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Can we prepare a gas medium in which we can travel faster than light?
This question struck me while reading a sci-fi where a scientist prepared such a gas medium. He sat in a chamber filled with that gas and stayed there for sometime, then came out and from outside he could see a past version of himself in the chamber. Can this anyhow be scientifically described?
The speed of light in a material is $c = 1/\sqrt{\epsilon\mu}$. Very slow light therefore means either a very high permittivity (high $\epsilon$) or a very high permeability (high $\mu$).
High $\epsilon$ means high electric polarizability, which implies high van-der-Waals force. I highly doubt that a substance with such a high permittivity that you could see light come out after a macroscopic time could be a gas at temperatures you could survive; I'd expect the forces between the atoms to be strong enough that it would be a solid body (which clearly would preclude entering and leaving).
I'm less sure about permeability, but I highly suspect it would have a similar effect on magnetic attraction between the atoms.
Therefore I highly doubt that in our universe there could be a substance that has those properties.
However, since this is worldbuilding.SE, not physics.SE, we can hypothetize some substance which would interact with yet another field (not available in our universe) which causes repulsion between the atoms. That way you could have a gas despite strong electromagnetic attraction. Alternatively you could hypothesize that the scientist wears a suit that protects him from very high temperatures (however one then has to additionally handwave why his image is not drowned in thermal radiation, that is, glowing of the hot gas).
Already been done (The light-freezing/slowing part).
However the scale is too small, and the temperatures would instantly kill the scientist. Also, the scientist's body heat would free up the gas cloud, releasing the light.
However, if the scientist was in a glass box where the walls were filled with a light stopping/slowing substance, then it might work.
The speed of light in a vacuum is a fixed constant in physics. Putting additional material in the way of a moving object, even if it's a gas, can only slow the object down, not make it go faster.
You could use a very long optic fiber. But why not transduce the light into another form and back again? In modern tech we just use a camera and monitor with a programmed delay. If you want a pre-tech idea that works fairly directly with materials, how about a "slow holograph". The light hits the inside surface and causes a chemical reaction. The slow (human time scale) reaction cascades through the thickness of material until reaching the opposite side, where a delayed image is visible. A delayed photograph is very plausable indeed and might be engineered today, in fact. But that means projecting an image onto the inner surface with lenses, at the very least like a camera obscura. In pre-ellectronic times that might be useful in fact. But without lenses, just having it as the wall in a room like a window, the light from all angles needs to be handled. That can be plausible in a hand-wavy manner by requiring special illumination on both sides and saying it's like a hologram on the viewing surface. In fact, with coherent monochromatic light and the right beam setup on the inside, the photograph woukd be an interference pattern (that's how you make a hologram on photo film) and have that slowly pass through the material.
No. You can't have a gas or another material where a macroscopic object such as human moves faster than light. Interactions between the gas and object would either slow down the speed object can move or allow the light to move faster. Generally both.
You can have a geometry where the light travels much longer thru the gas as than you do, though. But at that point it is easier to simply not have you disturbing the gas at all and hold it in a separate chamber with transparent walls. And as celtschk noted, it is pretty hard to have a gas where light speed is small enough anyway. So just using a video camera with time delay would be more practical. Or use a transparent solid, if non-technological solution is needed.
