Since photon has zero rest mass, it will has zero mass when the velocity is zero. We are now being able to slower down the photon in experiment. Is the mass of photon reduced with the decreased velocity. Or it will remain the same, but it will decreased to zero only when the velocity is zero? The deeper question behind it would be that what does it mean for the observer if the object is under observation is in another medium with different speed of light.
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A photon has no mass. Ever. It has momentum - and there is a relationship between its energy and momentum, and because we know its speed, we can pretend it has mass $m = \frac{p}{c}$. But mass of something traveling at the speed of light is not something we can relate to things not traveling at the speed of light.
When light travels in a medium with a refractive index > 1, it slows down. That means that the energy that the photon conveys is propagating more slowly - because of interactions with the electrons / atoms in the medium. But you can tell (by observing the frequency of the photon) that its energy did not change. The only way to change the observed frequency (as opposed to wavelength, which changes in a refractive medium) is to change your frame of reference.
All the tenets of special relativity are related to light traveling in vacuum. And photons cannot be slowed down to an "apparent" speed of zero.
Floris
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To answer your question, we need to clarify:
1.photons have mass, that is equal to E=h*f which comes from frequency
photons always travel at the speed of light, when measured locally (because they always travel in vacuum, or they are absorbed and re-emitted)
EM waves travel slower in dense medium, when measured locally
EM waves are a herd of photons, and the wavefront slows down in dense medium, because phase shifts, but mainly because the photons are absorbed and re-emitted and the EM interactions take time, that is about the time needed for the ravage lifetime of the excited state of the atom (when the atoms absorb the photon, the electrons are in excited state, then when they re-emit the photon, they go back to ground state)
photons travel slower next to the sun then the speed of light, when measured from the earth, because the sun has a stronger gravity field. This is the Shapiro effect.
It is because the clocks tick slower next to the sun, when viewed from the earth, and the clock here on earth ticks faster. So we divide the path of the photon with a bigger time, so we get a slower speed. The slowing is because of the spacetime being not flat next to the sun, so the photon has to travel a longer path. So a longer path divided by a bigger time gives you a slower speed.
The photon's mass is still it's energy in this case, E=h*f, which comes from it's frequency, which should not change.
The photon's frequency can change when it is redshifted because it is coming from a galaxy that is getting further from us, because of the expanding universe. In That case it's mass which is it's energy, can change.
Árpád Szendrei
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