In classical physics, protons are considered to have the same amount of energy if they are at rest, since their energy is solely determined by their mass. However, in quantum mechanics, particles such as protons can have additional energy due to their motion, known as kinetic energy, and their interactions with other particles or fields.
At any given time, protons can have different amounts of energy in certain contexts. For example, protons in an accelerator like the Large Hadron Collider (LHC) can be accelerated to high speeds using electromagnetic fields, resulting in significantly higher energies compared to protons at rest. The energy of a proton in such a scenario is determined by its kinetic energy, which increases with its speed.
In addition to kinetic energy, protons can also possess potential energy due to their interactions with other particles or fields. For instance, protons in a strong magnetic field can acquire magnetic potential energy. The total energy of a proton in such cases would be the sum of its kinetic and potential energy.
It's important to note that in quantum mechanics, particles can also exhibit energy fluctuations due to the inherent probabilistic nature of the quantum realm. These energy fluctuations are described by the uncertainty principle, which implies that the precise energy of a particle at a given instant may not be well-defined.
Therefore, while protons at rest can be considered to have the same energy in classical physics, in the context of quantum mechanics and when considering factors such as motion, interactions, and fluctuations, protons can have varying amounts of energy at any given time.