Anyone who says the white dwarf would is wrong. But wait. Anyone who says the pulsar would is also wrong (even though pulsars are superdense). Under the gravitational strong equivalence principle (SEP) in Einstein’s theory of general relativity (GR), it doesn't matter that a teaspoon of pulsar material would weigh a billion tons on Earth, compared to only several tons for the same amount of star stuff from a white dwarf. Scientists studying this phenomenon found that since both are under the same gravitational pull — orbiting the same dying star — neither can move faster than the other.
“Pulsars that are orbited by white dwarf companions provide an excellent laboratory, where the extreme difference in binding energy between neutron stars and white dwarfs allows for precision tests of the SEP via the technique of radio pulsar timing,” said Guillaume Voisin of the University of Manchester, whose team recently published a study in Astronomy & Astrophysics.
Think of the hypothetical feather and bowling ball falling from the same height, which would drop at the same rate anywhere on Earth despite the enormous difference in mass. That is SEP at work. Both objects are subject to the same pull of gravity since they are on the same planet, so therefore, if they drop from the same height, neither falls faster than the other. It is no different for stars that may be orbiting the same star somewhere in the far reaches of deep space.
To really put SEP to the test, the scientists tried to find something that violated this principle in the orbiting pulsar and white dwarf. Pulsar-white dwarf systems are known to have eccentricities. Whether anything eccentric would prove Einstein wrong was the question. If there were an SEP violation, that would suggest cracks in general relativity. However, finding no violation would further strengthen general relativity. Alternative theories of gravity often claim that the self-gravity of an object determines its gravitational properties. These were also tested as part of the experiment, to see which, if any, the celestial bodies would violate.
Because of the difference in mass between a pulsar and a white dwarf, it may be easy to assume that the pulsar would move faster. Alternate theories of gravity that the team looked at took factors such as mass and spin frequency into account. Some of these predicted that the pulsar’s behavior would differ from that of the white dwarf it orbited with and the white dwarf it orbited around, but they always ended up breaking somewhere. Both orbiting objects were proven by SEP to react the same way to the object they orbited, regardless of mass, density, spin, or anything else that was outside of the realm of general relativity.
Somewhere in the fabric of spacetime, Einstein is probably throwing a party over this.
“Our results are fully consistent with the predictions of [general relativity]. This limit strongly constrains SEP violation and any alternative theories of gravity that predict a violation of the universality of free fall for self-gravitating masses,” Voisin said, adding that “In all of these experiments, no … violation can be detected; gravity behaves, to within observable precision, as described by GR, which is conjectured to be the only viable theory which fully embodies the SEP.”
While there are videos of bowling balls and feathers out there that prove SEP, too bad no one can actually drop a pulsar and a white dwarf at the same time. That would go viral.