A Magick Carpet Ride

A young woman and her two wyrd sisters are practicing their mysterious magicks tonight.  They will exercise their telekinetic and mathematical skills with the levitation of a massive material object.   In their alchemical experiment they will test whether two events that would appear simultaneous in a reference frame that is at rest, would these events still appear simultaneous if the reference frame were in motion? Can she make the invisible, visible?

It is a windless night, during the witching hour (air / medium at rest relative to earth).  Since her youth, a thousand years in the past, she has known that three is a magick number, so the sisters can begin their session under a beneficial sign.  The young woman stands at the centerline of a soccer field with one sister at each endline.   This field has the length L meters.

Now, beforehand, the thrice wyrd sisters had planned their rite.   The young woman’s sisters have agreed to take certain actions in response to her initiations.  While in a mystical trance she conjures up two digital stopwatches which hover in the air before her, stacked, so that they are perpendicular to a line that runs from endline to endline.   She continues her dark rite by whispering the secret words.  Then, the entire green turf (and the reference frame attached to it) lifts itself from the dust, and rises above the ancient high treetops. It begins to fly away at the constant velocity c, straight and level, like a magick carpet, off into the starry night.   Then, it turns, and flies similarly back to the stadium.  A warlock soccer fan, with his supporters scarf, was observing the sisters rehearse their magicks from his stationary stadium seat in a reference frame attached to the earth (at rest).

The Blue Djinn on her Magick Carpet

As the carpet tandem passes once again through the stadium, within view of the warlock she will, with some incantations, make a ball of golden light appear above her head.   At this flash of light, her sisters, with their supernatural reflexes, will let out a banshee’s wail upon seeing the nearly instantaneous flash from this light.   In the same instant, two disembodied bony fingers waft as smoky wisps awaiting, for at the appearance of the light they will start the timing devices. The warlock sees this flash and begins each of his two hidden clocks.  Now their clocks are synchronized, so they will measure the same time intervals between these events in their separate reference frames.

As each of her sisters’ wail reaches her, the ball of golden light flashes to green when the first sound wave arrives at her central position, then to red when the second sound wave arrives at her central position, the warlock will witness each arrival flash.  The difference in arrival times of each sisters’ sound wave is due to the carpet’s forward motion. If the sound waves had arrived at the same time then that would mean the tandem was not moving through the still air and the light would instead flash to blue.

Thrice Wyrd Sisters ~ MacBeth

They have made a three-seated tandem (aligned parallel to the direction of motion) so that they maintain the same distances relative to each other, no matter how quickly, or slowly, the tandem moves through space; or possibly not even moving at all.  The distance L moves through space, neither increasing nor decreasing. So, each pair of clocks will measure two times, one from the forward sister and one from the rearward sister.  The following equation adds these two times for a total time T (both the witch at the center position and the warlock seated nearby do this addition):

♦T = t₁ + t₂ = [0.5L / (c + v )] + [0.5L / (c – v )] = Lc / (c² – v² ) = [L / c ] × (1 – [v² /c² ])^-1

If the carpet were at rest (v = 0) then this formula would reduce to:

♦ T_r = t₃ + t₄ = [0.5L / (c + 0)] + [0.5L / (c - 0)] = L / c

The zero velocity airy particles allow the porous conceptual walls of the reference frames to pass by without hindrance, so the air molecules velocity will neither increase nor decrease the velocity of the sound wave c travelling through the still air.  It will remain constant despite the motion, or lack of motion, of the wailing banshees.

The magick carpet will move straight, level, and true at the same time as the sound waves are in flight.   The length L of the tandem will neither increase nor decrease.  As the carpet moves forward, the distance from one sister to the center will appear to shorten, while the distance from the other sister to the center will appear to lengthen.  This equation will account for this by inserting the velocity v.

She puts some numbers into the calculator that she has been carrying beneath her pointed witchy hat; L = 100 meters; c = 343 meters / second; assume v = 30 meters /second; T_v = total time measured by each pair of clocks:

♦T_v = t₁ + t₂ = [Lc ] / (c² – v² ) = [100 m × 343 m/s] / [(343m)² – (30 m/s)² ] = 0.294 s

as compared to the total time measured when the carpet is at rest:

♦T_r = t₃ + t₄ = L / c = 100 m / 343 m/s = 0.292 s

thus, her velocity is:

♦v = √c² – [(Lc ) / T_v )] = √(343 m/s)² – [(100 m × 343 m/s) / 0.294 s] = 31.3 m/s

Thus, she has made her velocity form from the night’s shadows (detecting her absolute motion relative to the still air/medium) using sound waves.  She can make her magick carpet fly, through the night sky.  This will contradict Galileo, Newton, and Einstein and their precious principle of relativity, which says that what she has done is impossible.