Does Impermanent Loss Occur If Both Tokens’ Prices Double Simultaneously?
No, impermanent loss does not occur if both tokens' prices double simultaneously, because the price ratio between the two tokens remains unchanged. Impermanent loss is solely a function of the divergence in the price ratio from the time of deposit.
If the ratio is constant, the pool rebalancing mechanism does not trigger, and the LP's portfolio value relative to a hold strategy is identical.