Are there really witches, floating daggers, and invisible spots of blood—or do the spooky, supernatural occurrences merely reflect the characters' interior thoughts?

There is no right or wrong answer to this question. In the beginning of the story, Shakespeare allows the apparition to appear to more than one person...... as do the witches, thus, the playwright does illustrate the working of the supernatural in the text. None-the-less, there are moments when apparitions, like the dagger or Banquo's ghost are only visible to Macbeth. These instances might point to impeding madness.

The supernatural is addressed in two of Gradesaver's theme analysis for the play.

Ghosts and Visions

Just as an overwhelming guilty conscience drives Lady Macbeth mad, so too does Macbeth’s “heat-oppressed” brain project the vision of a dagger before he murders Duncan (II i 39). In what concerns ghosts and visions, the relation of the natural to the supernatural in Macbeth is unclear. The three apparitions that the witches summon, for example, are usually taken to be “real”—even if only as supernatural occurrences. But the matter is less clear when it comes to Banquo’ ghost. Macbeth is the only one who sees the ghost in a crowded room; is this yet another projection of his feverish mind? Or is it really, so to speak, a supernatural occurrence? Such ambiguities contribute to the eerie mood and sense of uncanniness that pervade the play, from the very opening scene with the three bearded witches.

The Natural/Supernatural

If the witches’ prophecy is understood to be imposing a supernatural order on the natural order of things, the natural order can also be understood as responding with tempestuous signs. Following Duncan’s death, Lennox describes the “unruly” night in some detail. Similarly, Ross notes that “the heavens, as troubled with man’s act, / Threatens his bloody stage” (II iv 5-6). In the same scene, the Old Man and Ross both agree that they saw horses eat each other. Even the events leading to the conclusion of the play can be understood as a negotiation of the natural and supernatural. Whereas Macbeth believes that he will live the “lease of nature”—since Birnam Wood cannot possible come to Dunsinane Hill—the forest is literally uprooted by the English army in accordance with the prophecy. The dichotomy between the natural and the supernatural forms a backdrop that suggests the epic proportions of the struggle over the Scottish crown.