No, it would not be possible to "go back in time" by using trillions of nanobots to place every atom back to its exact position after an explosion.
The concept of going back in time, as commonly understood, involves reversing the progression of time itself. However, in our current understanding of physics, time is considered a unidirectional dimension that moves forward. The laws of thermodynamics, which govern the behavior of energy and entropy, make it highly improbable to reverse the effects of a macroscopic event like an explosion.
Even if trillions of nanobots were somehow able to meticulously reconstruct the exact positions of every atom in a system, there are several fundamental challenges that would prevent this scenario from resulting in a "reversal" of time:
Conservation of energy: An explosion involves a significant release of energy, which is dispersed into the environment in the form of heat, light, sound, and other forms of energy. Even if the atoms were restored to their original positions, the energy that was dispersed would still exist and would not be reversed. Energy disperses and dissipates, making it practically impossible to fully recover the initial state.
Entropy and information loss: Entropy is a measure of the disorder or randomness in a system. Entropy tends to increase over time in isolated systems, according to the second law of thermodynamics. An explosion leads to a dramatic increase in entropy as the system goes from an ordered state to a highly disordered one. Even if the atoms were placed back precisely, the information about the initial state and the specific arrangement of atoms would likely be lost, making it impossible to fully recreate the original conditions.
Quantum effects and uncertainty: At the microscopic level, quantum mechanics introduces inherent uncertainty and probabilistic behavior. Even with precise knowledge of the initial positions of atoms, quantum effects would come into play, and the system would evolve differently due to the inherent uncertainty in quantum behavior.
In summary, the idea of "going back in time" by perfectly reconstructing the positions of every atom after an explosion goes against our current understanding of fundamental physical laws, such as the irreversible nature of time, the increase of entropy, and the conservation of energy. Time travel concepts, if they were to be explored, would require a much deeper understanding of the fundamental nature of time and the laws of physics beyond what is currently known.