The New Physics

It's often said that when offering new ideas, it best not to attack the old stuff, but to build the new. So here is a deliberate attempt to do that and show what a MiHsC-ian (quantised inertia) world would look like. Just a warning: I am thinking far ahead here.

I'll start with the obvious. The gravity well would be broken because it would become possible to launch objects fuelessly into space by making a gradient in the zero point field. This is, according to MiHsC, what the emdrive does. The launches will be far safer as well, no huge explosions would be needed to blast atoms downward to get Newton's momentum accountant to move the rocket the other way. You just need to put some meta-materials (a metal structure that bends electromagnetic waves) above or in your satellite or human-rated capsule to damp the wavelength of Unruh waves that are likely to form above it, and it'll glide slowly into space. Similarly it would revolutionise satellite station-keeping, as the Chinese have already recognised. Ground transport would also be revolutionised: no wheels would be required: put metamaterials above cars and they will be pulled up by the Unruh-void and glide along frictionlessly. Want a floating house? Floating city? No problem, given a big enough damper above. The problem is to have a metal structure of the right size to damp the Unruh waves that are likely to form. For terrestrial accelerations these are a light year long! In the emdrive, photon accelerations are huge so the Unruh waves are as short as the cavity, so its small size can do the job.

Energy. No longer will big companies own the means of energy production, huge oil or nuclear installations, and be able to charge up to the limit. Energy will be obtainable by everyone at home, by putting horizons in the zero point field in a way that makes rotational movement, for example using a nano-construction like this.

Physics will not be taught in the same schizophrenic way: as quantum mechanics for the small and relativity for the fast or large. MiHsC shows that the two halves link up if you consider the effect of relativistic horizons on the quantum fields as I discuss here. The assumption of smooth fields will go too, the cosmos is broken up into reference-frame dependent information cliffs (horizons). Dark matter and dark energy are not needed in the MiHsC-ian framework so we can close the dark matter detectors down and divert the millions in funding to horizon engineering (some reading this will fear for their funding - they will have to change topic, that's all). Dark matter, like the Michelson and Morley experiments, will be regarded as a null result.

String theory, and its 11 dimensions, will also be out, but will get some credit for its discovery of the holographic principle, and the EPR paradox will be solved because in MiHsC, time does not exist for quantum systems that are not able to perceive it, so quantum systems have no sense of time and this means the future is known to them.

No longer will engineering just involve sticking bits of existing matter to other bits. We will be able to create matter by setting horizons up for photons. In MiHsC, matter or particles are just confined photons so this will make Star Trek technology like the holodeck or food replicators possible. Another name for MiHsC or quantised inertia is 'Horizon mechanics' (this name was suggested to me by John Dorman, and I like it: it's more general). Horizon mechanics will replace the whole of present engineering.

The philosophy of MiHsC is that if something can't be seen in principle, then it does not exist, so you can delete space and step over it. This was the basis for my sci-fi novel (yes, OK, I've been told to "stick to physics", but the ideas in it are valid). Also, we previously assumed that mass->energy and the cosmos ends up in a depressing heat death. MiHsC makes it clear that the heirarchy is information->mass->energy, and information is always being created. So the cosmos can grow instead of die. Which brings us on to biology. Do organisms make use of MiHsC? Why are cells the size they are? Are they precluding Unruh waves longer than they are and so regulating their temperature?

Coming back to space, the galaxy will be open to human colonisation. The emdrive, explained by MiHsC as just being a metamaterial (metal structure) that creates a gradient in the zero point field, doesn't need to carry fuel with it and so, although it accelerates very slowly, it will get us as close as we like to the speed of light, so that we could get to Proxima Centauri in four or so years of Earth time, and less time for those in the ship (given that special relativity still applies and slows time down for the travellers).

Who could possibly give anything else a second of their time, given the fact that quantised inertia / MiHsC / horizon mechanics is unbelievably simple, works perfectly to explain the data in the galaxy rotation problem for all galaxies, and galaxy clusters, cosmic acceleration and predicts many other anomalies as well (see the 12 journal papers that I have published), and it predicts all of the above applications?

References

Video clip to provide serious background: Mary Poppins flies in on her metamaterial .. sorry, umbrella: https://www.youtube.com/watch?v=5BHoDW9f7vY

Game over for dark matter

Back in 2006 when I had not yet published MiHsC / quantised inertia, I went to an evening seminar at Exeter University by someone who'd been sitting in the Boulby Mine in Yorkshire for ten years, isolated from cosmic radiation, looking for (hoping to detect) dark matter. Afterwards, being the tactful person I am, I went up to him and said that I had an alternative to dark matter. It is a tribute to the centuries of civilisation we stand on, that he didn't go for my throat, and we discussed things in a rational manner. Back then, I already believed, somehow, that quantised inertia would replace dark matter, but I did not have solid observational proof. I now have a lot of evidence, including this plot:

The plot shows the expected Newtonian rotational acceleration of stars orbiting in galaxies on the x axis, and that observed on the y axis. The line predicted by Newton is of course the diagonal dotted one (expected=observed). The data, binned from 153 galaxies in the SPARC catalogue, that was sent to me recently by Prof Stacy McGaugh, is shown by the grey squares. It shows that at low accelerations (at the outer edges of galaxies, left hand side of the plot) the acceleration is higher than expected: the squares are above the diagonal line. This means that galaxies spin too fast for Newtonian gravity and they should explode with centrifugal force. This would be a cool, but brief, sight to see, but they don't explode. They just sit there, anomalously spinning too fast. The old solution to this of course is to arbitrarily add dark matter to the galaxies to hold them in by gravitational force, rather as governor Tarkin tried to hold The Empire together by force, but this is obviously bogus because you have to add a different arbitrary amount of dark matter to each galaxy.

The solid line in this plot shows the predictions of MoND, which has been fitted to the data by varying its adjustable parameter a0, so it's not that big a deal that it fits. It has been made to fit by that adjustment, and without a physical reason, but it is at least less adjustable than dark matter. 

The dashed line shows the prediction of quantised inertia (MiHsC) using only the visible matter, the co-moving diameter of the cosmos, and the speed of light: all well-known parameters that are unadjustable. Quantised inertia (MiHsC) therefore beats dark matter and MoND in fitting this data without any adjustment at all. This is why I claim dark matter is finished, and why I claim that quantised inertia explains the empirical relation that was MoND. A paper on this is now going though review, but really it is only a slight update to the paper I published back in 2012 (see references). The title of this paper (Testing quantised inertia on galactic scales) had a pun (double meaning) that I was proud of, but no-one seemed to notice (galactic scales could imply size, or weighing scales for inertial mass. Ho ho ho!). Hopefully the new paper will be published soon and noticed, and all that dark matter funding can be put to better use, and that guy down the mine, who usefully got a null result, can finally get some vitamin D.

References

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. ApSS, 342, 2, 675. http://arxiv.org/abs/1207.7007

Notes on EMdrive and MiHsC

Here are some notes that I made (to anticipate likely questions) to prepare for a radio interview on the EMdrive and how MiHsC explains it, that was recorded yesterday (on 'Hotel Mars' with John Batchelor and David Livingston). The audio interview is available here (this version has better audio) and The Space Show here.

What is the emdrive?

The emdrive is a truncated-cone made out of a copper shell with microwaves resonating within it. A bit like a microwave oven built into a metal megaphone. Roger Shawyer from Britain & Guido Fetta from Italy discovered that such a thing moves slightly towards its narrow end. The thrust is tiny: ~1mN per kW so the acceleration is on the order of 0-60 mph in 3 days, so it won't be on The Grand Tour anytime soon, but the crucial thing is that it accelerates without expelling propellant, an ability that gets rid of the need to carry heavy fuel and therefore revolutionises the prospects for interplanetary/interstellar flight.

Why is it controversial?

It is the equivalent of moving your car by sitting in it and pushing on the dashboard. Physics disallows this because if you push forward on the dashboard, your backside pushes back on the seat and the two forces cancel. This is due to the conservation of momentum, which has never been seen to be broken before. Physics says you can’t move unless you leave something behind. If you throw your shoe out of the back of the car then the car (if the brake is off) will move forward, because you expelled something. That is how rockets work. The emdrive does not expel anything so physics says it shouldn’t move.

Why is it important?

It violates a central part of physics (the conservation of momentum) which has never failed before, so if it is confirmed physics will need a radical change (see below). Also, the applications are huge: hovercars, launching without rockets, new energy sources from apparently ‘nothing’, and interplanetary and interstellar travel becomes practical because this engine works without having to carry heavy fuel.

How many groups have tested it?

UK. Shawyer, 1999-. Many experiments have been done. Several reports have been published on the SPR website.
China. Juan et al., 2012. They got a larger thrust than Shawyer, but later found an error, and their recent results are null, but consistent with the other results since their apparatus is unable to measure the likely thrust.
US. Guido Fetta, 2014. The Cannae drive has a much flatter shape, but they also found positive thrust.
Germany. Tajmar et al., 2015. They also saw a thrust, but the emdrive also thrusted when upright, which needs to be looked into.
US. NASA, 2014. Tested positive for thrust, but in air.
US. NASA, 2016. Tested positive in vacuum and published a peer reviewed paper.

What is different about the new NASA paper?

1. NASA tested the emdrive in a vacuum. One of the earlier criticisms was that the thrust was being caused by air currents. This is obviously now ruled out since they saw the same thrust in a vacuum.
2. It is a peer reviewed, checked by other scientists. Most of the experimental papers on it before this have been conference reports, not subject to the same rigour. It was apparently a very long and difficult process too, so Dr Harold G. White of NASA should be commended for having the courage to do this in the first place, and for his hard work through peer review.
3. It is NASA, so it has raised the profile of the emdrive.

The NASA emdrive results (see the recent paper) are interesting because they get weaker thrusts than everyone else so far, and also they tend to put dielectrics in the narrow end of their cavity. Quantised inertia predicts that the dielectric should thrust the other way, cancelling the force due to the taper of the cavity. I need to look into this in more detail.

So what is your suggestion?

I can use an analogy with ships at sea. Usually waves hit ships from all around so they don’t push them on average, but if you put two ships together there’s a sheltered zone between them, so suddenly more waves hit the ships from outside then from between them, so they move together. If the crew don’t know about the waves they’ll think it odd, like physicists think the emdrive is odd.

Quantum mechanics predicts there’s a quantum sea all around us called the quantum vacuum and the Casimir effect and Lamb shift have proven its existence. Relativity predicts that when objects accelerate, information horizons appear in the opposite direction to the acceleration vector, since information cannot catch up to the object from behind that horizon, and relativity has been tested. I’ve suggested that relativistic horizons damp the quantum vacuum, just as the ships damp the sea waves, making a void that pulls the objects back against their acceleration. This model, called quantised inertia or MiHsC, predicts the old property of inertia (which suppresses accelerations). It also predicts galaxy rotation exactly without dark matter or any adjustment and cosmic acceleration. I have published 12 papers on this and a book called ‘Physics from the Edge’.

Quantised inertia can model the emdrive too because it allows more quantum waves to exist at the wide end of the cavity so microwave photons that go to that end gain inertial mass, they’re heavier. This is like a rocket expelling mass at the wide end. Another way to think about it is that the microwaves’ centre of mass is continually being shifted towards the wide end, so the emdrive cavity itself moves towards its narrow end to conserve momentum.

An analogy is a person on a ship who keeps walking from the front to the back. Every time he goes to the back he picks up a weight from the deck. This moves the centre of mass of the ship backwards, so the ship has to move forwards slightly to conserve momentum.

What is MiHsC/QI in a nutshell?

A summary: quantised inertia says that relativistic horizons damp the quantum vacuum, making it non-uniform, creating new forces.

A poem: Go to the right, the left’s out of your sight. A horizon appears, damps zero point fields, dragging you back. Inertia is that!

What has been the response of the scientific community to MiHsC?

They have mostly ignored it, so far. Two criticisms they have made are that the Unruh radiation (quantum vacuum) I’m using has not been seen, but it is a widely-accepted prediction akin to Hawking radiation and may have been seen in experiments recently. The second criticism is that I’m varying the speed of light in the vacuum, but this is not so serious since special relativity only demands that light is emitted at a constant speed, c. Apparent speed of light changes happen in general relativity all the time but are explained away with bent space. Also, NASA tests may have shown light changing speed (space bending) in the cavity.

Interest is growing and a few people are now working with me: including Dr Jaume Gine who recently worked with me on this paper, and Prof Perez-Diaz who is a very capable experimenter. He recently visited me and we designed some experiments, including the LEMdrive, that he is now doing.

What other theories are there?

Many people have said there must be an experimental error, but no one has suggested an error that fits the data. For example, the heating/expansion of the cavity can offset the centre of mass and make the cavity move to conserve momentum, but that and other errors were calculated in the NASA paper and found to be too small.

Roger Shawyer has a theory that uses special relativity to explain it, and while I respect him for the experimental emdrive discovery, I don’t accept his theory because relativity should also obey the conservation of momentum. The emdrive does not.

Grahn, Annila and Kohlemainen from Finland have an interesting idea that photons in the emdrive are pairing up and cancelling each other out, so they can leave the emdrive undetectably through the wide end, pushing it towards the narrow end. However, this theory relies on many assumptions and ‘invisible stuff’ and I haven’t seen a comparison with data yet.

In their new paper, NASA propose that the particles in the quantum vacuum are ‘real’ (a non-standard view due to David Bohm) so that sound waves can exist in the quantum vacuum and it can act as a momentum sink. An interesting approach, but again it is adjustable and complex so it’s easy to get the right answer for the wrong reason. Also, I’ve not seen a comparison with the emdrive thrusts.

What’s Next for the Emdrive?

It has been given a boost by the positive NASA test, and I admire the NASA Eagleworks people, eg: Dr Harold G. White, Paul March and others, for having the curiosity and courage to test it.

The next step is that universities need to get involved and perform rigorous tests, and do some crucial experiments, that those who have theories can suggest.

There should also be a test in space. The Earth is a messy environment, and you never know what electromagnetic forces might be around. In space, it’s cleaner. Guido Fetta aims to test an emdrive in space using a 6U cubesat (small satellite), possibly in 2017. It’ll have a solar panel to power it and be pointed narrow end up, so if it stays in orbit longer than expected that’ll be a sign that it is thrusting upwards. If it works, it’ll change the satellite industry completely.

Also, the quality factor of the cavity is a crucial parameter. This is the number of times microwaves can bounce around inside without being absorbed. So Guido Fetta and Roger Shawyer are now trying out emdrives coated inside with a superconducting layer, because they have much better Q factors: far more photon bounces.

Cannae has also proposed a deep space probe, that uses 10 em-/Cannae-drives powered by RTGs to accelerate at 8.66x10^-3 m/s^2 from low Earth orbit to Sol escape velocity in 2 months. It could travel 0.1 light years in 15 years (1.35% c). This could be the first interstellar probe. To do this with a rocket you would need to carry a Ceres-sized amount of fuel.

Isn’t there a suggestion that dark matter can predict the emdrive?

Someone wrote a blog saying it could be dark matter. But, dark matter is an awful hypothesis. It has been forgotten that in 1980 or so physics failed to predict the newly-observed galaxy rotation: they rotate so fast they should explode, but don’t. Instead of changing the theory, they added ten times as much dark mass to galaxies as there is visible mass, to hold them in by gravitational force, but they have to add it by hand to each galaxy differently. Some galaxies are 92% dark, some are 99.3% but there’s no reason behind these numbers, and dark matter is not falsifiable: if your multimillion pound experiment can’t find it, you can say “OK, maybe it’s in this other more difficult regime” and that can go on for ever. In the same way you can glibly say "dark matter drives the emdrive" but until you point out a specific process that can be tested or falsified it is meaningless hand waving. In contrast quantised inertia predicts all galaxies (and the emdrive) without any adjustment, and Unruh radiation is something that can be looked for in one place and is either there or not. It is falsifiable.

Is the emdrive a warp drive?

Well, it’s not based on Alcubierre’s warp theory, but I’m suggesting that the speed of light changes within it. This can happen in relativity if you bend spacetime to make sure the change in c is not measurable to an observer, say a bug inside the cavity, so maybe space-time is bending in there. NASA found something like that when they fired a laser through, but couldn’t quantify.

Do you think the emdrive is really anomalous?

Yes. Of course there is always doubt in science, but as Captain Kirk says in the film Star Trek: Generations "You have to take some risk if you want to sit in that chair", and the emdrive has now been successfully repeated in 4 independent labs. So you have to pay attention to that. It's vital in science to value new observations over old theories.

Concluding thought?

It’s a time to be excited: anomalous observations such as galactic rotation, cosmic acceleration, the flyby anomaly, the emdrive and many others are forcing a rethink of physics. In my opinion they are all telling us that mass-energy can be created from information horizons, this is the basis of quantised inertia, and the theoretical and practical implications are huge. I’m hoping now that universities will get involved in tests.

Emdrives & dielectrics: the NASA shift

The NASA paper further supporting the previous emdrive experiments (in which a microwave-filled conical cavity moves towards its narrow end without expelling anything, as standard physics says it just shouldn't do) has finally been published. Apparently Eagleworks had a terrible time publishing it, so well done to them.

It is interesting that all the NASA results are anomalous in comparison with results from the other teams: Shawyer's, the Cannae group and Tajmar's. The plot below shows the thrust predicted by quantised inertia (MiHsC) on the x axis, and the y axis shows the thrusts observed in the lab. It would be great if all the diamonds representing the different emdrive experiments were along the diagonal line (a perfect agreement). The Shawyer, Cannae and Tajmar experiments are, but the NASA experiments are all shifted rightwards. This shows that MiHsC over-predicts the thrust for NASA's tests by a factor that can be as much as ten.

I may have an explanation for this. MiHsC predicts the emdrive's thrust by saying that the inertia of the microwave photons is caused by Unruh radiation (a radiation you only see if you accelerate). At the wide end of the cavity more Unruh wavelengths fit within, and are 'allowed', due to the bigger space available, but at the narrow confined end fewer are allowed (as for the Casimir effect). Thus, MiHsC is continually shifting the photons' collective centre of mass towards the wide end so that to conserve momentum the cavity has to shift the other way, as indeed it does, but more slowly as it is far more massive than the microwaves (more detail).

A new possibility to explain NASA's anomaly within an anomaly (the NASA shift) is as follows. Most of the NASA experiments, including the latest one, put a dielectric at the narrow end of the cavity. A dielectric means that Unruh waves will be slower and have shorter wavelengths, and so more of them will fit at the narrow end. MiHsC therefore predicts that having a dielectric at one end is rather like widening that end, and if you put it at the narrow end, then you reduce the taper and reduce the thrust.

I've already worked out some of the maths for dielectrics, after I read an interesting, but inconclusive, 2016 report by a group at CalPoly (Kraft and Zeller, 2016) who tested a cylindrical emdrive with a dielectric at one end. I just need to account now for both a dielectric and taper and see if the numbers fit the NASA shift.

References

McCulloch, M.E., 2015. Testing quantised inertia on the emdrive. EPL, 111, 60005. Preprint

K. Zeller and B. Kraft, 2016. Investigation of a partially-loaded resonant cavity. CalPoly research report.

White, H., P. March, J. Lawrence, J. Vera, A. Sylvester, D. Brady, P. Bailey, 2016. Measurement of impulsive thrust from a closed rf cavity in vacuum. AIAA J. of Propulsion and Power. Online

Experiments with balls: the mystery of big G

I've written a few blogs of late, showing how quantised inertia (MiHsC) predicts galaxy rotation and other things perfectly without adjustment, but to avoid sounding like a advert I also want to talk about the new things I am puzzling over. So this blog entry will be a bit messier, but perhaps more fruitful.

I've mentioned before that the gravitational constant (big G) is in trouble. Well, it still is. I recently read an interesting paper on this by Norbert Klein (see references) who analysed two of the recent experiments to measure big G in light of the galaxy rotation problem. The experiments typically measure G using a development of the Cavendish experiment. For example Quinn and Speake (2014) suspended four 1.2kg masses arranged in a circle radius 120mm (see the 4 small balls in the diagram below) from a fibre (the vertical line) and then put four much larger masses (11 kg) on a 214 mm radius circle around them, and then rotated this outer circle by 18.9 degrees so that the tiny gravitational force between the four pairs of masses twists the inner arrangement, so that they can work out from the twist what the force is. Since they know the masses M and m, the force F and the distance (r) very well they can work out G from Newton's gravity law: F=GMm/r^2.

The trouble is that the two different values of G they found disagree by more than the uncertainty in the experiments! Which they just can't do, unless something 'unknown' is going on. Schlamminger measured G=6.674252x10^-11 m^3kg^-1s^-2 and Quinn and Speake found G=6.67545x10^-11 m^3kg^-1s^-2. The observation that got me excited was that Norbert Klein, in his paper, points out that in the Schlamminger experiment (the low G value) the gravitational acceleration between the two balls (if they'd be free to move) was relatively high, but in Quinn and Speake's experiment (the high G value) it was very low.

This agrees with quantised inertia since a low acceleration should mean the small ball has lower inertial mass and so is more sensitive to the large ball, so it should 'appear' that G is bigger, as indeed Quinn and Speake found. I have done a rough calculation assuming the mutual acceleration is four times the gravitational acceleration between each pair of balls (there are four pairs), and quantised inertia predicts that the apparent change in G divided by G (dG/G) should be 11.3x10^-4 whereas Quinn and Speake measured a change from the standard value of G of dG/G=3x10^-4.

The prediction is a factor of 3.8 out, but there are large uncertainties in the calculation. For example, what is the correct acceleration to plug into MiHsC/QI? Is it, as I have assumed, the along-inner-circle component of the acceleration that the small mass would have towards the bigger one, times four? Does the rest of the environment contribute? How about the curve of the ball around its circle as it moves? That is an acceleration too. Also, what is the 'raw' value of G, that MiHsC/QI predicts should only be seen at high accelerations? This affects dG. It's something interesting to think about anyway.

My family must think I'm training for a boxing match since I can often be found these days walking round the house holding my fists up to represent two balls and mumbling to myself.. Saying that, maybe I should learn to box: given some of the online responses to MiHsC/QI, if I ever attend another conference, such a skill might be needed!

References

Quinn, T., C. Speake et al., 2013. Phys. Rev. Lett., 101102. Link

Schlamminger, S., 2014. Phil. Trans. Roy. Soc., 372, 20140027. Link

Klein, N., 2016. Are gravitational constant measurement discrepancies linked to galaxy rotation curves? https://arxiv.org/abs/1610.09181

Critique of Verlinde's Gravity

People have been sending me Verlinde's new emergent gravity paper wanting me to comment on it. I started reading it and I'm afraid I stopped at the sentence 'code subspace in microscopic bulk Hilbert space'. I skimmed the rest. He focuses on gravity, and just assumes inertia, and is proposing a new force that starts to appear at large scales. Although there are similarities to MiHsC in that he uses the Unruh temperature formula and information, there are many observations that falsify Emergent Gravity:

1) Emergent gravity predicts an anomalous effect that occurs only on large scales, and so it is falsified by the many tiny globular clusters and small satellite galaxies that show even more of an anomalous rotation effect than big galaxies (MiHsC is successful with these minnows too because it predicts anomalies at low accelerations, instead of just large scales, see paper). Emergent Gravity also cannot deal with many other anomalies like the cosmic acceleration, the flybys and the emdrive. MiHsC explains all of these.

2) Entropic gravity has been falsified by a detailed comparison with galaxy rotation curves: https://arxiv.org/abs/1609.05917 (Lelli et al., 2017, to be published in MNRAS letters).

3) Emergent Gravity has been falsified by experiments in which uncharged neutrons were confined in the vertical direction by making them bounce off a mirror below, and allowing gravity to pull them down. It was found that, in agreement with quantum mechanics, the neutrons did not move continuously along the vertical direction, but jumped from height to height like mountain goats. Entropic gravity predicts the wrong heights (see the Kobakhidze reference).

4) Emergent Gravity relies on something called code subspace, which is something we cannot directly see, so it is another kind of informational dark matter that is difficult to test for directly.

It is strange people that people are considering Emergent Gravity and are not discussing MiHsC / quantised inertia which is far simpler, requires less new physics, is based only on observable things, and predicts far more. To summarise:

1. MiHsC/quantised inertia is deliberately based only on things we can see (empiricism): visible matter, the speed of light, the cosmic diameter, and Unruh radiation that was already predicted and is at least observable, and may have been seen already (Unruh confirmed?).

2. MiHsC is simple. Emergent gravity is complex and Byzantine, and needs more untestable assumptions (like code subspace) than you can shake Occam's razor at, MiHsC needs only one new assumption and 6 lines of maths to predict galaxy rotation and many more anomalies on a huge range of scales.

3. The new assumption in MiHsC: that quantum mechanics (the zero point field) and relativity (horizons) interact on all scales via the uncertainty principle simply gets rid of the dark sector and unifies physics.

4. The same mathematics that leads to MiHsC, also predicts gravity, so MiHsC predict both gravity and inertia.

5. MiHsC predicts the many anomalies that have been seen in recent years (29 or so of them), but also makes very specific predictions for new things that can be looked for (eg: early galaxies span faster at the same visible mass, the emdrive can reverse if you change its aspect ratio..)

Of course, it's good that Verlinde is at least trying to solve galaxy rotation without vague dark matter, but he is still suffering from the excess-baggage problem of theoretical physics. He had to start from general relativity and try to add invisible elements to it. The result is complex, contrived and doesn't fit the data.

Quantised inertia / MiHsC fits the data, and is far simpler because you don't have to add anything unobservable. All you have to do is admit that quantum mechanics and relativity interact via horizons and the uncertainty principle (summary).

References

Kobakhidze, A., 2011. Once again gravity is not an entropic force. arXiv

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. arXiv

Verlinde, E., 2016. Emergent gravity and the dark universe. arXiv

Based on Leonard Cohen's Hallelujah - Hallowed Data

Just for fun I've just written this, based on Leonard Cohen's song "Hallelujah", but with a science/MiHsC theme.

Hallowed Data

Thales of Miletus, in Ancient Greece
said the Gods were not the keys
and we should only assume things we can see, yeah.
Putting data first
gave us gravity
and Einstein's relativity.
Humanity was rising towards the stars with Hallowed Data.

Hallowed data
Hallowed data
Hallowed data
Hallowed data

Their faith was strong, but they needed bread.
They went for funding, lost their head.
The beauty, & the aura, overthrew them.
She tied them up
in darkness then
and broke Occam's razor, when
they threw out that essential hallowed data.

Hallowed data
Hallowed data
Hallowed data
Hallowed data

They say I aspire far too high
but I just want to pierce the sky,
and if I did, well really, what's it to you?
MiHsC was born
outside the herd.
It doesn't matter what you heard.
It's simply and surely based on Hallowed data.

Quantised inertia
Quantised inertia
Quantised inertia
Quantised inertia

I did my best, it wasn't much.
I couldn't join, but I tried to push.
I've told the truth, I didn't come to fool you.
And even though
I'm on the edge
I'll stand before the garden hedge,
with nothing on my tongue but Hallowed data.

Hallowed data
Hallowed data
Hallowed data
Hallowed data.

A Test using Redshift

Galaxies further away from us, are moving away much faster than close ones, and therefore the light coming from them is red-shifted. So the redshift of star light is a measure of its distance, and of increasing age, since when we look far off we are also looking back in time since the light has taken aeons to reach us. Like an ice core in climatology, this gives us a record of the distant past.

The minimum acceleration predicted by Quantised Inertia / MiHsC is given by: a = 2c^2/CosmicDiameter, and 'CosmicDiameter' varies with time as the cosmos expands. This means that as we look at galaxies further away, and further back in time, the CosmicDiameter was smaller and the minimum acceleration was bigger (This might also explain the inflation of the early universe, but that's another story). The prediction then is that earlier galaxies, ones at higher redshift, have to rotate more rapidly, with the same visible mass, to remain above the minimum acceleration. I proposed this as a test in McCulloch (2007) (see paragraph 4 of the Discussion), but at the time the data did not seem to be good enough.

I was reminded of this test by various insightful people on my last blog entry and in a few emails (see the guilty names below). Thanks to them I've looked into it again and added it to the discussion of my latest paper (just submitted to MNRAS) which includes the plot below. Along the x-axis we have the log of the stellar acceleration expected given the visible matter and Newton's laws, and along the y-axis the log of the acceleration observed directly from the movement of the stars. Newton and Einstein would expect the results to lie on the dotted line. The observations, taken from McGaugh et al. (2016) are shown by the squares with their size indicating the uncertainty, and they are obviously at odds with dear Albert and Isaac. At low accelerations (on the left hand side) the stars orbit the galaxies far too fast. This is the famous galaxy rotation problem, that is usually solved by stuffing in huge amounts of dark matter wherever it's needed (the second worst hypothesis in history in my opinion, since it is unfalsifiable).

The black line shows the prediction of MoND which fits the data (the squares) and is much more falsifiable than dark matter, but despite the great respect I have for Milgrom's bold step, MoND has been adjusted to fit the data using its parameter a0, so it's not surprising that it fits. The MoND prediction also shows no dependence on time.

The coloured lines show the predictions of quantised inertia / MiHsC. Uniquely, among all the theories QI/MiHsC predicts the observations correctly without any adjustment, and, also uniquely, its prediction varies with redshift. The light blue line shows the curve for a redshift of Z=0 (nearby galaxies in this epoch). This agrees with McGaugh et al. (2016)'s data (which was for Z=0). The dark blue curve shows the prediction for Z=0.5, purple for Z=1 (for which the cosmos was half its present size) and the red curve for Z=2. As you can see the galaxy rotation problem is predicted by QI/MiHsC to have been worse when the cosmos was young (all other things being equal). If two galaxies have the same visible mass, then according to QI/MiHsC the one further away (earlier in time) should spin faster.

Does this prediction agree with the data? Well, the data still seems noisy, but earlier galaxies do seem to have faster spin, see for example Figure 6 in the Thomas et al. (2013) reference below (a paper found by airenatural). With a bit more data this could be the definitive proof that QI/MiHsC needs..

Acknowledgements

Thanks to S.S. McGaugh for sending his binned data, and R. Ludwick, T. Short, Magnus Ihse Bursie and J.A.M. Lizcano (airenatural), for advice ...and anyone else I may have forgotten.

References

McCulloch, M.E., 2007. The Pioneer anomaly as modified inertia. MNRAS, 376, 338-342. https://arxiv.org/abs/astro-ph/0612599

McGaugh, S., F. Lelli, J. Schombert, 2016. The radial acceleration relation in rotationally supported galaxies. Phys. Rev. Lett., (accepted).

Thomas, D., et al., 2013. Stellar velocity dispersions and emission line properties of SDSS-III/BOSS galaxies. MNRAS, 431, 2, 1383-1397. https://arxiv.org/abs/1207.6115

Strong evidence for MiHsC/QI

A few days ago Prof Stacy McGaugh kindly sent me the binned galaxy acceleration data they used in their paper (McGaugh, Lelli and Schomberg, 2016, see below) and I've been comparing MiHsC with it. The result is shown in the figure. To explain: the x-axis shows the log of the expected acceleration for stars within galaxies, g_bar. They looked at about 2693 stars, in 153 galaxies and calculated the expected acceleration using Newton's gravity law from the visible distribution of matter. Higher accelerations are shown to the right. The y-axis shows the acceleration of the stars derived from their observed motion, g_obs - a faster more curving path, means more acceleration. Higher accelerations are shown to the top. The data all lie between the two dashed lines, which represent the uncertainties in the values.

If Newtonian physics or general relativity were right without any fudging, then the two estimates of acceleration (g_bar and g_obs) would agree and you would expect all the data (between the two dashed lines) to lie along the dotted diagonal line. It doesn't. For low accelerations, at the edge of galaxies (on the left side of the plot) the observed acceleration is greater than Newton or Einstein predicted, which pushes the two dashed lines up away from the dotted line. This is the galaxy rotation problem. Stars at the edges of galaxies are moving so fast, they should escape from the galaxy, so dark matter is usually added to hold them in by gravity.

However, McGaugh et al.'s study showed that the acceleration is correlated with the distribution of 'visible' matter only, which implies there is no dark matter. Also, dark matter is an unscientific hypothesis because you have to add the stuff to galaxies just to make a theory (general relativity) fit the data and this is a bit like a cheat, especially since so much has to be added with no physical 'reason' for it (beyond saving a theory). Also it means you can't actually predict the motion of stars in a galaxy from its visible mass: you have to add the dark matter arbitrarily, and you can't double check you got it right because dark matter is invisible!

A slightly less fudged alternative is MoND (Modified Newtonian Dynamics) which is a empirical model that does not have an explanation, but fits the data if you set an adjustable parameter to be a0 = 1.2x10^-10 m/s^2. The MoND result is shown by the blue line in the plot. It works, but this is not surprising because the value of a0 is set manually to move the blue curve up and down on the plot so it fits the data.

The red line shows the prediction of quantised inertia (QI), otherwise known as MiHsC, which also fits the data (it is between the dashed lines). Now, this is surprising because MiHsC/QI fits the data without any adjustment. It predicts the observed galaxy rotation from just two numbers: the speed of light and the diameter of the cosmos. I should point out that in this work I am using the co-moving diameter of the cosmos 'now' which is 8.8x10^-10 m/s^2, see Got et al. (2005) and which I now think is correct, rather than the diameter when the light we see was emitted which is 2.6x10^-10 m/s^2. This latter is the value I used in my earlier papers, which means that the MiHsC flyby predictions will worsen, the predictions in my 2012 galaxy paper will improve and the MiHsC emdrive predictions are unaffected (there it depends on the cavity size). Nevertheless, this plot is evidence that MiHsC/QI is a very simple solution to the galaxy rotation problem (see also my 2012 paper). It also elegantly unifies quantum mechanics and relativity, predicts cosmic acceleration, and other MiHsCellaneous anomalies like the emdrive.

References

McGaugh, S.S, F. Lelli, J. Schombert, 2016. The radial acceleration relation in rotationally supported galaxies. Phys. Rev. Lett. (to be published). Preprint.

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophysics and Space Science, 342, 342-575. Preprint

 Gott III, J. Richard; M. Jurić; D. Schlegel; F. Hoyle; et al. (2005). "A Map of the Universe". The Astrophysical Journal. 624 (2): 463–484.

Star Trek, Birmingham

This is a more light-hearted blog than normal since I have just been to a Star Trek convention. I know that it is irrational (Star Trek is fiction), but I did enjoy it immensely, like the previous one. Why go? Well, although the people Trekkies come to see are actors, it's interesting to hear the back-story to episodes that you like, to meet people with similar scientific and moral interests, and also when the actors get up on the stage they often talk about the amazing ideas that science fiction writers have forced them to enact. Where else can you hear such ideas presented by passionate and humorous actors?

My friend and I first saw the dignified George Takei (Sulu), who talked about how in World War 2 the US interned even ethnic Japanese orphans, "What's so dangerous about orphans?" and how when his ethnic Japanese family were taken away to the internment camp their neighbours stole their stuff.

The Next Generation panel was a blast with Marina Sirtis who played Troy, Gates McFadden (Dr Crusher) and Will Wheaton (Wesley). Marina Sirtis was hilarious and was the opposite of her psychological 'careful what you say' Betazoid character, and kept dropping loud shock-bombs. When someone said 'When Gene Roddenberry left in 1991..' as if to give the impression that he'd abandoned Star Trek. Sirtis corrected him: 'Actually, he died'. When someone asked her to talk about Shatner's new documentary she said: "Why should I make Shatner richer than he already is!?".

Will Wheaton was in good form, having just rested up in Scotland. He used the collapse of the quantum mechanical wave-function in an analogy, very Big Bang, and when a fellow in a wheelchair apologised for not standing up, Will Wheaton told him not to apologise for something outside his control, which is common sense, but is very Star Trek. My friend and I also met some German Trekkies and we had a frank chat about the terrible corporate-rigged US-western system. Star Trek gives me the sort of feeling that the local church used to give me as a child, that I was with people who at least said decent things, with the huge added bonus that Star Trek is based on logic and science and so is endlessly interesting and makes sense.

William Shatner is always surprising. When I got him to sign something at a convention in 2012 I gave him a short speech about how I've developed a hypothesis that might make faster than light travel possible (see here) and how Star Trek was of course an inspiration, and he showed no interest in astrophysics and just said "You're very welcome". Yesterday, he would not shut up about astrophysics! He's been chatting to bigwigs like Machiu Kaku, DeGrasse Tyson and Stephen Hawking. Hawking apparently, through no fault of his own of course, took half an hour to ask Shatner a question, who was on tenterhooks thinking what profound question it would be, and it turned out to be "What is your favourite episode?". Shatner talked a lot about dark matter, though admirably he teased these three guys for not knowing what it was. I felt like standing up and shouting: "Dark matter does not exist (link) and I have a far better explanation for galaxy rotation!" (see here).

To mix healthy fact in with the science fiction, I was very glad that Al Worden was there too: the Apollo 15 astronaut who orbited the Moon. Worden said he was flying over the Moon one day and when he woke up in the 'morning' the craters looked awful big. He was concerned and phoned Houston who said "Yeah. You're a little close", "How close?" "31 km +/- 10 km" (or something). He then said in his pragmatic American way: "When people give you numbers in a circumstance like that, with a plus or minus after it, you pay attention!". That made me laugh, because I'm always trying to get my students to use error bars. I can use that story in class.

Gravity from Quantum Mechanics

Three years ago I wrote a little chit of a paper that was accepted and published by Astrophysics and Space Science without any modifications (the only time that has happened to me). I thought at the time that it was absolutely beautiful in form, but probably nothing to do with MiHsC/quantised inertia. It is fascinating that recently I have managed to derive MiHsC from this method as well, and it is so suggestive, that it is now taking over my work.

Heisenberg's uncertainty principle is part of quantum mechanics, and says that for a quantum particle the uncertainty in momentum dp (or energy, dE) and uncertainty in position, dx, when multiplied, equal a constant: a very small number called Planck's constant: h-bar. See equation below:

This means that the more you know a particle's position, the less you know its momentum or energy, and vice versa. Hence the joke wherein a policeman stops Prof Werner Heisenberg speeding on the Autobahn "Do you know how fast you were going?". "Nein.." says Heisenberg, "but I know where I am!". This principle has only been applied to tiny quantum particles and not on the Autobahn scale let alone for planets, but a law should be a law at all scales. So why not apply it at planetary scale?

Imagine you have a big planet, with a smaller Moon orbiting it which is quantum-jiggling slightly at random and we apply the Heisenberg uncertainty principle (HUP) to the situation, adding up the uncertainty for every possible interaction between all the Planck masses in both bodies. Let us imagine the uncertainty in position dx is the Moon's orbital radius and suddenly by chance the random perturbations push the two closer together. Now dx decreases and dE must increase. There is now more uncertainty of energy. "But this isn't REAL energy!" I hear you say. True, but what if we, just to see what happens, assume that this energy uncertainty becomes real kinetic energy. What then? Well, I showed in this little paper that you get Newton's gravity law! (You still have to assume the value of G). When you recover from the shock, do read the paper below, which is available for free on research gate (The arXiv refused to accept it, even though it had been accepted and published by ApSS).

This is a derivation of classical gravity, simply (in only eight lines) from quantum mechanics: two theories that are not supposed to be compatible. It suggests that gravity is not fundamental, but emerges from quantum mechanics (QM). This makes sense to me because there's a lot of evidence that QM is a better theory than general relativity (GR). Admittedly QM is completely nuts (but so what: "Nature will come out as she is" - Feynman), but it is fairly simple and very accurate, whereas GR is a lovely idea to us parochial humans, but is complex and is not working right at low accelerations (for example, with galaxy rotation, where it needs the ad hoc dark matter). MiHsC/quantised inertia, which is based on quantum mechanics with relativistic horizons chucked in, is far more successful (no dark matter is needed to predict galaxy rotation, see here) and I can now derive MiHsC from the uncertainty principle approach too (I have submitted a paper). This forms the outline of a new paradigm: what is conserved in nature is not mass-energy, but mass-energy plus uncertainty or information.

I can now quote Francis Bacon, with a nice double meaning:

“If a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubt (uncertainties), he shall end in certainties.” - Francis Bacon.

References

McCulloch, M.E., 2014. Gravity from the uncertainty principle. ApSS, 349, 957-959. Journal (not free)
PDF is free on research gate: Preprint (free)

Video discussing the paper: https://www.youtube.com/watch?v=4ge_ukRbuOw

MiHsC/QI vs New Galaxy Data

It is crucial to pay close attention to new data, and observational astrophysicist Prof Stacy McGaugh has a habit, like John Anderson, of writing nicely concise analyses of new data that are easy to test against. McGaugh, Lelli and Schombert have just published a paper comparing the data from 153 different galaxies across a large range of scales from dwarfs to large disc galaxies, looking at two things 1) the acceleration within them as predicted using standard dynamics from their baryonic (visible) mass only (g_bar, x axis in the Figure), and the actual acceleration as determined from the observed motion of their stars (g_obs, y axis). The result is shown on a log-log plot here (from McGaugh and Lelli, 2016):

If Newton or Einstein's general relativity were right (without the crutch of dark matter) then you would expect the data to lie along the faint straight diagonal line, so that the predicted acceleration would equal that observed. It does not. As you can see the data lifts from the straight line on the left hand side because for lower accelerations the stars' orbital speed, and therefore acceleration, is greater than expected. This is the famous galaxy rotation problem noticed by Zwicky (1933) and Rubin & Ford (1980). The majority of astrophysicists fix this by adding dark matter to the galaxies where it's needed, but that is an ad hoc solution that no-one should have to resort to in a scientific age. In the paper, McGaugh and Lelli fit a curve to this data using this formula

and show it predicts well if the fitting parameter 'gt' is set to the value 1.2x10^-10 m/s^2 and both McGaugh and Lelli, and Milgrom in a note published soon after, say this looks like some of the possible variants of MoND (Modified Newtonian dynamics). Milgrom in his note even says 'nothing else can give this behaviour' but this is simply not true. MiHsC / quantised inertia also predicts this behaviour far more plausibly and simply than MoND, and without any adjustment at all. The MiHsC formula can be found in McCulloch (2012) (see Eq. 6 in the ref below, and note the comments on a' therein. The Eq. I showed before is based on Eq. 7 and is less general). The MiHsC formula (note, only strictly valid at a galaxy's edge) is

This formula is based on a specific physical model (MiHsC: Unruh waves harmonise with horizons and cause inertia) unlike MoND which is just an empirical relation with no physical model. It is obviously much simpler than McGaugh & Lelli's formula, and crucially there are no fitting parameters in MiHsC/quantised inertia at all! Its predictions of g_obs are exactly right see Figure below and are predicted from just the known quantities of the speed of light (c) and the size of the observable universe (Theta=8.8x10^26 m):

I do feel a bit like a broken record going on about this, but it's necessary because it has not yet been widely appreciated that a theory that predicts real data without any fitting parameters, like MiHsC does, is like a diamond in the mine. Like special relativity, it is a sign of something fundamental.

(Note: MoND is a bit like the early twin patchwork formulas of Wien & Rayleigh-Jeans for blackbody radiation, whereas MiHsC/QI is like the quantum mechanics of Planck et al. which predicted it more concisely with a shocking new assumption).

References

McGaugh, S.S, F. Lelli, J. Schombert, 2016. The radial acceleration relation in rotationally supported galaxies. Phys. Rev. Lett. (to be published). Preprint.

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophysics and Space Science, 342, 342-575. Preprint

Unruh Radiation Confirmed?

One of the criticisms of MiHsC (quantised inertia) is that "it relies on Unruh radiation which has not been seen". The fact that MiHsC predicts a whole range of important anomalies is some evidence for its use of Unruh radiation, but it is not direct evidence. In this blog entry I'd like to show you why I'm fairly confident that Unruh radiation has also been directly detected, based on papers by Beversluis et al. (2002) and Smolyaninov (2008).

Unruh radiation is usually difficult to see, to put it mildly, because its wavelength is L=8c^2/a, where a is acceleration and c is the speed of light, so for a typical acceleration of 9.8 m/s^2 the wavelength is eight light years. You'd have to wait eight years for the wave to pass by and be confirmed. It would make for a nice quiet sinecure, but there is a quicker way to see them. The formula shows that to produce Unruh waves near the more familiar EM spectrum you need to increase the acceleration, hugely!

This was done unwittingly by Beverluis et al, 2002. They shone a 780 nm laser at a gold nanotip, a very sharp pin if you like, so that the 'plasmons' (quantised waves of free electrons) formed had to travel over the very sharp tip (radius of curvature, r=10^-6 m) at a very fast speed (v) and were therefore accelerated by

a = v^2/r = c^2/10^-6 = 9x10^22 m/s^2.

They noticed an anomalous photoluminescence from the nanotip with a wavelength of about 900 nm (see the Figure below, from Beversluis et al., 2002, which shows the intensity of the radiation emitted on the y-axis, as a function of wavelength, on the x-axis. See the peak at 900 nm). Beversluis et al. proposed a complex 3-stage process to explain it but also stated that each step was implausible.

Enter Smolyaninov (2008) who claimed that their suggested 3-step process for explaining this 900 nm radiation was indeed implausible, and showed how the conversion of 780 nm laser light to 900 nm photoluminescence could be due to Unruh radiation instead. It works as follows: the 780 nm laser light impacts the gold surface and creates 'plasmons' (quantised waves of free electrons) which zoom around the sharp bend at the tip (this is well known). The plasmons' acceleration generates Unruh waves of wavelength L = 8c^2/a = 8000 nm. The newly-incoming laser photons excite the gold molecules and normally they'd then drop back to the ground energy state and emit the same frequency photon (Rayleigh scattering), but the ground state is now higher because of the Unruh excitation so the molecules don't lose as much energy as they gained, and the light they emit now has a lower energy (a longer wavelength). In more typical, non-Unruh, cases this is called Raman scattering and is usually undetectable, but for rough surfaces it can be enhanced (a well-known process called Surface Enhanced Raman Scattering, discovered first by Martin Fleischman in 1973, well before he co-discovered cold fusion / LENR). So the emitted light has a lower energy and frequency as follows:

f(emitted) = f(laser) - f(Unruh)

Replacing frequencies with wavelengths, L, given f = c/L

c/L(emitted) = c/L(laser) - c/L(Unruh)

L(emitted) = 1/(1/L(laser)-1/L(Unruh)) = 864 nm.

This predicts the emission of light of wavelength 864 nm (or above, from the less curved parts of the nanotip), which agrees with the observed anomalous photoluminescence seen by Beversluis et al. of around 800 nm and above (see figure) and so this is good evidence that Unruh radiation has been indirectly seen, since other explanations have been implausible, so far.

This interests me not only because it provides more direct evidence for Unruh radiation, but also that it implies that Unruh waves, seen only in the reference frame of the accelerated object, can cause directly testable effects in the laboratory frame, and this makes me wonder about sonoluminescence (which MiHsC predicts) and LENR (which it doesn't yet, but might if high accelerations are involved).

One way to confirm that this experiment shows Unruh radiation would be to vary the curve of the nanotip and see if the emitted wavelength varies as expected (for example, a spherical nanotip, of uniform curvature, with a cylindrical stem should show a narrower Unruh-peak). Another more direct test of MiHsC (quantised inertia) itself would be to try to interfere with these shorter Unruh waves by shielding them, to see if the plasmons' inertia (trajectory) is affected.

References

Beversluis, M.R., A. Bouhelier, L. Novotny, 2003. Continuum generation from single gold nanostructures through near-field mediated intraband transitions. Phys. Rev.B., 68, 115433.

Smolyaninov, I.I., 2008. Photoluminescence from a gold nanotip in an accelerated reference frame. Preprint

MiHsC: from Hubble scale to Emdrive

A comment on my previous blog entry (by qraal) pointed out something that is obvious to those familiar with MiHsC, but needs to be more widely known: MiHsC does not just predict galaxy rotation like other models (eg: MoND and MOG) but, as I've shown in my papers, it can explain many other eclectic (varied) anomalies that have been seen, from cosmological scales right down to the lab scale (emdrive).

As an introduction for those who are new to this blog. Unruh radiation is like Hawking radiation but is predicted to be seen only by accelerating objects. Its wavelength gets longer as accelerations reduce. MiHsC says that the long-taken-for-granted property of inertial mass is caused by the relativistic Rindler horizon that opens up behind objects when they accelerate. This horizon then damps the Unruh waves on that side but not in front, thus making a radiation pressure that resists the original acceleration and causes humans to say 'that's inertial mass'. This force is also weakened when objects have tiny accelerations because the Unruh waves get long enough to be damped by the spherically symmetric Hubble horizon leading to a new prediction: a weakening of inertia at very low accelerations. MiHsC is encapsulated by the equation below, which is an approximation to the real process of Unruh waves being deselected by horizons

where mi is the inertial mass, mg is the gravitational mass, c is light speed, |a| is the magnitude of the acceleration of the mass and the Theta is the Hubble scale (2.6x10^26 metres). The good thing about this equation is that it is inevitable, being based on an intuitive physical model and all these quantities are well defined and known, so any agreement with data that I talk about here has not occurred because I've 'tuned' the model. The model can only make one prediction, which happens to agree with nature.

On cosmic scales MiHsC correctly predicts the recently observed cosmic acceleration. This drops straight out when you put the above formula for mi into Newton's 2nd law and gravity law. You can try it yourself! At the same scale MiHsC predicts the recently-observed unexpected smoothness of patterns in the Cosmic Microwave Background (the so called low-L CMB anomaly). The Hubble horizon is damping long waves.

MiHsC predicts the rotation of all galaxies from tiny dwarfs, through discs to galaxy clusters, and just from the equation above, whereas MoND has to be 'tuned' by parameter a0, and dark matter has to be packed-in differently for each galaxy to make the rotation curve fit general relativity. MiHsC also predicts why the oddities start when accelerations go below a particular value: the Hubble horizon then starts deselecting the long Unruh waves (see diagram below).

MiHsC predicts the Pioneer, Galileo and Ulysses anomalies, with its weakening of inertial mass at low accelerations. The Pioneer anomaly has been also explained by a complex thermal model, but the emphasis here being on complex.. I distrust complex adjustable models. MiHsC predicts the flyby anomalies, close, but not perfectly, as being due to the weakening of inertia since mutual accelerations between passing spacecraft and the spinning Earth are lower near the poles, reducing the inertia mass of the craft and by conservation of momentum (mass times speed) boosting their speed.

It predicts the anomalous effects seen by Tajmar when he spun a supercooled disc and noted that a nearby accelerometer moved slightly with the disc (with no frictional contact).

It predicts the Emdrive, a truncated metal cavity with microwaves inside, which, In MiHsC, is rather like joining a big cosmos (the wide end) which allows more Unruh waves (more inertia) to a small cosmos (allows fewer waves, less inertia) so that objects, microwave photons in this case, going from the small end to the big end gain mass (ie: the mass shifts rightwards, see diagram) so to conserve momentum (mass x speed) the cavity has to go the other way, as it does. The numbers agree with the data quite well.

This list represents successes from a cosmic scale of 10^26 metres, right down to the lab scale of a 0.1m! I'm now working on the proton radius anomaly which may give me another 10 orders of magnitude of scale. I should say also, that MiHsC reduces to the standard model for high accelerations (in the equation above hen a is huge then mi = mg, the famous equivalence principle) so it is not contradicted by any empirical data.

MiHsC can also be called quantised inertia, which is a more accessible name. Another possible name is 'horizon mechanics', which was suggested recently by someone who's read my book: John Michael Dorman. More theoretically, it is another step consistent with the history of science, which has always progressed by debunking invisible quantities, like the Greek gods (Thales), epicycles (Newton), the aether (FitzGerald, Einstein). Now we can jettison dark matter (well, most of it). MiHsC also links together relativity and quantum mechanics in a natural way.

Mathematically, MiHsC is not complete, instead of the equation above, it ideally needs a formula to describe exactly how Unruh waves are allowed or disallowed by horizons of a complex shape, and then how the remaining Unruh waves push the object around. There lots of scope for mathematicians here..

Experimentally, the best way to prove MiHsC would be to try and accelerate an object so much that the Unruh waves it is assumed to see, become small enough (they're usually light years long) to be interfered with by our technology. For example if you set up a spinning disc or resonate light within a cavity, and then block the Unruh waves on one side only, MiHsC predicts the object should move towards the blockage.

A marriage of relativity & quantum mechanics

I'm often accused of being a radical, but I'd like to point out that MiHsC is actually far less radical than dark matter. Consider dark matter. Its supporters believe that 96% of the universe is in the form of a new and invisible form of matter and energy that has a weird structure, as dark matter for example must cling to the edges of galaxies and stay away from their centres, so it needs an entirely new dark-sector physics to explain it.

In the meantime, MiHsC says only that we need to fully accept both relativity and quantum mechanics and therefore the horizons and Unruh waves that they have already predicted and, here's the crucial new bit: assume that inertial mass (never understood before, and Higgs only predicts 0.01% of it) is caused by the Unruh waves being modified by the horizons. The result is a dynamics far better than the usual one since it predicts all dwarf galaxies, spirals and clusters without any tuning, whereas the dark matter hypothesis needs a new type of matter and its physics to be added, and a different amount for each galaxy. This is why it is strange that dark matter-ists accuse MiHsC of being a weird theory out of the blue. The pot calling the kettle black.

MiHsC is simply a particular marriage of relativity and quantum mechanics that happens to predict inertial mass. Of course, people have been trying to marry these two theories off for a long time and have failed because they didn't want to break the equivalence principle or they worried about non-locality, but these breaks are theoretical and not necessarily forbidden by experiment.

The bride (quantum mechanics) and groom (relativity) were first introduced to each other by Hawking, Fulling, Unruh and Davies who predicted Hawking-Unruh radiation. People like Jennison, Milgrom and Haisch and Puthoff offered hints but without a plausible method. I disliked the complexity of the arrangement and suspected there was actually a baby coming (a better model of inertial mass), got my shotgun and rammed the two theories together, and damn the consequences. I've been able to continue because all the consequences that were feared for decades turn out not to disagree with experiment and in fact they predict many of the anomalies that the dark sector was invented to fudge. It just shows that sometimes you just have to suck it and see.

To make this point even more simple mathematically than before, I've recently submitted a paper showing I can derive MiHsC (with an annoying factor of 1.26 probably caused by my simplification of the shape of the Rindler horizon) in 10 lines just from Heisenberg's uncertainty principle and special relativity, similar to my approach to gravity in 2014 (see ref). So I'm just waiting patiently for the standard first rejection...

References

McCulloch, M.E., 2014. Gravity from the uncertainty principle. A&SS, 349, 957-959. Video

Dragonfly 44: a fudge too far.

Yesterday, a few people online kindly sent me the news that a galaxy called Dragonfly 44 has been found apparently containing 99.99% of the so-called 'dark matter' (see reference). Many, for example Sean Carroll, said that this supports the dark matter hypothesis. However, in reality it worsens the outlook for dark matter, which has to be added in different ad hoc amounts to each galaxy, in huge amounts to this one, and so it further supports MiHsC (quantised inertia) which works for all galaxies without any arbitrary tuning needed...

For each separate galaxy they find, the darkmatterists have to add dark matter in different amounts, 90% for the Milky Way, 99% for dwarf satellite galaxies, 99.99% for this one. This number is arbitrary, they chose it incestuously to make general relativity work for the data, and it has no reason behind it except to save GR. That means that the dark matter hypothesis is not only not falsifiable (you can look for dark matter for ever), it is also not predictive. Given the visible light distribution, dark matter cannot predict the velocity of stars. So dark matter is a bit like Peeves at Hogwarts: useless, but you can't get rid of him.

In contrast MoND and quantised inertia / MiHsC are both predictive. Given the visible mass M (it's best to base theories on visible stuff) MoND says the stellar velocity is v=(GMa0)^1/4 (a0 is a fitting parameter) and MiHsC says v=(2GMc^2/Hubblescale)^1/4 (no fitting parameter, and a slighly higher velocity, see equation below) and both predict the velocity dispersion of Dragonfly 44 within the uncertainty and without the need for any dark matter.

The important advantage of MiHsC over MoND is that MiHsC has no adjustability, at all! MoND was an inspiration for me, but it is not a theory, it is an empirical formula that happens to fit galaxy rotation if you 'tune' the adjustable parameter a0 against the data, so it is not surprising that it fits the data, because it has been fitted to it. The parameter a0 has no 'physical reason'. MoND is a bit like an engineering formula with its tune-able a0. In contrast MiHsC has been derived from first principles, says the velocity has to be one value with no tuning possible, and every parameter in the MiHsC formula below is known from observation and is there for a good physical reason, so it is remarkable that it works on all galaxies including Dragonfly 44:

In this way MiHsC resembles special relativity in that there is no arbitrariness about it, no input numbers, but it will need input from better mathematicians than me to properly describe higher order effects due to the interaction of Unruh waves with relativistic horizons or cavities.

A loose analogy to this crisis in astrophysics would be holding a competition to see who can make a shoe to fit a foot they've only seen from a distance (like a theory that must predict galaxy rotation from observed quantities to be useful). Shoemaker 1 comes with his shoe, says 'It fits', but you see nothing. 'It's invisible!' he says (GR and dark matter). Shoemaker 2 comes with a shoe that has an adjustable strap and he adjusts the strap to fit it (MoND). This is better. Then shoemaker 3 comes with one unadjustable shoe, and it fits (MiHsC). Obviously, the third shoemaker is the best one.

I cannot emphasise enough the difference between tunable theories like dark matter, and to a lesser extent MoND, and a non-tunable theory like MiHsC. Only a non-tunable theory gives a real understanding of the physics.

References

van Dokkum, P., 2016. A High Stellar Velocity Dispersion and ~100 Globular Clusters for the Ultra Diffuse Galaxy Dragonfly 44. http://arxiv.org/abs/1606.06291

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophys. & Sp.Sci., 342 (2), 575-578. http://arxiv.org/abs/1207.7007

The Emperor's Naked!

Karl Popper made a statements that should by engraved above the entrance to every proud physics department:

"A theory can never be proven, but it can be falsified, meaning that it can and should be scrutinized by decisive experiments. If the outcome of an experiment contradicts the theory, one should refrain from ad hoc manoeuvres that evade the contradiction merely by making it less falsifiable."

In 1915 Einstein finished general relativity and this theory has been successful in regimes where the acceleration is high (such is in the inner Solar system and close-orbiting binary stars. Then in 1933 (by Fritz Zwicky) and in 1980 (by Vera Rubin) it was found that galaxies were orbiting so fast at their low-acceleration edges that, if they had any decency at all, they should explode centrifugally. Yet they don't: they generally persist in sensible bound/round shapes.

This means that most of the observed cosmos, the bit with a low acceleration, does not agree with general relativity. The theory has been hugely falsified, but tell that to a mainstream physicist at a conference (I have done) and you'll be pigeon-holed in a category somewhere below holocaust denier and they'll walk away in disgust. Speaking objectively, given GR's failure with 90% of the data, you can either claim that general relativity is wrong, and invent a new theory (for example I have suggested MiHsC, which reduces the outward centrifugal force in galaxies) or you can claim that there is a huge amount of invisible matter holding the galaxy together by gravity: dark matter.

There are several reasons why it is obvious that the problem is a failure of theory and not due to dark matter:

1) The galactic problems always start at a radius where the acceleration goes below about 10^-10 m/s^2 which is also the cosmic acceleration, so it is obviously linked (in a way that MiHsC explains simply).

2) Globular clusters and wide binary stars, which are far too small to have any dark matter, also show the same anomaly, starting at the same critical acceleration.

3) Many other well known anomalies, eg: cosmic acceleration, the low-l CMB anomaly, the flyby anomaly, the Pioneer anomaly, Tajmar's spinning disc results, the emdrive and the proton radius puzzle are all consistent with the galactic rotation anomaly if you look within the framework of MiHsC.

4) Dark matter is just a mess. It needs huge amount of new matter to be added in an ad hoc way and it also needs new physics to keep it spread out in a galactic halo.

5) There is no evidence for dark matter even after 40 years of very expensive looking.

6) Philosophically: dark matter defends a theory (GR) that failed to predict galaxy rotation properly, by inventing an ad hoc manoeuvre that makes it less falsifiable (see Popper's warning above). If a theory uses an ad hoc fix that is, even worse: as vague as a bad politician's promises, then beware!

As a result of these points I'm amazed that the rest of physics is spending most of its money (each dark matter detector is on the order of $100 million dollars) to defend general relativity by looking for dark matter and almost no-one is challenging the theory. I agree the dark matter option should have been looked at, a null result, like Michelson and Morley's is useful, but it must be in proportion to other options. Instead dark matter is tacitly assumed in journal papers and magazines articles, and there are even dark matter conferences which are inherently unscientific, since they pre-assume the solution they're looking for!

As Popper suggested, instead of trying to defend the status quo, it has always been more effective to attack the prevailing theory. It is easy to attack general relativity since the counter-evidence is already plentiful (see above), so why don't they?

After ten tears of fighting it, I think the obsession with dark matter is like the age-old story of the Emperor's new clothes. People are told that only the cleverest can see the clothes (dark matter), so everyone of course says that they can see them when the Emperor goes on walkabout awarding post-doc positions, but eventually some idiot comes along and says 'Ho Ho The Emperor's Naked!' and the spell is broken. Well, I'm willing to be the idiot, and I have suggested MiHsC, and, although I say it myself, MiHsC is far more successful than GR, absolutely beautiful and simple in form, joins quantum mechanics and special relativity for the first time, and offers a new way to get energy and propulsion (by learning to put horizons in the zero point field). Since we're talking about invisible fashions, it seems appropriate to quote Coco Chanel:

The most courageous act is still to think for yourself. Aloud.