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If I'm in a car and hit the gas, an outside observer on the ground sees my car accelerate to some speed, and given the mass of my car and the horsepower of my engine, this obeys Newton's second law.

From my standpoint, the principle of relativity says I can claim the car is stationary and the Earth and everything on it is moving backwards. But that seems to require saying that my 300 hp car (say) is pushing the entire planet from 0 to 60 mph in 15 sec, or whatever it may be. In clear violation of Newton's laws. So it seems like I would know my point of view to be false, and the Earth is a truly "preferred" reference frame.

What am I missing?

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Your frame of reference, i.e. the car is accelerating. So it is not an inertial frame of reference. If you were travelling with constant velocity, then both the observers and your interpretation would be equivalent. But you are accelerating. And you can feel the effects of that acceleration as you feel a pseudo force pushing you backwards when you hit the gas pedal. It is impossible to differentiate between two inertial frames. Here you clearly know that you are not in one.

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  • $\begingroup$ Thanks. Follow-up question: if we are talking about accelerated reference frames, I recall reading in one of the critiques of Einstein's formulation of General Relativity (in the 1910s, before it was proven) that the idea of "acceleration = gravity" seemed to require a passenger on a train to ascribe all the jostles and bumps he experienced to small planets which formed and vanished around his train, if he used his own reference frame. Do you have any comment on this? Does it mean the "locally flat" inertial frame in that case must be much smaller than a person? $\endgroup$
    – RC_23
    Sep 15 at 5:49
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    $\begingroup$ I'm a mechanical engineer with a basic understanding of the theory of relativity. Maybe you should ask the follow-up question as a separate question. $\endgroup$
    – Mechanic
    Sep 15 at 5:51

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