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It is currently understood that gravity is not actually a force, and a fact that is often used to show this is that an object in free fall doesn't "feel" that it is accelerating and is thus an inertial frame.

However, it seems to me that Newtonian mechanics can already predict that this will be the case. Since all the parts of the object are being accelerated by the same amount simultaneously (at least approximately, like near the surface of the Earth) there won't be a tendency for this object to contract, and thus "feel" that it is accelerating. This isn't the case, for example, when I push the same object. In my understanding, the force needs to be communicated from the point I apply it to all the rest of the object, and this delay is the cause of a contraction/increase in internal forces or tension, allowing it to effectively "feel" that is accelerating.

Now, suppose that there is a uniform field that accelerates any particles with constant acceleration. Like gravity, a free object in this field will not be able to detect that it is accelerating, since all of its particles are accelerating equally at the same time. My question is: Is this object inertial, or is it only inertial if this field is a gravitational one?

Qmechanic
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2 Answers2

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Now, suppose that there is a uniform field that accelerates any particles with constant acceleration. Like gravity, a free object in this field will not be able to detect that it is accelerating, since all of its particles are accelerating equally at the same time.

That field isn’t like gravity, it is gravity.

My question is: Is this object inertial, or is it only inertial if this field is a gravitational one?

Unfortunately, the question cannot arise since such a field is a gravitational field.

Dale
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If there is a uniform field (in a small region of space, since gravity is not uniform in general) accelerating any particles with an acceleration that is different from the gravity, and you're not able to "cancel" gravity, you're ending up with a resulting field equal to the vector sum of your uniform field and the gravitational field in that region of space.

So, you're accelerating w.r.t. a ``classical mechanics'' inertial frame with acceleration $\mathbf{a}$. If you take a 3-axis accelerometer with you its measurement reads $\mathbf{g}-\mathbf{a}$.

  • You're in a "classical mechanics" (that considers gravity as a force) if you read $\mathbf{g}$ on the accelerometer, and thus $\mathbf{a} = \mathbf{0}$
  • You're in a "general relativity" (that considers gravity as a result of the curvature of the space and not an actual force) if you read $\mathbf{0}$ and thus $\mathbf{a} = \mathbf{g}$, and thus you're in free fall.

In every other situation, you need to introduce a new definition of inertial frame, considering $\mathbf{g}-\mathbf{a}$, the measurement read on the 3-axis accelerometer (torques should be zero) by every point in motion with you or in relative uniform rectilinear motion w.r.t. you as the constant ``real force'', playing the role of gravity we perceive as an example in a small region on the Earth.

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