What does the Uncertainty Principle say about the location of photons?

DrChinese

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Light gets absorbed and emitted over and over ...
Just to amplify on this: it is not absorbed and re-emitted in the classical sense. There are probabilities that activity occurs. I.e. various paths or histories. The probabilities (paths) then sum (integrate) in a way that has the overall result averaging to a value lower than c.
 
Light gets absorbed and emitted over and over (and over and over). You can think of it like a busy man walking to work from the train station. If a pan-handler asks him for money, it'll slow him down, even though when he's walking, he's always walking as quickly as he can without appearing to be in a hurry :)
Well:
Originally Posted by JJRittenhouse
Isn't the speed still the same in another medium, just interrupted by electron interaction?
AFAIK, the photons of visible light do not have enough energy to excite the electrons of a transparent material. The photons just pass through having lower speed.
What happens with visible light then? it can't have a different explanation.


Edit: Understood Dr.Chinese
 

DrChinese

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AFAIK, the photons of visible light do not have enough energy to excite the electrons of a transparent material.
This is not accurate, and I probably should have commented earlier. The excitation energy of electrons does not determine whether a material is transparent or not. It is more closely related to field effects of the atomic structure. I.e. the arrangement and type of atoms/molecules. They create a virtual field and this leads to the effects of color we see.

ZapperZ has commented on this in the Physics FAQ in much better words than I could provide:

This question appears often because it has been shown that in a normal, dispersive solid such as glass, the speed of light is slower than it is in vacuum. This FAQ will strictly deal with that scenario only and will not address light transport in anomolous medium, atomic vapor, metals, etc., and will only consider light within the visible range.

The process of describing light transport via the quantum mechanical description isn't trivial. The use of photons to explain such process involves the understanding of not just the properties of photons, but also the quantum mechanical properties of the material itself (something one learns in Solid State Physics). So this explanation will attempt to only provide a very general and rough idea of the process.

A common explanation that has been provided is that a photon moving through the material still moves at the speed of c, but when it encounters the atom of the material, it is absorbed by the atom via an atomic transition. After a very slight delay, a photon is then re-emitted. This explanation is incorrect and inconsistent with empirical observations. If this is what actually occurs, then the absorption spectrum will be discrete because atoms have only discrete energy states. Yet, in glass for example, we see almost the whole visible spectrum being transmitted with no discrete disruption in the measured speed. In fact, the index of refraction (which reflects the speed of light through that medium) varies continuously, rather than abruptly, with the frequency of light.

Secondly, if that assertion is true, then the index of refraction would ONLY depend on the type of atom in the material, and nothing else, since the atom is responsible for the absorption of the photon. Again, if this is true, then we see a problem when we apply this to carbon, let's say. The index of refraction of graphite and diamond are different from each other. Yet, both are made up of carbon atoms. In fact, if we look at graphite alone, the index of refraction is different along different crystal directions. Obviously, materials with identical atoms can have different index of refraction. So it points to the evidence that it may have nothing to do with an "atomic transition".

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.

A solid has a network of ions and electrons fixed in a "lattice". Think of this as a network of balls connected to each other by springs. Because of this, they have what is known as "collective vibrational modes", often called phonons. These are quanta of lattice vibrations, similar to photons being the quanta of EM radiation. It is these vibrational modes that can absorb a photon. So when a photon encounters a solid, and it can interact with an available phonon mode (i.e. something similar to a resonance condition), this photon can be absorbed by the solid and then converted to heat (it is the energy of these vibrations or phonons that we commonly refer to as heat). The solid is then opaque to this particular photon (i.e. at that frequency). Now, unlike the atomic orbitals, the phonon spectrum can be broad and continuous over a large frequency range. That is why all materials have a "bandwidth" of transmission or absorption. The width here depends on how wide the phonon spectrum is.

On the other hand, if a photon has an energy beyond the phonon spectrum, then while it can still cause a disturbance of the lattice ions, the solid cannot sustain this vibration, because the phonon mode isn't available. This is similar to trying to oscillate something at a different frequency than the resonance frequency. So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. The emitted photon may encounter other lattice ions as it makes its way through the material and this accumulate the delay.

Moral of the story: the properties of a solid that we are familiar with have more to do with the "collective" behavior of a large number of atoms interacting with each other. In most cases, these do not reflect the properties of the individual, isolated atoms.
 
The controlling rule is in fact the Uncertainty Principle. So answering your question with anything else ends up stretching the language in a fashion which leads to either contradiction or confusion. (Which is why Fredrik is correct.)

It is probably easiest to say that when a photon has a known velocity (momentum actually), it's position is essentially undefined.
we were getting bogged down in the mechanics of the speed of light through a medium, I was just drawing that to a close where it could be asked in a different topic.

Thanks for the help, though guys.
 
On the other hand, if a photon has an energy beyond the phonon spectrum, then while it can still cause a disturbance of the lattice ions, the solid cannot sustain this vibration, because the phonon mode isn't available. This is similar to trying to oscillate something at a different frequency than the resonance frequency. So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. The emitted photon may encounter other lattice ions as it makes its way through the material and this accumulate the delay.
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So the idea of absorption and emission is correct, but not with the electrons within atoms, but the collective nature of the material in which is passes.

Was this discovered after Feynman was writing QED, or was he simply mistaken or using obsolete information?
 

DrChinese

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Was this discovered after Feynman was writing QED, or was he simply mistaken or using obsolete information?
Feynman was quite aware of this, especially since he discovered and/or formulated a lot of it. Sometimes the ideas get mangled a bit when you move from the language of mathematics to a conversational language. That is part of the reason that quotes like that - even from the physics gods - are not really considered authoritative references in and of themselves.
 
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This is not accurate, and I probably should have commented earlier. The excitation energy of electrons does not determine whether a material is transparent or not. It is more closely related to field effects of the atomic structure. I.e. the arrangement and type of atoms/molecules. They create a virtual field and this leads to the effects of color we see.
Is this effect (absorption/re-emission by the field effect of the atomic structure) ever observed? It is hypothesized that light will travel faster than c in Casimir vacuum. Couldn't the field effect of the atomic structure effect the speed of light?
 

DrChinese

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Is this effect (absorption/re-emission by the field effect of the atomic structure) ever observed? It is hypothesized that light will travel faster than c in Casimir vacuum. Couldn't the field effect of the atomic structure effect the speed of light?
The net effect (of the various paths that a photon can take) is that the probability packet moves at less than c through various materials. Even though the photon itself is essentially moving at c. So I would say that the speed of light (and other optical properties) in a particular medium is a function of its structure.
 

zonde

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So the idea of absorption and emission is correct, but not with the electrons within atoms, but the collective nature of the material in which is passes.

Was this discovered after Feynman was writing QED, or was he simply mistaken or using obsolete information?
Explanations like that are only speculations.

So I can propose different speculation.
When you go down to length scales of photon wavelength photon is traveling as a wave i.e. it travels many available paths. In material these paths are not straight and when you average over all the paths the photon travels within one wavelength it is shorter then straight path would be. So while you can still say that it travels at c average speed will be less than c.
 
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Explanations like that are only speculations.

So I can propose different speculation.
When you go down to length scales of photon wavelength photon is traveling as a wave i.e. it travels many available paths. In material these paths are not straight and when you average over all the paths the photon travels within one wavelength it is shorter then straight path would be. So while you can still say that it travels at c average speed will be less than c.
We know that gravity changes the space making it curved. The same is valid for charged particles in EM field. Unlike gravity where only "pits" are possible, in EM field we will have "pits" and "hills". Also these "pits" and "hills" can be packed very tight depending on material density. More dense material means more pits and hills. So photon traveling through this EM field curved space will need more time to cross it compared to the straight line defined by the local gravity field.

That is my speculation. :devil:
 

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