Idle thoughts of a freshly non-idle lady

What if Star Trek transporter made a new copy of you every time you got beamed somewhere, and the old you just got disintegrated in the energy beam? Your original consciousness terminated, never to be recovered again? For the outsiders, there would be no way to perceive that the new copy is a new individual, imbued with all your traits, experiences, and memories, so they'd just figure you got beamed up. How would we ever know?