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The State of rest and the state of uniform linear motion are equivalent. Why?

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  • $\begingroup$ Because if you were in empty space these two states would be the same. That would be the short answer. $\endgroup$ Sep 25, 2021 at 10:33
  • $\begingroup$ See also: this, as well as this $\endgroup$ Sep 26, 2021 at 2:49

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It's one of the postulates of special relativity

The first postulate is "The laws of physics take the same form in all inertial frames of reference."

This means that an experiment done (and viewed) by an experimenter in the moving frame would give the same result as the same experiment done (and viewed) by an experimenter in the stationary frame.

So the state of uniform motion can also be regarded as stationary.

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Why ? Because there is no absolute state of rest in the universe - we can only measure the relative velocity between two reference frames that are in uniform motion, not their absolute velocity. Contrast this with acceleration, where we can measure absolute acceleration because Newton's first law does not hold in an accelerated reference frame.

Why is there no absolute state of rest in the universe ? We don't know. That's just how things work here.

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As others have said, this appears to be how the world is built. Physicists are better at answering ‘what’ questions than ‘why’ questions.

But we can ask: what would the world be like if it were not the case that rest and uniform linear motion were equivalent? This would mean there was some sort of preferred rest frame – where Rule #1 applied and all the other frames – where Rule #2 applied. We could then ask: at rest, relative to what? Surely not the Earth – for we know that the Earth rotates around the Sun and the Sun rotates around the galaxy. So there would be some preferred frame of reference and the world would not be isotropic (the same in all directions).

Depending on what you assume for Rule # 1 and Rule #2, this would make for a very different world than the one we observe. For example, things would behave differently depending on how they were moving relative to the preferred frame of reference.

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Take the uniform linear motion and observe it from the viewpoint of a co-moving observer. When looking at a train from a parallel train with the same speed, the train appears at rest.

When applying such a transformation to the observer (called a Galilean Transformation) it does not change the nature of the problem. Newton's laws still apply just the same.

So the 1st law isn't really about the state of motion of an object, but about the state of motion of the observer.

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