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DallasDad
23rd March 2011, 08:15 AM
Okay, we all know that the speed of light in a vacuum is ~186,000 miles/second (299,792,458 meters/second). This is constant for all observers.

Yet the measured speed through a transparent medium (a sheet of glass, for example) is less. The standard explanation is that the speed doesn't change, but as the light travels through the medium, there is an absorbtion and reemission of photos from atom to atom within the medium, correct? The apparent slow-down is caused by the time-delay imposed by the absorbtion and reemission -- that is, the photon exiting the far side of the sheet is not the photon that entered the near side, rather it is a new photon popped out in response to the absorbtion of the entering photon.

My question: How is this measured? What instruments do we have that are subtle enough to detect what is happening?

Follow-up question: If I'm reading special relativity right, the constantness of c is only valid in vacuuo. Would it therefore be possible for observers in different frames to observe/measure the propagation through the glass happening at different rates? How would they square the incoming and outgoing measurements (which must equal c for all observers) with a different propagation time? Something else in the equation would have to give to make the sums equal. I'm guessing they'd measure a different thickness to the glass?

Follow-up to the follow-up: If all the foregoing is correct, what is the proper way to describe the glass existing in multiple thicknesses simultaneously? Can it only be described via one of the transformation equations, or does it have a value? If there were only one observer, would he be justified in calling that value a constant?

ehcks
23rd March 2011, 08:28 AM
Don't know how relevant it is to your first question, but police in the US use a LIDAR speed detector that's accurate to the tenths of miles per hour. .1 mph is .04 m/s. Even 1 mph is .4 m/s, and that's what they base tickets around.

There's been tests of sending light through super-cooled sodium gas that slowed the transmission of photons to 17 m/s. There's nothing subtle about that.

sol invictus
23rd March 2011, 08:31 AM
The model for light propagation you described it too over-simplified to be tested. But one can observe the interaction of a single photon with a single atom or molecule (and e.g. measure how long it takes to get re-emitted) - that's done all the time in a huge variety of experiments.


Follow-up question: If I'm reading special relativity right, the constantness of c is only valid in vacuuo. Would it therefore be possible for observers in different frames to observe/measure the propagation through the glass happening at different rates?

Yes.

How would they square the incoming and outgoing measurements (which must equal c for all observers) with a different propagation time? Something else in the equation would have to give to make the sums equal. I'm guessing they'd measure a different thickness to the glass?

Yep - that's called "Lorentz contraction". But they would also disagree on the times when the light entered and exited the glass.

Basically the glass itself defines a special rest frame. Physics as seen by someone embedded in the glass will not look invariant under Lorentz transformations. For example, light would propagate at different speeds in different directions in any frame where the glass is moving.

Follow-up to the follow-up: If all the foregoing is correct, what is the proper way to describe the glass existing in multiple thicknesses simultaneously? Can it only be described via one of the transformation equations, or does it have a value? If there were only one observer, would he be justified in calling that value a constant?

I don't understand the question.

DallasDad
23rd March 2011, 08:41 AM
Sol,

You answered my third question ("Can it only be described via one of the transformation equations?") with part of your answer ("Physics as seen by someone embedded in the glass will not look invariant under Lorentz transformations") to my second question. I worded the question badly.

I knew one of the transformations would be required, but I didn't think Lorentz-Fitzgerald was correct, because I've always associated it with contraction in the direction of flight -- that is, changes to the measured length of moving body as it accelerates to relativistic speeds. You're telling me it's really the same function in this example, even though the sheet of glass is at rest in a theoretically inert frame?