In quantum physics, there is a topic on something called retrocausality, which addresses whether the future can affect the present and whether the present can affect the past.
In terms of deja vu and dreams, are they the result of future information being transferred to the present/past?
Actually, I'm wondering whether psychology and quantum physic are related in any way.
Short answer
Déjà vu and dreaming are closely related to memory and memory formation. However, they have nothing to do with future events. The brain cannot recall what it never has processed in the past.
Background
Déjà vu is thought to be related to the tip-of-the-tongue feeling, in the sense that it is a memory phenomenon. It can occur when someone encounters a scenario that’s similar to an actual memory, but they fail to recall the memory. In other words, it's not an actual memory but an erroneous retrieval of a memory, if you like (sources: PsychCentral & New Scientist).
Dreams are basically stories and images our mind creates while we sleep. It has been proposed that dreams reflect biological processes of long-term memory consolidation. Consolidation strengthens the neural representations of recent events (i.e., their memories) and embeds these new memory fragments into older, existing memories. This also maintains the stability of existing memory representations in the face of subsequent experiences (Payne & Nadel, 2004). In sleeping rodents, for example, neurons in the hippocampus fire in patterns remarkably similar to those recorded during a previous maze-running session—almost as if the animals replay the experience in their sleep (source: Science Magazine).
In all, déjà vu and dreaming are indeed closely related to memory, and memory formation. However, they have nothing to do with future events. The brain cannot recall what never has perceived in the past. Hence, déjà vu experiences and dreams have nothing to do with what the future may bring, other than cases of pure coincidence.
Reference
- Payne & Nadel, Learn Mem (2004); 11(6): 671–8
Actually, I'm wondering whether psychology and quantum physic are related in any way.
There's no conclusive evidence insofar that quantum processes play a distinctive role in brain, although some hypothesis or another typically relating qubits (or entanglement) to consciousness seems to endure on the fringes.
Note that retrocausality is fringy even without involving the brain, as in not being strictly necessary to formulate entanglement.
Part 1
I'm wondering whether psychology and quantum physic are related in any way.
One possible connection between psychology & quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics) is quantum cognition:
Quantum cognition is an emerging field which applies the mathematical formalism of quantum theory to model cognitive phenomena such as information processing by the human brain, language, decision making, human memory, concepts and conceptual reasoning, human judgment, and perception.
From Preparing a (quantum) belief system:
In quantum cognition, the system of interest is the decision-maker’s mental representation of the world. It is represented by a cognitive state. This representation of the world is modelled as a quantumlike system so the decision relevant uncertainty is of non-classical (quantum) nature. - pg.2
Part 2
When a reporter asked Asher if quantum teleportation could teleport the soul as well as the body, Asher answered, characteristically, “No, not the body, just the soul.” -Source (pdf)
If at some point in the future we build tachyonic antitelephones (or something equivalent), it might be hypothetically possible to communicate backwards in time via déjà vu and dreaming since both are subjective (eg. "déjà vu is a feeling" & "dreams are the stories the brain tells during sleep" - which is to say they are not objects in the sense that chairs or cars or other physical things are).