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From one book, I read that if we release a ball horizontally on earth, its velocity does change in very accurate observations. If we track its motion, we get full information of its motion (incl. acceleration respect to an true inertial frame).

And we can then compare it to the ideal linear uniform motion, then we get our acceleration to an true inertial frame (in which newtons 1st law is true), right? So with the developed formulas, we get all things we ever wanted in an exactly true inertial frame, can't we?

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    $\begingroup$ What are you asking? What exactly is an absolute inertial frame? $\endgroup$ – Jim Aug 11 '15 at 14:58
  • $\begingroup$ Define absolute inertial frame. $\endgroup$ – Shing Aug 11 '15 at 15:09
  • $\begingroup$ @Shing Though it's figurative as i understood, that's the true inertial frame while the earth or the sun are our approximations. $\endgroup$ – YiFei Aug 11 '15 at 15:12
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    $\begingroup$ Actually, Newton defined inertial frame quite well in his 1st law. What exactly meant by "true inertial frame"? $\endgroup$ – Shing Aug 11 '15 at 15:14
  • $\begingroup$ @Shing Yes, it's consistent. I just think because how much the ball turns describes how good the approximations are, we can finally theoretically find the Newtonian inertial frame $\endgroup$ – YiFei Aug 11 '15 at 15:16
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There is no absolute inertial frame because all motion is relative. The earth is a good approximation, and the frame of reference we use for most situations. However the earth is accelerating around the sun (i.e. towards the sun, that acceleration keeps the earth in orbit). The closest thing to an absolute inertial frame might be a space ship traveling with uniform velocity in a straight line -- however even this is relative it it's surroundings. What appears to us as a uniform velocity straight line may not be from other frames of reference. Furthermore keep in mind such a straight line would have to continue forever staying far away from any material bodies (such as planets and stars) which curve space and therefore re-define what is a straight line in their vicinity.

The failure of science to experimentally determine and absolute inertial frame (for example, the Michaelson-Morley experiment, and others like it) is what ultimately lead to the theory of relativity. When Lorentz first proposed his time-space transformations, many scientists still believed there would be found an absolute inertial frame, that space and time were constant, and that the transformations were merely a correction to account for some as yet undiscovered error in their calculations. Einstein came along and said, no, the speed of light is constant, and the Lorentz corrections are real. In other words, there is no absolute inertial frame. All frames of reference are relative. This is our current understanding of the nature of the universe.

To summarize, after many, many failures to find an absolute inertial frame, Einstein effectively proposed that there is no such thing. His theory explained all the experimental results so well (by assuming no such thing as an absolute inertial frame) that it has generally become accepted that the universe does not have an absolute inertial frame. Keep an open mind. Perhaps someday we will discover something new and realize that there is an absolute inertial frame, but for now all the physics we do works best assuming that there is none.

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  • $\begingroup$ So in short, do you mean the result of the experiment I stated above cannot be explained with newtonian mechanics? $\endgroup$ – YiFei Aug 11 '15 at 15:37
  • $\begingroup$ I'm not completely sure what you mean by "release a ball horizontally on earth" and by "it does turn in very accurate observations" (what do you mean by "turn in?"). That said, the statement that we "get ... acceleration respect to an absolute inertial frame" is NOT correct. There is no absolute inertial frame. We are using the earth as our inertial frame. It is not perfect, as an inertial frame, but for the accuracy of most situations (measuring the motion of a ball for example) it is close enough that we can explain the results with newtonian mechanics. $\endgroup$ – Daniel Goldfarb Aug 11 '15 at 18:22
  • $\begingroup$ I edited the problem. If the ball is running in an uniform gravitational field (to eliminate gravity), we get all the acceleration by inertial force, which returns its true acceleration $\endgroup$ – YiFei Aug 11 '15 at 22:56
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Consider this previous exchange on the Cosmic Microwave Background

The crucial bit is this:

However, the crucial assumption of Einstein's theory is not that there are no special frames, but that there are no special frames where the laws of physics are different. There clearly is a frame where the CMB is at rest, and so this is, in some sense, the rest frame of the Universe.

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There is nothing called an absolute inertial frame however in an inertial frame obeying the laws of motion your calculations will hold true.

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    $\begingroup$ Would you just point out where it went paradoxical? $\endgroup$ – YiFei Aug 11 '15 at 15:27
  • $\begingroup$ Your concept of frames is very confusing $\endgroup$ – Dhritiman Banerjee Aug 11 '15 at 15:29
  • $\begingroup$ It is rather comment-like. Better elaborate & expound your argument; otherwise it can't be an answer:| $\endgroup$ – user36790 Aug 11 '15 at 15:30
  • $\begingroup$ See the whole concept of reference points and franes is very vague as motio is mainly something with respect to something else therefore no absolute frame exists $\endgroup$ – Dhritiman Banerjee Aug 11 '15 at 15:47

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