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I just read Galileo's Relativity Hypothesis from this website: http://physics.ucr.edu/~wudka/Physics7/Notes_www/node47.html

It states that - "any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments"

Now imagine two people, one inside the hull of a ship, moving at a constant velocity relative to another stationary observer, on land. Lets say both of them are holding identical magnetic compasses. The person inside the ship can observe a movement of his compass needle, whereas the person on shore will not record any such observation. Moreover, using this, the person inside the ship can conclude that he is indeed moving!

Is this argument really inconsistent with Galileo's Relativity Hypothesis? Or is there a flaw in the argument? Or I havent understood the hypothesis correctly?

PS - I haven't read much about Einstein's theory. So I would love to know if this theory was later modified by him or someone else, which would be consistent with this argument (if it is indeed foolproof).

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    $\begingroup$ the person in the ship cannot tell for sure if he is moving or if the magnetic field is changing $\endgroup$ – user83548 Nov 28 '15 at 23:25
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Technically, experiments involving magnetic interactions are not really "mechanical experiments". But this is not the main issue. Right after the OP quote there is a stipulation, "it is understood that the apparatuses they use for these experiments move with them". Although it might seem that the apparatus, the compass, is moving along with the person on the ship this is misleading, because the compass is only a part of the "apparatus". What the stipulation really means is that everything involved in the experiments has to be isolated from any external interactions with objects that do not move along with the observers. The compass, on the other hand, is interacting with the magnetic field of Earth, the other part of the "apparatus", which is illegitimately left out of the picture.

If something like this is allowed we do not need a compass, we may simply let the moving observer observe a lighthouse on the shore with binoculars, and deduce that he moves that way. The binoculars are moving with the observer, just like the compass does, but it is the lighthouse, just like the magnetic field, that allows him to "violate" the relativity principle. And if we do not let our moving observer deduce that he is moving from the fact that the lighthouse does (i.e. to assume that the lighthouse is stationary), then we similarly should not allow him to deduce that he is moving from the movement of the magnetic needle.

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