Testing the strong equivalence principle with the triple pulsar PSR J0337+1715

Three conceptually different masses appear in equations of motion for objects under gravity, namely, the inertial mass, $m_{\cal I}$, the passive gravitational mass, $m_{\cal P}$, and the active gravitational mass, $m_{\cal A}$. It is assumed that, for any objects, $m_{\cal I} = m_{\cal P} = m_{\cal A}$ in the Newtonian gravity, and $m_{\cal I} = m_{\cal P}$ in the Einsteinian gravity, oblivious to objects' sophisticated internal structure. Empirical examination of the equivalence probes deep into gravity theories. We study the possibility of carrying out new tests based on pulsar timing of the stellar triple system, PSR J0337+1715. Various machine-precision three-body simulations are performed, from which, the equivalence-violating parameters are extracted with Markov chain Monte Carlo sampling that takes full correlations into account. We show that the difference in masses could be probed to $3\times10^{-8}$, improving the current constraints from lunar laser ranging on the post-Newtonian parameters that govern violations of $m_{\cal P}=m_{\cal I}$ and $m_{\cal A}=m_{\cal P}$ by thousands and millions, respectively. The test of $m_{\cal P}=m_{\cal A}$ would represent the first test of Newton's third law with compact objects.