Monthly Archives: August 2018

Dark Acceleration: The Acceleration Discrepancy

Are Newton and Einstein both wrong?

Maybe Dark Matter has been going by the wrong name all along, ever since the cantankerous Swiss astronomer Fritz Zwicky coined the name, when his observations of the Coma cluster of galaxies showed the velocities were very much higher than expected.

He assumed Newton’s laws, and indeed general relativity, are correct. And that has been the canonical assumption ever since.

“Dark matter” has been studied on the scale of individual galaxies, clusters of galaxies, and the universe as a whole. The measurements of rotation velocity of spiral galaxies decades ago set the tone.

But the effects have been seen in the velocity dispersions of elliptical galaxies, in clusters of galaxies, and indeed in the cosmic microwave background temperature fluctuations.

What effects? Well for galaxies, whether for rotation or for dispersions within elliptical galaxies, what is actually observed is extra acceleration.

We all know F = ma, force equals mass times acceleration, for Newtonian dynamics.

In the case of galaxy rotation curves, the outer regions of the galaxies rotate faster than expected, where the expectation is set by the profile of visible matter and the modeling of the relationship between stellar luminosity and masses.

What is actually measured is the rotational (centripetal) observed acceleration of outer regions as being higher than expected, sometimes very much so.

But is m the problem? Is there missing ‘dark matter’? Or is ‘a’ the problem; does the Newtonian formula fail for the outer regions, or more specifically in environments where the acceleration is very low, less than about one ten billionth of a meter per second per second (less than 1 Angstrom per second per second)?

Now general relativity is not the explanation for the discrepancy, because we see departures from Newtonian behavior towards general relativistic formulae when acceleration is quite high, not when it is very low. So if Newton is wrong at very low accelerations, so is Einstein.

It turns out that the extra acceleration is best correlated not with the distance from the galaxy center, but with the amplitude of the expected Newtonian acceleration. When the expected acceleration is very low, the observed acceleration has the biggest discrepancy, always in the direction of more acceleration than expected.


Figure 3 from Lelli et al. 2016 “One Law to Rule Them All” This shows the observed gravitational acceleration on the y-axis (log scale) displayed vs. the expected Newtonian acceleration on the x-axis. Over 2000 data points drawn from 153 galaxy rotation curves would lie on the dotted line if there were no extra acceleration. There is very clear extra acceleration and it is correlated to the Newtonian acceleration, with a larger proportional effect at lower accelerations. At these very low accelerations the observed values are about an order of magnitude above the Newtonian value.

From an Occam’s razor point of view it is actually simpler to think about modifying the laws of gravity in very low acceleration environments. It is only in these actual astrophysical laboratories that we are able to test how gravity behaves at very low accelerations.

Explanations such as emergent gravity and other modified Newtonian dynamics approaches need serious theoretical and experimental investigation. They have been playing a distant second fiddle to expensive dark matter searches for WIMPs and axions, which keep coming up short even as the experiments become more and more sensitive.


F. Lelli, S. McGaugh, J. Schombert, M. Pawlowski, 2016 “One Law to Rule Them All: The Radial Acceleration Relation of Galaxies”