Special Relativity and Lorentz Transformations Quiz

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Questions and Answers

What is the equation for mass variation?

The equation for mass variation is $M = M_0 / \sqrt{1 - v^2/c^2}$.

What is the equation for Lorentz transformation?

The equation for Lorentz transformation is $x' = \gamma (x - vt)$, $y' = y$, $z' = z$, $t' = \gamma (t - vx/c^2)$.

What is the equation for momentum?

The equation for momentum is $p = \gamma mv$, where $p$ is momentum, $m$ is mass, $v$ is velocity, and $\gamma$ is the Lorentz factor.

What is the condition for Lorentz transformation to remain invariant?

<p>The condition for Lorentz transformation to remain invariant is $x^2 + y^2 + z^2 - (ct)^2 = x'^2 + y'^2 + z'^2 - (ct')^2$.</p> Signup and view all the answers

What is the equation for time dilation?

<p>The equation for time dilation is $t' = \gamma (t - vx/c^2)$, where $t'$ is the dilated time, $t$ is the proper time, $v$ is the relative velocity, $c$ is the speed of light, and $\gamma$ is the Lorentz factor.</p> Signup and view all the answers

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Study Notes

Relativity Equations

The equation for mass variation is: m = γ(m₀), where m is the relativistic mass, m₀ is the rest mass, and γ is the Lorentz factor.

Lorentz Transformation

The equation for Lorentz transformation is: t' = γ(t - vx/c²), x' = γ(x - vt), y' = y, z' = z, where (t, x, y, z) are the coordinates in one frame, (t', x', y', z') are the coordinates in another frame, v is the relative velocity, c is the speed of light, and γ is the Lorentz factor.
The condition for Lorentz transformation to remain invariant is that the spacetime interval (c²t² - x² - y² - z²) remains the same in all inertial frames.

Momentum and Time Dilation

The equation for momentum is: p = γ(m₀v), where p is the relativistic momentum, m₀ is the rest mass, v is the velocity, and γ is the Lorentz factor.
The equation for time dilation is: t' = γ(t), where t is the time in one frame, t' is the time in another frame, and γ is the Lorentz factor.