The Zen anti-interpretation of quantum mechanics (2021)
Sure, I&#x27;d like to read Aaronson and tried.<p>My difficulty with quantum mechanics is much earlier, that is, more elementary and basic than what Aaronson considers. I&#x27;ve watched MIT lectures, looked into books by experts, ..., and I get nothing I can believe in.  Right in the first hour, I get questions with no answers.  E.g.,<p>(1) Wave Function.  Okay.  I can&#x27;t find a definition of a wave function. Nothing subtle but just the most elementary objection possible:  What are the range and domain of the function?  That is, for a function f, we usually write<p>f: A --&gt; B<p>for sets A and B meaning that for each element x in set A there is an element y in set B so that f(x) = y.  For function f, set A is the <i>domain</i> and set B is the <i>range</i>.  Fine.  Now for a wave function, what are the sets A and B?  No joke -- I can&#x27;t find a clean, clear, unambiguous, simple, beginning, first step definition.<p>(2) Everything.  There is a common statement that the wave function has everything we can know about the particle, molecule, whatever.  Okay: What about Schrödinger&#x27;s Cat -- where in the wave function is the color of the cat?  Simpler, for an electron, where in the wave function is the spin of the electron?<p>(3) Probability Density.  We are supposed to take the complex valued wave function, take its absolute value, scale the function so that its integral is 1, and then, presto, bingo, since it is continuous, non-negative, and integrates to 1, it can be a probability density.  In particular it can be the probability density of the current location of the particle.  Okay, it CAN be.<p>Now, what is the evidence that it actually IS the probability density of the particle?  That is, so far I can&#x27;t find any argument, justification, reason to conclude that the probability density of the particle is not something else.  E.g., the probability density of the particle might be Gaussian.<p>(4) Hilbert Space.  I&#x27;ve read so many times, more than I can count, that the set of all wave functions form a Hilbert space.  Tilt.  The definition of Hilbert space I saw in math, e.g., W. Rudin, <i>Real and Complex Analysis</i>, is that a Hilbert space is a complete inner product space where <i>complete</i> means that every Cauchy convergent sequence converges.  Well, the wave functions have to be differentiable and, thus, continuous, and it&#x27;s easy enough to have a sequence of such functions converge to a discontinuous and, thus, not differentiable function and not a wave function.  So, wave functions might be points in a Hilbert space, but they can&#x27;t form a Hilbert space.<p>(5) Superposition.  Some definitions  say that superposition is just linearity.  But if I have complex numbers a and b and wave functions f and g and form the linear combination<p>h = af + bg<p>that seems to be an example of <i>superposition</i>.  Okay.<p>Now, is h actually also a wave function?  Its absolute value might not integrate to 1.  Okay, scale it so that we do get 1.  Now what particle has wave function h?  That is, what <i>physics</i> does this linear combination describe?  What does h in<p>h = af + bg<p>have to do with physics?  E.g., from the Pauli exclusion principle, maybe h can&#x27;t correspond to anything in physics.  What is going on with <i>superposition</i>?<p>(6) Can&#x27;t Know.  We are told that as an electron goes by, we can&#x27;t know anything about it except its wave function unless we take a measurement at which time we change the wave function, what the electron might do, or some such.<p>Hmm.  The electron has a negative charge and mass.  As it goes by, it has to emit from its electric charge an electrostatic force, that is, a Coulomb field and since it has mass, a gravitational wave.<p>If that situation is not strong enough, then have the electron go past a strong Coulomb field so that it moves in a curve.  Such a curve is acceleration so that the electron might generate a photon.  We detect the photon and then &quot;know&quot; that the electron went by.  And, even if we don&#x27;t have a strong Coulomb field, our universe is awash in Coulomb fields that might deflect the electron.  So, the wave function can&#x27;t be &quot;destroyed&quot; merely by some Coulomb field.  Then we just use a strong Coulomb field, detect the photon, and, thus, know a lot about the electron without changing its wave function.  So, the claim that we can&#x27;t know seems wrong.<p>(7) The Other Half.  We take a beam splitter, such as in the Mach-Zehnder interferometer, and shoot an electron at it.  The wave function splits into two parts, say, f and g.  For part f, we have a detector.  For the last electron we shot, we got a detection from part f.  Now, what happens to part g?<p>No fair saying that part g does not exist since the Mach-Zehnder interferometer can bring such f and g back together and generate interference fringes that part f or g can&#x27;t generate alone.  So, part g does exist.  So, what happens to it?<p>(8) Domain.  For the wave function, a guess at the domain is the set of all ordered pairs (x, t) where x is a point in three space and t is time. Well, three space is a big place, and we usually believe that nothing can travel, propagate faster than the speed of light.  So, all the wave functions so far are still traveling, still expanding.  Right?  What happens to them?<p>Just a few, simple, obvious, elementary, first day questions.  I can&#x27;t find any answers.