6. Being in two places at the same time

Article 6 Module 3



Fast moving objects

If things are moving very fast on the same path, say a metronome, the composite of all the images would make the final picture that we see as a blur of a thousand metronome pendulums in a fluid arc.

Similarly, the tick-tick-tick of the metronome would blend into one sound as the frequency of the beats increase. In a youtube video, the beats start at 90 BPM and move to a speed of 10,000 BPM. As the sound moves into the thousands beats/minute, the beats no longer become separable by our senses. At 10,000 beats, the sound is one long high-pitched tone.

There are many examples of single entities blending into a composite image when motion is added. The hub of a car’s wheel looks as a flat disc rather than individual spokes; the individual ferris wheel gondolas look like a colored circle; the ribbons of a maypole are a vista of color as the children run around the pole.

Round table with 4 legs

Round table with 4 legs

A four-legged table

Here’s an analogy: take a 4 legged table, with one leg at each corner of the table. If we removed 1 leg , the table would be slightly unbalanced. If we removed 2, the table may be able to balance if the remaining legs were diagonally across from each other and the weight of the table were perfectly matched. If we removed 3 legs, the table would topple over. 

Now suppose that remaining leg could rapidly move from its position to the 2nd, 3rd, and 4th positions. At any split instant, only one of the positions has a leg. How fast does that leg have to transpose itself from one position  to the next for the table not to topple over?

We could imagine that if the leg changed its position in space at a relatively slow speed of 100 transpositions/second, the table would remain standing. 

It may look a little wiggly as it tilts every so slightly in one direction - when the leg disappears from that corner - then tilts to another, as the leg comes back to its first position.

White cube

White cube

Creating a 3-dimensional reality

What do we see as we look towards that table with its one leg zooming from position to position?

We see a blurred square prism (a "cuboid") holding up the table. The prism is a composite of all the movements that the one leg has gone through. This prism - even though it is functionally made up of one leg - has enough substance as if there were a multitude of wooden legs. When the leg continuously repositions itself, the table has a stable position in space.

The one-legged prism is - for all practical purposes - a solid structure. Attempting to throw a ball through the "legs" would fail. The fast moving leg would block the ball from going through (unless the speed of the ball is faster than the speed at which the legs are changing positions).

Similarly, 1 electron can create a forest of electrons surrounding the nucleus.

This is the dual reality of electrons: They can create stable, "solid" structures; but they are in continuous motion.

In the next article, I will highlight Platonic solids. This will set the stage for seeing how Platonic solids form the basis for electron orbitals. 

Picture credits: 

  1. Matt Ryall Ferris wheel., Taken on May 9, 2009.
  2. Paco. Metrónomo., taken on August 4, 2002. 
  3. By Khusnul Faizin. Shutterstock, ID: 1313382593. Round table with four legs. 
  4. By Topuria Design. White vector cube isolated on the transparent background. Shutterstock, ID: 1858571896.