One of the things that kept us commentators up all night during the original series run was trying to find an explanation for the island time travel.
It still remains elusive.
The Alcubierre drive or Alcubierre metric is a speculative idea based on a solution of Einstein's field equations in general relativity as proposed by theoretical physicist Miguel Alcubierre, by which a spacecraft could achieve faster than light travel if a configurable energy-density field lower than that of vacuum (example, negative mass) could be created. Rather than exceeding the speed of light within its local frame of reference,
a spacecraft would traverse distances by contracting space in front of
it and expanding space behind it, resulting in effective
faster-than-light travel. This is the theory behind Star Trek warp drive.
Objects cannot accelerate to the speed of light within normal
space time; instead, the Alcubierre drive shifts space around an object
so that the object would arrive at its destination faster than light
would in normal space.
Although the metric proposed by Alcubierre is mathematically valid in
that it is consistent with the Einstein field equations, it may not be
physically meaningful or indicate that such a drive could be
constructed. The proposed mechanism of the Alcubierre drive implies a
negative energy density and therefore requires exotic matter,
so if exotic matter with the correct properties does not exist then it
could not be constructed. However, at the close of his original paper.
Alcubierre based some of his ideas on analyzing traversable wormholes that the Casimir vacuum
between parallel plates could fulfill the negative-energy requirement
for the Alcubierre drive. Another possible issue is that although the
Alcubierre metric is consistent with general relativity, general
relativity does not incorporate quantum mechanics, and some physicists
have presented arguments to suggest that a theory of quantum gravity which merged the two theories would eliminate those solutions in general relativity which allow for backwards time travel of which the Alcubierre drive is one.
If one goes back to look at the numerous community posts on the subject, you would find references to the Casimir Effect, wormholes, warp drive spacecraft, as possible elements to the LOST time travel puzzle.
Dark energy appears to be the unknown substance that is a part of space itself; it is thought to explain why space is always expanding outward. To harness an energy like this is one of the theoretical basis for time travel since the expansion (or contraction) of space is the fundamental element of warp space drive.
The Fermi Lab has been colliding matter for years to create very small exotic matter through the burst of gamma rays. Gamma Rays are the greatest energy concentration force. However, capture, storage and application of gamma rays as an energy source is unproven. However, contact with other matter can generate electromagnetic fields. The faster than light speed could be accomplished when the dark energy or gamma rays come into contact with any other matter; the reaction between the two phases could generate more energy because it would come all the mass of the elements into pure energy.
Black holes have such intense gravity
that, once inside their event horizons, not even light can escape. Outside of the
event horizon, the hole's intense gravity draws matter into a
disk and raises it to very high energies. The disk emits lots of light
on its own and sends out jets of high energy particles that emit even
more as they interact with the surrounding interstellar material.
It was thought that the radiation emitted by the black hole starts driving off
the surrounding matter, effectively cutting off its own food supply, called the Eddington limit. But now, researchers have found that the Eddington
limit isn't an absolute cap on the amount of energy a black hole can
emit out into its surroundings. Their observations suggest that this
particular black hole sends out almost as much energy in the form of
accelerated particles.
In theory, the use of pull of a wormhole or black hole with associated intense energy could create the warp bubble around a spacecraft. However, the math states that the encapsulated craft would need to be shielded from intense heat greater than that our the center of our sun.
If we start to piece together some of these elements, we can possibly see the light (literally and figuratively). The light cave may be in reality a gamma ray generator (natural or alien). The disruptive electromagnetic release (which destroyed the Hatch) is caused by the gamma rays to interact with other matter. The safeguard to keep the gamma ray generator and other matter from coming together could be the efficient placement of a tiny worm hole. A tiny wormhole in front of a spacecraft (or in this case, the island is the craft), could bend space time around these opposing fields to create time travel jumps.
I can guarantee that none of the LOST writers ever thought of this. The series did not dwell on scientific explanations. It relied on vague illusions. Their time skips were thrown out to create "separation" anxieties among the various surviving 815ers.