Examples of special relativity in the following topics:
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- The twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more.
- This occurs because special relativity shows that the faster one travels, the slower time moves for them.
- However, this scenario can be resolved within the standard framework of special relativity (because the twins are not equivalent; the space twin experienced additional, asymmetrical acceleration when switching direction to return home), and therefore is not a paradox in the sense of a logical contradiction.
- Nevertheless twin paradox is useful as a demonstration that special relativity is self-consistent.
- Explain the twin paradox within the standard framework of special relativity
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- Special relativity is based on Einstein's two postulates: the Principle of Relativity and the Principle of Invariant Light Speed.
- In his "Special Theory of Relativity," Einstein resolved the puzzle and broadened the scope of the invariance to extend the validity of all physical laws, including electromagnetic theory, to all inertial frames of reference.
- With two deceptively simple postulates and a careful consideration of how measurements are made, Einstein produced the theory of special relativity.
- Einstein accepted the result of the experiment and incorporated it in his theory of relativity.
- Imagine that you can throw a baseball at a speed v (relative to you).
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- Special relativity changed the way we view space and time and showed us that time is relative to an observer.
- After 1905, however, the Special Theory of Relativity destroyed this old, but intuitive, view.
- This factor shows up frequently in special relativity.
- Another radical finding that was made possible by the discovery of special relativity is the equivalence of energy and mass.
- Formulate major changes in the understanding of time, space, mass, and energy that were introduced by the theory of Special Relativity
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- In special relativity, as the object approaches the speed of light, the object's energy and momentum increase without bound.
- In special relativity, an object that has a mass cannot travel at the speed of light.
- In order for these laws to hold in all reference frames, special relativity must be applied.
- The Lorentz factor is equal to: $\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$, where v is the relative velocity between inertial reference frames and c is the speed of light.
- When the relative velocity is zero, is simply equal to 1, and the relativistic mass is reduced to the rest mass.
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- When both the fly and the ship are moving slowly compared to speed of light, it is accurate enough to use the vector sum $s = u + v$ where $s$ is the velocity of the fly relative to the shore.
- According to the theory of special relativity, the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed.
- Since special relativity dictates that the speed of light is the same in all frames of reference, light shone from the front of a moving car can't go faster than light from a stationary lamp.
- For collinear motions, the velocity of the fly relative to the shore is given by the following equation:
- Composition law for velocities gave the first test of the kinematics of the special theory of relativity.
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- Gravity is a geometrical effect in which a metric matrix plays a special role, and the motion of objects are altered by curved space.
- Special relativity indicates that humans live in a four-dimensional space-time where the 'distance' $s$ between points in space-time can be regarded as:
- General relativity, or the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1916.
- General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or space-time.
- Minkowski space is the special space devoid of matter, and as a result, it is completely flat.
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- A a motional EMF is an electromotive force (EMF) induced by motion relative to a magnetic field B.
- An electromotive force (EMF) induced by motion relative to a magnetic field B is called a motional EMF.
- Therefore, the motional EMF over the length L of the side of the loop is given by $\varepsilon_{motion} = vB \times L$ (Eq. 1), where L is the length of the object moving at speed v relative to the magnet.
- In fact, the equivalence of the two phenomena is what triggered Albert Einstein to examine special relativity.
- In his seminal paper on special relativity published in 1905, Einstein begins by mentioning the equivalence of the two phenomena:
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- The relativity of simultaneity is the concept that simultaneity is not absolute, but depends on the observer's reference frame.
- According to the theory of special relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York.
- The question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in other frames (in a different state of motion relative to the events) the crash in London may occur first, and still in other frames, the New York crash may occur first.
- If the two events are causally connected ("event A causes event B"), then the relativity of simultaneity preserves the causal order (i.e.
- Formulate conclusions of the theory of special relativity, noting the assumptions that were made in deriving it
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- In this context it is sometimes called Newtonian relativity.
- Galilean relativity can be shown as follows.
- Suppose S' is in relative uniform motion to S with velocity v.
- It is this simple but crucial result that implies Galilean relativity.
- Albert Einstein's central insight in formulating special relativity was that, for full consistency with electromagnetism, mechanics must also be revised, such that Lorentz invariance (introduced later) replaces Galilean invariance.