A Scientist and a Spin

Top left box evolves into a superposition of the other two

When introduced to quantum physics the first example we encounter is usually that of a single particle.  We are shown that experiment demonstrates a particle left alone evolves into a superposition of states.  These states may be position states or they may be momentum states, or if the particle has spin it may be a superposition of spin states.  It doesn't matter, the point is that fundamental particles can be in a superposition of states.  That's because they are small, we are told, so you wouldn't expect them to behave like big things do, we are told.

The next thing we are shown is how the Schroedinger equation governs the evolution of this superposition.  The particle is not usually in every state equally, it is more in one position state (or momentum state, or spin state) than it is in another.  The distribution over these so-called basis states evolves with time and the Schroedinger equation describes how.  A distribution over basis states is also known by a snappier term: wavefunction.

Much later - if you stick with the subject - you learn about quantum systems of more than one particle.  This is where it gets interesting because this is where it becomes clear the story "quantum theory is about how small things don't act like big things" just isn't true.  Because when you have two particles, you don't have two distributions over basis states - two wavefunctions - you have one!  To give an example, a single particle with spin has two basis states: up and down.  A system containing just one of these particles can be in a superposition of up and down and the wavefunction therefore consists of just two numbers.  If superposition was a feature of individual particles, of small things, then a system of two spins would be a system of two independent wavefunctions.  Thus if particle A is equally likely to be up or down and particle B is equally likely to be up or down then all four possibilities (up,up), (up,down), (down,up), (down,down) would be equally likely to be found on inspection.  However, the truth - predicted by the theory and confirmed by experiment - is that it is possible to put the system in a state where (up,down) and (down,up) are each equally likely but (up,up) and (down,down) are never observed.  This tells us that the superposition is over ensemble states: combined states of the entire system.

when we observe a spin we don't see it in a superposition of up and down we see just up or just down.  Likewise each scientist in the superposition sees either up or down, but not both

Going one step further, we can imagine applying the Schroedinger equation to a more complicated system.  This one involves a scientist and a spin.  In the initial state the scientist is intending to measure the spin and the spin is in a superposition of up and down.  Although it would be difficult to do the mathematics, there isn't much controversy about what the result would be.  One minute later the system would - according to the Schroedinger equation - be in a superposition of many states.  In half of these the scientist thinks she has observed an up spin and the spin is up, and in the other half she thinks she has observed a down spin and the spin is down.  Just like the system of two spins, half of the possibilities are missing (in this case, thinking it's down but it being up, and thinking it's up but it being down).  This is known as entanglement.

Note that what the Schroedinger equation predicts is completely consistent with our observations, for when we observe a spin we don't see it in a superposition of up and down we see just up or just down.  Likewise each scientist in the superposition sees either up or down, but not both.  So there is no need for an additional "wavefunction collapse" postulate, in which "observation" reduces a superposition of states to a single state.  In fact, the phenomenon of entanglement predicts the subjective experience that observation collapses the state.

The persistent belief in wavefunction collapse - and the refusal to believe in the multiverse - is a little bit like our persistent belief in gods.  In early western civilization, gods - such as Mars, Venus, and Jupiter - were created in an attempt to explain the erratic paths of wandering stars.  Eventually a simple physical theory that was able to predict these paths was developed, and these "wandering stars" were shown to be planets orbiting the Sun, just like Earth.  To continue to believe in these gods after this discovery would be absurd.  It would be not wanting to let go of an explanation that is no longer needed.  It would be saying "yes, I accept the laws determine exactly how that planet moves, but I still think it's a god".

Likewise, wavefunction collapse was created to explain a phenomenon we didn't understand.  That, although our experimental results require an object to be in a superposition of states when we're not looking at it, we never see it in a superposition when we are looking at it.  Eventually an experimentally verified theory arose (the Schroedinger equation) which - as a by-product - predicted the subjective appearance of wavefunction collapse.  But the additional postulate of collapse is still maintained by many despite no longer being needed.  (And despite the unresolved issues it creates: who, exactly, can collapse what?)  This seems to be purely out of a desire to not accept the most interesting corollary of the Schroedinger equation, namely that the universe is in a superposition of states.  Or, put differently, that we live in a multiverse.