So where do the probabilities come from? If there’s “an” electron that we’ve calculated has 1⁄4 of it’s amplitude here, and 3⁄4 of it’s amplitude across the street, and we have detectors set up in both places, then after the electron has interacted with the detectors and I’ve read their outputs there should be two big blobs of amplitude. One blob with 1⁄4 of the amplitude that represents I-who-saw-the-electron-here, and one blob with 3⁄4 of it that represents I-who-saw the-electron-across-the-street. Why shouldn’t I bet $1 for $2 if the electron is here? What difference does the amplitude make? I’m either one blob or the other.
So where do the probabilities come from? If there’s “an” electron that we’ve calculated has 1⁄4 of it’s amplitude here, and 3⁄4 of it’s amplitude across the street, and we have detectors set up in both places, then after the electron has interacted with the detectors and I’ve read their outputs there should be two big blobs of amplitude. One blob with 1⁄4 of the amplitude that represents I-who-saw-the-electron-here, and one blob with 3⁄4 of it that represents I-who-saw the-electron-across-the-street. Why shouldn’t I bet $1 for $2 if the electron is here? What difference does the amplitude make? I’m either one blob or the other.