So, I'm taking a course of Classical Field Theory here are IMSc. I was just reading Tong's notes, the way he wrotes is extremely motivational! Also listening to some really nice relaxing music by Kevin Kern. The moment I read this.
Well, I thought I landed up with some good idea this time. Sadly, nothing new and this is resolved very easily. In Special Theory of Relativity, we have the postutate about the speed of light being the maximum speed of transmission. Now, with this postutate and a few other postulates about measurement of position,time and being same in all interntial frames, we can get nice results. One of them being the Invariance equation.
Question: Now what would happen if I use a similar signal in a medium? We know the "effective velocity" of light that we observe in a medium is . (If this wasn't the case, then when it exists the medium it would be c" /> which isn't possible.Does it imply I can make measurements only using this upper bound of velocity on the medium?
Answer: It's fairly straight forward. There are two ways of looking at it this. Either, I can remove the medium entirely and make the measurements of events the same as in vacuum and then replace the medium back. This is more of a frame by frame approach. If you want a more convincing answer then you could argue that, we send signals of light even before any interaction with the molecules of the medium. We consider such a scale and hence in that scale, it is effectively the same concepts of SPR we use. We can extend this throughout the whole of the medium as this through bits.
Had this doubt while reading GR.
So today, an interesting question was raised in my Optics lecture.We know that velocity of light in medium is less than . Therefore, we can move in an inertial frame where the photon has no velocity. Hence it would be possible to compute the rest mass of a photon. (Which is obviously not true, as photon has no mass.) Where are we going wrong? Further, adding to the confusion, we have cherenkov radiation which says that a charged particle traveling at a speed greater than the "phase velocity" photon emits electromagnetic radiation which gives rise to the blue color in the above picture. Answer: Thanks to a senior of mine. He was able to give me an outline of what is the reason. It is often misunderstood that velocity of light changes in the medium. But in effect, this isn't true. The velocity of light is and always will be in any medium. Just that, when the photon enters the medium, the dielectric of the medium absorbs the light and emits another photon. If the medium is a crystal, due to its isotropic nature, the absorption and emission of light is more systematic and the effective velocity due to the time delays between this process gives a "net" reduction of velocity of light. This is an outline of what happens but a clear understanding can be got by looking more into the quantum mechanical aspects of refraction. Kudos!
I've decided to start this trend of writing something that I learn everyday which really is due to misunderstood fundamentals.
It is often misconception in high school physics that momentum . But it actually isnt, a generalised definition of momentum comes from the concept of conjugate momentum where we see that it is obtained from the action of the system (Lagrangian Mechanics). In simpler terms, you see that where is the vector field.
Why is the high school definition wrong? A simple thought experiment which goes by the name Feynmann angular momentum paradox shows you why.
The angular momentum is still conserved, but just that there is some influence of magnetic field of the system on the momentum at the beginning itself. It is NOT a mere change of 0 momentum to some a non zero momentum.
Where did I learn this? While analysing the action principle in General Relativity! Kudos