Does light always travel at light speed?

[George K]

See the link in post #5.

I have already read that. However, it doesn't say anything about that. Let's consider the following: Suppose that you have a "transmitter" that emits a photon and a "receiver" that receives this photon, and that the "transmitter" and "receiver" are both located in the vacuum and very close to each other (at a distance similar to the distance between the atoms of a medium). (This "transmitter" and "receiver" could be two atoms of a gas -one transmitting a photon and the other receiving this photon- which happens to be so close to each other.) What is the speed of light in this case? As the photon travels inside the vacuum, it's speed should be c (no matter how short its travel is). If this is correct, then what is the difference between this case and the travel of light inside the "vacuum areas" (i.e. between the atoms) of a medium?

 

[sophiecentaur]

what is the difference between this case and the travel of light inside the "vacuum areas" (i.e. between the atoms) of a medium?

I would say that you are mixing your models up. Photons don't travel from molecule to molecule. The propagation is in the form of waves and individual photons cannot be regarded as 'being' anywhere at any given time. It has been said many times before but you cannot treat photons as little bullets. They are essentially only 'there' when they interact. If the whole wave is being involved than where can you say the individual photons are? Stick a tiny light sensor in the middle of the medium and you can say that, when it 'sees' light, it has interacted with a particular few photons - defining where they are at the time.
It is not a good idea to try to bend the accepted terms to your own model.

 

[George K]

I would say that you are mixing your models up. Photons don't travel from molecule to molecule. The propagation is in the form of waves and individual photons cannot be regarded as 'being' anywhere at any given time. It has been said many times before but you cannot treat photons as little bullets. They are essentially only 'there' when they interact. If the whole wave is being involved than where can you say the individual photons are? Stick a tiny light sensor in the middle of the medium and you can say that, when it 'sees' light, it has interacted with a particular few photons - defining where they are at the time.
It is not a good idea to try to bend the accepted terms to your own model.

Ok, I agree that I should not use the term photon. But actually the question remains. In my example, one atom of the gas emits light (ok, as a wave) and another nearby atom of the gas receives this light (yes, as a wave). What is the speed of light in this case? I suppose that the speed must be c, no matter how close to each other these atoms are (and that's because there is only vacuum between them). Am I right?

 

[sophiecentaur]

Ok, I agree that I should not use the term photon. But actually the question remains. In my example, one atom of the gas emits light (ok, as a wave) and another nearby atom of the gas receives this light (yes, as a wave). What is the speed of light in this case? I suppose that the speed must be c, no matter how close to each other these atoms are (and that's because there is only vacuum between them). Am I right?

I'm going to throw something else in, here. You are talking about "light" but any model you come up with should also be applicable to 1500m long waves and the shortest of gamma waves.
In a 'condensed' substance, the spacing between atoms / molecules will probably be less than one wavelength of visible light. So it is not realistic to talk in terms of launching a light wave (or photon, if you must) and then it arriving at another atom. (That would be like what happens in a low density gas, where the effect is random scattering from individual atoms.) The fields around each atom (and all the other nearby atoms) will all be involved in setting up the energy levels and the transitions. The model to use is much more classical - coupled oscillators or a transmission line with masses on springs. The 'space' in between (where you could say that c applies) is only part of it; it's the interaction between the charge systems along the line that counts. The contribution to the delay along each step the journey is, of course, affected by the 'c' delay of the fields but each atom is also contributing a significant delay as it reacts with the fields around it and the fields of its neighbouring atoms. This 'loads' the line.
RF model:
If you take a line of parallel dipoles (say each one is 1m long) and you feed the first one with a 150MHz RF signal, that signal will propagate along the line. Some of the power will couple with the each dipole- they each have an equivalent cross section- but slower than c because each dipole introduces a phase shift as the currents flowing will cause a re-radiated signal that lags behind the incoming signal. The signal that emerges from the other end will be the net sum of the incident signal and each of the re-radiated signals. But there's something else here. Each element will be interacting with its neighbours (depending on the spacing). Appropriate spacing can produce a Null in the emerging RF wave in the direction of the line.
In a solid, the system is three dimensional but the same principle is at work and the majority of the power will travel in a straight line.

 

[nasu]

In a 'condensed' substance, the spacing between atoms / molecules will probably be less than one wavelength of visible light.

It is definitely so.
The typical spacing in a solid is of the order of angstroms or at most tens of angstroms.
The wavelength of visible light is of the order of a micron. 3 to 4 orders of magnitude larger than the spacing.
So even the notion of propagation between two neighboring atoms is not so clear, at this scale.

I think the image of the solid being composed of mostly empty space is not such a good idea. It gives some image about the smallness of the atomic nucleus, at some elementary level. But this space (in solids) is filled by electrons which may have no volume but have strong electric fields. So propagating thorough this "vast" empty space is nothing like going through vacuum. Most of the time, the spacing in the lattice is very close to the ionic or atomic diameter, no matter how you define these.

 

[sophiecentaur]

. . . . . . which probably means that the basic model would fit for optical wavelengths all the way up. For short wavelengths, it could be different - the Bragg formula for X ray diffraction is based on point scatterers, where the photon energy is too high to be interacting with the valence electrons.

 

[nasu]

I am not sure what you call the "basic model".
But the Laue theory of x-ray diffraction seem to be similar to what you describe about the line of dipoles. Without assuming a discrete line of scattering objects but a distribution of electrons with periodic structure.
The result is again that most radiation goes forward and some of it is scattered at some very specific angles, depending on the details of the periodic structure.
Still don't need to introduce photons to get the results.

 

[Nick Martin]

To throw in a wobbler, it has been on my mind for some time that nobody knows for sure what speed light travels at in interstellar or intergalactic space. We have plenty of evidence within our own solar system that it travels at C. We assume that outside the solar system it is traveling at C in a vacuum, and work out all our distances between objects on that basis, but we don't know if it is
a) truly a vacuum (we don't know where the dark matter is) or
b) how that area of space reacts to light if it is teeming with dark energy.
For all we know it may go really slowly once it gets out of our solar system, or indeed much faster. We'd have no way of measuring it given that conditions were consistent, we'd just always get our interstellar distances wrong. All we do is record it arriving at C and work backwards.
Having said that there's zero evidence to say that it doesn't travel at C, but the idea that it does is based on some reasonable assumptions and no more.
I'd love to see this idea refuted by someone with more physics or maths than me. (most of you I guess!)

 

[DrStupid]

For all we know it may go really slowly once it gets out of our solar system, or indeed much faster.

That would result in refractions which could be detected by astronomically observations but we do not see any variations in the speed of light which could not be explained with the Shapiro delay.

 

[Nick Martin]

Thanks for that, I will go off and read aboout Shapiro delay!

 

[George K]

I'm going to throw something else in, here. You are talking about "light" but any model you come up with should also be applicable to 1500m long waves and the shortest of gamma waves.
In a 'condensed' substance, the spacing between atoms / molecules will probably be less than one wavelength of visible light. So it is not realistic to talk in terms of launching a light wave (or photon, if you must) and then it arriving at another atom. (That would be like what happens in a low density gas, where the effect is random scattering from individual atoms.) The fields around each atom (and all the other nearby atoms) will all be involved in setting up the energy levels and the transitions. The model to use is much more classical - coupled oscillators or a transmission line with masses on springs. The 'space' in between (where you could say that c applies) is only part of it; it's the interaction between the charge systems along the line that counts. The contribution to the delay along each step the journey is, of course, affected by the 'c' delay of the fields but each atom is also contributing a significant delay as it reacts with the fields around it and the fields of its neighbouring atoms. This 'loads' the line.
RF model:
If you take a line of parallel dipoles (say each one is 1m long) and you feed the first one with a 150MHz RF signal, that signal will propagate along the line. Some of the power will couple with the each dipole- they each have an equivalent cross section- but slower than c because each dipole introduces a phase shift as the currents flowing will cause a re-radiated signal that lags behind the incoming signal. The signal that emerges from the other end will be the net sum of the incident signal and each of the re-radiated signals. But there's something else here. Each element will be interacting with its neighbours (depending on the spacing). Appropriate spacing can produce a Null in the emerging RF wave in the direction of the line.
In a solid, the system is three dimensional but the same principle is at work and the majority of the power will travel in a straight line.

I've never thought of that (i.e. the light wavelength compared to the distance of the atoms in a solid medium). That's a good point. However, is it correct to assume that the light-wave doesn't travel at speed c if its full wavelength is not "completed" through its travel? (It's like to say that the sound doesn't travel at the speed of sound if the the distance between the transmitter (speaker) and the receiver (microphone) is less than a full wavelength, which is not correct.)
As an electronic circuit designer, I'm familiar with your "dipoles' array" example and I'm trying to understand the connection with our issue. I think that you say that (as in the "dipoles' array" example) the medium's atoms are stimulated by the incident light and they re-transmit light themselves. And that the "net sum" of the incident (initial) and re-transmitted light is a wave with a speed less than c. Is this correct?
(BTW, I'm already convinced that the light in a transparent medium travels at a speed lower than c in a continuous manner through the whole structure. However, I'm struggling with the details. And the vacuum space between the medium's atoms always bothers me.)

 

[Svein]

Every medium consists of 99,99999... % vacuum. So, what happens when the light travels inside these "vast areas" of vacuum (as it travels inside this material)? Is its speed slower than c? (And if yes then how is this possible?)

How do you know that the wave equations are valid inside the atoms?

 

[sophiecentaur]

However, is it correct to assume that the light-wave doesn't travel at speed c if its full wavelength is not "completed" through its travel?

That's a reasonable question but the answer is that you don't need a 'whole wavelength' to pass in order to be affected by the speed of the wave. Any change in the E field is delayed by a time x/c where x is the distance. A 200kHz signal (λ = 1500m) is still delayed by 3ns over a distance in space of 1m. A minuscule amount of phase shift (delay) but it's there.

the medium's atoms are stimulated by the incident light and they re-transmit light themselves.

Except that the 're-emission' is not from individual atoms but the whole region of 'charge systems' that the wave is passing through. That ensures that a ray will pass through without being dispersed so much that it is not recognisable (which would happen if single atoms were involved.)

 

[George K]

That's a reasonable question but the answer is that you don't need a 'whole wavelength' to pass in order to be affected by the speed of the wave. Any change in the E field is delayed by a time x/c where x is the distance. A 200kHz signal (λ = 1500m) is still delayed by 3ns over a distance in space of 1m. A minuscule amount of phase shift (delay) but it's there.

That's exactly what I meant. E.g. the propagation velocity of an AC signal on a wire is (somewhat less than) c. It doesn't matter if the signal's wavelength is very large and the wire's length is very small (i.e. much smaller than the signal's wavelength). The propagation velocity is always the same (≈c). That's why I think that your specific citation (i.e. the light's wavelength compared to the atom's distance, as mentioned in your previous post) was rather pointless.

 

[George K]

Except that the 're-emission' is not from individual atoms but the whole region of 'charge systems' that the wave is passing through. That ensures that a ray will pass through without being dispersed so much that it is not recognisable (which would happen if single atoms were involved.)

Yes, of course, the incident light is interacting with a whole region of the lattice. (The interaction with the single atoms is a rather wrong and misleading explanation.)

 

[George K]

How do you know that the wave equations are valid inside the atoms?

How do you know that are not valid?

 

[Svein]

How do you know that are not valid?

Remember what happened when they thought Newtonian mechanics were valid inside the atom?

 

[sophiecentaur]

That's why I think that your specific citation (i.e. the light's wavelength compared to the atom's distance, as mentioned in your previous post) was rather pointless.

I think it was rather that either you didn't get my point or you weren't clear about what point you were making. (Was I actually disagreeing with you?)

 

[nasu]

@GeorgeA
At least part of the problem, and a quite common one in the discussion on the forum, is the attempt to mix two models of electromagnetic waves.
If you want the wave theory of Maxwell, this is fine and good, it works very well to describe all the optical phenomena. But in this model the speed of light is given by the macroscopic properties of the medium and this (the medium) can be considered a continuum. At macroscopic propagation path the speed of light is uniquey determined by the medium.

If you want to look at subatomic distances and individual photon-electron interactions, these are described by QED. The classic theory does not work at these scales. Otherwise why come with QED in the first place? And in QED, the photons does not have to propagate with the same speed on all their paths. The "speed of light" does not have the same meaning as at macroscopic scales.
If you want to get some idea about how to treat the propagation in a medium in terms of photons you can try Feynman's book on QED.