Wave function is described using imaginary numbers. If we “taking the wave function seriously as a physical entity”—does it mean that imaginary part have physical sense? For example, if a cat has amplitude (0;1) does it mean that real part of doesn’t exist, but imaginary is full of life?
I wouldn’t get too hung up on “real” and “imaginary”. A complex number is just a mathematical object. You can equally well say that there are no complex numbers in quantum mechanics at all … only ordered pair of real numbers like (x,y). You can “add” two pairs by (x,y)+(z,w) = (x+z,y+w), and you can “multiply” two pairs by (x,y) × (z,w) = (xz-yw, xw+yz). (See here.) To answer your question more directly, you can multiply all states simultaneously by an arbitrary phase factor like −1 or i or -i and it makes no difference—global phase factors are unobservable. Sometimes people say that quantum states are complex rays, or points in a complex projective space, to make that point more clear. That actually makes the math more complicated and annoying in some cases … I learned this lesson by getting it wrong when writing the original version of this wikipedia article.
Wave function is described using imaginary numbers. If we “taking the wave function seriously as a physical entity”—does it mean that imaginary part have physical sense? For example, if a cat has amplitude (0;1) does it mean that real part of doesn’t exist, but imaginary is full of life?
I wouldn’t get too hung up on “real” and “imaginary”. A complex number is just a mathematical object. You can equally well say that there are no complex numbers in quantum mechanics at all … only ordered pair of real numbers like (x,y). You can “add” two pairs by (x,y)+(z,w) = (x+z,y+w), and you can “multiply” two pairs by (x,y) × (z,w) = (xz-yw, xw+yz). (See here.) To answer your question more directly, you can multiply all states simultaneously by an arbitrary phase factor like −1 or i or -i and it makes no difference—global phase factors are unobservable. Sometimes people say that quantum states are complex rays, or points in a complex projective space, to make that point more clear. That actually makes the math more complicated and annoying in some cases … I learned this lesson by getting it wrong when writing the original version of this wikipedia article.