A teaching tape for ME-01, opposite pulses and two ledgers
the two pulses
A body at rest emits two light pulses of equal energy in opposite directions. Turn the pair, and each pulse's share changes while their sum in the moving frame does not.
Open ME-01 with these settings
Where it starts
| Setting | Value |
|---|---|
| Observer speed v/c (frameSpeed) | 0.6 |
| Emitted energy L (emittedEnergyRestFrame) | 1 |
| Emission angle phi (emissionAngle) | 0 |
What it changes, and what to expect
Where it starts, before anything changes
Both pulses forward and back along the motion
The two pulses carry L = 1 between them in the rest frame. In the frame moving at 0.6c they carry 1.25, which is L times the factor 1.25, and the body's kinetic energy falls by 0.25 = L(1.25 - 1). The low-speed form Einstein takes next, half L v^2/c^2, would give 0.18 here: 39 per cent low, which is why he takes it only for small speeds.
What the author recorded that a reader should see here. Quantity Expected Under pulseSumMoving 1.25 J modern-si-2019 kineticEnergyDifference 0.25 J modern-si-2019 pulseEnergyRatio 0.25 1 modern-si-2019 Set Emission angle phi (emissionAngle) to 45 changes what the run starts from
The pair turned to 45 degrees
One pulse gains what the other loses: their energy ratio goes from 0.25 to 0.4042. The sum is still 1.25 and the kinetic-energy difference is still 0.25. This is the cancellation the argument rests on, and it is worth seeing rather than being told.
What the author recorded that a reader should see here. Quantity Expected Under pulseSumMoving 1.25 J modern-si-2019 pulseEnergyRatio 0.4042339787513938 1 modern-si-2019 Set Emission angle phi (emissionAngle) to 90 changes what the run starts from
Broadside: the two pulses are equal again
At 90 degrees the ratio is exactly 1, the two pulses sharing the moving-frame energy equally, and the sum is still 1.25. Three different directions, three different splits, one sum. The result does not depend on which way the body fired.
What the author recorded that a reader should see here. Quantity Expected Under pulseSumMoving 1.25 J modern-si-2019 pulseEnergyRatio 1 1 modern-si-2019 Set Observer speed v/c (frameSpeed) to 0.1 describes the same world from somewhere else
The same emission watched from 0.1c
The kinetic-energy difference is 0.005038, and half L v^2/c^2 is 0.005: 0.76 per cent apart, where the same comparison at 0.6c was 39 per cent apart. That gap closing is the whole content of Einstein's 'to within magnitudes of the fourth and higher orders'.
What the author recorded that a reader should see here. Quantity Expected Under kineticEnergyDifference 0.005037815259212077 J modern-si-2019 pulseSumMoving 1.005037815259212 J modern-si-2019
These are the values the tape's author recorded, not a result this page computed. Nothing here runs the instrument. Open ME-01 with these settings: the link opens it with them already in place. Compare what it gives you with what is recorded here. The settings travel in the link and the laboratory reads them as it loads, so without JavaScript it opens at its worked example instead.