Generalized Uncertainty Principle (GUP) was obtained in string theory andquantum gravity and suggested the existence of a fundamental minimal lengthwhich, as was established, can be obtained within the deformed Heisenbergalgebra. We use the deformed commutation relations or in classical case(studied in this paper) the deformed Poisson brackets, which are invariant withrespect to the translation in configurational space. We have foundtransformations relating coordinates and times of moving and rest frames ofreference in the space with GUP in the first order over parameter ofdeformation. For the non-relativistic case we find the deformed Galileantransformation which is similar to the Lorentz one written for Euclidean spacewith signature $(+,+,+,+)$. The role of the speed of light here plays somevelocity $u$ related to the parameter of deformation, which as we estimate ismany order of magnitude larger than the speed of light $u\simeq 1.2 \times10^{22} c$. The coordinates of the rest and moving frames of reference forrelativistic particle in the space with GUP satisfy the Lorentz transformationwith some effective speed of light. We estimate that the relative deviation ofthis effective speed of light $\tilde c$ from $c$ is ${(\tilde c-c)/ c}\simeq3.5\times 10^{-45}$. The influence of GUP on the motion of particle and theLorentz transformation in the first order over parameter of deformation ishidden in $1/c^2$ relativistic effects.
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机译：通过弦论和量子引力获得了广义不确定性原理（GUP），并提出了一个基本的最小长度的存在，该长度是可以确定的，可以在变形的海森堡代数中获得。我们使用变形的换向关系或在经典情况下（本文研究）使用变形的Poisson括号，它们对于构型空间的平移是不变的。我们已经发现，与GUP的变形参数相关的一阶变换，与空间中参考坐标的运动和时间以及静止参考帧的变换有关。对于非相对论的情况，我们发现了变形的伽利略变换，它类似于为欧几里德空间写的带有符号$（+，+，+，+）$的洛伦兹变换。光速的作用在这里起着与变形参数有关的一定速度$ u $，正如我们估计的，它比光速$ u \ simeq 1.2 \ times10 ^ {22} c $大许多数量级。 GUP空间中相对论粒子的静止和静止参照系的坐标以一定的有效光速满足Lorentz变换。我们估计该有效光速$ \波浪线c $与$ c $的相对偏差为$ {（\波浪线c-c）/ c} \ simeq3.5 \乘以10 ^ {-45} $。在$ 1 / c ^ 2 $相对论效应中，GUP对粒子运动和一阶洛伦兹变换的影响超过了变形参数。
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