The Evidence For A Strong Equivalence Principle Violation Explained

Stacy McGaugh at his Triton Station blog explains a recent (previously blogged) paper showing convincingly that the External Field Effect predicted by MOND is real, even though it violates the Strong Equivalence Principle of General Relativity.

A weird consequence of the EFE in MOND is that a dwarf galaxy orbiting a large host will behave differently than it would if it were isolated in the depths of intergalactic space. MOND obeys the Weak Equivalence Principle but does not obey local position invariance. That means it violates the Strong Equivalence Principle while remaining consistent with the Einstein Equivalence Principle, a subtle but important distinction about how gravity self-gravitates.

Nothing like this happens conventionally, with or without dark matter. Gravity is local; it doesn’t matter what the rest of the universe is doing. Larger systems don’t impact smaller ones except in the extreme of tidal disruption, where the null geodesics diverge within the lesser object because it is no longer small compared to the gradient in the gravitational field. An amusing, if extreme, example is spaghettification. The EFE in MOND is a much subtler effect: when near a host, there is an extra source of acceleration, so a dwarf satellite is not as deep in the MOND regime as the equivalent isolated dwarf. Consequently, there is less of a boost from MOND: stars move a little slower, and conventionally one would infer a bit less dark matter.

The importance of the EFE in dwarf satellite galaxies is well documented. It was essential to the a priori prediction of the velocity dispersion in Crater 2 (where MOND correctly anticipated a velocity dispersion of just 2 km/s where the conventional expectation with dark matter was more like 17 km/s) and to the correct prediction of that for NGC 1052-DF2 (13 rather than 20 km/s). Indeed, one can see the difference between isolated and EFE cases in matched pairs of dwarfs satellites of Andromeda. Andromeda has enough satellites that one can pick out otherwise indistinguishable dwarfs where one happens to be subject to the EFE while its twin is practically isolated. The speeds of stars in the dwarfs affected by the EFE are consistently lower, as predicted. For example, the relatively isolated dwarf satellite of Andromeda known as And XXVIII has a velocity dispersion of 5 km/s, while its near twin And XVII (which has very nearly the same luminosity and size) is affected by the EFE and consequently has a velocity dispersion of only 3 km/s.

The case of dwarf satellites is the most obvious place where the EFE occurs. In principle, it applies everywhere all the time. It is most obvious in dwarf satellites because the external field can be comparable to or even greater than the internal field. In principle, the EFE also matters even when smaller than the internal field, albeit only a little bit: the extra acceleration causes an object to be not quite as deep in the MOND regime. . . .

The figure above shows the amplitude of the EFE that best fits each rotation curve along the x-axis. The median is 5% of a0. This is non-zero at 4.7σ, and our detection of the EFE is comparable in quality to that of the Baryon Acoustic Oscillation or the accelerated expansion of the universe when these were first accepted. Of course, these were widely anticipated effects, while the EFE is expected only in MOND. Personally, I think it is a mistake to obsess over the number of σ, which is not as robust as people like to think. I am more impressed that the peak of the color map (the darkest color in the data density map above) is positive definite and clearly non-zero.

Taken together, the data prefer a small but clearly non-zero EFE. That’s a statistical statement for the whole sample. Of course, the amplitude (e) of the EFE inferred for individual galaxies is uncertain, and is occasionally negative. This is unphysical: it shouldn’t happen. Nevertheless, it is statistically expected given the amount of uncertainty in the data: for error bars this size, some of the data should spill over to e < 0.

I didn’t initially think we could detect the EFE in this way because I expected that the error bars would wash out the effect. That is, I expected the colored blob above would be smeared out enough that the peak would encompass zero. That’s not what happened, me of little faith. I am also encouraged that the distribution skews positive: the error bars scatter points in both direction, and wind up positive more often than negative. That’s an indication that they started from an underlying distribution centered on e > 0, not e = 0.

This is huge. While it is model dependent, it is the strongest evidence of a violation of General Relativity shown to date anywhere.

Many quantum gravity theories predict equivalence principle violations, although not necessarily the one observed in this case that was predicted by MOND:

Modern quantum theories, however, often require that at some scale the EP must be violated. Usually, the scale is small, no more than a few centimeters.

What sorts of forces violate the equivalence principle? In a way, one type of EP violation is familiar: any vector field which couples to a mass must violate the equivalence principle. To see this, consider electromagnetism, which is a vector field. There are two electrical charges; a positive charge behaves quite differently from a negative charge in an electric field. The existance of a charge and an anticharge is a general feature of vector fields. Then, if a vector field coupled to mass, there would have to be a mass and an antimass which would behave oppositely in the same gravitational field and therefore violate the EP.

Scalar fields also produce EP violations. Scalar charges, unlike vector charges, are not conserved. The statement of charge conservation for a vector charge is Lorentz invariant. The charge of an object is the integral of the time component of its vector current density, which picks up a factor under Lorentz transformation, over a volume element, which picks up a factor 1/. Therefore, the integral as a whole is Lorentz invariant. For a scalar charge, the relevant integral is a charge density (a Lorentz scalar) integrated over a volume; only the volume picks up a factor under a Lorentz transformation, so scalar charges are not conserved and depend on .

Now, strange things can happen because of that factor. Quarks inside the protons and neutrons are highly relativistic; electrons surrounding the nucleus move more slowly (v/c ~ Z). We therefore expect scalar interactions to be composition dependent, since larger atoms' electrons are much farther away from the nucleus and move much more slowly.]

See also here.