Quantised Inertia & Galactic Lensing

One of the most frequent criticisms of quantised inertia is that it does not predict galactic lensing. The good news it that it does, at least qualitatively. I'm sure you all know, but galactic lensing is the bending of light by the gravity of a galaxy, which causes the images from behind it to be bent by a parameter called alpha, and focused just as light rays are focused by a magnifying glass. Here's a schematic of it, with our point of view from the blue planet at the bottom.

Lensing has the effect of making the background of any galaxy (shown in orange) look distorted, just like a magnifying glass distorts a page of text. The Sun does this as well and in the future we might well use QI thrusters to send telescopes to large distances away from the Sun, say an easy 1000 AU, and use the Sun itself as a gravitational lens to see whether exoplanets might have any versions of the great wall of China. Mainstreamers are always saying that dark matter is needed to produce the lensing that is seen around galaxies. The observed lensing or deflection is indeed far more than what would be expected from the visible matter alone, given Newton or general relativity, but even with dark matter added these old models predict that the lensing should still decline as you go away from the galaxy, being insignificant further away than 100-250 kiloparsecs (kpc) because the usual dark matter halos are supposed to fizzle out there.

But, what is this? A paper by Mistele, McGaugh et al., 2024 used data from the KiDS (Kilo-Degree Survey) data base of isolated galaxies, and found that the amount of lensing does not decrease with radius from the galaxies beyond 100 kpc: it remains at a constant value out to even 1000 kpc (though it is debatable how accurate the data is beyond 300 kpc).

How could lensing be flat when it should fall off, even with a dark matter halo which should not extend much beyond 250 kpc? Well, that flatness is just what quantised inertia predicts. You remember that QI says that there is a minimum acceleration in nature? Well, that means that you can't have a beam of light travelling in a straight line because that would have no acceleration, so even when the attractive force from a galaxy is weak the light should bend a little. I've performed some calculations for a galaxy of the size of Andromeda based on Eq. 7 from my 2017 paper (see the references) and the plot below shows the inferred orbital speed (y axis) you would get at various radii from the galactic centre (x axis). The predictions of general relativity (the orange curve) and QI (the green curve) are shown here along with the inferred observations from Mistele et al., 2024 (the blue curve and the grey area which shows their uncertainty).

You can see here that the old physics (Newton or general relativity, orange curve) predicts a decay of deflection or orbital speed slowly down towards zero beyond 100 kiloparsecs. Even adding a dark matter halo would not help much past 250 kpc, because there's not supposed to be any dark stuff out there. However, QI predicts that the orbital speed stays flat, as has now been seen. This is only a qualitative agreement so far. I hope to compare the actual numbers more closely and look at some differences between disc and elliptical galaxies that have been seen, that might be uniquely explainable by QI. Proper testing is all about simply predicting what the other theories cannot.

This weak lensing data is new at the moment and subject to debate. The deflection of light in the weak lensing regime (far from the galaxy) is hard to measure because you can't be entirely sure that the objects you are looking at are part of that galaxy or behind it, but better data is coming from NASA's newly-launched Roman telescope which is ideal for weak lensing studies and might offer an order of magnitude improvement in the data. Veni, vidi, vici?

References

Mistele, T., S. McGaugh...et al., 2024. Indefinitely Flat Circular Velocities and the Baryonic Tully-Fisher Relation from Weak Lensing. ApJL, 969, L3. https://arxiv.org/abs/2406.09685

McCulloch, M.E., 2017. Galaxy rotations from quantised inertia and visible matter only. Astrophys. & Space Sci., 362,149.

Responding to Criticisms

This morning I asked google for a summary of the criticisms of quantised inertia (QI) from mainstream physics and I received this useful list. I can rebut them all, some do require a lot of explanation, some are just plain wrong and one is actually backwards! I'm grateful to google for summarising the misconceptions being said in the mainstream media. The criticisms are in bold with my response below:

QI violates the conservation of momentum.

The way to get something moving without expelling propellant in QI is to damp the Unruh waves seen by the object on one side. This is analogous to a ship in a wavy sea. Image that suddenly you put a wall to the side of it and damp the waves on that side, of shelter the ship from them on that side. The ship now feels more wave impacts from the seaward side and gets pushed towards the wall. If the crew could not see the waves they’d think there was some magic afoot and Newton’s third law was being violated, but if they could see the waves they would conclude that on a microscopic level Newton’s third law is perfectly satisfied. It is the same with quantised inertia. Damping the Unruh waves on one side of the object you want to move, shifts the centre of mass of the Unruh field to the other side compensating for the movement of the object the other way. This comes through very well in my later emdrive papers (e.g. 2017). When you consider the Unruh radiation, you get the conservation of momentum back.

QI violates relativity by giving photons mass inside the emdrive

Photons inside cavities can give that cavity mass while not technically having mass themselves (which is a different and difficult debate). This was shown in a paper by Einstein (1906) and later updated by Jennison (1979).

Abandoning the Equivalence Principle

The equivalence principle was Einstein’s assumption that the gravitational and inertial masses are exactly the same. In quantised inertia the inertial mass is modified slightly, but the point is that the change is independent of mass which means that this change will not be seen in the torsion balance tests used to test the equivalence principle. These tests are just subtle variations of Galileo dropping two balls of different masses off the tower of Pizza – was he trying to hit his critics, who were slimeballs? – they both hit the ground together and so would they in QI, just both slightly faster.

Unruh Radiation is too Weak

It is true that Unruh radiation is weak, but as I show in my 2013 paper on the asymmetric Casimir effect, it is acting at the level of tiny Planck masses and so the effect is the right size to reproduce inertia.

The Maths is Wrong

Renda (2019) usefully pointed out some shortcoming of my previous derivations of QI in which I failed to consider the whole Unruh spectrum, and only looked at the peak, so I responded by deriving the same formula in a more robust manner from the uncertainty principle (see my 2024 book) and the erasure of information by horizons (see my 2020 paper and 2024 book).

Toy Models

It is true that my models tend to be simple, but in my opinion that is an advantage. A simple model is easy to understand, nothing can be hidden and nature tends towards simplicity (Occam). I think the mainstream models are far too complex and they can hide behind that complexity.

Changing Universe Problem

Apparently Prof Stacy McGaugh has said that if the QI minimum acceleration was true then galaxy rotation speeds would vary in time and they don’t. Well, this was the point of my 2017 paper on galaxy rotation. QI indeed predicts that early galaxies should spin faster for the same mass and there is now evidence that that does happen, as I show in that 2017 paper and you can also see it in the recent discovery of the Little Red Dots by the James Webb Telescope.

Falsification by Wide Binaries.

This is the weirdest criticism them all. It is backwards. I published a paper with J. Lucio in MNRAS (2019) to show that wide binaries are the best proof of quantised inertia. These twin stars show the same orbital anomalies as galaxies, but dark matter cannot be used to correct them. QI predicts the odd wide binary orbits exactly.

Publication Issue

This criticism was that QI papers are almost impossible to publish, but that has not been my experience. I’ve published 28 of them, 1 or 2 per year. Perhaps one third of the ones I’ve submitted have been accepted and all my papers (almost all) have eventually found a home. QI is new but I always show that it predicts the data simply which reviewers find it hard to complain about.

References

Einstein, A., 1906. Ann. Phys., 20, 627–633.

Jennison, R.C., 1979. What is an electron. Wireless World, June 1979. 42-46.

McCulloch, M.E., 2013. Inertia from an asymmetric Casimir effect. EPL, 101, 59001.

McCulloch, M.E., 2017. Galaxy rotations from quantised inertia and visible matter only. Astro. Sp. Sci., 362,149.

McCulloch, M.E., 2017. Testing quantised inertia on emdrives with dielectrics. EPL, 118, 34003.

McCulloch, M.E. & J. Lucio, 2019. Testing Newton/GR, MoND & quantised inertia on wide binaries. Astrophys. Sp. Sci., 364, 121.

Renda, M., 2019. A sceptical analysis of quantised inertia., MNRAS, 489, 1, 881-885.

McCulloch, M.E., 2020. Quantised inertia and galaxy rotation from information theory. Advances in Astrophysics, 5, 4, 91-94.

McCulloch, M.E., 2024. Quantised Accelerations. Polaris Books.

How to Make a (Safe) Black Hole in Your Garage

As you know, quantised inertia predicts that a new kind of propulsion can be extracted from charged capacitors. This is essentially the Casimir effect and charging the cathode so that electrons stream across to the anode pushing the whole thing a little bit more than expected. In 2021 (see also my 2024 book) I derived this thrust using dimensional and physical arguments to be

F = 0.00014 x IA/d^2

where I is the Fowler-Nordheim leakage current, the A is plate area and d is the plate separation. This predicts the thrust measurements from several laboratories, one in California (Becker and Bhatt), Virginia (IVO Ltd), Italy and the one I set up with Richard Arundal at Plymouth University, and the thrust has also been seen in a few high-powered 'garages' or home labs. I have recently repeated and improved the derivation of this that I had before, but recently Morgan H. Lynch suggested to me another way to derive the same formula that is more speculative, but is rather elegant and couples the down to Earth component of this with black hole physics.

Imagine a small black hole, shown above. It is emitting Hawking radiation of power P (the red arrows). The total force coming off it is P/c, where c is the speed of light. Now imagine someone extremely brave goes up to the event horizon and puts a capacitor (grey //) on it so that the cathode is just on the horizon. What would the force on the electrons be? It would be P/c times the ratio between the plate area (A) and the area of the whole black hole radius d, so

F = PA/(4pi.cd^2)

Now let us imagine that the leakage current observed in the capacitor is equivalent to Hawking radiation. The mass energy flux rate is P = (I/q)mc^2, where q and m are the charge and mass of an electron, so

F = (mcIA)/(4pi.qd^2)

Now let's just put the known numbers in here and see what happens.

F = 0.00014 x IA/d^2

Compare this with the formula I derived before. The same! In other words, in some sense, that is not entirely clear yet, the QI thrust capacitor is analogous to a black hole. In a sense it is, because, for a highly accelerated object like an electron, the Unruh waves are short enough to be damped by the plates so the area between the plates is a sub-vacuum bounded by a metal horizon. Not a million miles from the concept of a black hole.

After I told him this my son asked if there was any danger. The answer is no. It's just another horizon. They form whenever anything moves (strictly - accelerates) and based on billions of years of experience they do not swallow the universe. So you too can make a 'black hole' in your garage.

By the way, I'm now making short videos about QI and related issues. The videos are available on my YouTube channel:

https://www.youtube.com/channel/UC0LWcVMLjdw7duQRVsqzZNQ

References

McCulloch, M.E., 2021. Thrust from symmetrical capacitors using quantised inertia. Research Gate: https://www.researchgate.net/publication/353481953_Thrust_from_Symmetric_Capacitors_using_Quantised_Inertia

Light is a Quantum Pressure Wave?

 I've been writing a new book, made up so far of mini-papers, but I've been sticking them all together and two of the bits taken together are pretty exciting so I'm writing a paper on that. The paper has four steps to it:

Step 1. Thesis. I've shown that light looks like a sound wave in the quantum background. When you assume that, it predicts a speed that agrees with the speed of light within 10%, which is the uncertainty of some of the parameters I'm using anyway. So that was my initial observational test and it passed.

Step 2. Based GR. If you apply quantised inertia to this, you get the equation for the propagation of light from general relativity. It predicts general relativistic effects not from curved spacetime, but from the inhomogeneity of the quantum background around matter. This is a much more scientific model than curved space because you can see both the effect (light bending) and in principle also the cause of it (inhomogeneities in the quantum background).

Step 3. A Test. This model predicts that if you fire a laser through a cavity then the light should slow down. That is a test that can be done quite easily and as I recall was done by Harold White once. He fired a laser through an emdrive just for the heck of it and saw anomalous results.

Step 4. Application. What this means is that by engineering the vacuum (not sure how yet) we should be able to increase the speed of light and travel faster than the usual light speed limit. Perhaps this already happens in some parts of deep space?

If I can get this past the reviewers or censors this will be a great paper. It represents conceptual progress, but is also testable and applicable. If I can't publish it that way, I'll just go to Plan B and continue with the book. It was supposed to be about time, but that's a concept so big to think about, that a lot of other things are dropping out along the way.

A Tale of Two Satellites

In March 2025 SpaceX launched a Rogue Space Systems cubesat with an IVO Ltd Quantum (QI) Drive on it. Up till Christmas I was monitoring its trajectory, almost every day and it did seem to push up by about a few metres when it seemed from personal communications that they had turned it on, but analyses like this are very subjective.

Unfortunately, as you may know, there was a engineering glitch so the thruster could not be turned on for more than a minute before problems arose, so the hoped-for orbit raise of kilometers did not come to pass. Which leaves us in a less than ideal position. Can we see if there is QI thrust? We probably cannot do this for certain, but I collected a lot of data from SatNOGS DB (nearly every day for several months) so it makes sense to see what we can get from it.

They always say "Don't compare yourself with others," but in science that is a valid method. One thing we can do is to use a control: a similar satellite without a QI drive. The IVO Sat (Norad ID = 63235) had a close twin brother (Norad ID = 63220) which was the same shape and mass and was launched by the same Falcon 9 rocket into about the same orbit. So, we can look at their fall over the last three months and see if the IVO Sat fell less than the control satellite. IVOsat fell from 506.3 km on 30/9/25 to 501.42 km on 30/12/25, a fall of 4880 metres. The other satellite fell from 504.98 km to 499.5 km so a fall of 5480 metres. Therefore the IVOsat fell 600 metres less over three months. Does that mean the QI Drive thrust it up by 600 meters over that time? Possibly. Is that the rise we expect give the thrusting they did?

The thrust generated by the QI quantum drive was expected to be 1.75 mN and the mass of the satellite is 20 kg which means that the along track acceleration (a) will be

a = F/mass = 0.00175/20 = 8.75x10^-5 m/s^2

Since I happen to know that the typical burn time was about a minute, and if we assume it was fired once every other day, a reasonable guess, then the change in speed per day (dv) is

dv = 8.75x10^-5 x 60 /2 = 0.002625 m/s

The change in height (dH) is

dH = 2.dv.sqrt(r^3/GM) = 5 metres per day

The observed rise (compared to its twin) was 600 metres in 90 days, which is 6.6 metres per day. Therefore the IVOsat moved up relative to its twin satellite by about the height you might expect if the Quantum Drive was being fired every other day for one minute on average. It looks plausible, but it could be that the drive was generating a Lorentz force and pushing off the Earth's magnetic field. My calculation of the Lorentz force suggests it's too small but I do not have detailed knowledge of the circuitry in the drive. We had hoped to have thrust large enough to avoid ambiguities like this but that has not been the case.

If this QI Quantum Drive was indeed thrusting then it means a radical change to the entire satellite industry because we can now have onboard thrusters that are silent and do not need to carry heavy fuel so they will last much longer, but we are not in a position to say that yet. Anyway, a big thank you to IVO Ltd, Rogue Space Systems and SpaceX who got the test up there (an amazing feat in itself) and have produced some results. I hope they will soon make a more detailed press release on it.

Elephants in the Room (JuMBOs)

The fantastic news is that the journal Astronomy has just peer-reviewed, accepted and published my new paper on the Jupiter Mass Binary Objects (JuMBOs). Since it was an invited contribution I do not have to pay £1000 to make it open access.

As you know, quantised inertia predicts there is a minimum acceleration in nature of around 2x10^-10 m/s^2. This is such a small acceleration that it would take the lifetime of the universe to get from zero to the speed of light (there a big clue to something right there). How do we test this? Look where nature tests the limit. Stars at the edge of galaxies are doing that and move faster to stay above this minimum, that’s why they orbit faster than expected, not because they contain invisible dark matter. Galaxy clusters, wide binaries and even our nearest neighbour Proxima Centauri all hover just above this limit and these are all on different scales, thus proving that the reason is not dark matter since this has to be spread out specifically on galactic scales.

When a paper was published by McCaughrean and Pearson (2023) finding what looked like 42 wide binaries in the Orion nebula, I thought “I’ll bet they too hover just above the QI minimum.” Sure enough, when I checked, they did! QI never fails. Hence the plot below which shows the separation of each binary (x axis) against the orbital acceleration (y). As they get wider, they still stay above the minimum predicted by QI (red line, but see the caveat below).

I always have the confident feeling on testing QI that it is going to work, but it is still a great thrill when it does. There are a couple of data points that are strictly below the QI minimum but this minimum also has an uncertainty, mostly due to uncertainties in the cosmic scale.

In any good paper, there’s always a testable prediction and a caveat. The QI prediction is that the widest of these binary objects should be orbiting up to 70 metres per second faster than expected and this prediction could be tested by the HARPS (High Accuracy Radial Velocity Planet Searcher) telescope which is used to spot exoplanets and can determine orbital speeds, they say, to an accuracy of 1 m/s. The main caveat is that we need to find more of these JuMBOs to be sure they are binary objects and not just coincident objects. Their being just random coincidence is very unlikely, as stated in the observational paper, because the line of sight points out of the galaxy so there isn't much situated behind them, but you know sceptics! I've been through quite a long, and useful, review process on this one so it's great to end the year with a success.

If you liked this, find much more at my patreon site: https://www.patreon.com/OneSteptoTauCeti

References

Pearson, S.G. and M.J. McCaughrean, 2023. Jupiter mass binary objects in the Trapezium cluster. https://arxiv.org/abs/2310.01231

McCulloch, M.E., 2026. Jupiter Mass Binary Objects Show a Minimum Acceleration. Astronomy, 5(1), 1. https://www.mdpi.com/2674-0346/5/1/1

3I/Atlas Bound?

This month's great leap forward is that I have written a fortran model to simulate complete QI dynamics for the first time. The great thing about having a fortran model is that you can run experiments with it. I've suspected for a while that these interstellar comets like Oumuamua, Borisov or 3I/Atlas are actually bound to the Solar system, or 3I/Atlas at least. This was based on little more than my QI intuition that objects at low acceleration, in other words out in the boondocks, tend to be bound when they are not supposed to be. This is because at low accelerations QI reduces the inertial mass and also the centrifugal force, so there's less tendency than expected for objects to go in straight lines and with a circular orbit, this means less tendency to veer off into deep space. Galactic edge stars and wide binaries are unexpectedly bound. Unexpected unless you know about QI.

As a test, I initialised 3I/Atlas at its perihelion, taking the data from the JPL Horizons website and then modelled it as it shot off into the outer solar system. With Newtonian physics it kept on going and was an interstellar comet as everyone expects. With QI, it first slowed down in its trajectory as it lost inertial mass and was more easily attracted back to the Sun, a bit like the Pioneer craft. This was very obvious after about 100 years. Then at about 1500 AU distance it came to a virtual stop and started on a very slow turn-aroud back to the Sun. On other words. Despite its present breakneck speed, of 68,000 m/s, it's bound and someday it will be back. This is as much of a shock to old physics as when Rutherford fired alpha particles at atoms in gold foil and saw them bounce back thus proving the existence of the hard central nucleus, or the day an Australian native threw away a bent stick and it came back and hit him on the head.

This realisation with QI that 3I/Atlas is bound solves so many of the problems that have been pointed out by Avi Loeb. It arrived in the plane of the ecliptic, and the random chance of that was very low. More importantly, 3I/Atlas is so massive: one million times the mass of the first 'interstellar' object Oumuamua and 1000 times the mass of Borisov. It is just crazy that we should see something so big. We should see 1000 Oumuamuas before we see one Borisov, and 1000 Borisovs before one 3I/Atlas. But 3I/Atlas is what it is. It would be a shock if there is so much mass in interstellar space. It is far easier to assume that 3I/Atlas is part of the Solar system, just coming in from the Oort cloud, if that exists. I suspect it might be closer in than expected. This accounts for it being in the ecliptic plane - it is just derived from the same condensed, flattened cloud that all the planets are, and its huge mass is no longer a mystery. I love simplifications, and QI always provides a few for free.

So is 3I/Atlas bound? Newton says no. QI says yes, and remember that the data is with QI in these low acceleration regimes. QI predicts galactic edge stars and wide binaries, whereas Newton does not without a ridiculous amount of arbitrary (dark) help. Anyway, this is bound to change our view of the Solar system.