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I came across this paradox after trying to teach myself special relativity (which I finally understand)
Given an observer in a racecar, with no windows, accelarating in a straight line at 1g, 9.8m/s/s, he is strapped in his car seat with an accelerometer.  Since he is accelerating, he feels himself being pushed into the seat at 1g, his accelerometer also registers 1g.

Now, imagine the same observer skydive out of a plane at 20,000 feet, in a car, with no windows, also with an accelerometer.  He is strapped in, with the seat facing towards the earth.  He does not feel himself being pushed into the seat, even though he is accelerating!.  His accelerometer regesters zero acceleration.  How could this be? He should feel something, since he is accelerating.  In fact a observer stationed in a fixed frame of reference in both scenarios could measure a straight line acceleration of 9.8 m/s/s. How does one resolve this paradox of him accelerating  - in both examples, an observer in a fixed frame can tell the driver is accelerating, with car power,he can do tests with 2 tools: 1.his sense of touch (he feels the seat) and 2. the accelerometer to  confirm he is accelerating, whilst in free-fall, he cannot use the same tools to confirm he is accelerating.  Please explain!  Also, I have read somewhere that an observe in free fall is in an inertial frame of reference, but I don't believe that, becasue he could do a third test: punch a hole in his car and point a laser rangefinder and infer that he is accelerating w/ respect to the earth, however, I thought inertial frame of reference means non-accelerating frames.  What gives?!???

The problem is that the detection of acceleration is due to the relative acceleration of the observer and an external clue. In the case of the race car you feel a normal force between you and the structure of the car. In the case of the falling system both you and the structure are accelerating at the same rate due to the external gravitational force and as a result there is no normal force between you and the structure.
To put things another way, in the first instance the structure of the race car is applying an external force to your body resulting in your acceleration while in the second case your acceleration is not being supplied by the falling plane but is, instead, being supplied by the gravitational force of the Earth directly and so there is no normal force between you and the structure of the plane. In the first case your acceleration is being supplied by the race car while in the second case your acceleration is being supplied by the Earth. There is no contradiction.
By the way, the accelerometer would not work in freefall for the same reason! The accelerometer works when an outside force, not gravity, acts on the structure of the accelerometer. Drop an accelerometer in freefall and it will not work at all.


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James J. Kovalcin


I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.

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