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Science

Physics

Relativity and Space-Time

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Lorentz Factor

\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}

, where

v

is the relative velocity and

c

is the speed of light. It quantifies the amount of time dilation, length contraction, and mass increase experienced by an object moving at a velocity

v

General Relativity

A theory of gravitation that describes gravity as a curvature of spacetime caused by matter and energy. The presence of mass and energy warps spacetime around it.

Special Relativity

A theory that describes the physics of moving bodies at speeds close to that of light and how they are observed in different inertial frames of reference.

Schwarzschild Radius

The radius of a sphere such that, if all the mass of an object is compressed within that sphere, the escape velocity from the surface would equal the speed of light. It is defined as

R_S = \frac{2GM}{c^2}

where

G

is the gravitational constant,

M

is the mass of the object, and

c

is the speed of light.

E=mc^2

Einstein's mass-energy equivalence formula, stating that the energy ( $E$ ) of a system is equal to its mass ( $m$ ) times the speed of light squared ( $c^2$ ).

Twin Paradox

A thought experiment involving identical twins, one who makes a journey into space in a high-speed rocket and the other who remains on Earth. Due to time dilation, the traveling twin would age slower than the twin on Earth, so upon return, the traveling twin would be younger.

Time Dilation

The difference in the elapsed time measured by two observers, due to the relative velocity between them or the difference in their gravitational potential.

Length Contraction

Objects in motion are measured to be shorter along the direction of motion compared to when they are at rest. This is given by the equation $L = L_0 \sqrt{1 - \frac{v^2}{c^2}}$ , where $L_0$ is the proper length.

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