Matter density should only matter if the density is sufficient to change the refractive index of space and yet remain transparent to light. It's not really significant, as it represents a potential effect on a small fraction of observations. Still if the value of c is not constant the field equations can only approximate the shape of space, where c differs from the assumed value. I guess if the value were to vary smoothly in empty space GR would remain valid, but everything we think we know about how far a light year is would be out the window. A variation in the speed of light is not like an expanding universe. A LY would still be a LY, we just would not be able to associate that with a light time independent measurement of distance. On the other hand the whole dark matter debate stems from GR's inability to explain observed galactic orbital velocities. I guess I need to open up some dusty books, made of paper. I have become to dependent on a digital library. I am pretty sure that I have seen some of these issues addressed in the past. Perhaps not in the same context...
Well, I said that the average flight time would still be c, despite the variance in arrival time increasing. Therefore a photon could arrive sooner, or later, than distance/c. Quantum mechanically light is only constrained to travel at c on average. You still can't send information faster than light though (on average), because you can't tell which photons will arrive sooner and which will arrive later, so you can't encode any information in them. I'm still not really clear on why you think the process of emission and absorption "takes longer" for longer wavelength photons. I will give you this much: If you look at the wavefunction for a photon/atom system as the system is emitting a photon, over time the wavefunction will change from a well-isolated, higher energy state of the atom, to a blurry entangled mess of atom and photon all around each other, to well seperated, unentangled lumps of wavefunction representing the atom and the photon having seperated. The entangled phase will last longer for a longer wavelength photon, which generally will be emitted in a "bigger" wavepacket, because it takes longer for the wavepacket to move far enough away from the atom for you to really say for sure that the photon has definitely been emitted. Before this though, the system exists in a crazy superposition of having emitted and not having emitted a photon, similar to if it was a radioactive system or something and the emission was totally random (I am assuming we are "kicking" the atom somehow to get it to emit a photon, so we have some knowledge about when this should happen). However, the measurement side of things is different, because the photon interacts with a large system which very very quickly causes decoherence and wavefunction collapse. Admittedly exactly how this process occurs is a deep mystery, but I think for a photon interacting with a big system like a detector the collapse happens so fast that it is effectively instantaneous. I can see that you might say that my argument about the entangled emission phase taking longer for longer wavelengths could just be reversed here, but in this instance I think it just collapses back to my previous argument that the flight time variance is increased. The entangled absorption phase is just the superposition of "detected/not detected" combined photon/detector state. Hmm that was a bit long, apologies if it doesn't make sense. Well, is it really capable of absorbing any photon whatsoever? Real materials only absorb photons which are the right energy to kick their electrons into higher orbitals, which ok for most solids is practically continuous but in principle it is still quantised. And why should the exclusion of some energies of photon mean the absorption of those that are allowed should take a different length of time?
This reasoning is flawed because 1) I don't need to "encode information" in the transmission of a photon...the transmission of a bit is sufficient. (e.g. "When I shine my lamp at you, it means that the British are attacking!!") I think you might be confusing this with not being able to encode information using the collapse of a wavefunction; and 2) this whole concept of photons arriving with an average velocity of c is troublesome because, as I said, it implies that I just need to shower the distant photon receptor with photons that are sufficient in number and wavelength such that ONE of them arrives reasonably consistently faster than c. This cannot be the case. Yes, "black bodies" are hypothetically perfect absorbers of all photons by definition. Also, the material itself does not change in any way just because we "make the oven bigger", right?
I have a few questions, but first some context. My primary interest in physics te nds more to both Newtonian Dynamics and Special and General Relativity, as gravity models. I understand some of particle physics but am by no means an authority. Can you provide some reference. It seems I need to do a bit more thinking on the substance, of this conversation. And secondly, since the wavelength of visible light is between about 390 and 750 nm (?) is essentially instantaneous really essentially instantaneous? 800 nm is not very long in light time. Since my knowledge is not exhaustive, the discussion itself could be hypothetical. If reference is available, it would be helpful.
Well sure, but even then you have no idea if the signal will actually be transmitted faster than c, you just have to hope you get lucky. It will be transmitted slower than light with equal probability. I don't think this can cause causality problems. I'm confused. I am saying that if you shower a distant detector with photons prepared in the manner we are discussing then they will arrive both faster and slower than c in equal proportions. There is no way to shift the probability distribution so that more than 50% of them arrive faster than c (barring some kind of weird casimir lower energy vacuum perhaps or some exotic thing outside the scope of this discussion). If you pick an individual photon its arrival time will be drawn randomly according to this probability distribution, you can't affect this choice at all. Ok, sure. But in the normal analyses "black bodies" are also assumed to be much larger than the wavelength of light incident on them because small objects cannot absorb long wavelength photons efficiently (and black bodies have to do it with 100% efficiency). Which is related to the fact that long wavelength photons can't resonate in a black body cavity.
Hmm ok I will try to find you some references. The instantaneousness of wave function collapse is essentially a postulate of quantum mechanics though. I don't think I or anyone else really believes that, and there might be some experiments probing the limits of this somehow but I am not familiar with them. It is instantaneous as far as most experiments are concerned in the very least.
Thanks kurros, that is what I had thought. The banter back and forth got me to wondering. Don't need to go hunting up reference.
Kurros, this is all obviously incorrect. I just don't believe you're thinking completely about the implications of your description. I don't care if "some" photons arrive sooner than others, I only care that a single photon arrives faster than c. That's it. It doesn't matter that you qualify this by saying that "luck" is involved because we can run the experiment as many times as we wish. A single photon arriving at a distant detector with a non-zero probability (a probability which, according to the description we're discussing, is apparently influenced by the red-shift we have imparted to our photons as well as the number of photons we have emitted) is sufficient for us to break Relativity and encounter causality violations. I don't even understand how this can be debatable. In other words, if I send out a "virtually infinite" number of photons that are extremely red-shifted towards a very distant receiver, there is a "virtually certain" possibility that he will receive a photon with an apparent velocity > c. We can agree that ANY photon reaching him shall signal that the British are attacking our shores, for example, and the receiver shall therefore be in possession of information which has been delivered in a manner which violates Relativity.
Hmm, ok so it's more subtle than I perhaps made it out to be. This is a common effect though and it is similar in nature to EPR correlations, I am just having a hard time thinking about what really happens. I think the explanation is something like that the probability of seeing a photon traveling faster than c is similar to the probability of one popping out of the vacuum and going into your detector instead. You can't tell them apart so you can't extract any information from the fact that one has arrived. Your attempt to send me some photons will introduce correlations between your counting of sent photons and my received photons, but we can't figure that out until we compare our data. Or something like that. I will go try and learn a better explanation, because there are some things in there I'm not happy with and probably you won't be either.
Ok I give up for now, I have searched hard but found nothing satisfying me. I will think about it more later. The thing I said about a particle popping out of the vacuum is no good, we shouldn't see those in a detector.
Well don't give up because I have a deep affinity for the reality that you're trying to describe (a world in which EM and other fields are similar to if not precisely equated with wavefunctions). This is also why I'm critiquing it, because I "want" it to work.
I haven't given up totally, I am going to go ask some people Please Register or Log in to view the hidden image!. Besides I am willing to concede I might be somewhat wrong here. Definitely what I am saying is 100% true for virtual photons, in a very dramatic fashion, and I had some intuition that it must still be true to a more limited fashion for "real" photons, but for slightly different reasons, but I am not sure anymore so I am going to go find out Please Register or Log in to view the hidden image!. I feel like the uncertainty principle must make it true. I'll get back to you.
Light does travel forever in space, but that is assuming it does not come into contact with anything to absorb or scatter it.
I believe that current theories predict that light waves expand or Gravitational Red Shift. This would mean that as a light particle/wave travels over great distances the frequency of the particle/wave, red shifts, and the wavelengths get longer over time.
