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Photons seldom travel at light speed. The c in Einstein equation is an impossibility. There is no 100% vacuum. For example photons travel slower in glass in comparison with space.
Special Relativity (SR)says that the mass of a particle will increase with its velocity according to the Lorentz transformation. Photons have no rest mass but photons always travel at light speed. General Relativity (GR)states that gravity can bend a light beam, and this has been observed. GR explains this in terms of the geometry of spacetime. Quantum mechanics (QM) proposes the graviton as the carrier of the gravitational force. As such, it interacts with particles with mass. However it's clear from E=mc^2, it seems that if m=0, photons have no 'energy' at light speed or energy equivalent mass. If rest mass is zero, it seems photons cannot acquire mass by virtue of moving.
Quote1. Mass doesn't vary with speed.OK. Let's say total energy varies with velocity. Nevertheless if you substitute '0' for mass in the equation E=mc^2, you get 0 energy. How should we interpret this result?
1. Mass doesn't vary with speed.
Lightarrow,Ok. But the classical definition of momentum is p=mv. So how do we deal with mass in this equation? Do we take 'm' as equal to the mass equivalent of the photon's energy which is given a priori?
Quote from: stevewillie on 30/09/2008 21:01:10Lightarrow,Ok. But the classical definition of momentum is p=mv. So how do we deal with mass in this equation? Do we take 'm' as equal to the mass equivalent of the photon's energy which is given a priori? Your 'classical' definition of mv of momentum refers to objects with mass. For an electromagnetic wave, the momentum of a photon is h/λ where λ is the wavelength and h is the Planck constant.Using these two definitions describes accurately what happens when photons run into objects - so it works. (Light pressure etc).)
Does the compton effect prove that light behaves like a particle? Thus photons have mass.
A particle must have mass.
Not only general relativity says that gravity bends a light beam, newtonian mechanics does it too.
Quote from: lightarrow on 30/09/2008 12:25:52Not only general relativity says that gravity bends a light beam, newtonian mechanics does it too.Apologies for coming late to the table, but would you elaborate? I thought Newtonian mechanics predicts no bending, and that's why Campbell's solar-eclipse measurements in 1922 were such an important confirmation of GR.
The bending depends on the field, not on the mass; so, regardless of the mass, all other factors being equal, the bending is the same
It turns out that General Relativity predicts a bending which is double the one predicted by newtonian mechanichs, and this is exactly what they discovered in 1922.
QuoteThe bending depends on the field, not on the mass; so, regardless of the mass, all other factors being equal, the bending is the sameSo in this respect, Newtonian mechanics and GR are in agreement.QuoteIt turns out that General Relativity predicts a bending which is double the one predicted by newtonian mechanichs, and this is exactly what they discovered in 1922.That's really interesting because Einstein revised GR shortly before the 1922 eclipse when he realized an earlier version's prediction was off by 1/2. So it turns out that earlier prediction would have matched Newtonian mechanics' and, had he not made the change, the eclipse results would have resolved nothing. (They would have embarassed Einstein, though.)Apparently, this Newtonian prediction wasn't recognized at the time, i.e., the thinking then was that any bending at all would be a violation. So it's a more recent refinement (?)
This is all even more interesting than the "bending vs. no bending" version of the story I've always heard before.I think it's a stretch for the text to call the Mercury shift an "observational confirmation" because Einstein was aware of it. The agreement he found was a major reason he believed his final equations were correct. If we accept this characterization of the shift, any data he considered would have to be added to the list.Thanks very much for the lesson and the pointer to the article, lightarrow!
Can both ideas coexist?