There are multiple ways of observing this : including multiple types of imagery and animal models.
For instance you can use Functional Magnetic Resonnance Imagery (fMRI) to see in real time blood flow to different parts of the brain, indicating brain activity. There are techniques to assess the activity of specific neurons of groups of neurons and their activity is monitored while the subject is tasked to recall a memory.
There are also experiments where you can use drugs to affect recalling and rewriting of memories in humans and animals, and draw conclusions from there.
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