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Now far more information than that/what was carried by 10 to 20 wires can be carried by a single thread-sized strand of fiber-optic material.

Which is the right choice? and why is it?

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This sentence would require "what". If you were making a comparison to a previous discussion of the information carried by 10 to 20 wires, you could say, "Now far more information than that can be carried by a single thread-sized strand of fiber-optic material." "That" is a placeholder referring to the person, thing, or idea indicated, mentioned, or understood from the situation - M-W

You're making the entire comparison in one sentence, so you need to define what will be compared to fiber optics. "what was carried by 10 to 20 wires" describes the thing you are going to compare. "What" in this case means that which -M-W: "that which was carried by 10 to 20 wires".

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In this sentence:

A train car nowadays can carry freight much heavier than that carried by a wooden wagon.

that can be understood as a demonstrative adjective with "freight" as the tacit reference:

.. much heavier than that [freight] carried by a wooden wagon.

In this sentence:

A train car nowadays carries freight much heavier than what was carried by a wooden wagon.

what is a nominal, or at least a placeholder for a nominal; it heads the phrase "what was carried by mules and wagons". That phrase in its entirety is a sort of periphrasis for "freight".

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