I'm always looking for ways to simplify quantised inertia since it is not the easiest concept to get across, and also simplification usually leads to a deeper understanding. My usual argument using Unruh waves and horizons is equivalent to what follows below, but there is now a simpler way to frame quantised inertia, which I published in 2016. First of all, just as Einstein assumed that physics should not be frame-dependent, quantised inertia assumes that physics should not be scale-dependent. To explain: a huge entity the size of a galaxy (say) should agree with us on the physics it sees. Therefore, Heisenberg's uncertainty relation (below) should apply to stars too

dp.dx~hbar/2

This is illustrated by the diagram which shows a large object (black ball) and its uncertainty in position (solid envelope) and momentum (dashed envelope). Since hbar must be kept constant, then the more an object knows its position (dx smaller, the solid line is closer to the ball) the more it does not know its momentum (dp is bigger, the dashed line is further from the ball).

dp.dx~hbar/2

This is illustrated by the diagram which shows a large object (black ball) and its uncertainty in position (solid envelope) and momentum (dashed envelope). Since hbar must be kept constant, then the more an object knows its position (dx smaller, the solid line is closer to the ball) the more it does not know its momentum (dp is bigger, the dashed line is further from the ball).

Now let us forget for a moment that quantum mechanics and relativity usually get on like two cats in a bag, and combine them. If the object accelerates to the left (red arrow) then information from far to its right can never catch up and a relativistic horizon (like a black hole event horizon) appears at a distance of

d=c^2/a

in the rightward direction (see the solid right-angle). So the uncertainty in position is reduced since the object's space has been curtailed from the cosmic scale to a scale 'd'. As a result, the uncertainty of momentum to the right is increased (the dashed line is far from the ball) and the ball will jiggle more rightwards: against its original acceleration. This predicts the inertial force (blue arrow) in the modified form needed for quantised inertia, and so it predicts galaxy rotation without dark matter and cosmic acceleration without dark energy. QI is, simply put, the quantum and relativistic equations shown above rammed together in the way shown in the diagram. To put it more physically: new mass-energy (dp) appears if information about space (dx) is curtailed. Put another way: what is conserved in nature is not mass-energy, but M-E plus information (conservation of EMI).

Now imagine putting a large mass next to an object. To some extent this mass will block information from that direction, reduce dx in the uncertainty principle and increase the momentum (or quantum jitter) that way. The two objects will then jitter-themselves together. This looks very much like gravity, and in the 2016 paper I show that you get Newtonian gravity from it. To get something like general relativity (in a QI form) the same derivation will have to be done fully relativised.

Now imagine that instead of putting a large mass next to the object, we put an information horizon there that reduces 'dx' in that direction and increases the quantum jitter (dp). The object should see a thrust. Since quantum waves are partly electro-magnetic, a conducting metamaterial should do. In my opinion this has already been seen in the emdrive, since QI predicts it well, and everything I have published over the last 11 years implies that this new thrust is possible. Can it be powerful enough to oppose gravity? I think so. Good news: solid lab tests are coming.

References

McCulloch, M.E., 2016. Quantised inertia from relativity and the uncertainty principle. EPL, 115, 69001. https://arxiv.org/abs/1610.06787