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Gravity from the uncertainty principle

Abstract

It is shown here that Newton’s gravity law can be derived from the uncertainty principle. The idea is that as the distance between two bodies in mutual orbit decreases, their uncertainty of position decreases, so their momentum and hence the force on them must increase to satisfy the uncertainty principle. When this result is summed over all the possible interactions between the Planck masses in the two bodies, Newton’s gravity law is obtained. This model predicts that masses less than the Planck mass will be unaffected by gravity and so it may be tested by looking for an abrupt decrease in the density of space dust, for masses above the Planck mass.

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Acknowledgements

Thanks to B. Kim for encouragement.

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Correspondence to M. E. McCulloch.

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McCulloch, M.E. Gravity from the uncertainty principle. Astrophys Space Sci 349, 957–959 (2014). https://doi.org/10.1007/s10509-013-1686-9

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  • DOI: https://doi.org/10.1007/s10509-013-1686-9

Keywords

  • Gravity
  • Uncertainty principle
  • Quantum gravity
  • Space dust