Cardinal Kasper, writing in Jesus the Christ, observes that the resurrection kerygma [preaching] is older than the resurrection accounts, by which he means that the church was proclaiming the resurrection before it put into writing the four gospels. The result of writing them down several years after the events and having gone through a period of oral transmission means that there can be some loose ends that don't fit together and no one has been able to construct a coherent pattern that includes all recorded experiences. However, judges who deal with eye witness testimony will say that a thoroughly consistent testimony between several witnesses often suggests collusion, and eye witness testimony can have rough edges.
There is no doubt that members of the early church experienced something. Maurice Casey, not a believer, writing in Jesus of Nazareth, states that the experiences are explicable in terms of the hallucinatory sightings of dead relatives often seen by the bereaved, though he excepts Paul's vision from this explanation. But Casey thereby contradicts himself, as he is accepting that there is one experience that does not fit his explanation, and if one, why not others? Furthermore, the accounts given in the gospels do not fit into the this bereavement hallucination model. If you read Luke 24, the encounter on the road to Emmaus, you see that the disciples do not recognize Jesus until he breaks bread with them. then they say that they should have known him by his inspiring scriptural explanations that had their hearts burning within them. The sighting in a bereavement hallucination is not an unidentified person only recognized later. The failure to initially recognize Jesus also occurred in Mary Magdalen's encounter, so the bereavement hallucination model does not work here either. Of course the objection could be that the gospels are making up the facts. You could say that, but the question the objector must answer is whether he has a source of facts better than the gospels and if so, what is it.
Furthermore, when Jesus met the apostles in the upper room he not only is said to have eaten some fish, but allowed them to touch him. Again, Casey's simplistic explanation does not work in this case. I do not deny that there may have been some hallucinatory experiences, but to say that all, particularly the ones reported here, were hallucinatory, is erroneous.
Nothing can be proved or disproved, but like the empty tomb the resurrection calls for a decision. Did he rise or not? The negative answer fits in with the modern world-view; the positive answer challenges it and opens the door to a confidence in the power of God to defeat evil.