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Imagine we've got two massless particles in an otherwise empty Newtonian world, both at the same position, with zero velocity in t0. One is without acceleration, but the other has a constant acceleration of 1.

Now, is my understanding correct that each one sees/measures the other one accelerating at the same rate, and there's no way for any of them to tell if it is really accelerating, i.e. if it has absolute acceleration?

(Imagine they have synchronized clocks and are also able to measure the distance between any two points at any moment; so strictly speaking, they're not the the only occupants of their world.)

Âloh
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  • Stripping out the unnecessary stipulations that the particles be massless and the Universe be otherwise empty, this question has already been answered: https://physics.stackexchange.com/questions/173/is-acceleration-an-absolute-quantity – D. Halsey Oct 06 '20 at 23:16
  • Massless particles travels at the light speed for every frames, so they can not be at a given position. – Claudio Saspinski Oct 07 '20 at 00:47

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Newton believed that there was an absolute spatial frame of reference:

Absolute space, in its own nature, without regard to anything external, remains always similar and immovable.

So as far as Newton was concerned, acceleration could always be detected relative to this absolute reference frame, because Newton's laws of motion would not hold in an accelerated reference frame (unless fictitious forces were introduced). So even in a universe with only two objects, it would always be clear which of them was being accelerated.

On the other hand, Newton's contemporary Leibniz believed that there was no absolute space, and that space only made sense as the relative location of bodies. So for Leibniz, Newton's laws of motion could only apply in a universe in which there were enough distant objects more or less stationary with respect to each other (the "fixed stars") to define an inertial frame of reference. In a two object universe Newton's laws of motion would not apply. If there was relative acceleration, both objects would see themselves as stationary and the other object as accelerating.

Ernst Mach expanded on Leibniz's point of view and encapsulated it in Mach's principle. He is reported to have said "When the subway jerks, it's the fixed stars that throw you down". Mach's thinking was a guiding factor in Einstein's development of general relativity.

gandalf61
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  • It is my understanding that an inertial guidance system can measure the acceleration of your airplane without reference to anything outside of the plane. – R.W. Bird Oct 07 '20 at 15:00
  • @R.W.Bird Then you would agree with Newton and disagree with Leibniz/Mach. Since we cannot gravitationally isolate an inertial guidance system (or anything else) we do not know who was right. – gandalf61 Oct 07 '20 at 15:45
  • Many thanks for your clear and informative response! In the (awkward) Newtonian scenario described in the question, I tried to limit what each particle is able to measure to the time passed since their departure and their mutual spacial distance at any moment. Now, it seems to me, although there’s a fact of the matter as to which one is stationary and which one is actually accelerating, none of them is able to know this; they only find each other accelerating at the same rate. (This, if true, might seem to be a useless or trivial point, but I needed to understand it for pedagogical reasons.) – Âloh Oct 07 '20 at 16:05
  • If you were in a rocket ship in outer space, you could measure the acceleration caused by your engines, but not that caused by a gravitational field, since gravity would also act on the reference mass in your accelerommeter. – R.W. Bird Oct 08 '20 at 14:09
  • A person in a rocket with the engines firing may feel like he is in a gravitational field but he can certainly tell the difference between that and being in free fall with the engines off. – R.W. Bird Oct 08 '20 at 17:46
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How about if we say this: A powered change in acceleration can be experienced and measured. An acceleration caused by gravity can only be measured relative to the associated sources of gravity. Which is to say, If you were in an enclosed lab in a space ship in free fall (with the engines off) there is no way to determine the acceleration you might be experiencing due to the gravity of a nearby planet or star. (When I refer to a “change in acceleration”, I mean that it is in addition to the continuous accelerations that we are subject to from various concentrations of mass.)

R.W. Bird
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