In the double-slit experiment, the behavior of light or particles is not directly influenced by the speed of light delay in observation. The concept of "observation" in the context of the experiment refers to detecting or measuring the outcome of the experiment, rather than the physical act of perceiving or recording it.
When performing the double-slit experiment with light, for example, the interference pattern is typically observed by detecting the light on a screen or photographic plate placed behind the slits. The light waves or particles interact with the screen, and the resulting pattern can be recorded and analyzed.
However, it's important to note that the light or particles do not require a specific amount of time, based on the speed of light, to "realize" they are being observed and change their behavior accordingly. The interference pattern arises due to the inherent wave-particle duality of light and matter, and it can be observed regardless of the specific time it takes for the information about the observation to reach the system.
According to the Copenhagen interpretation of quantum mechanics, the act of observation collapses the wave function and determines the outcome of the experiment. This collapse occurs instantaneously in terms of the quantum mechanical formalism, without any delay associated with the speed of light.
It's worth noting that there are other interpretations of quantum mechanics that explore the role of time and the process of measurement differently, such as the pilot wave theory or the many-worlds interpretation. However, in the standard interpretation of the double-slit experiment, the concept of "observation" does not involve a delay based on the speed of light.