The Journal of Space Exploration has just accepted my latest paper in which I focus far more on applying quantised inertia to propulsion, and which also shows an even simpler way to derive and understand QI, just from the uncertainty principle and relativity. This is a path I've been tending towards for a long time (see references). Werner Heisenberg showed, for a quantum object, the uncertainty in its momentum (dp) times the uncertainty in its position (dx) always has to be larger then Planck's constant divided by two Pi (hbar), over two (aka hbar/2). So: dpdx > hbar/2.

The assumption of quantised inertia is that you can apply quantum mechanics on the macroscale, if you take account of relativistic horizons. So, imagine we have a highly-accelerated system that excites the quantum vacuum (another way to say that is to say it sees Unruh radiation). For example, this might be a cavity with microwaves or a discharge spark inside. Imagine we now increase 'hbar' to represent the energy in this macroscopic system - bringing quantum mechanics to the macroscale. Now make the cavity asymmetrical so that the Unruh waves on the left side are blocked by a shield but those on the right side are not. Since you are blocking information from the left from getting to the system you are decreasing dx on the left side (the uncertainty in position in space is decreased because so far as the system knows there is no space beyond your shield), and so dp must increase to the left. This means that the normal quantum jitter (dp) usually very weak, is now magnified by the large accelerations (Unruh radiation) and also must be larger towards the left hand side. The system on a statistical average will move towards the left. As I show in the new paper, this predicts, to the right order of magnitude, the thrusts seen in the emdrive, the Woodward drive and also some intriguing results from asymmetrical capacitors.

The thrust of the argument :) is that quantum mechanics may not just apply to the small, and relativity to the fast: quantised inertia implies that at very high accelerations they join up to produce observable, and very useful, behaviour. Thrust without propellant means much lighter (cheaper) launch systems, and the possibility of interstellar travel in a human lifetime.

**References**

McCulloch, M.E., 2013. Gravity from the uncertainty principle. Astrophy & Space Science, 349, 957-959 Preprint

McCulloch, M.E., 2016. Quantised inertia from relativity and the uncertainty principle. EPL, 115, 69001 Preprint

McCulloch, M.E., 2018. Propellant-less propulsion from quantised inertia. J. of Space Exploration (in press). Preprint

## 4 comments:

Mike - congratulations on making the idea even simpler than it used to be. It seems you may be able to use visible light to produce the thrust as well, if you have a resonant cavity where one end is a thick plane mirror and the other is a very light, thin, and slightly concave reflector. Feed the laser in via a small off-centre hole in the thick mirror, and slightly off-axis. This off-axis would be corrected by the concavity of the thin mirror after a few bounces, after which the resonance would remain centred. Adjust the separation of the mirrors to achieve peak resonance - maybe an easy way to do this would be to vary the pressure inside the cavity (also allows for adjustment of the concavity). This thrust would not have been seen before because normally people would use all thick mirrors, even though the basic setup must have been done many times. I'd suspect maximum Q would be of the order of 1000 or so, given the reflectivity of Silver. Not as good as the microwave Qs available, but there may be even better reflectors using multilayer dielectric mirrors.

I'm sorry but I don't follow your 2013 Gravity paper. The study of "neutron-in-a-box", neutrons in a vertical gravitational well show unambiguously that the Newtonian gravitational potential yields the proper quantum mechanical energy levels. See:

V. Nesvizhevsky, et al., "Quantum states of neutrons in the Earth's gravitational field," Nature 415 297-299 (2002)

C. Krantz, Quantum States of Neutrons in the Gravitational Field https://www.physi.uni-heidelberg.de/Publications/dipl_krantz.pdf (2006)

So it seems that gravity is not "cut off" at ca 10^-5g, but at least remains valid down to 10^-27g.

Hi Mike:

I love the number two in Equation (4) in your new (2018) paper! Wow! F = delta(E)/2delta(x) and this equals having to divide the Unruh temperature by two, F = (T(Unruh)/2)(delta(S)/delta(x) as suggested by the Unruh temperature Greens function analysis, but I couldn't figure out the logic of having to divide by two even though the math went through. The logic is now clear.

Thank You

George Soli

@mikenyc

McCulloch has acknowledged elsewhere/repeatedly that 2013 paper is a sketch of the idea rather than a rigorous theory by itself. The mechanisms are of course more complicated than that in the same way that any model may fail at extremes.

I am personally a huge supporter of Mike's work and horizon mechanics in general, but I saw at the time that the mass restriction in the 2013 paper was really just a mathematical artifact.

McCulloch just didn't have the insight to build a superior model at the time. The Planck mass math is a dirty, cheap shortcut that informs the point.

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