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Concerning Rest Frame Wikipedia states:

For example, in the rest frame of a neutrino particle travelling from the Crab Nebula supernova to Earth the supernova occurred in the 11th Century AD only a short while before the light reached Earth, but in Earth's rest frame the event occurred about 6300 years earlier.

If a neutrino has a rest frame, why can't a photon have one as well?

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Nobody ever observed “neutrino in its rest frame”. Physicists only conjecture that neutrinos have rest masses and such frame might exist for a neutrino. It is convenient to (exhaustively) classify particles to massive and massless ones, for no better reason than Occam’s razor. But all evidences about rest masses of neutrinos are indirect and no values are currently known with any reasonable precision. –  Incnis Mrsi yesterday

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up vote 16 down vote accepted

Neutrinos have mass and travel slightly below light speed, therefore an inertial frame for the neutrino exists, while it doesn't exist for a massless photon which travels exactly at $c$. We don't know the masses of the neutrinos, but neutrino oscillations tell us that the three neutrino families must have a mass difference. For all we know, one of the three neutrinos could still be massless, but it is assumed that all neutrino families have a non-vanishing mass.

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There are 3 types of neutrino: electron neutrino $\nu_e$, muon neutrino $\nu_\mu$ and tau neutrino $\nu_\tau$, here's image that shows masses and other details: click here (Note that Electron neutrino has very low mass $<2.2$ $eV$ but it's not zero) –  Gigi Butbaia May 2 at 18:28
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It could still be $0$. Moreover, the flavor eigenstate of the neutrino does not coincide with the mass eigenstate, therefore the mass of an $\nu_e$ is ill defined. To be precise, one'd need to write $\nu_1 < 2.2$ eV, where $1$ denotes the lightest mass eigenstate of the neutrino. –  pfnuesel May 2 at 18:46
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The mass limit exhibited by @GigiButbaia is very much obsolete. That limit is from direct observation of beta decay kinematics, but cosmological observation put strict limits on the sum of the masses of the neutrino species that are much less than 1 eV. –  dmckee May 3 at 4:14

Disclaimer: in this answer “photon” refers to an excitation of electromagnetic field, not to a fundamental particle as understood in QED and Standard Model.

Possibly unexpectedly for some readers, a photon can have its rest frame in a homogeneous medium that moves w.r.t. the frame with speed equal to the light speed in this medium (that is less than c because of refraction). Note it does not cause the photon to become a massive particle, see What if we could give photons some mass? for details. These photons are not “true” particles obeying “standard” laws of dynamics at all.

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You are mixing classical wave descriptions with quantum descriptions and doing so incorrectly. In a medium photons are constantly interacting with atoms---being absorbed and re-emitted or undergoing coherent forward scattering. Either process is described by annihilation and creation operators so it it not sensible to talk of a single slower than light photon. –  dmckee 21 hours ago
    
It’s me who doing it wrong, really? We all know that photons and electrons are elementary particles in vacuum. In a continuum, both photons and electrons “are constantly interacting with atoms, being absorbed and re-emitted”, as @dmckee said. But millions of people talk about electrons in semiconductors and metals, in spite of these “electrons” being (theoretically) quasiparticles. Why me, Incnis Mrsi, should be deprived of right to refer to EM field excitations in continuum media as to photons? The quibble doesn’t pass. –  Incnis Mrsi 18 hours ago
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The problem is not using these wonky, almost-right ways of talking, it's trying to answer this question in this way. You give an impression that will only lead the beginning student astray. –  dmckee 17 hours ago

Photons travel at exactly light speed, rather than just close to light speed. That means that for photons, the time and space axes collapse to a single axis, reducing the number of dimensions the photon "sees" to one. Unfortunately, a single dimension is not sufficient for a frame of reference for four dimensional space time, so the photon cannot have a rest frame.

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I am confused here :"Unfortunately, a single dimension is not sufficient for a frame of reference for four dimensional space time" . Can you please explain it elaborately? –  user22180 Aug 5 at 13:48
    
The photon exists in a one dimensional world, so it can't have a four dimensional rest frame. –  Warren Dew Aug 5 at 23:51
    
I deleted some inappropriate comments and their responses. Remember to be nice! –  David Z 7 hours ago

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