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The linguistic relativity hypothesis, also known as the Sapir-Whorf hypothesis, proposes a relationship between the structure of one's language and the way one thinks. It suggests that the language we speak shapes our perception and understanding of the world.

Let's evaluate each option to determine which one captures the essence of the linguistic relativity hypothesis: A. one's language determines the nature of one's thought -> This option aligns well with the hypothesis, stating that the language we speak directly influences our thoughts. B. one's thought determines the nature of one's language -> This option contradicts the hypothesis, as it suggests that thoughts shape language rather than the other way around. C. language and thought are separate and independent processes -> This option does not support the linguistic relativity hypothesis, as it claims that language and thought are unrelated. D. language and thought interact, with each influencing the other -> This option is also in line with the hypothesis, stating that language and thought mutually influence each other.

From our analysis, options A and D both align with the linguistic relativity hypothesis. However, option D is a more accurate description, as it emphasizes the mutual relationship between language and thought. Therefore, the correct answer is: D. language and thought interact, with each influencing the other.