Two Poisson processes cannot be negatively correlated due to the inherent positivity of Poisson random variables, which ensures that their joint distribution remains non-negative. The Frechet bounds can be applied to demonstrate this relationship, highlighting that the correlation between two independent Poisson processes cannot fall below zero. While some discussions suggest the possibility of constructing a negatively correlated Poisson distribution, this contradicts established results from copula theory. A relevant survey article by Embrechts provides insights into these concepts, although it indicates that the initial conjecture about negative correlation may not hold true. The conversation underscores the importance of understanding the mathematical foundations behind Poisson processes and their correlations.