It isn’t even physically continuous. There are multiple mechanisms to rebuild, resync, reinterpret, etc the reality. Because our vision is blurry, sound has low speed in the air, and nerves aren’t that fast either. Even the internal clarity and continuity is likely a feeling, the opposite being “something wrong with me”, space/time teleports, delays and loops and other well-known effects that people may have under influences. You might jump back and forth in time perception-wise by default all your life and never notice it because the internal tableau said “all normal” all the way.