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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)

Questions:

  1. Is it true that most physicists do not accept quantized inertia theory?

  2. 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)

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    $\begingroup$ It seems for someone outside of physics it is quite an effort to ask a question as lots needs to be studied to understand what is mainstream and what is not. Imho instead of deciding something as not "main stream" and remove from the site (physics) one should put the contradictions of the viewpoint. There are many many unknowns so any prior assumptions may block innovation, learning process. $\endgroup$
    – Creator
    Oct 27, 2018 at 18:21
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    $\begingroup$ @user48956, I have the same questions but did not get any answer. I had no idea that I was asking a controversial question, after reading the comments I realized, I have devalued my name (although I am in the lowest rank) in the community. By the way i did not delete the question as I really want the answer to my question. $\endgroup$
    – Creator
    Jan 29, 2019 at 19:22
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    $\begingroup$ @Qmechanic -- your cited cite rule does not cover this case. The work is published (@Creator provided a reference) and "is a new theory in the context of established science". Why is this still closed? $\endgroup$
    – user48956
    Jan 29, 2019 at 19:26
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    $\begingroup$ I edited the question, which sends it into the review queue for a second opinion. $\endgroup$
    – Qmechanic ♦
    Jan 29, 2019 at 19:45
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    $\begingroup$ This site has already accepted many questions on MoND (modified newtonian dynamics) a "fringe" theory that explains galactic rotation without needing dark matter. It is unclear why quantised inertia is different from MoND in being "fringe" especially since it has beed discussed in legitimate physics journals and is therefore not an example of "unpublished personal theories". $\endgroup$
    – matt_black
    Feb 4, 2019 at 0:55

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