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- Thread starter aditya23456
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HallsofIvy

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A.T.

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According to GR, no.Am I in an "inertial coordinate system" sitting here in front of my computer?

Because your frame is non-inertial.If I were to toss a coin in the air, itwouldcome back to my hand!

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As long as the net real force is zero an object may be subject to multiple external forces and still be inertial. Similarly with the various sub-parts of an extended body.

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HallsofIvy

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DrGreg

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Yes, although to be precise and avoid ambiguity it would be better to say "non-zero acceleration relative to the Earth's surface". A free-falling room has zero "proper acceleration" i.e. acceleration relative to a local inertial observer.Ah. So a room stationary on the surface of the earth is "non-inertial" and a room falling with non-zero acceleration due to gravity is "inertial".

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A.T.

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Yes. In GR gravity is an inertial force which appears only in non-inertial frames. An answer to the OPs question valid for both: Newton and GR is:

The difference is only the classification of gravity as a interaction or inertial force respectively.

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Matterwave

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You cannot convert a non inertial frame to an inertial frame. The proper force experienced in a non inertial frame cannot be transformed away. We can sometimes use the concept of an "instantaneous co-moving inertial reference frame" to study non inertial frames. For example let us say we have a rocket accelerating with a constant proper acceleration of one g. In an initial reference frame S, the velocity of the rocket is zero. At a later time the rocket is momentarily at rest in inertial reference frame S' which is moving at 0.6c relative to S. At an even later time the rocket is momentarily at rest in an inertial reference frame S'' moving at 0.8c relative to S and so on. In inertial reference frames, S, S' and S'' the rocket is always measured to have an acceleration of g when the rocket is momentarily at rest, but in frame S for example, the initial acceleration is g but progressively the acceleration gets slower as the velocity of the rocket increases relative to S.

Now if we have object accelerating with constant proper acceleration then there exists a non inertial reference frame, in which the object will appear stationary. If we have an inertial object that is accelerating from the point of view of a non inertial reference frame, then there is also exists an inertial reference frame in which the object appears to be stationary. This is trivially obvious. However, if we have a non inertial object experiencing proper acceleration, then there is no inertial reference frame where the object appears stationary for more than an instant. Conversely, if we have a inertial object with coordinate acceleration as measured in a non inertial reference frame, then there is no non inertial reference frame where the object appears stationary for more than an instant.

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DrGreg

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In relativity this is taken account of by the difference between a coordinate derivative and a covariant derivative. Newton's law in a non-inertial frame becomes[tex]

F^\alpha = \frac{\mbox{D} P^\alpha}{\mbox{D} \tau} = \frac{\mbox{d} P^\alpha}{\mbox{d} \tau} + \Gamma^\alpha_{\beta\gamma} U^\beta P^\gamma

[/tex]The term involving [itex]\Gamma^\alpha_{\beta\gamma}[/itex] is the "fictitious force" term and becomes zero in an inertial frame.

In general relativity, gravity becomes a fictitious force. A free-falling inertial observer feels no force of gravity. An observer on the Earth's surface is experiencing a proper acceleration upwards and zero acceleration relative to the Earth. The fictitious weight of the observer makes Newton's Law work relative to the Earth's surface.

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