# Effect of Acceleration on (Special) Relativity of Simultaneity

We often refer to the train/station analogy of inertial frames to determine the relativity of simultaneity. So, if the experiment was done on Earth, the train is one inertial frame, and the station is another inertial frame. But in reality the Earth is accelerating in a number of ways - revolving once a day, orbiting the sun once a year, and orbiting the galaxy centre once every 250mil(?) years. So both the train and the station are not in reality inertial frames. So my question is - can we treat them as inertial frames, because they are both subject to the same acceleration, or do we in reality need to invoke some other correction or indeed General Relativity?

Note, I'm not a physics student, so if it's possible to give a "for dummies" answer, that would be great.

A train car is 50 feet long, and the speed of light is 1 foot per nanosecond. That mean it takes 50 ns to traverse it, so it falls about 40 femtometers (1 fm $=10^{-15}$ m)--that is roughly the width of 40 protons, or several thousand times smaller than the diameter of an atom. These corrections are insignificant.
• Frankly you can't build a light projector inside a physically sized train car with opening angle less than $3 \times 10^{-15}$ radians which is what would be needed for this "systematic" to affect your experiment. – dmckee --- ex-moderator kitten Mar 27 '18 at 13:45