Ciencia ficción

The transformations of Galileo indicates the group of transformations which makes it possible to bind two frames of reference of two reference frames galiléens, i.e. moving uniform relative in Newtonian Mécanique.

The equations of the transformation, apparently obvious, are erroneous when the relative speed of the reference frames approaches the Speed of light. Under these conditions, they should be replaced by the group of the Transformations of Lorentz.

Are (X, there, Z, T) the punctual coordinates in a reference frame has, and (x', y', z', you) the coordinates of this point in a' reference frame. If A' is moving uniform speed v in direction X, relative with has, then one a:

\ left \ {\ begin {matrix}
t'&=&t \ \ x'&=&x - vt \ \ y'&=&y \ \ z'&=&z \end{matrix}\right.

The first line expresses that time does not depend on the reference frame in which one measures it and It is very simple to then deduce the law from it from addition speeds by simple derivation compared to the time T which is an absolute:

\ left \ {\ begin {matrix}
dt'&=&dt \ \ \ frac {dx'} {dt} &=& \ frac {dx} {dt} - v \ \ \ frac {dy'} {dt} &=& \ frac {Dy} {dt} \ \ \frac{dz'}{dt}&=&\frac{dz}{dt} \end{matrix}\right.

Thus the fact that in Euclidean geometry \ vec {OM} = \ vec {OO'} + \ vec {O' M} and that time is an absolute (independent of the reference frame), it is obtained immediately that: \ frac {D \ vec {OM}} {dt} = \ frac {D \ vec {OO'}} {dt} + \ frac {D \ vec {O' M}} {dt} is the law of addition speeds \ vec {V} = \ vec {v'} + \ vec {V'}

See too

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