# Quantised Inertia

• B
Gold Member
Dearly Missed
I do not know if this has been discussed before, but it is one solution to Dark Matter, Can inertia even be quatised?

arXiv:1709.04918 [pdf, other]
Galaxy rotations from quantised inertia and visible matter only
M.E. McCulloch
Comments: 9 pages, 2 figures. Published in Astrophys Space Sci
Journal-ref: McCulloch, M.E. Astrophys Space Sci (2017) 362: 149
Subjects: Astrophysics of Galaxies (astro-ph.GA)

It is shown here that a model for inertial mass, called quantised inertia, or MiHsC (Modified inertia by a Hubble-scale Casimir effect) predicts the rotational acceleration of the 153 good quality galaxies in the SPARC dataset (2016 AJ 152 157), with a large range of scales and mass, from just their visible baryonic matter, the speed of light and the co-moving diameter of the observable universe. No dark matter is needed. The performance of quantised inertia is comparable to that of MoND, yet it needs no adjustable parameter. As a further critical test, quantised inertia uniquely predicts a specific increase in the galaxy rotation anomaly at higher redshifts. This test is now becoming possible and new data shows that galaxy rotational accelerations do increase with redshift in the predicted manner, at least up to Z=2.2.

Mike McCulloch

kimbyd
Gold Member
To me, this kind of thing isn't worth paying attention to unless they can actually match galaxy cluster data using the same model they're using with galaxy rotation curves. The word "cluster" doesn't appear in their paper.

Explaining galaxy cluster behavior has long been a sticky point with MOND-style theories.

And then they'd also have to explain the CMB data.

Mike McCulloch
Jorrie
Gold Member
Quantised inertia does predict galaxy clusters, unlike MoND. See: https://arxiv.org/abs/1207.7007
I'm not sure if you want to discuss your papers here, but I have a number of questions.

1. Inertia shows up when we have a proper acceleration. But the edges of galaxies move on geodesics, so presumably there is no proper acceleration there, as I understand it. So are you using coordinate acceleration?
2. You seem to sometimes refer to the Hubble radius and sometimes to the radius of the observable universe, which is usually understood to be the particle horizon. And then we also have what is called the cosmological horizon, at yet another radius in our present models. Can you please clarify.

Mike McCulloch
1) It is best to think of it without GR for now, so this is just the acceleration a=v^2/r, what you might call the co-ordinate acceleration. This should be ideally the mutual acceleration between the star and other visible matter (since only that is measurable).
2) I use the co-moving diameter of the Hubble volume, 8.8x10^26m. This is then the particle horizon.

Jorrie
Gold Member
2) I use the co-moving diameter of the Hubble volume, 8.8x10^26m. This is then the particle horizon.
In cosmology we have different different definitions for the Hubble radius and the particle horizon (observable universe), but I suppose if we talk order of magnitude, they are numerically about the same. What you have given is the observable diameter. The Hubble diameter is about 2.7x10^26m, which defines the present cosmic event horizon.

Correct me if I’m wrong, but my understanding of this is a new model for inertia using Unruh radiation:

In this way quantised inertia explains galaxy rotation without the need for dark matter (McCulloch, 2012, 2017) because it reduces the inertial mass of outlying stars and allows them to be bound even by the gravity from visible matter. It also explains the recently observed cosmic acceleration (McCulloch, 2010) and the experimental tests on the emdrive (McCulloch, 2015).

My question is this: If Unruh radiation is dynamically equivalent to Hawking radiation, is its effect significant enough to affect the inertial mass of gravitationally bound objects?

PeterDonis
Mentor

What makes you think it is? Can you give a reference?

What makes you think it is? Can you give a reference?
From the OP paper:

Fulling (1973), Davies (1975) and Unruh (1976) proposed that when an object accelerates it perceives Unruh radiation, a dynamical equivalent of Hawking radiation (Hawking, 1974), and Unruh radiation may now have been seen in experiments (Smolyaninov, 2008).

PeterDonis
Mentor
From the OP paper

Hm, ok. "Dynamic equivalent of Hawking radiation" might be misleading. Unruh radiation doesn't cause anything to lose mass the way Hawking radiation causes a black hole to lose mass. There is an analogy between the two, but it doesn't go that far.

As for the overall proposal of the paper, Unruh radiation is so weak at ordinary accelerations that I'm not sure how they get it to predict "standard inertia", as the paper claims. That claim is referenced to another paper, which I'll have to take a look at when I get a chance.

stoomart
Bandersnatch
The Hubble diameter is about 2.7x10^26m, which defines the present cosmic event horizon.
This is tangential to the subject matter, but isn't the present-epoch event horizon farther than the Hubble radius? Shouldn't they coincide with one another only in de Sitter universes?

Jorrie
Gold Member
This is tangential to the subject matter, but isn't the present-epoch event horizon farther than the Hubble radius? Shouldn't they coincide with one another only in de Sitter universes?
The terms during the pre-de Sitter epoch are a tad confusing. The Hubble radius is the present proper distance where the recession rate equals 'c', so no particle emitted there now can ever reach us, because it will forever be taken away from us.

The cosmic event horizon is the farthest (present) proper distance that a particle emitted by us now can ever reach, because again, the particle is forever taken away from us by the expansion (as I understand things).

Mike McCulloch referred to the Hubble diameter in his paper https://arxiv.org/abs/1302.2775 (just below equation (1)), not the latter.

Bandersnatch
The terms during the pre-de Sitter epoch are a tad confusing. The Hubble radius is the present proper distance where the recession rate equals 'c', so no particle emitted there now can ever reach us, because it will forever be taken away from us.

The cosmic event horizon is the farthest (present) proper distance that a particle emitted by us now can ever reach, because again, the particle is forever taken away from us by the expansion (as I understand things).
I don't think you have it right. It could never reach us only if we were living in a de Sitter universe. Since we aren't, and the Hubble radius is increasing, a particle emitted at the H_r now, will tomorrow find itself within the radius and start making its approach - which means it can be observed, and that by definition it was within the event horizon at emission.
Even your own calculator gives different values for the H_r and the horizon.

Whether we're talking about a signal emitted by us or received by us doesn't matter, since the situation is symmetrical.

Jorrie
Gold Member
Even your own calculator gives different values for the H_r and the horizon.
But I don't think what I wrote contradicts that. The Hubble radius increased faster then one lyr/yr ("c") only when the metric expansion was decelerating. If our models and data are correct, it is today 14.4 Glyr away and increasing at a rate somewhat below "c", so it does not catch up with photons released beyond that, where proper distances increase at greater than "c".

However, a photon that we send today can reach a galaxy that is presently ~16.5 Glyr from us - our communication horizon. I think what McCulloch referred to is the effect of the Unruh radiation from the Hubble horizon on us. IMO, the symmetry that you mentioned only means that an observer presently at our Hubble radius will find the same values than what we do, but that's a different 'perspective', so to speak.

Bandersnatch
(once again, I have nothing to say about the papers in the OP, so if you think this is clogging the discussion we can take it to the conversation feature)

If our models and data are correct, it is today 14.4 Glyr away and increasing at a rate somewhat below "c", so it does not catch up with photons released beyond that, where proper distances increase at greater than "c".
But it doesn't have to increase at rate higher than c to catch up with these photons, because they are not comoving with the Hubble flow.
The net velocity of a photon emitted at H_r (towards the observer) is 0 (recession velocity + photon velocity), so H_r needs only grow at any rate higher than 0 to be able to catch up with and overtake photons released at itself.
The rate of growth of H_r determines how far beyond it a photon can be emitted and still be caught up with, i.e. the distance to the event horizon, which is why the difference between these two distances diminishes as we approach de Sitter expansion.

This should be visible on the third (conformal time) light cone graph in Davis' paper - it shows that the event horizon is just the past light cone of an observer at infinite future, and that it encompasses events currently beyond H_r.

I don't think there's any kind of a different perspective here. After all, if you look at your second paragraph above, it suggests that a galaxy beyond H_r can receive our signals - but your first paragraph contradicts that, since it suggests those photons are already beyond H_r, and will never be caught up with by the growing Hubble radius.

I believe @bapowell wrote about this in his Insight on cosmological horizons. Maybe he can back me up (or set me straight).

kimbyd
Gold Member
Quantised inertia does predict galaxy clusters, unlike MoND. See: https://arxiv.org/abs/1207.7007
That's a step. But seems to me to be far too superficial to be of all that much value. It only barely examines the data, and does so using only very simple formulas. I'm particularly worried that the model doesn't match dwarf galaxies (dwarf galaxies tend to be particularly rich in dark matter, making them good testing grounds for any alternative DM theory).

But the main thing that worries me is that nearly all of the citations on this paper are from the paper's author. This strongly indicates somebody who hasn't managed to catch the interest of the broader cosmology community, which makes demonstrating correctness basically impossible. It takes lots and lots of work to do the detailed calculations necessary to match rich data like the CMB or the Bullet Cluster. That's just not happening as long as there's only one person involved. And the current lack of interest indicates that it's very likely that others have found his papers very flawed. I don't have the expertise to dig in and find the flaws myself (I'm not experienced with galaxy dynamics). But the lack of interest seems to indicate that there are very significant flaws.

Bandersnatch
Jorrie
Gold Member
This should be visible on the third (conformal time) light cone graph in Davis' paper - it shows that the event horizon is just the past light cone of an observer at infinite future, and that it encompasses events currently beyond H_r.
Yes, you are right! The Hubble radius is not an event horizon. Sorry for the confusion.
A photon emitted precisely at Hr "hangs there" for a period and then Hr increases beyond its coordinate, so it starts to make headway toward us. So I guess that the horizon McCulloch should use for the (hypothetical?) Unruh radiation is the cosmic horizon at 16.5 Glyr.

Last edited:
Greg Bernhardt
MiHsC assumes that the inertial mass of an object is caused by Unruh radiation resulting from its acceleration with respect to surrounding matter, and that this radiation is subject to a Hubble-scale Casimir effect. This means that only Unruh waves that fit exactly into twice the Hubble diameter are allowed, so that an increasingly greater proportion of the Unruh waves are disallowed as accelerations decrease and these waves get longer, leading to a new gradual loss of inertia as acceleration reduces.

This would have to improve a lot to be considered wrong. Unruh radiation pertains to local observables, and can be derived making reference only to local quantities. A horizon, even if we had cause to suspect it might impose boundary conditions on radiation (we don't, and in fact it makes very little sense to even pose the question), is a nonlocal thing by its very nature. For Unruh radiation to be affected by the structure of the causal horizon in the manner desired by this author, information would have to travel faster than light. Big no-no.

Another aspect of the same coin is that the Rindler horizon only exists for observers that perpetually accelerate. Observers that accelerated for a while, and then got tired and/or ran out of fuel need not apply. For these, the horizon is at best approximate and will be pierced by any sufficiently patient light wave: light always catches up. How can an observable that I measure here, in my lab, depend on the entire history of the detector? How does it know whether I'll accelerate forever or eventually stop?

(related: https://arxiv.org/abs/1407.7295)

Plus, the Unruh effect is so small that even the word "tiny" can't do it justice. Even an acceleration of the order of 10^20 m/s² results in an Unruh temperature of a single measly kelvin. As a result, this radiation was never detected directly and probably never will. Yet somehow ordinary everyday observations such as _things have mass_ are explained by Unruh radiation?

John Baez had a field day with this a few years ago: https://plus.google.com/+johncbaez999/posts/E1ecoYsa5ae

mfb, stoomart and Bandersnatch
Which appears to be this one:

https://arxiv.org/abs/1302.2775

Equation 2 in that paper reads:

$$F = \frac{uA}{3}$$

which is said to represent the force experienced by an accelerating object due to Unruh radiation.

I thought the author was supposed to be deriving the existence of inertia, which F=ma subsumes. Using F=ma to derive F=ma makes no sense.

Of course, F = ma has already has an explanation in the form of Ehrenfest's theorem, so any putative explanation of inertia would have to explain first why quantum mechanics works and why the standard model Lagrangian is what it is. It is clear that an argument based solely on classical physics (and with a clear circularity) cannot do that.

Gold Member
Dearly Missed
Thank you Mike McColloch.

Dwarf satellite galaxies of the Milky Way appear to be gravitationally bound, but their stars’ orbital motion seems too fast to allow this given their visible mass. This is akin to the larger-scale galaxy rotation problem. In this paper, a modification of inertia called quantised inertia or MiHsC (Modified inertia due to a Hubble-scale Casimir effect) which correctly predicts larger galaxy rotations without dark matter is tested on eleven dwarf satellite galaxies of the Milky Way, for which mass and velocity data are available. Quantised inertia slightly outperforms MoND (Modified Newtonian Dynamics) in predicting the velocity dispersion of these systems, and has the fundamental advantage over MoND that it does not need an adjustable parameter.

kimbyd
Gold Member
Just to correct some comments on this thread: quantised inertia predicts dwarf galaxies well, unlike other theories. I published a paper specifically to point that out: https://link.springer.com/article/10.1007/s10509-017-3039-6 A preprint is here: https://arxiv.org/abs/1703.01179
This states that this model does better than MOND. It does. But it still has a strong tendency to predict much smaller velocities than observed. Some of the dwarf galaxies are within the error bars. Many are not.

I don't think it can be reasonably stated that this model "predicts dwarf galaxies well".

timmdeeg
Gold Member
I might be wrong, just wonder if it is not a contradiction in itself that an observer-dependent effect like Unruh-radiation can be the cause of something which is not observer-dependent like the rotation curve of bound systems. Whats wrong with this reasoning?

PeterDonis
Mentor
just wonder if it is not a contradiction in itself that an observer-dependent effect like Unruh-radiation can be the cause of something which is not observer-dependent like the rotation curve of bound systems

"Observer-dependent" in this case doesn't mean what you think it means. Unruh radiation does not depend on your choice of coordinates; it depends on the state of motion of an object--specifically its proper acceleration. But proper acceleration is an invariant, independent of coordinates. And the quantum field state transitions involved in the Unruh radiation are also invariant, independent of coordinates. So there's no issue in principle with using such effects to explain galaxy rotation curves. That's not to say this model is correct, just that it doesn't suffer from the particular issue you raise.

(It is true that the description in ordinary language of what is happening with Unruh radiation depends on the observer. The accelerated observer describes it as radiation being absorbed by a radiation detector that moves with him--he therefore says that there must be radiation coming from his Rindler horizon, in order to explain why his detector is absorbing it. But an inertial observer watching the process would describe it as radiation being emitted by the accelerated detector and flying off into empty space. What this really illustrates is that in QFT, the notion of the "vacuum state" of a quantum field depends on your state of motion.)