This recent news article reports that DARPA is doing work with "quantized inertia", despite their claim that it's not widely accepted by physicists:
The Defense Advanced Research Projects Agency (DARPA) recently awarded a $1.3 million contract to an international team of researchers to study quantized inertia, a controversial theory that some physicists dismiss as pseudoscience.
Quantized inertia (QI) is an alternative theory of inertia, a property of matter that describes an object’s resistance to acceleration. QI was first proposed by University of Plymouth physicist Mike McCulloch in 2007, but it is still considered a fringe theory by many, if not most, physicists today. McCulloch has used the theory to explain galactic rotation speeds without the need for dark matter, but he believes it may one day provide the foundation for launching space vehicles without fuel.
–"DARPA Is Researching Quantized Inertia, a Theory Many Think Is Pseudoscience", Motherboard (2018-10-02)
Is it true that most physicists do not accept quantized inertia theory?
Would quantized inertia imply that the conservation of momentum is only approximate?
I also found a paper on arXiv:
It is shown here that if we assume that what is conserved in nature is not simply mass-energy, but rather mass-energy plus the energy uncertainty of the uncertainty principle, and if we also assume that position uncertainty is reduced by the formation of relativistic horizons, then the resulting increase of energy uncertainty is close to that needed for a new model for inertial mass (MiHsC, quantised inertia) which has been shown to predict galaxy rotation without dark matter and cosmic acceleration without dark energy. The same principle can also be used to model the inverse square law of gravity, and predicts the mass of the electron.
–"Quantised inertia from relativity and the uncertainty principle", M.E. McCulloch (2016-10-13)