The only objects which can constitute [the space-time framework essential to interpersonal communication] are those which confer upon it their own fundamental characteristics.
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The construction X confers Y upon Z means that X causes object or person Z to have attribute Y.
So your example sentence means that objects cause "the space-time framework essential to interpersonal communication" to share in "their own fundamental characteristics".
"To exchange one's opinion, thoughts, views etc." or "to give or grant a thought of yours to others".
Confer means "to grant or bestow a title, degree, benefit, or right"; upon is a preposition that has the same meaning of on, but it is more formal.
You can also use it to mean "to give a characteristic, feature, or quality".
[Reference: the New Oxford American Dictionary, third edition.]