person may not be simultaneous for another person in relative motion. 2. Length Shrinking: Objects are measured and appeared to be shorter in the direction that they are moving with respect to the observer. 3. Mass – Energy Equivalence: Study of relativity lead to one of the greatest inventions i.e., E = mc2 where E is Energy, m stands for mass and c for the velocity of light. Many scientists observed that the mass of the object is increased with the velocity but never knew how to calculate it. This equation is the answer to their problem, which...

    General Relativity theory developed by Einstein in the year 1907-1915 states that being at rest in the gravitational field and accelerating are identical physically. For example, an observer can see the ball fall the same way on the rocket and on Earth. This is due to the acceleration of the rocket, which is equal to 9.8 m/s2. This theory relates to Newton’s gravitational theory and special relativity.

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  4. Apr 13, 2018 · Special relativity is ultimately a set of equations that relate the way things look in one frame of reference to how they look in another — the stretching of time and space, and the increase in...

    • 3 min
  5. Theory of Relativity explained in simple words – Astrogeekz › 2018/08/18 › theory-of-relativity

    Aug 18, 2018 · Theory of Relativity explained in simple words Posted on August 18, 2018 August 19, 2018 by astrogeekz ‘Theory of Relativity’ is a generalized term used for two different classes of theories given by Albert Einstein namely special relativity and general relativity.

  6. 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.

  7. 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.

  8. Einstein's theory of general relativity | Space › 17661-theory-general-relativity

    Jun 04, 2021 · The theory, which Einstein published in 1915, expanded the theory of special relativity that he had published 10 years earlier. Special relativity argued that space and time are inextricably ...

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

    May 28, 2021 · E = mc2, 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.

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