Is consciousness continuous?

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Imagine if we cloned someone by copying their atoms in a spot 2m away from the original. We probably believe that this would create two conscious beings, each experiencing there own experiences 2m away from each other, the original could not suddenly see out of the clone's eyes.
Now imagine just instantaneously translating someones atoms 2m away. This is equivalent to cloning the original and then deleting the original. So this should be a NEW consciousness, right?
Finally imaging translating someones atoms through another dimension; time. As we do each living moment of our lives!
TLDR: am I only alive in a single instant and some other consciousness experiences the next?