REL-24

Relativistic Doppler

Receding longitudinal Doppler.

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GoverningRelativistic Doppler

Governing equation

f=f_0\sqrt{(1-\beta)/(1+\beta)}

$beta \in \left[0, 0.9\right]$

where

f0: f0 (Hz)
beta: beta (—)
f: Relativistic Doppler (Hz)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

f=f_0\sqrt{(1-\beta)/(1+\beta)}

$beta \in \left[0, 0.9\right]$

$beta = 0$ $f = 1\times 10^{9}$

Along the curve

②

Domain of the variable — blue

beta_{\min} = 0,\quad beta_{\max} = 0.9

$beta \in \left[0, 0.9\right]$

$beta = 0$ $beta = 0$

Along the curve

③

Response curve — green

f=f_0\sqrt{(1-\beta)/(1+\beta)}

$beta \in \left[0, 0.9\right]$

$beta = 0$ $f = 1\times 10^{9}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}f}{\mathrm{d}beta}

$beta \in \left[0, 0.9\right]$

$beta = 0.006$ $f^{\prime} = -9.94\times 10^{8}$

Along the curve

Lecture brief

Historical brief

Einstein’s 1905 Lorentz kinematics and 1915 field equation, then Schwarzschild (1916) and Hawking temperature, recast time, mass and gravity. The lab computes dilation, E=mc² and horizon scales. This sheet (REL-24 — Relativistic Doppler) is the form associated with Relativistic Doppler. Working symbols: $f0$ , $beta$ $\rightarrow$ $f$ . Receding longitudinal Doppler. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

f

from

f0

beta

in Relativity via

f=f_0\sqrt{(1-\beta)/(1+\beta)}

Receding longitudinal Doppler. Use it when a real relativity question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

f0 = 1.000e+9\,\mathrm{Hz}

beta = 0.200\,\mathrm{—}

, the governing relation

f=f_0\sqrt{(1-\beta)/(1+\beta)}

yields

f = 8.165e+8\,\mathrm{Hz}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

f0 f01000000000 Hzbeta beta0.2 —

Outputs

Relativistic Doppler f816496580.928 Hz

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Receding longitudinal Doppler. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube