This posting explores the possibility that insights from consideration of Flatland may be extended to higher dimensionality and shed light on Particle-Wave Duality and Super-Luminal (faster than light) effects such as those that may be associated with the EPR (Einstein-Podolsky-Rosen) experiments.
This is the second of a series. The first Flatland, Dimensionality, and QM Hidden Variables utilized "Flatland" analogies to explore what Feynman called "quantum weirdness" and Einstein called "spooky action at a distance". In particular, could it be that what we perceive as conflicts between ""particles" and "waves" are due to the limits of our perception to 3-D Space plus Time? If we imagine 4-D Space or higher dimensionality, could that help us better understand the "weirdness" and "spooky" nature of Quantum Mechanics (QM)? Could we resolve questions about the Nature of the Universe such as deterministic vs probabilistic, discrete vs continuous, brain vs mind, and so on?
(a) and (b) in the graphic visualize "Particle-Wave Duality" based on the famous Double-Slit Experiment. In that experiment, sub-atomic objects, such as electrons or photons, act like either particles or waves, depending upon whether or not they are made to pass through a SINGLE or DOUBLE slit. If there is a SINGLE slit, they act like particles. If there is a DOUBLE slit, they act like waves.
(c) in the graphic visualizes "Super-luminal" (faster than the speed of light) effects such as those that may be associated with the Einstein-Podolsky-Rosen experiment. In the EPR experiments, the actions of an experimenter "A" appear to instantly affect the results measured by distant experimenter "B".
In the animation, we start with a 3-D object that is a bent red plastic tube:
(a) The bent tube is dropped into Flatland and lands on a Flatland shape that has a SINGLE-width slit in it. As the slit is too narrow for the bent tube to pass thru in that Horizontal orientation, the bent tube bounces and rotates 90° to a Vertical position and penetrates Flatland, leaving only a portion of a nearly vertical part of the bent tube in Flatland. The Flatlanders explore that part (the tiny yellow circle) and call it a "PARTICLE".
(b) The bent tube is dropped into Flatland and lands on a Flatland shape that has a DOUBLE-width slit in it. As the slit is wide enough for the bent tube to pass thru in that Horizontal orientation, the bent tube lands there and lies flat in a Horizontal position. The Flatlanders explore that part (the yellow wave) and call it a "WAVE".
Note that a 90° rotation in 3-D Space changes a "PARTICLE-like" object into a "WAVE-like" object for Flatlanders, and vice-versa.
Recall that in the first posting of this series Flatland, Dimensionality, and QM Hidden Variables a 90° rotation in 3-D Space changed the appearance of a Cola can from a CIRCLE to a RECTANGLE as viewed by Flatlanders.
A 90° rotation in higher-dimension world appears to change the basic form of an object in a lower-dimension world. A PARTICLE appears to be a WAVE, a CIRCLE appears to be a RECTANGLE, and vice-versa.
Although not illustrated in the graphic, it turns out that a 180°rotation in a higher-dimensional world changes an object into its MIRROR-image as viewed in a lower-dimensional world.
(c) A human hand penetrates Flatland and is viewed by Flatlanders as five disconnected small yellow circles (or "PARTICLES"). A Flatland triangle-shape happens to touch the pinky of the human hand and the hand reacts by thrusting out its thumb, which happens to push a Flatland square-shape.The Flatlanders are amazed that touching one PARTICLE (the pinky) causes a totally disconnected and distant PARTICLE (the thumb) to react "instantly" with no apparent means of communication. If we assume the highest speed of communication within Flatland is slower than the 3-D speed of light, to the Flatlanders this reaction seems to be SUPER-luminal (faster than light).
APPLYING FLATLANDER INSIGHT TO QUANTUM MECHANICS In my recent Dialog with Howard Pattee, we speculated on whether the Universe is actually probabilistic, which is the mainstream scientific view, or deterministic, which is definitely the minority view. I speculated that extending the Flatland scenario beyond 2-D and 3-D Space to 4-D and higher-dimensionality, might support an alternative QM interpretation such as that of David Bohm.
In a future posting, I plan to create an animated graphic that visualizes a 4-D Space world in which what we perceive as a PARTICLE-WAVE duality is actually a single object (Bohm's "pilot wave") as perceived by denizens of 4-D world.