  Globular clusters can form inside their host galaxies at high redshift when
gas densities were higher and gas-rich mergers were common. They can also form
inside lower-mass galaxies that have since been accreted and tidally disrupted,
leaving their globular cluster complement bound to higher-mass halos. We argue
that the age-metallicity-specific orbital energy relation in a galaxy's
globular cluster system can be used to identify its origin. Gas-rich mergers
should produce tightly bound systems in which metal-rich clusters are younger
than metal-poor clusters. Globular clusters formed in massive disks and then
scattered into a halo should have no relationship between age and specific
orbital energy. Accreted globular clusters should produce weakly bound systems
in which age and metallicity are correlated with each other but inversely
correlated with specific orbital energy. We use precise relative ages,
self-consistent metallicities, and space-based proper motion-informed orbits to
show that the Milky Way's metal-poor globular cluster system lies in a plane in
age-metallicity-specific orbital energy space. We find that relatively young or
metal-poor globular clusters are weakly bound to the Milky Way, while
relatively old or metal-rich globular clusters are tightly bound to the Galaxy.
While metal-rich globular clusters may be formed either in situ or ex situ, our
results suggest that metal-poor clusters formed outside of the Milky Way in
now-disrupted dwarf galaxies. We predict that this relationship between age,
metallicity, and specific orbital energy in a $L^{*}$ galaxy's globular cluster
system is a natural outcome of galaxy formation in a $\Lambda$CDM universe.
