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Suppose we have a ball filled half with water in space with nothing else around (nothing else in the whole space except the ball) and suddenly it accelerates for time t. obviously, there would be movement in water which will tell us that the ball underwent motion. But since we have nothing to compare the motion with how can we say that it was in motion? can we say that it was at point A inertially (in space) and then in point B (again in the empty space)?

Qmechanic
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Rahul Bhardwaj
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2 Answers2

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I don't know if you came with this thought experiment by yourself but if you did you are crazy smart. This is actually very close to the argument made by Newton, usually called Newton's Bucket. He believed that absolute space was a real physical scenario where physical processes were to happen. And something similar to that is his main argument for it's existence.

The truth is that today we don't consider this to be empirical evidence for that idea necessarily. To join a concept of relative space been the only one in existence with the results of this thought experiment you can just suppose that the objects of the rest of the universe are somehow mysteriously influencing the water communicating it what its movement relative to other objects is. In the extreme case were only your ball filled with water exists the believe is that water would actually not slosh at all. This is calles Mach's principle.

Today with the Einsteinian view we think in another way. Space is nothing more than a conceptual construct, an abstract aid for calculations, but space-time is something physically real and something entirely different.

Swike
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  • Thanks for such a quick response but why can't we say that it is in motion when we know it is in motion? – Rahul Bhardwaj Jun 22 '19 at 18:15
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    The only way you can *know* it is in motion is to measure its position at different times. But if the only thing in the universe is the ball, you can't measure anything. You can't magically sit *outside* the universe and somehow measure what is happening *inside* it - except in these books ;) https://en.wikipedia.org/wiki/The_Science_of_Discworld – alephzero Jun 22 '19 at 18:43
  • Motion is relative in principle. You know about motion from the perspective of a reference frame. If you assume motion is an absolute then it follows that space and time are absolute and you can refer motion to an absolute preferential frame. But since you are trying to prove that you can't start with that as a premise. So no, you wouldn't know if it is moving. Mach's argument is that not only you wouldn't know but that nature would have no means of applying the laws so the phenomena would actually happen in a different way as opposed to the universe having some other object in it. – Swike Jun 22 '19 at 19:14
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You are asking if we can take space as a universal reference frame. Now what we usually use as universal reference frame, is the CMB. But in SR and GR, there is no universal frame of reference in theory.

But let's disregard that, and say you want to move that bucket with water.

First of all, how would you say if the bucket was in motion (constant speed) in the first place? In an empty universe you could not tell (about constant speed).

Speed is relative. You need to specify what your speed is relative to. In your case, in an empty universe, there is nothing to compare it to.

Now if you want to move the bucket what you really do is you accelerate it (at least for a while). Now acceleration is absolute.

Even in an empty universe, you are able to tell if your bucket accelerates or not. First, as you say, the water will move differently from the bucket because of the acceleration.

But, you can also drop beacons from the bucket as it accelerates. With a laser, you can check the distance between the following beacons, and you will see that this distance increases with each new pair of beacons. Thus, the bucket is accelerating, and you can tell even in an otherwise empty universe.

Árpád Szendrei
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