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.