I’ve been studying MOND and some of the ideas behind theories put forward to explain MOND. Based on this I’m now going to describe the simplest, but most critical concept that’s used to begin understand why Newton’s inverse square law breaks down. Dynamics won’t be considered since they are complicated. I don‘t mind if you don‘t agree with it, I just hope it’s comprehensible. There are some concepts that need to be clarified before the concept can be understood Messenger particles. It is often theorized that force field interactions are propagated by ‘messenger’ particles, like for the electro-magnetic force, the photon, for gravity, the graviton. I was taught this at college. It is intuitive that such a messenger particle transfer between bodies might result in a repulsive force, because that is exactly what happens for the macro classical case e.g. a ball thrown between 2 people. But what about attractive force? My college teacher was quick to explain the repulsive model, but didn’t say much for the attractive force. How are attractive forces intuitively explained? Simple. As any good physicist knows, such small entities as messenger particles, theoretical or not, would not be well described simply as particles. Every object in the universe has a wave particle duality, and the wave aspect of a messenger particle helps in describing attractive forces. A messenger particle sent between 2 bodies would have an associated standing wave, which could create an attractive force. E.g. two people with a rope which is then oscillated to create a standing wave will be pulled towards each other. E.g.2. If I recall correctly, van der walls force has been shown to be a result of standing wave attraction. Might all attractive forces be a result of standing waves? Side note. A standing wave, viewed only at it’s nodes, appears much more particle like. Perhaps it is true to say particles are the nodes of standing waves. How many bodies are needed for a messenger particle exchange? 2 is the obvious answer, and up till the early twentieth century no argument otherwise would have been taken seriously. But, as physics went through the quantum revolution, it became clear a system under observation from outside acted differently to one which was unobserved, and the concept of a quantum jump became central to physics. E.g. the electron - proton interaction inside an atom is much more restricted when under observation, the system has fewer allowed states compared to when it is unobserved. More importantly, since observation itself is interaction, a system that is never in some way observed, is not considered to be part of the universe. This is observation in it’s broadest sense of course, not the familiar restricted meaning of electro-magnetic interaction ( e.g. a person looking, touching or smelling etc something ). Any type of interaction can be considered observation. So it has some real meaning to say 2 bodies are needed to interact, and a 3rd body is needed to observe the 2 bodies for the system to be part of the universe. * Conjecture : To observe a system, a 3rd body must have a standing wave messenger particle interaction with the system. If this seems unreasonable then consider that many physical dynamic are known to require this. E.g. Within an empty electric conducting box, all electromagnetic interactions within the box have to be standing waves. Other than this slight justification I won’t go into this here. The last bit of physics I need you to have in your mind… Wave - energy transfer association Every acceleration of mass can be said to have an associated wave. Acceleration of mass implies change of kinetic energy. And energy is associated with waves via the equation E=hf. Subsequently, acceleration can also be said to have an associated frequency and wavelength. High energy waves have high frequencies and short wavelength, low energy waves have low frequencies and long wavelengths. e.g. Electrons in a particle accelerator often emit high energy electro-magnetic radiation. This is clear example of wave - energy transfer association, but usually the acceleration - wave association is more theoretical. E.g. A car speeds up. Where is the associated wave? In theory it exists, but it is difficult to observe. The key principle for MOND a based theory Consider a galaxy, and in particular, the gravitational force between the galactic centre of mass and a star in one of the spiral arms. Gravitational attraction between such masses is very weak. The energy transfer in such interactions between an atom in the star and an atom in the galactic centre is typically much less than 1/10 that of the average energy transfers between atoms in the lowest temperature environments ever created on Earth, I.e. Bose Einstein condensate temperatures. And so, the theoretical acceleration waves associated with such star - galactic centre interactions are very weak, and so could be expected to have low frequency and long wavelength. It is assumed a 3rd body is needed outside the interaction to observe it. Another star in the galaxy seems a good candidate observer, but, and here’s the critical point, assuming * the largest wavelength standing wave between two stars in a galaxy is too short a wave length and thus too high energy to observe accelerations typical of star - galactic centre gravity. In fact this is a point migrom made in 1983. The gravity acceleration between star in a spiral arm and the galactic centre is so small that the associated wave would has a wavelength the size of the universe. c^2/R or c/T, where R and T are the length and age of the universe. ( note that R is the non expanding universe R ) This means it is possible the associated gravity waves between stars and their galactic centres can form standing waves with the galaxies on the edge of the observable universe. Now we can answer the question of why there is a cut off, and break down in Newton’s inverse square gravity field for galaxy rotation curves. For stars near the galactic centre, the gravity attraction and acceleration is strong, and so the associated wave has relatively short wavelength. Depending on the stars distance from the galactic centre, these waves can form standing waves with nearby to distant galaxies. But at greater distances from the galactic centre, the associated wavelength exceeds c/T, and since there are no observable galaxies at distances capable of containing a standing wave at distance of c/T, no standing wave can form. This associates the c/T galaxy rotation curve cut off to a principled theory that can be worked into the existing structure of modern physics. Summary of theory Messenger particles are better described as ‘messenger quantums’ - they can take on particle and wave behaviours. Observation and interactions have an associated wave, where the wavelength and frequency are dependant on the energy transfer of the interaction. Interactions between 2 bodies require a 3rd body to observe the interaction in order the 2 bodies can be part of the universe. To observe and interact, the messenger quantum between 2 bodies must be a standing wave. Only inter-galactic distances or greater will suffice for star - galactic centre gravity interactions observations, because the energy transfer between star and galactic centre is so small, the associated wavelength is very long. There is a necessarily a cut off for such observations and waves, because beyond the observable universe there are no galaxies to act as observers. This is the cause of the c/T discontinuity of galaxy rotation curves. One sentance Summary : The galaxy rotation anomaly\cut off is due to the size of the universe setting a lower limit on energy transfer via observer, standing waves principles. Hope that was understandable! Please give critical feedback if you feel I haven’t explained something well or if there’s a fault in my understanding.