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This is a very basic question about the concepts of force and acceleration. Consider the following situations:

  1. I sit on the floor of my room on earth
  2. I sit on the floor of a spaceship that accelerates with 1g (in a direction perpendicular to its "floor")

In both situations I feel the same (a force that presses me towards the floor). Both situations involve an acceleration of 1g. BUT: in situation (2) my velocity changes, while in (1) it does not.

My question: what is the essential difference between these situations?

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Your velocity in reference to the accelerating frames doesn't change in either case – yayu Apr 19 '11 at 19:09
point of order: sitting on the floor on earth your velocity is changing as you're traversing a circular orbit and hence your direction is changing. – Nic Apr 20 '11 at 14:02
@Nic: while true, this point is irrelevant to the problem at hand. One could imagine a stationary earth on which you are sitting and ask the question above. It isn't helpful to bring in unrelated facts that distract from the physics being asked about. – kbeta Jul 11 '12 at 5:53

General relativity rests on the fact that there is no essential difference. This means: It is absolutely impossible for you to design an experiment that distinguishes between (1) and (2). You can use this as the foundation of GR and do some cool Gedankenexperimente, such as this: If in your spaceship you shine a laser parallel to the floor, you will, due to the acceleration, observe that it gets bent (very slightly). On earth, you will observe the same, which shows that photons are affected by gravity.

In addition, in your accelerated framework, light experiences a frequency shift due to the relativistic Doppler effect. On earth, you will observe the same, but this time it's because photons lose energy in earth's gravitational field and since $E = h\nu$, so $\nu$ gets smaller.

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Photons have energy, not mass, but other than that, that's right. – David Z Apr 19 '11 at 20:37
You're right, of course. I've changed it/ – Lagerbaer Apr 19 '11 at 20:38

From what I know the difference lays in the fact that a body in a spaceship will be in a homogenous force field, while the proximity of a mass (e.g. Earth) will cause a slight deformation of the body due to the changes of gravity force throught the volume of the body.

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It is called the principle of equivalence. It was discovered by Albert Einstein probably in 1907. This is the central principle of his theory of gravity.

Simply speaking, it says that gravity and accelerations are equivalent. Sitting on an "accelerated frame" (w.r.t. an out side observer) an observer can not determine whether he is accelerating or there is simply a gravitational field around him. This is due to the fact that inertial mass of an object is the same as its gravitational mass as is shown by the experiments till date.

This equivalence ensures that all freely falling objects will fall towards ground with the same acceleration. It also ensures that there could be a metric theory of gravity (not necessarily GR). There are many metric theory of gravity and Einstein's GR is the simplest possible and experimentally confirmed theory of gravity till today.

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