Time dilation does not affect causality because the relationship between cause and effect remains intact regardless of the differences in the perception of time between observers in different frames of reference. Although time dilation may lead to different measurements of time between observers, it does not disrupt the causal order of events.
Causality is a fundamental principle that states that the cause of an event must precede its effect. Time dilation, on the other hand, describes the relative difference in the passage of time between observers moving at different velocities. It does not change the order of cause and effect.
From the perspective of each observer, cause and effect occur in the same order. They may experience different durations between events or perceive time passing at different rates, but the causal relationship remains unchanged. For example, if event A causes event B, all observers will agree that event A must occur before event B, regardless of any time dilation effects.
To illustrate, let's consider a simple scenario: two observers, one stationary and one moving at a high velocity relative to the stationary observer. From the stationary observer's perspective, they see the moving observer's clock running slower due to time dilation. From the moving observer's perspective, they see the stationary observer's clock running slower. However, regardless of the perceived differences in the passage of time, both observers will agree on the causal order of events they witness.
The consistency of causality is a fundamental principle of physics, and time dilation does not alter this principle. It merely introduces differences in the measurement of time between observers, but the cause-and-effect relationships between events remain preserved.