Why C in Vacuum? Time Dilation Formula Explained

[rbj]

Let's attempt a related thought experiment. Place a piece of glass with index of refraction n=c/v>1 between a light source and a detector and measure the time-of flight of a photon.

it's not the same photon. in a material, they're absorbed and re-emitted. that's what slows down the wavefront.

Would you conclude that the photon had a rest mass?

i'm one of these turkeys who don't like the application of the term "massless" to photons without some qualification, but whatever you say or think or whatever i say or think, photons do not have rest mass.

 

[rbj]

in a material, they're absorbed and re-emitted. that's what slows down the wavefront.

okay, i have to retract that (unless this Wikipedia article is wrong):

It is sometimes claimed that light is slowed on its passage through a block of media by being absorbed and re-emitted by the atoms, only traveling at full speed through the vacuum between atoms. This explanation is incorrect and runs into problems if you try to use it to explain the details of refraction beyond the simple slowing of the signal.

Classically, considering electromagnetic radiation to be like a wave, the charges of each atom (primarily the electrons) interfere with the electric and magnetic fields of the radiation, slowing its progress.

The full quantum-mechanical explanation is essentially the same, but has to cope with the discrete particle nature (see Photons in matter): The E-field creates phonons in the media, and the photons mix with the phonons. The resulting mixture, called a polariton, travels with a speed different from light.
...

Light that travels through transparent matter does so at a lower speed than c, the speed of light in a vacuum. For example, photons suffer so many collisions on the way from the core of the sun that radiant energy can take years to reach the surface; however, once in open space, a photon only takes 8.3 minutes to reach Earth. The factor by which the speed is decreased is called the refractive index of the material. In a classical wave picture, the slowing can be explained by the light inducing electric polarization in the matter, the polarized matter radiating new light, and the new light interfering with the original light wave to form a delayed wave. In a particle picture, the slowing can instead be described as a blending of the photon with quantum excitations of the matter (quasi-particles such as phonons and excitons) to form a polariton; this polariton has a nonzero effective mass, which means that it cannot travel at c. Light of different frequencies may travel through matter at different speeds; this is called dispersion. The polariton propagation speed v equals its group velocity, which is the derivative of the energy with respect to momentum.

so, i think the article you want to look up is the one on polariton.

 

[yogi]

From Post 32: "It is sometimes claimed that light is slowed on its passage through a block of media by being absorbed and re-emitted by the atoms, only traveling at full speed through the vacuum between atoms. This explanation is incorrect and runs into problems if you try to use it to explain the details of refraction beyond the simple slowing of the signal."

As one of the posters on this forum, I have long argued against the absorption/re-emission explanation. Its gratifying to see some new views on the subject.

 

[jtbell]

In a similar vein, see the following post from PF's own "Physics Forums FAQ" in the General Physics forum:

https://www.physicsforums.com/showpost.php?p=899393&postcount=4

 

[country boy]

it's not the same photon. in a material, they're absorbed and re-emitted. that's what slows down the wavefront.

i'm one of these turkeys who don't like the application of the term "massless" to photons without some qualification, but whatever you say or think or whatever i say or think, photons do not have rest mass.

Thank you for the Wikipedia passage; I had not read it. It shows how we fit refraction into our theory de jour without, perhaps, fully understanding it.

You are correct, of course, in the sense that a free photon doesn't have rest mass. When it interacts with matter it is something else, like a "virtual" photon.

The point of this thought experiment is to think about what goes on in the medium, and what it means to travel slower than c. If you don't know what is going on between the source and the detector, how do you know that the photon isn't traveling slower than c and possessing rest mass? If, instead of an n>1 material, what if the photon bounced back and forth between two mirrors before reaching the detector? That would be similar to your first description of absorption and re-emission.

 

[yogi]

jtbell - I read Zz explanation previously - in fact argued the point about absorption/re-emission with him some time ago - apparently, for the most part we were both saying absorption/re-emission is incorrect - but when I pressed him on how his theory explained a situation where light is slowed in a rarefied medium such as a gas, our dialog broke down. Whatever the mechanism, it must work in the case of a single atom as well as in the case of a crystalline or amorphous solid. Quoting from the Post:

"When atoms and molecules form a solid, they start to lose most of their individual identity and form a "collective behavior" with other atoms. It is as the result of this collective behavior that one obtains a metal, insulator, semiconductor, etc. Almost all of the properties of solids that we are familiar with are the results of the collective properties of the solid as a whole, not the properties of the individual atoms. The same applies to how a photon moves through a solid."

So my question remains, how does the explanation for the collective behavior of photon slowing in a solid translate to a gas or single isolated atom. The increase in transit time for a photon in a gas is almost linear over a wide range of density.

 

[jtbell]

Apparently, even in a dilute gas, the interaction of photons must be explained as a collective interaction with many atoms, and not just with a single atom at a time:

http://www.aip.org/pnu/2005/split/732-1.html

 

[ZapperZ]

jtbell - I read Zz explanation previously - in fact argued the point about absorption/re-emission with him some time ago - apparently, for the most part we were both saying absorption/re-emission is incorrect - but when I pressed him on how his theory explained a situation where light is slowed in a rarefied medium such as a gas, our dialog broke down. Whatever the mechanism, it must work in the case of a single atom as well as in the case of a crystalline or amorphous solid. Quoting from the Post:

"When atoms and molecules form a solid, they start to lose most of their individual identity and form a "collective behavior" with other atoms. It is as the result of this collective behavior that one obtains a metal, insulator, semiconductor, etc. Almost all of the properties of solids that we are familiar with are the results of the collective properties of the solid as a whole, not the properties of the individual atoms. The same applies to how a photon moves through a solid."

So my question remains, how does the explanation for the collective behavior of photon slowing in a solid translate to a gas or single isolated atom. The increase in transit time for a photon in a gas is almost linear over a wide range of density.

Most gasses are diatomic molecules, and thus have a vibrational spectrum. That's one form of absorption and/or re-transmission, depending on the frequency of the incoming photon and the vibrational spectrum itself.

You will note that in light transmission through dense gasses (where you can find any appreciable slowdown), the light transmitted can be highly diffused. The effect of scattering can no longer be neglected. The whole group velocity effect on this is similar to the scattering of the electron gas in solids as one increases the resistance of the material via increasing the scattering frequency.

And no, I'm not tackling the transmission in an anomalous medium such as those in the NEC experiment or metamaterial.

Zz.

 

[ZapperZ]

From Post 32: "It is sometimes claimed that light is slowed on its passage through a block of media by being absorbed and re-emitted by the atoms, only traveling at full speed through the vacuum between atoms. This explanation is incorrect and runs into problems if you try to use it to explain the details of refraction beyond the simple slowing of the signal."

As one of the posters on this forum, I have long argued against the absorption/re-emission explanation. Its gratifying to see some new views on the subject.

Why is this "different"?

It is the SAME explanation that I gave in the FAQ. I gave the "dumbed-down" version. If you read carefully what you are agreeing to, it is the SAME interaction of the photon with the phonon spectrum! What is being disagreed with is that it is NOT an absorption and re-emission due to the ATOMS of the solid being discussed, which is the point I was also making in the FAQ.

This is why we had a "breakdown" in such discussion before. It appears somehow that this very important point didn't get through to you.

Zz.

 

[yogi]

Thank you for the clarification

Yogi

 

[lightarrow]

Apparently, even in a dilute gas, the interaction of photons must be explained as a collective interaction with many atoms, and not just with a single atom at a time:
http://www.aip.org/pnu/2005/split/732-1.html

Ok, however, in the case of the experiment described in that document, they used a Bose-Einstein condensate, not exactly an ordinary gas as air in standard conditions.

 

[rbj]

No that is incorrect Tim Lou.
The water is just as much moving as the train is.

but it can't be just as much moving for every observer, MeJen. i think that that the same Eisteinian relativistic thought experiment can't be done for movement in media as it can for movement in nothing whatsoever. the fact that two observers, moving relative to each other, observing the same wave propagation of the same E&M wave must observe its speed the same is the central reason they can't observe the others' clocks as ticking the same as their own.

that's my take on it.

 

[MeJennifer]

i think that that the same Eisteinian relativistic thought experiment can't be done for movement in media as it can for movement in nothing whatsoever.

The principle of relativity works everywere in space, in empty space and in any medium.

 

[rbj]

The principle of relativity works everywere in space, in empty space and in any medium.

i agree that the physics (once everything is accounted for) is valid everywhere, empty or not. it's just the thought experiment in its basic form that takes place with two observers moving inertially relative to each other and observing the same beam of light.

hey, and whatever happened to Tim Lou's post? it vanished.