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Someone once tried to explain to me why neutrino oscillation implies that neutrinos have mass, and I understood it as follows:

  1. Change requires time.

  2. Massless particles travel at the speed of light.

  3. Objects travelling at the speed of light do not experience. time

  4. Therefore, if neutrinos oscillate, then they must have mass.

That argument seems to correspond to the most highly rated answer to Why do neutrino oscillations imply nonzero neutrino masses?.

Following from that argument, I considered that a massless particle than then be described as a line connecting two points in 3-space: the point where the particle was emitted, and the point where it was absorbed. Then time synchronization can be defined as follows: two events E1 and E2 occur at the same time if a photon emitted by E2 is absorbed by E2. But then I considered the scenario of an observer that is stationary with respect to a mirror t light-seconds away. When the observer views its own reflection, it will see itself as it was 2t seconds in the past. This contradicts the definition of time synchrony above, which requires that the light emission and observation take place at the same time (unless the process of reflection takes time, but then the time to reflect a photon depends on how far the mirror is from the observer, which also doesn't make sense). So clearly this understanding is faulty.

What is my mistake here?

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This argument isn't correct. A photon does change phase as it travels.

"Objects traveling at the speed of light do not experience time" is a common idea, but there is no such thing as a frame of reference traveling at the speed of light, so you can't consistently talk about what something traveling at the speed of light experiences.

See How does a photon experience space and time?, in particular, my answer

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