Milgrom's Comet

Mordehi Milgrom in the early 1980’s developed an alternative theory to explain the behavior of galactic rotation curves informally known as Modified Newtonian dynamics, less commonly known as Milgrom’s law.

MoND had been more or less kept on a shelf by the broader scientific community and it’s no secret it fails to explain the large scale structure of the universe, yet it doesn’t go away because it does make very precise predictions which have been shown true by observation, far more accurately in fact than dark matter theory on the galactic scale.

In simple terms Milgrom’s law proposes the force of gravity changes from an inverse square of the distance between two objects into just the inverse of that distance at a point relative to size and speed of the objects involved.

This may seem counter intuitive on the surface as there is no obvious mechanism to change the force of gravity, but this behavior of differing field strengths over distance is not unknown to science. In fact the only analogous energy field in the universe, the far stronger magnetic field, experiences precisely this kind of loss in the near and far field ranges. In the near field power over distance is measured by the inverse of the cube of the distance between two points, in the far field it is measured by the inverse square.

Milgrom basically says gravity does exactly that, and when the equations are run you get perfectly spun spiral and elliptical galaxies. When put in those terms it seems so symmetrical with standard theory to me it’s hard to imagine why there has been such resistance to look at trying to develop an underlying theory unless you know more of the story.

One reason it the idea of Milgrom’s law gathers dust on the shelf is it’s hard to prove. To do that we would need an analogous gravitational system that we could measure the speed of the furthest orbiting objects accurately. For us our best bet is our solar system, and that would mean measuring the speed of Oort cloud objects we can’t yet really see. Maybe one day we can dream up a mission to illuminate and survey these distant objects in the Oort cloud. I believe we would learn much more from that than we would dropping several more tons of ultra pure water down another mineshaft.

We can measure the speed of some Oort cloud objects though, those which sweep into the inner solar system, the comets. Some comets will take trajectories which represent little gravitational interaction to explain their velocities, though initial interactions can’t be ruled out, those velocities can none the less be compared to predictions made using Milgrom on similar bodies on similar long period orbits.

If there is any symmetry at all, whatsoever between those predictions and comet velocities, it would be evidence that maybe MoNd isn’t just a fringe idea, and might very well be on to something after all.

Milgrom’s comet would throw serious doubt on the mysterious and elusive dark matter particle if we found it. If any such symmetry existed between MoNd and the orbital velocities of comets or Oort cloud objects it would be a stunning validation of an idea which for years has clung to outside edges of mainstream thought and debate.

Perhaps it’s time we take another look…

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I believe that a fair number of MOND-based hypotheses were killed off by the observations of the recent neutron star merger. Admittedly, there are some that survive, but they appear to be an ever decreasing number. Every test of GR seems to confirm it to very high precision.
This article seems to do a good job of summarising the current state of affairs;

The fundamental assumption that prevents science from taking Milgrom seriously is the idea this needs to replace relatively. It does not, they are complimentary equations which on balance describe the whole behavior of a gravitational field.

The recent studies which attempt to eliminate MoND also rely heavily on fundamental assumptions to draw their conclusions even though the process was both rigorous and scientific the results pointed in a direction but were far from conclusive.

Einstein was limited by the extent of our ability to make observations at the time his theories and ideas were developed. We have no idea how he would have responded to the mystery of galactic rotation curves, but I feel he would have given Milgrom’s ideas which point to a duality of the gravitational field similar to the duality experienced by the magnetic field more weight than a magic particle designed to keep his ideas intact.

The jury is yet very much out…

Something that just occurred to me - what about the orbits of the stars around Sgr A*? Would this be a reasonable test of MoND? If I remember correctly these orbits, and the observed gravitational redshift, strongly support the standard model.
Is it reasonable to equate a comet at ~1 AU, in terms of mass and distance from the Sun, to a star hundreds of AU from a BH?

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I think this would work rather well actually. What we need are bodies at sufficient distance from center that their velocities should fall within the predictions of relativity as slower than observed.

The problem for MoND is that the observations seem to match very well with GR;

Detection of the gravitational redshift in the orbit of the star S2near the Galactic centre massive black hole
GRAVITY Collaboration.

I know, it isn’t that relativity is inaccurate, in fact it’s quite the contrary. However we have the entire theory of dark matter predicated on the assumption that relativity is applicable at all scales when we have yet to measure accurately the velocities of distant bodies in our own back yard. Milgrom proposes a kind of Schwarzschild radius at which gravity as a force changes from an inverse square of the distance between objects to simply the inverse. Using Einstein’s field equations the velocities of bodies slow the further away from the center of gravity, we see this clearly in the orbits of the planets. If relativity holds true on it’s own then even more distant bodies should orbit even slower relative to their mass. There hasn’t been any true survey done of these objects in our own back yard because they are so hard to spot. If there was and those objects orbit faster than they should relativity would have some explaining to do. Comets come in to the inner solar system faster than they should if that is their standard orbital velocity using relativity, so the assumption is they have been nudged and pushed into new orbits that swing close and can gain momentum from both the interaction and new orbital trajectory. Perhaps this is true, but I simply like to have my assumptions challenged as often as possible…

In computer programming world, my trajectory, you have C, C++, then C++/CLI as superset to C++, C#, F#…
Then you have C99(1999), C11(2011),C14, C18 etc.
If you ask me which one is superset in relation to previous programming language then I would take stance on simple C but newer and better versions of same. So preceding and mightier superset of C++ is not C++/CLI, which really is(in common sense) but just newer revision of previous in-chain little brother C. In this case C19(2019).
Maybe it’s just naming convention about GR and MoND.