I've suggested (& published in 21 journal papers) a new theory called quantised inertia (or MiHsC) that assumes that inertia is caused by relativistic horizons damping quantum fields. It predicts galaxy rotation, cosmic acceleration & the emdrive without any dark stuff or adjustment. My Plymouth University webpage is here, I've written a book called Physics from the Edge and I'm on twitter as @memcculloch

Thursday, 14 November 2019

From Galactic Scales to Lab Scales.

The best way to bring about the revolution in physics that we all need - getting rid of dark matter and dark energy, unifying physics and making propellant-less thrusters and new energy sources possible - is to demonstrate QI in the lab. That is being attempted by the two groups I am funding using DARPA funds. I am not at liberty to divulge what they are finding - not due to DARPA but because the experimenters wish their results to be held back till they are sure. This is understandable but their results at least have given me an indication of what might work. I'd like to get many groups to try horizon drives for themselves and this is my attempt to explain how to do that. Please note I am not an experimenter, yet, so my suggestions may be naive in some way - you may well know better, so feel free to tell us all in the comments below. Everyone is welcome, even careful unpublished results will be useful, though most useful would be groups who know how to be uber-careful about artifacts & how to publish in journals.

The Experiment:

1. Make or buy an asymmetric metal resonance chamber (emdrive shaped or similar) that has a reflective inside, so that light of the wavelength you are going to use will bounce around inside it many times before being dissipated as heat.

2. Place this cavity with its narrow end pointing up, on a digital balance (scale) capable of measuring a change in weight of 0.1 mg or preferably 0.01 mg (depending on your setup, see point 4), with a fast enough response time that sudden 'jumps' can be seen (see point 5) and able to log data to a PC.

3. Decide some way to get light into the cavity. This could either involve firing a laser in through a hole, use a fibre-optic or placing a light source in there, eg: an LED with attached battery/capacitor. Try to avoid having cables going into your cavity - they produce em forces & external mechanical forces.

4. Activate the light source. QI roughly predicts a thrust force of F ~ PQ/c, where c is the speed of light. So, for example for a light source with power P = 4W and for a cavity with a Q (number of internal reflections) of 100 the force is 1.3 microN and the weight change is 0.13 mg.

5. Plot a time series of the force before and after activation of the light. The QI thrust (if there) will show up as an initial jump at switch on. Any effects due to heating should be slower. These two effects can be isolated as Sonny White did in his 2016 emdrive paper (see references).

Please make sure that the expected QI thrust given by your P and Q is bigger than the scale's sensitivity (ie: watch your Ps and Qs!). The full QI thrust formula is F=PQL/c x ((1/wb)-(1/ws)) where L = length of cavity, and ws and wb are the width of the small and big ends. The way to enhance the QI effect is to improve the reflectivity of the inside of the cavity (higher Q), boost the power of the light source (higher P) or change the shape (L, wb/ws). I am intending to try this for myself, but as the German proverb goes "Einmal ist keinmal, zweimal ist immer". "Once is never, twice is forever", or to use the scientific expression "Things must be repeated to be sure". As I said above I am a theorist, so some of my suggestions here will be naive in some sense. Please tell all of us in the comments if you see a better way!

Acknowledgements. The above experimental plan has benefited from others such as M. Tajmar, J-L Perez-Diaz, Russ George and T. Taylor. Also many others on twitter who have made suggestions. Thank you!

References

McCulloch, M.E., 2018. Propellant-less propulsion from quantised inertia. J. Space Explo. 2018 Vol: 7(3). https://www.tsijournals.com/abstract/propellantless-propulsion-from-quantized-inertia-13923.html

White, H., P. March, J. Lawrence, J. Vera, A. Sylvester, D. Brady and P. Bailey, 2016. J. Propulsion and Power. doi:10.2514/1.B36120 https://arc.aiaa.org/doi/10.2514/1.B36120

Wednesday, 2 October 2019

Digesting Arp's Kebab

There is a certain comfort in these uncertain times, and I like doing this at any time, in focusing on a non-human puzzle that has a chance of making sense. The puzzle I've been focusing on over the past few weeks is one that is brilliantly explained in Halton Arp's book 'Seeing Red' (see the reference below) and after many weeks of boiling it down to its essentials I've summarised it in this plot.



The plot shows the Sol star system in the centre. Observations show that as you look at galaxies further and further away they are increasingly red-shifted. So I've varied the colours on the plot from blue-green in the middle to red around the edge. This red-shifting was discovered by Edwin Hubble in 1929 and was assumed to be a Doppler shift caused by the stars moving away from us, but not so fast!

Along came William Tifft in 1973 who found that these red-shifts are quantized or 'stepped' as shown in the plot by the areas of uniform colour. Galaxies appear to be moving away from us only at certain preferred speeds. This is still being contested, but on balance it looks to be true and this is incompatible with the Big Bang / expansion hypothesis. The mainstream usually explain cosmic expansion by talking about an expanding balloon. We are at one point on it, and as it expands all other galaxies move away from us, like dots on the balloon. The further ones move away faster. The problem is that the only way to get it to work for stepped speeds is to say that the Sun is at a privileged centre of the cosmos, and even cosmologists are not arrogant enough to claim that.

Then along came Halton Arp who started by looking at observations with an unusually clear sight, which is why I admire him. He spotted that some low-red-shift active galaxies (such as the green one in the plot) have quasars next to them that have high red-shift (red circles). The red-shift decays with distance, see the red-orange-yellow circles that look a bit like a kebab (someone on twitter sent me a picture of a kebab in response to the above plot). Mainstream astronomers insisted "No, the quasars are a long way behind the galaxies in the distant background & so they must be putting out a thousand times as much power as the Milky Way to be seen!!" but Arp was sure the quasars were connected to the nearby galaxies - sometimes even linking tendrils could be seen. This also meant that the quasars didn't have to be so ridiculously powerful - not so far away.

This convinced him that a high red-shift does not necessarily mean great distance, and once a barrier breaks down in one place, the chaos tends to spread, especially if you are as stubborn as Arp who has a certain similarity to Fritz Zwicky or Fred Hoyle. He applied this idea to the red-shifts seen in distant galaxies and suggested that that occurs because the light we see from them was emitted long ago when the cosmos was young and objects had a smaller view of the whole and there is 'some' intrinsic process that predicts a lower inertial mass for a young small cosmos (sounds familiar?). This means that when matter was/is first formed, it forms atoms whose electrons have less inertial mass, so the electron orbitals are closer together (less centrifugal force) and so they emit less energetic photons and produce red-shifted light. This accounts for the distant/early galaxies and also the quasars close to the galaxies which appear to have been newly-formed and emitted from those galaxies. An important point is that it is possible to explain the stepping or quantisation using an intrinsic red-shift but it is not using the Doppler/Hubble model.

Quantised inertia looks to be an excellent candidate to explain the above process. In QI the inertial mass is caused by the zero point field (Unruh radiation) which would have been weaker in the early cosmos because fewer quantum waves can exist in a smaller perceived volume (horizon). This explains the cosmic red-shifts and should explain their quantisation, though the numbers still elude me. It also fits with the quasars emitted from the galaxies: if this is new matter being formed then it sees a smaller cosmos (closer horizon) since it has not had chance to collect information from far away, so, again, inertia is weaker.. The proof of this will be in whether QI can predict the values of the quantisation. The observed red-shifts are for example: Z=0.06, 0.3, 0.6, 0.96, 1.41, 1.96 and 2.64. I am working on this now, looking at a Bohr model with varying 'qinertial' mass.

In any event, apparently Arthur C Clarke was ahead of Halton Arp in his imagination. Arp went to see him in Sri Lanka to tell him about it, and, he hoped, surprise him. He told ACC that "Unexplained gamma radiation was being emitted from the Local Group of galaxies..". "Ah, matter creation..." said Arthur C. Clarke immediately (see page 138 of the book below). Of course it is one thing to imagine it, quite another to prove it, but let's see if QI can provide the reason.

References

Arp, Halton, 1998. Seeing Red: redshifts, cosmology and academic science.

Wednesday, 18 September 2019

FTL, Wide Binaries, Uncertainty, Data & Arp.

So what have I been doing over the past few weeks apart from not updating this blog because I've been trying to decide what I can reveal now that I'm working with experimenters? A lot has happened, so here's a summary of some of it:

I attended the FISW workshop on interstellar travel, in the UK, and gave a talk showing how the propellant-less propulsion you can get from quantised inertia will do three things: 1) make it easier to get into space, 2) make it easier to accelerate towards the speed of light because no heavy fuel needs to be carried and 3) QI may even allow us to outpace light.. My talk, or rather half of it given that the camera was pointing at me and not the slides, can be found here and a paper on it here.

My postdoc and I published a paper on wide binaries. These co-orbiting stars are a little like mini-galaxy rotation problems in that when they are far from each other, they orbit at a speed that should send them zooming off to infinity. Strangely, just like galaxies, they remain bound. The crucial point is that dark matter can't be put in between them to hold them together because that must stay spread out smoothly or the mainstream would be unable to model full galaxies. It turns out that MoND can't model wide binaries either. The point is that only QI can model wide binaries. Experimentum crucis!?

Jaume Gine and I published a paper on an alternative derivation of quantised inertia from the uncertainty principle. I've done a similar derivation before in a paper, and the result was close to QI, but Jaume found that if we assume that the important parameter is not the distance to the horizon, but the width of the horizon, then the result comes out exactly.

I've also had two meetings with DARPA and those seemed to go well, so funding may be OK for awhile (touch wood). Regarding the experiments being done, I cannot tell you any details (because the experimenters have asked me not to), but I can summarise the experimental results so far as not conclusive, but I'm extremely encouraged by them. More conclusive tests will occur in November. It is possible that a couple more groups in the US will collaborate on QI experiments: one on extreme spin and one looking at asymmetric capacitors.

I've been playing around with ideas to develop a full QI cosmology, and reading books by A. Unzicker (Einstein's Lost Key) which discusses the variable speed of light version of GR, which predicts as well as the geometric one, another by Halton Arp (Seeing Red) which talks about intrinsic redshift, and papers by F.W. Kantor who had a model of the cosmos where physics was determined by how much of the cosmos an object could have seen in its lifetime. After a lot of scribbling on paper and getting to the same point where mass seems to equal area, a rough outline has been coalescing. If the cosmic redshift is not caused by recession of the stars from us but by something intrinsic (as suggested by Arp) then this fits better with quantised inertia which ties inertial mass to cosmic age. QI predicts that the inertial mass was lower in the past because objects had not yet had time to see very far off (remember Kantor?) so everybody' cosmos was smaller (although the cosmos itself was not). Therefore, transitioning electrons in atoms in the past likely emitted redshifted (less energetic) photons. So when we look at far stars we see a redshift. QI may also explain some peculiar high redshifts seen by Arp near to galactic axes (new matter?) and redshift quantisation..? For more details of this see my earlier comments here.

All in all, a nice mix of progress in theory, in experiment and in learning to collaborate.

Maths, science, history, unraveling a mystery that all started with the Big Bang. Maybe.
(suggested amended to the Big Bang Theory's TV theme)

Tuesday, 2 July 2019

Evidence for Unruh Radiation?

Last week I went for a very pleasant walk at lunchtime, into town and to a tea shoppe. I was trying to understand the recent paper by Hu et al. (reference 2) where they claimed to see 'simulated' Unruh radiation by exciting a Bose-Einstein condensate with a high frequency magnetic field. During the walk I realised that this is very similar to a paper I read way back in 2011 by Wilson et al. in Nature (reference 1) where they observed what they called a dynamic Casimir effect. Several people at the Interstellar workshop I've just attended also mentioned the DCE to me, including Heidi Fearn. This 2011 paper is closer to showing real Unruh radiation, & is simpler to understand as well.

In 1948 Casimir himself noted that mirrors produce a 'boundary condition' on electromagnetic waves (I understand this to be a horizon) since at the mirror the electric field must be zero at the surface. The implication is that if you move a mirror in the quantum vacuum, then it has to zero the vacuum fields as it goes through it. However, moving mirrors fast enough has always been the problem with testing this.

Enter the SQUID. Wilson et al first set up a transmission line with a SQUID (Superconducting Quantum Interference Device) on one end. A SQUID is a loop allowing current to go both ways around, with a Josephson junction along each path. The Josephson junctions and therefore the SQUID responds to changes in the applied magnetic field and the change in the SQUID changes the boundary condition of the transmission line so that it is as if it was getting longer or shorter. Its electrical length changes. This means you can make what is effectively a moving mirror (in my view, a moving horizon) since, as Wilson et al say "In the same way as for the mirror, the boundary condition is enforced by currents that flow thru the SQUID". This is much easier than physically varying the length, since nothing solid is moving and you can get much higher accelerations that way (great for seeing QI).

Wilson et al applied a magnetic field varying with a frequency of about 10GHz to move the boundary condition (aka horizon) back and forth, and they stated that the speed of movement of the apparent end of the line (horizon) was 10% of the speed of light. In the paper they go through a complex analysis to show that what they are getting are paired photons emitted from the end of the line due to its speed through the quantum vacuum.

When I first read this paper back in 2011, I immediately tried a back of the envelope calculation and found it can also be understood as Unruh radiation. Since the frequency of the oscillation (f) they applied was 10GHz and the speed of the boundary was 10% the speed of light, then the acceleration of the horizon is 2 x 0.1 x c/t = 0.2cf = 6x10^17 m/s^2. The predicted wavelength of Unruh radiation is then 8c^2/a = 1.2 m. The radiation Wilson et al detected in their experiment ran a range from 0.4 m to 1 m in wavelength, so it seems plausible that what they saw can also be thought of as Unruh radiation. Also, this is a different way to look at horizons. Usually, in quantised inetia, we consider the horizon made by an accelerating object. Here we are looking at an accelerating horizon!

If this really is Unruh radiation then it is a well documented example (in Nature after all). Two symmetric Unruh photons are being emitted in opposite directions, and if we can just add some asymmetry, then we would have thrust. Is this then a direct mainstream way through to a QI thruster?

References

Wilson C.M., G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori & P. Delsing, 2011. Observation of the dynamical Casimir effect in a superconducting circuit.
Nature, 479, 376–379. Journal: https://www.nature.com/articles/nature10561 arxiv: https://arxiv.org/abs/1105.4714

Hu, J., L. Feng, Z. Zhang, C. Chin, 2019. Quantum Simulation of Coherent Hawking-Unruh Radiation. https://arxiv.org/abs/1807.07504

Monday, 13 May 2019

Halton Arp vs the Big Bang

I've just been reading through the late Halton Arp's book 'Seeing Red' and I have loved it. He was a rare astronomer who was able to look at data with fresh eyes, and think about it without trying to shoe-horn it into standard theories. As an introduction to what he concluded in his decades of observing, I can show you this plot of NGC3516Arp, which is one of many similar examples.


The figure shows a Seyfert galaxy (NGC3516) in the centre with various x-ray sources (quasars) surrounding it (measured by Y. Chu). The Seyfert galaxy has a low red shift. The quasars have high redshifts (see the numbers). Redshift? All atoms emit radiation when electrons in them change energy level. If you look at hydrogen in deep space you can see the radiation emitted is due to the known energy levels, as in a lab on Earth. If the photons are red-shifted though, it could mean that the object was moving away from us and the photon has been Doppler shifted into the red. So, it has been assumed by mainstream astronomers that the high redshift-ness of these sources means that they are moving away from us at a great speed. Hence there has arisen the Big Bang Model where the universe is still expanding from an initial explosion so further regions are receding from us faster. In astronomy redshift is used as a proxy for distance.

However, Arp pointed out repeatedly over decades that these high redshift galaxies are often near low redshift galaxies, sometimes being connected with tendrils to them. So, they may not be far off at all! Also, these high redshift objects usually appear along the minor axes of the normal galaxies, as in this case, as if they have been ejected along the spin axis. Further, quasars closer to their parent galaxy have a higher redshift, whereas those further way have a lower redshift. Finally, these redshifts are quantised into the values of: 2, 1.4, 0.95, 0.6, 0.3, 0.06..!

Arp's own judgement here was that a Steady State theory by Hoyle & Narlikar (1964) might explain some of these observations. This theory also has similarities to the theory of Dicke (who I have also been reading about lately in a book 'Einstein's Lost Key' by A. Unzicker). In Hoyle and Narlikar's theory the mass of objects depends on the surface area of the sphere that they could be aware of given the finite speed of light. New matter, then (produced from energy, and information in QI) can only be aware of a tiny region of space, since it has not had time to collect information from anywhere else, and so new matter has lower mass. Therefore, the new electrons have lower mass and so when they make the transition between atomic energy levels the photons given off have less energy than expected - their emissions are red-shifted. Therefore light coming off the quasars newly ejected from the galaxy, have high redshifts, and redshifts decline as they move away. This also means that high redshift should be common in the early universe so the redshifted objects we see far away are not necessarily moving away, and therefore there is no need for a big bang. Hoyle and Narlikar's theory can not explain the quantisation - but quantised inertia can.

Of course, Arp's observations enjoyed about the same popularity in astrophysics as Galileo did in his tour of the Vatican since, if they are true, the big bang theory & all of modern cosmology, with its distance measures, is reduced to a pile of expensive rubble. His accounts of the bizarre lengths the mainstream community went through to silence him are tragic but also hilarious (I would recommend the book for entertainment as well as for information).

Arp's observations are music to my ears because they sound like quantised inertia. Arp states that his observations demand a theory with the following characteristics. It requires inertial mass to increase with cosmic time (as predicted by Steady State theories and QI). It requires inertial mass to be quantised (quantised inertia!). It has matter being ejected from the spin axes of galaxies (as QI predicts). It is a Machian theory in which the mass of an object is determined by the amount of matter the object could have been in contact with in its history, which links to Hoyle and Narlikar and QI in which the mass of objects is determined by the size of the cosmos they perceive. Note that in this new approach the cosmic boundary is still there, but is not caused by objects moving away at the speed of light, but because we have not had time to collect data from behind this boundary.

It is my instinct that raw anomalous observations are the key to truth. Halton Arp, despite being dead, has just proven in my opinion to be hugely more incisive than modern 'theory-first' cosmology and I hope this will provide the inspiration to finally complete QI which may be a quantum-enabled cousin of a whole range of early classical theories by Hoyle, Dicke, Narlikar..etc that were blown up by the big bang freight train. I can email Narlikar too - he's still around.

References

F. Hoyle; J. V. Narlikar (1964). "A New Theory of Gravitation" (PDF). Proceedings of the Royal Society A. 282 (1389): 191–207. http://ayuba.fr/mach_effect/hoyle-narlikar1964.pdf

Unzicker, A., 2015. Einstein's Lost Key. https://www.amazon.co.uk/Einsteins-Lost-Key-Overlooked-Century/dp/1519473435

Sunday, 7 April 2019

Models, Experiments & Theory

So much has happened over the last few months and thanks to my newly-funded collaborators, research into QI is now running on three cylinders instead of one: it was just theory, now the work includes models and experiments as well. My post doc, Dr Jesus Lucio is working very well. I asked him to write a matlab script that simulates wide binaries with ordinary Newtonian physics, and MoND and QI. His script has produced a very nice animation (see below) that shows that when you model a real wide binary, only quantised inertia (red) predicts the stars to be bound together (as they are in reality). Newton and MoND (blue and green) predict wrongly that the two stars should zoom off to infinity, and so they are falsified. He has extended this tool to also simulate the Solar system. It compares the predictions with the observed orbital trajectories. We are having fun simulating Oumuamua at the moment.


The other project I asked him to do is to develop a numerical COMSOL simulation of the asymmetric Casimir effect that underpins quantised inertia (reference 1). The process by which when you accelerate something to the right, say, relativity and the speed of light limit, implies there is a region of space to your left that you can no longer see and a horizon forms that damps the intensified (Unruh) quantum vacuum on the left side of the object leading to a net quantum force that resists the object's acceleration: inertia. Unfortunately COMSOL is having a hard time modelling a particle at the tiny Planck scale (10^-35 metres wide) moving within a cosmos approximately 8.8x10^26 metres wide. So, our first crude plan is to use a particle the size of a galaxy cluster, and then slightly smaller, and we will use the difference to extrapolate down to the Planck scale.

The two experimental teams I employed as part of my funded project are also getting started building light-emdrives. The Dresden team are building resonators, but the Madrid team are already experimenting and have seen some thrust of the hoped-for kind, that is over six sigma outside the noise. However, it will be a long struggle to show it is definitely The Big One. They are now slowly eliminating mundane effects that could also be causing it.

As well as thinking about thrust, I am trying to generalise and further extend QI to explain gravity. After reading a book by A. Unzicker (ref 2), it seems that Einstein may have been on a more QI-compatible course until 1911 when he was redirected into bent space by his geometer friend Marcel Grossman. The variable speed of light version of general relativity (VSL-GR) that Einstein published in 1911 had a flaw at the time, but that flaw was corrected by Dicke (1957) (ref 3) and this version is far simpler and agrees with all the predictions of standard general relativity. This VSL-GR is far more satisfactory to me than normal GR since it relies on a process (slowing photons) that can be measured directly, as opposed to standard GR which relies in bent space, which is an abstract thing that you cannot measure directly, except by virtue of the moving objects it was designed to predict anyway. I have had some success in building a mathematical bridge between quantised inertia and VSL-GR. I am still trying to decide whether the piles I built the bridge on (the assumptions) are solid or not. The best way to do this is to jump up and down on them a lot. I'll let you know if there is a splash.

References

McCulloch, M.E., 2013. Inertia from an asymmetric Casiir effect. EPL, 101, 59001. https://arxiv.org/abs/1302.2775

Unzicker, A., 2015. Einstein's Lost Key. https://www.amazon.co.uk/Einsteins-Lost-Key-Overlooked-Century/dp/1519473435

Dicke, R., 1957. Gravitation without a principle of equivalence. Review of Modern Physics, 29, 363-376.


Saturday, 9 February 2019

Wide Binaries 3.0

The best way to do incisive science is to find an empirical case that can discriminate between hypotheses, in this case dark matter, MoND and QI.

Galaxy rotation is not ideal in that respect. To recap: galaxies spin far too fast at their edges to be stable. They should fly apart, but they appear to be gravitationally bound. So astro-physicists have proposed that there is invisible dark matter in them to hold them together. One of the properties of this dark matter has to be that it stays spread out, otherwise it would collapse to the centre of the galaxy and not predict the rotation correctly. The problem is that although QI can predict galaxy rotation, dark matter can be 'fudged' to predict it too, and even MoND is tweakable (a0).

Something un-fudge-able is needed and wide binaries are brilliant examples of unfudgeability. I have discussed them before. They are binary stars so far apart that their accelerations are as low as they are at the edges of galaxies. Hernandez et al. (2018) have shown in some brilliant papers, that wide binaries orbit each other far too fast, just as galaxies do. The data I have used here is from his latest paper which uses brand-new GAIA data. The data is shown by the crosses in the Figure below (prepared by my new post-doc Jesus Lucio). The x axis shows the separation of the stars in parsecs and the y axis shows their mutual speed in km/s. The grey area shows the uncertainty in the data, so it means that the orbital speed at each separation is somewhere in the grey area.
The dotted line shows the prediction of Newton or of general relativity (the same in this case). Just as in galaxies, although Newton/GR says the orbital speed should decrease with radius/separation (dotted line), the observed speeds stay much higher. Beyond a distance of 0.2 parsecs both Newton and general relativity are falsified. These theories disagree with the data and dark matter cannot be added to these wide binaries to save them, because to fit the larger galaxy it must stay diffuse. Unless they now come up with quantum dark matter that can be simultaneously spread out and clumpy!

The prediction of MoND is shown by the dashed line here with its fitting parameter set to a0 = 1.3x10^-10 m/s^2. It under-predicts the data at 1 parsec but if we set a0 = 2x10^-10 m/s^2 then it just about fits. However, the MoND prediction should probably be closer to the Newtonian/GR curve because it is subject to the External Field Effect (still under debate) which means that external accelerations bring it back towards Newtonian behaviour. These wide binaries are close to the Sun, and so accelerations due to the galaxy are still on the order of 8x10^-10 m/s^2. So, MoND is possibly also falsified by this data.

The prediction of quantised inertia is shown by the solid line, with the error shown by the two lighter solid lines above and below it. QI agrees with all the data (just). I submitted a paper on this to MNRAS a few weeks ago including a plot similar to this one, but in which QI did not quite agree. Well, a sincere thanks to my post-doc who recently spotted a factor of two error in my calculations which was making QI seem worse than it is, and he corrected it. So we will now resubmit with the new result.

In summary, QI predicts the orbits of these 83 pairs of wide binary stars better than other theories. Furthermore, QI does it without the need for any arbitrary fitting parameters (MoND needs one). QI needs just the observed mass, the observed speed of light and the observed cosmic scale. QI can only predict one outcome, and that turns out to agree with the data.

References

Hernandez, X., R.A.M. Cortes, C. Allen and R. Scarpa, 2018. Challenging a Newtonian prediction through Gaia wide binaries. https://arxiv.org/abs/1810.08696

McCulloch, M.E. and J.H. Lucio, 2019. Testing quantised inertia on wide binaries. Submitted to MNRAS.