Since relativity postulates that the laws of physics are invariant in all inertial systems, why can't photons have an inertial reference frame?
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$\begingroup$ Photons are not moving at all. They are states of a quantum field that has modes that move at the speed of light in vacuum. The photons themselves only exist where they are being measured. These modes do not define valid coordinate systems, so one can't transform in and out of them. $\endgroup$– CuriousOneCommented Jan 31, 2016 at 10:55
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$\begingroup$ @CuriousOne what if we replace photon by any other massless particle? $\endgroup$– Mac164Commented Jan 31, 2016 at 11:02
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$\begingroup$ Which other massless particles? Gluons? Gluon fields don't propagate macroscopically. If we want to define a coordinate system we need, quite literally, massive rulers. $\endgroup$– CuriousOneCommented Jan 31, 2016 at 11:07
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3$\begingroup$ Possible duplicates: physics.stackexchange.com/q/16018/2451 , physics.stackexchange.com/q/71639/2451 and links therein. $\endgroup$– Qmechanic ♦Commented Jan 31, 2016 at 11:43
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$\begingroup$ "Which part did I overlook?" - that there are no inertial reference frames with relative speed $c$. By the Lorentz transformation, an object with speed $c$ in an inertial reference frame has speed $c$ in all inertial reference frames, i.e., there is no inertial reference frame in which a photon is at rest. $\endgroup$– Alfred CentauriCommented Jan 31, 2016 at 11:48
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2 Answers
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Your question is the one that Einstein pondered for long time and from which Special Theory of Relativity was born.
He wondered what could happen if you travel at the speed of light how would you see a ray light. The problem was that according to Maxwell's Electrodynamics, explained light as oscillating $E$ and $B$ vectors along space and time, so as a wave. But then you would see $E$ and $B$ oscillating statically, which was not observed in nature thus contradicting experience.
There lies the problem with that reasoning, which lead to admitting that light should be invariant for all inertial systems, and further to STR.
Baring this in mind, you can see why a photon cannot be thought of as a classical particle, and is only a working concept in Quantum theories where velocities and positions cannot be simultaneously known to infinite accuracy, thus paths are inconceivable.
So not in the scales where light behaves classically, nor in those where it does not, can a photon it be conceived as a standing in rest, because it contradicts observation.
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$\begingroup$ And also in a universe there is not just a single photon. There are trillions of them. And each travel in each of its own directions. How can the material objects in the universe travel at the opposite of all these directions at once? $\endgroup$– N.S.JOHNCommented Mar 14, 2016 at 12:13
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Elementary particles do not have consciousness, individuality or volition. They follow the rules of the boundary value solutions of the quantum mechanical equations they obey.
The relativistic quantum mechanical mathematics have zero mass particles moving at velocity c, and in all valid frames massive particles move at velocities less than c. It is the mathematics "xxxx", to use a popular paraphrase. There is no rest frame for zero mass particles and no velocity equal or larger than c for massive ones using Lorenz tranformations, which are imperative for relativistic velocities.
