We can model the motions of planets in the solar system fairly accurately using Newton’s laws of physics. But by the early 1970s, scientists found that this didn’t work for disk galaxies – stars at their outer edges, far removed from the gravitational pull of all matter at their centers – were moving much faster than Newton’s theory predicted.
This led physicists to believe that an invisible substance called “dark matter” is exerting an additional gravitational force that is accelerating the stars – a theory that has become very popular. In a recent review, however, my colleagues and I suggest that observations at a variety of scales are much better explained in an alternative theory of gravity proposed by Israeli physicist Mordehai Milgrom in 1982, called Milgromian Dynamics, or the Moon — which does not require invisible matter .
Mond’s main postulate is that when gravity becomes very weak, as it is at the fringes of galaxies, it begins to behave differently from Newtonian physics. This explains why stars, planets and gas in the fringes of over 150 galaxies spin faster than expected based on their apparent mass alone. But moon doesn’t just do that to explain such rotation curves, in many cases, it forecast She.
Philosophers of science have argued that this predictive power makes Moon superior to the standard cosmological model, which proposes that there is more dark matter in the universe than visible matter. Because according to this model, galaxies have a highly uncertain amount of dark matter, which depends on details of the formation of the galaxy – which we do not always know. This makes it impossible to predict how fast galaxies should spin. But such predictions are routinely made at Moon and have been confirmed so far.
Suppose we know the distribution of visible mass in a galaxy, but not yet its rotation rate. In the standard cosmological model one can say with some certainty that the rotation speed at the outskirts will be between 100 km/s and 300 km/s. Moon makes a more accurate prediction that the rotation speed must be in the range of 180-190 km/s.
If observations later reveal a rotation speed of 188 km/s, then this agrees with both theories – but Moon is clearly preferred. This is a modern version of Occam’s razor – that the simplest solution is preferable to more complex ones, in which case we should explain observations with as few “free parameters” as possible. Free parameters are constants – specific numbers that we need to put in equations to make them work. But they are not given by the theory itself – there is no reason why they should have any particular value – so we have to measure them by observation. An example is the gravitational constant G in Newton’s theory of gravitation or the amount of dark matter in galaxies within the standard cosmological model.
We introduced a concept known as “theoretical flexibility” to capture the underlying idea of Occam’s razor that a theory with more free parameters is consistent with a wider range of data – making it more complex. In our review, we used this concept when comparing the Standard Cosmological Model and Moon with various astronomical observations such as the rotation of galaxies and the movements within galaxy clusters.
Each time we gave it a theoretical flexibility rating between -2 and +2. A score of -2 indicates that a model is making a clear, accurate prediction without looking at the data. Conversely, +2 implies “anything goes”—theorists would have been able to fit almost any plausible observational result (because there are so many free parameters). We also assessed how well each model agrees with the observations, with +2 indicating excellent agreement and -2 reserved for observations that clearly show the theory is wrong. From this we then subtract the theoretical flexibility value for fitting the observations, since fitting the data well is good, but fitting everything is bad.
A good theory would make clear predictions that would later be confirmed, ideally a combined score of +4 on many different tests (+2 -(-2) = +4). A bad theory would get a value between 0 and -4 (-2 -(+2)= -4). Precise predictions would fail in this case – these are unlikely to work with the wrong physics.
We found an average score for the Standard Cosmological Model of -0.25 in 32 tests, while the Moon averaged +1.69 in 29 tests. The results for each theory in many different tests are shown in Figures 1 and 2 below for the Standard Cosmological Model and the Moon, respectively.
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It is immediately apparent that no major issues have been identified for Moon, which is at least plausibly consistent with all the data (note that the bottom two rows denoting fakes are blank in Figure 2).
The problems with dark matter
One of the most striking flaws in the standard cosmological model concerns “galaxy bars” – rod-shaped bright regions of stars – which often have spiral galaxies in their central regions (see keynote). The bars rotate over time. If galaxies were embedded in massive dark matter halos, their bars would slow down. However, most if not all of the observed galaxy bars are fast. This falsifies the Standard Cosmological Model with very high confidence.
Another problem is that the original models that proposed galaxies with dark matter halos made a huge mistake – they assumed that the dark matter particles gave gravity to the matter around them, but not the gravitational pull of normal ones matter were affected. This simplified the calculations, but does not reflect reality. When this was taken into account in subsequent simulations, it was clear that dark matter halos around galaxies do not reliably explain their properties.
There are many other errors in the Standard Cosmological Model that we examined in our review, with the Moon often being able to naturally explain the observations. The reason why the Standard Cosmological Model is still so popular may be due to computational errors or limited knowledge of its errors, some of which have only recently been discovered. It could also be due to people’s reluctance to tweak a theory of gravity that has been so successful in many other areas of physics.
The enormous lead of Moon over the Standard Cosmological Model in our study led us to conclude that Moon is strongly favored by the available observations. While we don’t claim the moon is perfect, we still believe it gets the big picture right – galaxies really lack dark matter.