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Theory: The island exists within or around a SpaceTime Singularity.
Many physicists have theorized the existence of numerous micro-singularities on Earth, too small to detect. What has been qualitatively studied remains what can bend visible light - collapsed stars, etc. However, Einstein (even before the first visible singularity) theorized with complex mathematics the possibility for various types of these phenomenon. Within the confines of the spacial location do normal physics and the understanding of time breakdown. I am narrowing this down to that of a SpaceTime Singularity.
Theories of singularities are so vast and complex, and our actual knowledge of them is so limited, the writers could easily base a foundation of this in the show; it allows for so much to all be theoretically possible so as not to tick off loyal viewers, while creating an intriguing mysticism to the whole place. Such a singularity would cause space/time distortions, alterations of a magnetic field, time delays (reaching the island air vs sea, light/dark on various parts of the island, etc), why the island can't be seen/found (gravitational lensing), and many other things.
A video was released at ComicCon in 2008 (not a spoiler, already happened) where Chang says he was there to study the Kerr Metric equations and application of Einstein's Theory of Relativity. Kerr metric is used to analyze the rotation around singularities.
When Caesar is in the hydra station he finds a map of the island. On this drawing are notes regarding "imaginary time". This is a concept put forth by physicists for the sole purpose of explaining singularities.
FDW: The wheel was something built to harness the power of this phenomenon. When it's turned it distorts the curviture of spacetime subsequently causing jumps. It has been discussed that dark matter exists behind the FDW; dark matter could be found at the compressed point of a singularity.
Flashes: To use Faraday's analogy of a record skipping: Imagine the singularity spinning everything in space/time to the center. When you turn the wheel you exert a force in opposition to the natural flow of the spin. This would cause the needle to jump until the wheel was stabilized and the needle could find it's groove again.