I've suggested (& published in 21 journal papers) a new theory called quantised inertia (or MiHsC) that assumes that inertia is caused by horizons damping quantum fields. It predicts galaxy rotation & lab thrusts without any dark stuff or adjustment. My University webpage is here, I've written a book called Physics from the Edge and I'm on twitter as @memcculloch. Most of my content is at patreon now: here

Tuesday 28 March 2023

How QI gets rid of the Gravitational Constant, Big G

Inertia has never been understood, it has just been assumed that “Things keep going in a straight line, unless you push on them”, but why? Quantised inertia (QI) explains why.

This diagram shows an object (the black circle) accelerating to the left. Quantum mechanics states that all accelerated objects see a warm bath of thermal (random) radiation called Unruh radiation (orange) that has now been observed at CERN (Lynch et al., 2021). Relativity states that information from the far right will never catch up to the object since it is limited to the speed of light (c) (the black area to the right). The new assumption of quantised inertia (QI) is that the object & horizon (edge of the black) damp the Unruh radiation between them, as in the Casimir effect (the blue area) so more radiation pushes the object from the left than the right – this model predicts inertia (McCulloch, 2013).

QI also explains galaxy rotation without dark matter, since at a galaxy’s edge the accelerations are tiny so the waves of Unruh radiation get too long to fit inside the observable cosmos (size=Θ), so they cannot exist (Mach: what you cannot ever perceive you should assume does not exist). There is no doubt that it is QI & not dark matter that explains galaxy rotation since the galaxy rotation problems starts at the exact radius where the Unruh waves get as long as the cosmos (McCulloch, 2017). This also predicts a minimum acceleration for nature of 2c^2/Θ.

This is how QI gets rid of the need for the gravitational constant G. The lower the acceleration, the longer the Unruh waves. Physics must act to make sure that the length of the Unruh waves is less than the cosmic diameter, so in any volume there must be at least enough gravity to keep the acceleration above the minimum acceleration, so

GM/r^2 >(2c^2)/Θ

Since Θ=2r and we’ll assume it is on the threshold, then

G=(c^2 Θ)/2M

This relation has long been known to work (try putting numbers in). Now quantised inertia explains it. Since we know the speed of light, c, the cosmic size Θ (to 10%) and the cosmic mass, to within a factor of 10, from counting galaxies, we can calculate G and replace G in all the equations with the right hand side above. This new physics also predicts that G varies in time, as Θ increases. So, next time someone mentions the gravitational constant, tell them it isn't, and furthermore that it is not needed at all!


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

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

Lynch, M.H., et al, 2021. Experimental observations of acceleration-induced thermality. Phys. Rev. D., 104, 025015. Link


Alexandre said...

Hi Mike,

Does QI need to consider a retarded (forward in time) and an advanced (backward in time) waves that form a kind of quantum interaction as a Wheeler–Feynman handshake or transaction to justify the instantaneous feeling by an accelerating object, of the existence of a Rindler horizon occurring far from it ?

Mike McCulloch said...

Yes, because the Rindler horizon only exists in the future of the accelerating object. I have an, IMO, more elegant version of the Wheeler-Feynman-Cramer mechanism. I assume that time dilates for quantum objects. See my paper with Gine: https://www.worldscientific.com/doi/10.1142/S021798492150072X

Alexandre said...


Did you have the opportunity to discuss with the science philosopher Ruth Kasner of this mechanism. I know she has published on Transactional Interpretation and Relativity.

Mike McCulloch said...

I sent her my paper to comment on it, but she politely declined as being too busy. I did swap a few emails with John Cramer who first proposed the TIQM.

Alexandre said...

Oh, sad !

Gregory said...

I have no idea if your theories are correct or not, but it is a shame they are not being investigated more seriously by the scientific community.

Alexandre said...

In your article you well cite the paper of A. Aspect, P. Grangier, G. Roger of 1982 on the experience rewarded by the Nobel Prize of Alain Aspect in 2022.
Philippe Grangier, who carried out most of the measurements concerning the fine verifications of Bell's inequalities in this experience, is still very interested in the philosophical interpretation of quantum mechanics. He has recently put forward proposals to integrate the context of measurement into the quantum mechanical description of reality. You can find his latest work on this topic on arxiv. The question of whether these proposals can lead to testable predictions is still open.
Even before John Bell's work on his so-called inequalities in the sixties, a mathematical version of these inequalities (about convexity in Banach spaces) was given in the fifties by the mathematician Alexander Grothendieck in his first works on functional analysis.
I am sure that Grothendieck would have been interested in your work. Grothendieck was an ardent supporter of homeopathy and thought that the rejection of its evidence by official circles was only a waste of time for true science.

Alexandre said...

Your article also refers to two very interesting papers by Alexey V. Melkikh. Alexey V. I see that this author has also published a work in 2015 with the title: "Nonlinearity of Quantum Mechanics and Solution of the Problem of Wave Function Collapse". Where the non-linearity is analysed as coming from quantum fields consideration with virtual particles creation and destruction.
I also see that Melkikh has published articles on quantum biophysics. This makes me think of Giuliano Preparata's work on condensed matter and in particular on the structuring of water into coherent micro-domains through its interaction with the vacuum quantum fields.

All this opens the mind for stimulating thinking!

Philosopher Rex said...

Great post Dr. McCulloch. Thank you.

Dan's Test Blog said...

With G being fairly accurately known, doesn’t this equation supposedly give you the Hubble constant? So, what’s the prediction for it, with error bars?

Name2751 said...

I am unable to understand how the issues with this hypothesis go unaddressed.

First, asymmetric absorption of Unruh radiation by an object being responsible for inertia isn’t viable just based on how radiation works. Radiation pressure is a pressure, i.e., a force per unit area. If I have a solid steel sphere and a hollow steel balloon, both of which I created from the same amount of raw material (so the balloon has a much larger surface area despite being the same amount of stuff) then the balloon would have to have a much greater mass. A greater amount of the radiation emitted from the warm Unruh bath that supposedly lies in front of the accelerating balloon would be intercepted than the solid steel sphere when both are accelerating at the same rate. In both instances the radiation pressure is identical, given that the radiation pressure is a function of Unruh temperature, and the Unruh temperature is a function of acceleration. Since F = (P)(A), we would see the mass of objects being a function of their surface area, which is clearly not the case. Aluminum foil doesn’t weigh more than the block of Aluminum it was made from.

Secondly, Unruh radiation is an Electromagnetic (EM) radiation (both classically and quantum). It’s interaction with materials is mediated by the material’s optical properties (absorbance, transmittance and reflectance) at the given frequency spectrum of the Unruh radiation. Therefore, materials with different optical properties would have to behave completely differently. If a material had perfect transmittance, it would have to be massless. If it had perfect absorbance, it would have some mass, and if it had perfect reflectance, it would have twice the mass of the absorbance case. The mass of an object would have to be a function of the optical properties of a material at the given spectrum of Unruh radiation arising from that object’s acceleration. This would be obvious if it were true, since materials that are highly transparent to infrared light (the spectrum of light produced by any reasonable acceleration) should be essentially massless. What’s more, the absorption of EM radiation doesn’t just impart momentum, but energy as well. If an objects mass were the result of asymmetric radiation absorption, you would see objects heating up as they accelerate, the same way a solar sail is heated by the suns rays at the same time as it is propelled by them. No evidence of this.

The first two points boil down to this: MiHsC requires that the inertial properties of a material are dependent on the optical properties and surface area of that material, not the density or volume. Clearly, the mass of an object is a function of volume, not surface area, and the optical properties of a material have no correlation to mass.

Additionally, at the core of MiHsC is this idea that somehow a horizon can be treated as being the same as the parallel conductive plates from the derivation of the Casimir effect. The parallel conductive plates demand EM fields at their surface be zero, but a horizon doesn’t have any such requirement. Neutrally charged black holes will have a non-zero gravitational field at their event horizon. Charged black holes will have a non-zero gravitational field and electric field at their event horizon. The “stuff” behind a horizon doesn’t cease to exist, it just exists in a form beyond the capacity of current theory to explain or experiment to measure; the field effects of the stuff behind the horizon crosses the horizon without issue. If they didn’t, then how do black holes gravitate? A horizon doesn’t have any of the same properties of the parallel plates from the Casimir effect, and so can’t be expected to create a similar result.

Interested in hearing why these three issues seemingly go unaddressed.

Mike McCulloch said...

Name2751. Here's the short answer to your three points.

1. The Unruh radiation in QI is assumed to interact with objects at the level of the Planck mass, so whether it is a dense ball or a distributed sphere makes no difference.

2. Unruh radiation is not entirely EM, it is a wave in all the fields, but, true, the part I deal with is. However, it does not depend on the reflective properties of the material that we know about because the wavelength is way outside our areas of experience. It is not IR light as in your example, it is a wave typically light years long.

3. A horizon does have a requirement that fields be zero, not for the same reason as a metal plate, mobile electrons, but for a more philosophical reason. A wave cannot be allowed to go partially thru because that would give us information about the other side & so it would not be a horizon.

Also, detailed arguments using black holes mean nothing, as they have not been observed, except in analogs. Unruh radiation has now been observed at CERN (Lynch et al., 2021).

SkyLoop said...


It is not common for you to expand on Unruh wave behavior, and maybe you should. It sure is welcome. Clearly, it is not understood. Reflecting more on this is necessary.

George Soli said...

Hi Mike: You are reference [48] in Lynch's paper "Experimental observation of a moving mirror"
November 2022, DOI: 10.48550/arXiv.2211.14774

"Modelling the Pioneer anomaly as modified inertia" from 2007.

My poster paper is posted at the American Physical Society, APS April 2023 virtual meeting, and now I get to post a 5 minute video. Aikyon theory has QI as a new fundamental force of nature, dubbed U(1)-gravity. The usual 4 forces, that includes normal SU(2)-gravity, plus the new QI U(1)-gravity and SU(3)-gravity, for a total of six fundamental forces. The U(1)-QI-gravity in the space-drives interact with the up-quark, but see the down quark as a singlet state. Guess we'll need to get some Giger-counters? George

phildelltablet said...

Hi Mike,

It would be nice if you add some numbers for a worked example.

Not that it is difficult, but depending on where someone is coming from (time or education) they might not know where to start.

Neat example though!


phildelltablet said...

Hi Mike,

I had a chance to sleep in it. I agree with what Dan says, if you have constants in c and 2M, changes in Θ directly states that in the past, G was less.

Say 1/2 Θ of today's size, what would be the size of stars limited by their G in the past?

Since we have evidence the universe is expanding, surely the conditions of life might require certain time to expand the thermodynamic state to sample "life giving structures". (life trades energy for entropy - your organism shape...).

In summary, if G was less in the past, that should be directly observable.


Unknown said...

I've seen claims that this can explain a lot of the 'just after the big bang' conditions that just don't make sense if G has always been constant.

phildelltablet said...

An alternative interpretation is that G is constant and the mass(2M) increases with time. Easier to accept, with respect to my previous comment (can't have star sizes changing...).

Since there is evidence the universe is expanding, do the vacuum fluctuations in new space represent new mass - "unpublished" as it were?

It might be that star formation *is* the mechanism for mass generation, especially when one considers the asymmetry of anti-particles.


Simon Derricutt said...

Mike - maybe an interesting point on the large-scale clustering/structures of multiple galaxies. If the acceleration asymptotes to around 2e-10 m/s², if some object is at a very large distance from two gravitation sources, looks like the acceleration will be either towards one or the other with no point at which the acceleration is zero. This absence of a zero acceleration would (I think) tend to produce agglomerations of galaxies rather than a random structure.

Your reference would need to be the universe as a whole rather than a reference mass, which would of course also have that same minimum acceleration.

dhuber said...

Greetings, Dr. McCulloch.

Could QI aid in resolving the "Hubble Tension"? Perhaps the smaller distance to the cosmic horizon in earlier epochs would yield differences in inertial mass and galactic rotation velocities?

Is it possible to chart changes in QI every billion years since the Big Bang event?