Slow glass / Conjecture about refraction

[md65536]

Part 1: Slow glass...

From a thread in the Relativity forum:

Reminds me of a book about something called slow glass, great stuff, lets you see back in time....

 

 

http://en.wikipedia....ight_in_fiction

"'Slow glass' is a material where the delay light takes in passing through the glass is attributed to photons passing '...through a spiral tunnel coiled outside the radius of capture of each atom in the glass.'"

 

Suppose you had complete control over the path of light through some volume.

Even with light traveling at c, a long curving path would take longer for light to travel, and could be used to delay light.

A fractal path on an arbitrarily small section of a plane can have an infinite length.

Quantum limitations might make a true fractal path impossible, but using arbitrarily large volumes of "slow glass" and being able to cross paths and use 3 dimensions should allow you to make an arbitrarily large path for light.

If you had the path determined by some repeated crystal structure, such that the path of light entering from any specific angle at some specific point, would be the similar to the path of light entering from the same angle at any other point, you might be able to implement slow glass (possibly restricted only to a specific incoming and outgoing angle, eg. you might make it work only for light that is normal to the surface).

 

 

Part 2: Refraction

Can refraction and the "slowing of light in a physical medium" be described as the light traveling a greater, curving distance through the medium than it would if it were traveling through a vacuum?

 

My (poor) understanding of refraction is that photons traveling through a medium with an index of refraction > 1 will interact with chains of molecules one after another, making light appear to have a speed lower than c, when instead it is just being delayed due to these interactions. But I can't make sense of that. The arrangement of molecules should make light behave differently depending on its angle through the medium. How can light through eg. glass be so perfect unless every path of given length through it intersected with the same number of molecules, regardless of direction? How could the atomic structure of glass be so isotropic?

 

INSTEAD... I imagine that, say you have a 1 cm thick pane glass, then the distance across that pane, as measured from inside the pane, is greater than 1 cm. It might be that the path of light is simply curved or bent in some uniform way as the light interacts with the matter (ie. all glass is a type of "slow glass"). Another possibility is that the matter of the glass curves its interior space so that what appears as a straight line of 1 cm from outside, becomes a straight line greater than 1cm inside. Then light need not directly interact with the matter; it just follows a longer curved path through a vacuum inside the glass (ie the mostly empty space between the subatomic particles of the glass), and the length of that path is determined by the curvature caused by the matter.

 

Can anyone imagine this?

 

One problem is that refractive index depends on light wavelength, so the curvature of space within a medium would need to be variable. I can imagine curving spacetime looking like a curved funnel of typical spacetime "rubber sheet analogy" drawings, with different wavelengths of light going on different locations on the funnel, resulting in different distances being traveled through the glass.

 

 

To rephrase the conjecture: Matter causes local spacetime curvature, that causes light of a specific wavelength to travel a longer path through the medium than it would through a vacuum.

 

Then it's easy to conjecture that if a material is opaque to light of a certain wavelength, that means that the curvature is too extreme for the light to escape, similar to a black hole. Could the absorption of light energy be equated to light entering a black hole?

Edited June 12, 2011 by md65536

[swansont]

Refraction is due to the slowing of light — light follows the principle of "least time" in getting to its destination — it gets there as fast as it can, and given that it has to slow down, that's not a straight line. It travels faster in the air, so by bending towards the normal line you minimize the time spent in the medium.

 

A piece of glass is pretty uniform, overall. If it weren't you would get distortions of the light. (If the nonuniformities were of a particular pattern, you'd have a lens) A chunk of glass 1cm on a side is going to contain about 10^21 molecules. Any small inhomogeneities are going to average out over the path the light travels.

[md65536]

Refraction is due to the slowing of light — light follows the principle of "least time" in getting to its destination — it gets there as fast as it can, and given that it has to slow down, that's not a straight line. It travels faster in the air, so by bending towards the normal line you minimize the time spent in the medium.

 

A piece of glass is pretty uniform, overall. If it weren't you would get distortions of the light. (If the nonuniformities were of a particular pattern, you'd have a lens) A chunk of glass 1cm on a side is going to contain about 10^21 molecules. Any small inhomogeneities are going to average out over the path the light travels.

 

 

A single 1cm "row" of glass molecules would have 10^7 molecules. The number of interactions of transmitted light could be far less (if photons bypass most molecules) or more (if photons interact with multiple rows of molecules). Smaller wavelengths (violet) refract more than longer (red) so the former must involve more interactions.

 

Have scientists observed or modeled the path of photons and the number of interactions?

 

 

If a photon is absorbed and then re-emitted when passing through glass, it would still have to obey causality. I assume that if a photon is absorbed at one point and time, and emitted at another point and time, the energy that makes up the photon will be found to have traveled some distance at a speed of c. Uncertainty might disagree with that. But I suspect that both uncertainty and causality apply: The exact location of energy is uncertain, but where it is observed, it is observed to have traveled at a speed of c.

 

Does it make sense to speak of the path of photons between when they are absorbed and re-emitted? They might not be considered photons after being absorbed. It might not even be the same energy that gets re-emitted??? But if it does make sense, you could call the path of the energy a curved path along which the energy travels at a speed of c?

 

 

 

The conjecture seems to be compatible with the principle of "least time".

The principle says that the path of light takes the least time to get from P to Q while traveling at different speeds through different media.

My conjecture would state that the speed of light is constant through all media, and follows a path of least distance (and thus least time) getting from P to Q. Since the distance inside the glass is different due to curvature than the same distance measured by an external observer, it doesn't appear to be the least distance to an outside observer. It might even be the case that the bent path "feels" straight to the photons??? A traveling photon (imagined to be moving in some pseudo-classical sense) might not experience any change in direction, nor any interaction with molecules, when passing from air to glass, but might instead experience a sudden warping of space as it passes from the spacetime curvature of one medium to the curvature of another. Infinite length contraction makes this impossible to imagine, and possibly meaningless.

 

However, this doesn't seem to be compatible with reflection, and I would assume that the behavior of reflected light is very similar to the behavior of refracted light, in terms of photon/matter interaction.

Edited June 12, 2011 by md65536

[swansont]

Have scientists observed or modeled the path of photons and the number of interactions?

 

I'm not sure. In general terms, you have Feynman diagrams. The paths that do not follow the least time will interfere and cancel.

 

If a photon is absorbed and then re-emitted when passing through glass, it would still have to obey causality. I assume that if a photon is absorbed at one point and time, and emitted at another point and time, the energy that makes up the photon will be found to have traveled some distance at a speed of c. Uncertainty might disagree with that. But I suspect that both uncertainty and causality apply: The exact location of energy is uncertain, but where it is observed, it is observed to have traveled at a speed of c.

 

Does it make sense to speak of the path of photons between when they are absorbed and re-emitted? They might not be considered photons after being absorbed. It might not even be the same energy that gets re-emitted??? But if it does make sense, you could call the path of the energy a curved path along which the energy travels at a speed of c?

 

The photon isn't observed while in the medium; as with my prior statement, the states where the photon has a different energy or momentum cancel. Only the path that follows Snell's law conserves those properties.