I came across the following as a result of Rajesh Trivedi's questioning of the momentum-frequency relation in a material medium: http://rsta.royalsocietypublishing.org/content/368/1914/927 (Originally I posted this in the thread on the speed of photons that was sadly moved to Pseudo after becoming wrecked by a vendetta, but thought it was interesting enough to be re-posted under Physics.) The implication of the article seems to be that in a material medium, a photon has not one but two values for the momentum, a "kinetic" momentum and a "canonical" momentum. It is all rather complicated and seems bound up with the issue of the difference between group and phase velocities in a medium - though I am not sure I have fully taken it all in. It certainly appears that when speaking about either the velocity or the momentum of light in a material medium, one has to be careful what exactly one is referring to. This again shows how the phenomenon of refractive index, which we all first learn about early in our schooldays and take for granted, involves all kinds of strange and challenging concepts when viewed from the perspective of quantum theory. Anyway, something I didn't know, so I thought I would share it…...
Hi exchemist....If you check also in the P+M section, I posted another article on the " The Quantum spin Hall effect: A Fundamental property of light: for the same reason. Rightly or wrongly I see these experiments to slow down light and/or stop light. which I think is what is entailed between group and phase velocities, as sort of tricks of the trade. But also I'm trying to get my head around this "Spin Hall effect" and polarisation.
OK steady on, I'm only someone with a chemistry degree from 40 years ago. Refractive Index is about my limit, I think - we did at least cover it in outline at university. The Hall effect is more solid state physics I think (voltage created at right angles to a current, when a magnetic field is applied, or something.) If I get time I'll try to read a bit about it but no promises. Please Register or Log in to view the hidden image!
Still a rung or three up the ladder from me ol fella! Please Register or Log in to view the hidden image!
Its nice if this thread helps. But for record sake, I did not question any momentum frequency relationship in material medium. You and few others were fixated with momentum being equal to hf/c, but thats true only in vacuum where refractive index n = 1. In material medium whether it is nhf/c or hf/nc, that interested reader can search for Abraham Minkowski controversy and explore further.
No no I am not fixated on anything at all, Rajesh and thanks for raising the question that led me to this issue. I am delighted to have learnt something new and that is why I decided to share it with other readers.
The quantum physics of light in a material medium is interesting and involved but has bugger-all to do with "unification" of any kind, so far as I can see.
This is just a hunch I have, so far I have not done the math so at the moment I am still assuming this, once I work out the math then I will have stronger evidence backing up my assumptions.
I have an idea, this is why I could be wrong, but how would I know I am wrong if I don't fully investigate? As for QM that was where the inspiration came from with my idea, as well as entanglement.
A photon doesn't have two actual momentum values in a material medium, but there are two ways to compute the momentum. RajeshTrivedi has mentioned these: the Abraham and Minkowski methods. Which one is correct has been a matter of debate: http://rsta.royalsocietypublishing.org/content/368/1914/927
Congratulations. You have just repeated my OP to this thread.Please Register or Log in to view the hidden image!
Yes, but your OP says there are two values for the momentum, which isn't the same as having two ways to compute the momentum. Note the article from the Royal Society says the difference is because electric and magnetic fields depend on the chosen frame of reference. It also concludes that both methods are equally valid--the Minkowski momentum is that part of photon momentum transferred to the medium, the Abraham momentum is that part which is not transferred to the medium. Either method is valid, but I don't think you can say it leads to a conclusion that photons have two momentum values in a medium, instead there are two choices (of a gauge).
I was thinking about your comment in the other thread and found this. I haven't read the royal society link but I suspect they correlate. http://www.physics.utoronto.ca/~colloq/Talk10/Presentation10.ppt
All you're doing is blowing smoke up your own ass. So if you're serious you need to get the scholarship which will allow you to recognize a real idea from the nonsense you're spewing now. The following is a great example of a good idea in physics based on scholarship. Guth and Linde both had the idea to combine quantum field theory with GR to derive an origin for this universe.
I like the link to the powerpoint, brucep. On my mac, it needed some repair before opening. I have read that this topic (especially as it applies to birefringence/polarization) is deep in quantum theory also, and I don't doubt it. A block of glass however is not birefringent, and has neither a fast axis nor a slow axis / index of refraction. We will assume for the purposes of discussion that the block of glass is on a frictionless table, and that the incident beam of unpolarized light is in a plane that is parallel to the plane of the surface of the table, but that the angle of incidence is theta and that theta is not perpendicular to the surface of the block of glass. The reason for this is that we should also consider whether or not there is momentum imparted to the block that is a result of any refraction. Snell's law can be found here: http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/refr.html but this is an incomplete description because if the indices of refraction of the block of glass is not equal to the air or vacuum outside of it, part of the incident beam will be reflected as it would be from a plane mirror according to Fermat's principle. The situation is analyzed in detail here: http://physics.stackexchange.com/qu...flection-still-transfer-momentum-to-an-mirror So a small quantity of momentum is transferred to the mirror by this process. The greatest amount (about 50% of the beam intensity) will be reflected at Brewster's angle, and the reflected and refracted beams will both become linearly polarized. While the beam of light is traveling through the transparent glass with a higher index of refraction, glass is a dispersive medium, so the light will bend toward the normal (toward a line that is perpendicular to the plane of the glass block face at the point of entry) in accordance with its spectral content. A sideways amount of momentum will also therefore be transferred to the block based on the beam's spectral content and intensity. For as long as the refracted beam remains confined to the interior of the glass block, the beam is BOUND energy, which is to say, the energy of the beam is transferred from one atom to the next, absorbed and re-emitted, until it reaches the exit face of the glass block. There is some loss of energy in this process as well, depending on impurities and imperfections, including atoms of any non-transparent substance of which the block is composed. There is momentum transferred by this method as well, the same as if the beam of light had fallen on a much thinner material with a composite opacity similar to the block in question. When the beam strikes the opposite face of the glass block from the inside, once again some of the incident light will be transmitted to the medium outside of the block, and some of it will be reflected back into the block of glass where it will continue to propagate until it is dissipated or manages to propagate beyond the confines of the faces of the glass block. Like the situation where the beam first struck the incident face of the block, additional momentum may be transferred to the block in this manner. After the beam has exited the glass block, there is no more momentum transfer to the block from whatever intensity of the beam remains. By far the easiest experimental setup for determining the amount of energy transferred to the block would be to measure the exit intensity and compare it to the incident intensity minus the intensity of any light that is reflected from either of the faces of the block (so now you understand why the problem was reworked in this manner). But you must also remember to subtract any momentum imparted to the source of the collimated beam in the direction opposite to the momentum imparted to the glass block. This is a finer point to the problem that most treatments will usually fail to pick up. Einstein's original thought experiment to derive e=mc^2 used this same experimental setup, and analyzed a treatment of the center of mass of the light source / absorber at the ends of a long spaceship. I never forget it. It is central to several extended thought experiments of my own related to the subject of bound energy and inertia that are based on it. As with any transfer of momentum or energy, the specifics of the energy of the beam of light and state of motion of the block before the beam strikes it are up for grabs. If the light originated from a laser cavity, for instance, it makes a difference to the dynamics whether the mirror of the cavity is at rest relative to the table or glass block, which are assumed to be at rest relative to each other at the beginning of the problem setup.
