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