  One of the main issues in measuring the speed of light when it only travels
from one spatial position into another position, known as the one-way speed of
light, is that the clocks belonging to each separated spatial position are not
and, in principle, cannot be synchronized with sufficient precision. This issue
is the main reason why all of the measurements of the speed of light until now
have measured the two-way speed of light, i.e., measuring the speed of light
that travels from a source to another location and back to the source, and so
there is a need for only one clock to measure the speed. Here, we show that it
is possible, in principle, to measure the velocity of particles that travel at
the speed of light without assuming a round-trip once we adopt a quantum
mechanical description under two boundary conditions to the state of the
quantum system followed by the two-state-vector formalism while assuming
non-synchronized quantum clocks with unknown time dilation. We show that the
weak value of velocity can be measured for a test particle that has a clock
that is not synchronized with the clock of the quantum particle. Following the
proposed setup, when the weak value of the velocity is known even without
knowing the time states of the system, such a weak velocity is the two-way
speed of light. Otherwise, one has to impose assumptions regarding the time
states of the quantum clocks, which then give weak velocities that can be
slower or even faster than the two-way speed of light. We further explore some
fundamental implications of the setup. The proposed approach opens a new avenue
toward measuring the velocities of quantum particles while overcoming
relativistic issues regarding the synchronization of clocks.
