The core of MiHsC / quantised inertia / horizon mechanics*, is the idea that the property known for centuries as inertia is caused by an asymmetry in Unruh radiation (an asymmetric Casimir effect). I have already discussed the evidence for Unruh radiation itself here (Fulling-Davies-Unruh radiation), and how quantised inertia (introduced here) predicts galaxy rotation exactly, and cosmic acceleration, without any dark stuff, but many people have asked how can a process based on the zero point field, so weak in the Casimir effect, could have such a large effect on matter that it produces inertia. How can it be?

Well, it can be. This can be shown with simple maths and the schematic below. The black circle is a Planck mass. Let us say that for some reason it is accelerating to the left (purple arrow), so a combination of quantum mechanics and relativity says that it sees a warm bath of Unruh radiation (orange colour). Relativity then says that information from far to the right (from the black zone) is limited to the speed of light and so cannot reach the mass, so this is its 'unknowable space'. A Rindler horizon forms to separate that space from the known space. Now as far as the mass is concerned, there is no space beyond the horizon and waves need space to wiggle in. So this horizon damps the Unruh waves on the right, creating a colder Unruh bath there (blue area). The gradient in the Unruh radiation means that more thermal energy bangs into the Planck mass from the left than from the right and so it is pushed back against its initial acceleration. Another way to think about this is that energy is now extractable from the difference in (virtual) heat.

Maths helps us to be specific. The wavelength (L) of the Unruh radiation seen by a mass of acceleration 'a' is

L = 8c^2/a

The c is the speed of light, a huge number, so that the c^2 in the numerator makes the Unruh wavelength usually very long. A sperm whale falling in Earth's gravity would see Unruh waves a lightyear long, but probably wouldn't last long enough (a year) to measure one passing by. The energy in the Unruh field on the left is then

E1 = hc/L = hca/8c^2 = ha/8c

The energy in the Unruh field on the right is

E2=0

Using normal physics, the force on the mass is the energy gradient from left to right across the diameter of the mass

F = dE/dx = ((E1-E2)/d = ((ha/8c)-(0))/d

F = ha/8cd

This looks suspiciously like Newton's second law: F=ma, and suggests that m=h/8cd

For a Planck mass d is the Planck length so the predicted mass is m=1.7x10^-8 kg. The accepted Planck mass is 2.2x10^-8 kg. In other words, at least in this case of the Planck mass, the Unruh effect is strong enough to produce inertia. It predicts the accepted numbers quite well even in this simple analysis which leaves out a lot of detail. As I said in my 2013 paper on this (see below): to make this process work for larger particles, you can't just put in a larger diameter d. You have to add up the effect of each Planck mass.

References

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

*EPL*, 101, 59001. Preprint

--

Horizon mechanics* = A new name suggested to me by J.M. Dorman.

## 18 comments:

From what I understand, this does not work for big object.

however my intuition is that it is absurd to consider big object. they are made from small one who each interact with fields...

afterward they interact between each other...

question is that when a particle pair appear, both particle have inertia, suffer gravity...

before they were just... ok they were energy...

so mass is energy... I've heard that somewhere.

take a big fat proton...

I imagine that your equation does not work like daily inertia because d is too big...

however we should not forget there is only quarks, gluons, which are the mass, and are tiny... are they plank scale ?

same for whale...

how many plank scale objects are needed for one electron ? one proton ? one atom of hydrogen ? one gram of matter ? to have the usual inertia ...

is the number absurd, or absurdly promoting existence of many plank-scale objects.

I am unable to raise more than kid's questions...

Do any interesting consequences arise if you plug in the masses and radii of black holes of various scales, rather than Planck masses and lengths?

The energy of the Unruh radiation you've used is just a single photon. That doesn't seem quite right...

Just for the LOL.

https://www.sciencenews.org/article/dark-matter-still-missing

New Data released from Xenon100 Dark Matter Detector:

https://arxiv.org/abs/1701.00769

/Begin Rant

How long will it be until we finally come to terms with the idea that our relentless search for Dark Matter is going to come up just as empty and Michelson and Morley's Famous experiment looking for non-existent Ether.

In my opinion the evidence is increasingly showing that the entire idea of using Dark Matter to account for the missing mass problem is a giant fudge factor that is glossing over our incomplete and incorrect understanding of Gravity/Inertia, ESPECIALLY as it relates to ultra low acceleration environments (< 10x10^-10 m/s^2) at which scales General Relativity has NEVER been empirically tested (everything in our known solar system is experiencing a much higher acceleration than that) and in fact the only evidence we have from such low acceleration environments (towards the edges of spiral galaxies) points to a totally different observational behavior than we would predict and yet instead of trying to figure out what causes this difference we invent "Dark Matter" to be magically placed at just the right spots to account for the difference and then turn off our brains to the possibility that the equations we are using might not be complete in the same way that Newtonian Dynamics eventually got superseded and corrected by Special Relativity on certain scales.

At this point I would be willing to accept pretty much any wager on the idea that using Dark Matter to explain the missing mass problem will eventually seem every bit as discredited as Epicycles, Phlogiston, and the idea that EM radiation needs to travel through Ether as a medium. I'd LOVE to be proven wrong with a groundbreaking discovery of even a potential Dark Matter Candidate Particle (WIMP, Axion, or other) by LUX, Xenon100, or LHC but I wouldn't hold my breath and I suspect the Dark Matter Theorists will continue moving the goalposts on how small the interactive nucleon cross section could be before giving up entirely and declaring that it must be a magic unknown untestable particle with zero interaction of any type except for the exact amount of gravitational influence to correct the current Incomplete Einstein Field Equations!.

/RANT OVER

Keep up the great work Mike, your papers are great and so is your book though it is a shame it costs so much that nobody is reading it, information like that should be free to everyone! Sooner or later the tide will have to turn and people will start to accept the idea that the data shows the exact behavior your equations predict for low acceleration environments without any tuning variables. Unfortunately, if history is any guide they will ignore that you were screaming about it for years and someone else is going to steal all the credit but at least we'll be headed down the right path again in Physics instead of spinning our wheels for the past 40 years on a failed understanding of gravity/inertia! I do have one quick question for you, can you think of ANY explanations other than Unruh radiation that might still yeild the exact same equations and predictions or are you pretty settled on that exact physical mechanism?

What I can see positive on MiHsC theory is, it converges to explanation of mass and gravity with deDuillier-LeSage effect, i.e. with shielding of longitudinal waves of vacuum with massive objects. But these waves are extradimensional and superluminal by their very nature - they cannot have nothing to do with Unruh radiation, which is just form of light.

The main problem of dual model of MiHsC is, the projection of Unruh radiation from distant Rindler horizon would always take some time, so that the sufficiently temporary objects (like the resonances of particle physics) shouldn't exhibit any inertia and very fast changes of location should be also followed with temporal lost of inertia.

The explanation of inertia with radiation pressure of Unruh waves is sorta recursive by itself, as it depends on inertia of Unruh waves. And how large/distant the Rindler horizon is in comparison to cosmic horizon? The Unruh radiation propagates with speed of light, so that no inertia induced by its shielding can be a momentary effect. In relativity the Unruh radiation is essentially black body radiation: it's neither monochromatic, neither superluminal.

I even exactly understand, from where this misunderstanding comes from in an effort to quantify the vacuum ZPE field effects. IMO the actual contribution in MiHSC theory is in 1st order approximation of quantum effects, which modulate relativity at low energy density scales due to ZPE fluctuations. The energy density of these fluctuations can be estimated from cosmological observations, as they also result into red shift and scattering of light. MOND theory therefore considers its acceleration to product of Hubble constant and speed of light, whereas MiHSC utilizes diameter of observable Universe, which is also determined with this scattering (acceleration of the microwaves of 1018 m/s2 (~c2/L).

But the correlation doesn't imply causation: the fact, that the period of solar eclipses can be calculated from epicycle model and the results even fit the reality well still doesn't imply, that the Sun is revolving the Earth in epicycles. No matter how well the formal model works in some circumstances - Galielo could talk about it.

Errata: "they cannot have nothing to do" = "they have nothing to do" or "they cannot have something to do"...

I may be asking a stupid question but how do shielding work with Unruh radiation?

As inertia is experienced by all mass, there should not be any mass transparent to it.

Yet intertia properties close to a large shield (say the earth) doesn't seem affected by it even though half the horizon would be blacked-out.

Similarly, only the surface of matter should be affected by unruh radiation, but inertia affects objects in bulk.

For EMDrive effect though, it appears a thin sheet of copper is sufficient for shielding.

Gabriel Good question, easy to answer: The wavelength of Unruh waves is L=8c^2/a, where a is the acceleration. Objects on the Earth have accelerations of 9.8 m/s^2, so the Unruh waves they see are light years long and can't resolve the Earth. On the other hand photons in the emdrive have huge accelerations and their Unruh waves are similar in size to the cavity, so they do feel the cavity.

The above picture brings the resemblance to wake waves after moving objects at the surface of pond. The similar model is applied to so-called pilot wave model of deBroglie theory. This pilot wave is also the primary source of inertia of moving objects - by its deform of 4D space-time it exposes the extradimensional vacuum fluctuation, which are source of mass (Higgs field). This explanation is local and it doesn't require any distant horizons to work - the only problem is, how to quantify it.

And this is just the moment, where formal models of Mr. McCulloch or Milgrom enter the scene: we must somehow quantify the effects of vacuum fluctuations. In dense aether model these fluctuations are also source of the Hubble red shift and cosmologic parameters, which are observable easily, because they apply to large scales. McCulloch is utilizing diameter of observable Universe, Milgrom the Hubble constant. But this constant has a tendency to change with distance, so that the diameter of observable Universe (in comoving coordinates) is somewhat more precise, being an integral effect.

Actually, every physics theory ever formulated seem to violate at least one of these: relativity, causality symmetry (however: this may be artifact of human language, trying to describe them)

MISHC seems to me to be from the family of theories, which violate causality (is acceleration reason for horizon, or vice-versa?). Sci-fi author Charles Stross specificaly warns us, that Eschaton would harshly fight those trying to violate causality :-)

The consequences for causality are many, even the existence of Rindler horizons needs an extrapolation of the present dynamics into the future. I am arguing elsewhere (paper submitted) that causality is broken anyway for quantum systems, as is (probably) shown by the EPR-Bell test experiments).

You can remove the causality fear by reconsidering what is the theory.

People imagin things happens as theory says, no... the outcome is what theory says.

for EPR paradox for example, you know the outcome only when you gather the two results from the two branches, never before...

you can pretend that there was an answer on each branch, but you could only compare them later, respecting speed of light....

causality is a final result, the practical result.

MiHsC says something coherent, that things don't exist if you cannot see them yet/anymore.

You cannot argue on something you don't have in the hand.

You cannot argue that information on one branch reached the other branch, unless you have both measurement in your hand.

all that seems caused by equations, by convergence to eigenvalue where time is just a dimension.

In you hand both branch results converged to the "same" value, but did they have value until that moment?

you cannot say, so NO.

Dear Mike,

I had an idea for a slight variation of your seminal MiHsC theory. It occurred to me that a quantum version of gravity, entailing the existence of spin-2 gravitons, might substitute for Unruh waves in your theory. Appealing to quantum physics perhaps there is a phase transition, in a yet to be developed quantum version of gravity, where a particular graviton wavelength correlates to an acceleration regime corresponding to the Hubble Constant and Milgrom’s acceleration threshold (1.2 x 10^-10 m/s^2).

In the quantum view of gravity the g-field is mediated by a continuous flux of virtual gravitons. The question is, why should virtual gravitons distinguish between inertial and gravitational acceleration? If they don’t, could this then be the basis for the Equivalence Principle, and thus, by default, the origin of inertia for physical masses? So from this perspective, there’s a potential linkage between inertia, acceleration, and gravitons.

According to the response at physics.stackexchange.com, (below), the wavelength of real gravitons emitted by a body, is related to the acceleration that body is subject to. In the example given, an apple subject to 9.8 m/s^2, (Earth’s surface gravity), emits real gravitons of 90 light minutes wavelength, or 1.62 x 10^12 meters. The energy associated with such, (infrequent), real graviton emission is vanishingly small, so obviously not connected to the property of inertia, but perhaps this doesn’t necessarily rule out virtual gravitons in that role.

Now, assuming the wavelengths of virtual gravitons, for a given acceleration, are the same as for real gravitons, in the example above, we can calculate the virtual graviton wavelength associated with Milgrom’s acceleration threshold of 1.2 x 10^-10 m/s^2. As with photons, the energy of a graviton is inversely proportional to its wavelength. From this relation, and the above considerations, the graviton wavelength associated with Milgrom’s threshold comes out to 1.32 x 10^23 meters. This is about 1/2000 of the Hubble Diameter (2.7 x 10^26 m.).

What’s interesting about that ratio, is that it is quite comparable to the ratio between the de Broglie wavelength of super-cooled rubidium atoms, and the condensate’s physical diameter, in the first atomic BEC ever achieved in 1995. The Cornell/Wieman group’s rubidium BEC was about 0.1 mm across (1.0 x 10^-4 m.), while the deBroglie wavelength of the rubidium atoms at 3 micro-Kelvin was 2 x 10^-7 meter. That yields a ratio of 1/500, or within a magnitude of the ratio between the graviton wavelength associated with Milgrom’s threshold (per the assumptions), and the diameter of the visible Universe.

The analogy between a laboratory BEC composed of Bosonic atoms/molecules, and a cosmic-scale BEC composed of a Bosonic ‘gas’ of long wavelength/low energy gravitons is intriguing. As ponderable matter in the outskirts of galaxies descends to an acceleration, for which its intrinsic graviton wavelength matches the cosmic graviton wavelength, perhaps it might undergo a phase transition where its effective inertial mass begins to decrease, thus allowing such matter to remain gravitationally bound to the galaxy.

The big problem with this idea, as it relates to inertia in particular, is the requirement for instantaneous backreaction from long wavelength gravitons spanning interstellar distances, thus violating the universal velocity limit of C. However, if such graviton waves naturally occur in both retarded and advanced versions, as electromagnetic waves do in John Cramer’s Transactional Hypothesis, then that could account for such instantaneous action.

http://physics.stackexchange.com/questions/10582/the-energy-of-a-graviton

Dear David,

It is worth consideration, but the agreements you have are quite far from the mark (2000x out) and you need a couple of assumptions: gravitons and an analogy to BECs). I'm trying to come at gravity from the other direction: using Unruh radiation only. This is a simpler approach and involves something that has probably now been seen (Unruh radn) and which fits the acceleration a0 exactly. In my view gravity is caused by a sheltering of Unruh radiation by protons...etc, and this can also be thought of in more informational-horizon terms (see my latest paper in EPL, 115, 69001).

I like your final comments re Cramer.. though again I think there is a simpler way to do it (I've submitted a paper on that too!).

Mike

Mike, I've got to agree with what you're saying, and the graviton is hypothetical, with some physicists doubting their existence entirely. I very much like the relativity aspect of MiHsC, in which relative motions can affect inertia, if I'm interpreting it correctly. I did read your link about the experiment that appears to have detected Unruh radiation, which is extremely exciting. I'll definitely check out your latest paper. I guess EPL stands for European Physics Letters.

David: EuroPhysics Letters. Yes, MiHsC is a return to the type of thinking that led to relativity and QMechs, ie: consider only what you can see in principle.

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