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In the TNG episode We'll always have Paris, a time experiment allows a man to be partially in our dimensions and partially in other dimensions. How does the manipulation of time allow contact with other dimensions?

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In-universe, the answer is that Manheim's theories are being explained by a layperson (Jenice Manheim) who seems to have only the vaguest understanding of her husband's work. She isn't a scientist and was kept well away from his experiments and locked in a safe-room.

DATA: Do you know the nature of Doctor Manheim's work?

JENICE: Paul's always been interested in time. He's never believed that it was immutable, any more than space is immutable. Over the last decade, he came to believe that we reside in one of infinite dimensions, and what holds us here is the constancy of time. Change that and it would be what he called opening the window to those other dimensions.

In the earlier versions of the script, Manheim's own explanation is barely more coherent and is subject to an airy hand-wave as being too complex for someone as smart as Picard to understand, let alone us mere mortals out in TV-Land.

PICARD : I'd rather hear it from you personally, a condensed version.

MANHEIM : There is hardly a condensed version of the most complex theory of the twenty-fourth century, Captain Picard, but if you insist, I'll attempt one that even you will be able to understand.

A star four light years away went nova. I have been able to mathematically... "latch" onto the incredible gravity of this smooth black globe and direct that energy, that nearly immeasurable force, into space.

PICARD : So -- this energy, directed into space, then what?

MANHEIM : Then, abracadabra, Captain Picard, we all see God! A window to another dimension, isn't that how you put it? So pedestrian.

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