Mach’s principle and its possible connection with general relativity are discussed. Feynman’s idea about the influence of distant galaxies on the space-time scale, which he expresses in terms of the speed of light, Planck’s constant and an electron’s mass, is discussed. The hypothesis of the dependence of these fundamental constants on the global distribution of matter in the Universe is discussed. It is assumed that Planck’s constant decreases near massive bodies. The calculation is made for the assumed change in Planck's constant, depending on the height above the Earth's surface. A quantum mechanism of gravitational attraction is proposed: a large mass limits the uncertainty in motion of a particle and, as a result, attracts it. The concept of a degenerate space without definite laws... of motion and its connection with the origin of quantum uncertainty in the microcosm are discussed. A new interpretation of Mach's principle is proposed with allowance for quantum uncertainty. The calculation of the potential gravitational energy is performed taking into account the change in the rest energy of the body in a gravitational field. A solution of the problem posed by Feynman on the relationship between the space-time scale and the global distribution of galaxies is proposed. The appearance of a negative sign in the Schwarzschild equation for the square of the interval is investigated. A modification of the Schwarzschild solution for the square of the interval is proposed to achieve agreement with Mach’s principle. A laboratory experiment is proposed to verify Mach’s principle.