In my story, there is a VR world. A victim is chosen to be put into that world, and his/her job is to decide whether he/she is actually in the real world.
The VR world is implemented is a way such that the victim feels extremely real. So the victim does not only carry headsets and motion sensors. He/she also has some cognitive changes, for example, under the influence of drugs. So even though the victim feels wide awake, he/she may not actually be.
Now, I am asking how the victim can decide that he/she is actually in the real world. I can think of some conditions/constraints:
The victim is originally in the real world. When the VR developers have to put the victim into the VR world, they have to ensure that the victim is unaware of such an action. Therefore, the developers can only do so when the victim is unconscious (e.g. when he/she is drunk or sound asleep).
The drugs have non-lasting effects. To prevent overdosage the developers must stop injecting the drugs after several (perhaps 3-4) days of the first intake. After that the victim thinks that he/she wakes up normally in the morning.
The victim can keep some secrets, perhaps in his/her memory. There is no way the developers can get them in the real world, but they can fully control the VR world so that they obtain such secrets when the victim disclose them in the VR world.
For the victim to proof that he/she is in the real world, he/she doesn't need a logical proof. Instead he/she accepts a probabilistic or cryptographic proof. For example, I consider it to be a valid proof when the victim has 99.9% confidence that he/she is in the real world.
The victim has no responsibility to keep him/herself staying in the real world. In other words, it is OK if the victim found him/herself in the VR world in 10 consecutive days. His/her only job is to distinguish one world from another.
You can assume the victim is powerful (a normal guy having good physique, knowing how to fight/use weapons, knowledgeable, fluent in major languages, smart etc), as the idea of such a VR world comes from a fiction series I've read before.
Is it possible for the victim to do so?
Edit: After reading some answers I am going to clarify something. I will not downvote existing answers, but amendments are welcome. As I have mentioned earlier, the idea comes from a fiction series. Some drugs were injected into a guy. He did find something special/unusual, but the information was insufficient. He was put into a situation without communication devices and weapons. He saw her (dead) girlfriend as a clone, and eventually he was tricked to disclose something. So essentially he (1) was emotionally controlled (2) appeared to be less analytic (3) was "identical" to the one in the real world under the influence of drugs. I mean something like dreaming -- you aren't going to think that that self in the dream is different from yourself. Originally I wanted to figure out a probabilistically secure way to verify the world's integrity, and so I didn't intend to make it too philosophical. Anyway, thanks for any help and sorry for any misleading information.