The importance of Schrödinger’s Cat.

The dogma of the Copenhagen school was that nothing exists if it cannot be measured.

“What is in principle unobservable should not at all be contained in our conceptual scheme”  Schrödinger.

Scott Murray saw this as arrogance. The idea that physicists ego could not accept that there existed things which they could not measure. I think he missed the point and the real point is well illustrated by Schrödinger’s cat.

I’m not a paid up member of the physics brotherhood so I’m still permitted to use common sense.

The common sense interpretation goes as follows – life is the antithesis of death. One excludes the other so before the box is open the cat is either dead or alive and the only thing which changes when the box is opened is our knowledge – and perhaps the smell in the room :o). Common sense says that if the cat is alive then it was before the box is
opened. If it is dead then by retrospective analysis (autopsy) one can to some extent determine how long it has been dead. If autopsy shows it has been dead at least 4 hours then it would appear clear that it was dead before the box was opened.

Theoretical physics says no. The act of opening the box determines both the state of the cat and its history. In the many worlds interpretation there are an infinite number of universes and the action of opening the box means that in one universe it is alive and in another it is dead and has been for at least 4 hours. Put simply not only is the cat both dead and alive before the box is opened but continues to be both dead (in one universe) and alive (in another) when the box is opened.

This to the layman seems absurd. Why on earth, he would think, would physicists take such an extreme view. The point is that what is at stake here is the credibility of theoretical physics itself or at least the methodology.

If the common sense interpretation is accepted it means that there is more to physics than maths. That maths must be interpreted in terms of context and in order to do so one must understand the context i.e. one must understand what the maths is describing. In theoretical physics mathematics is paramount. An equation is considered a full description uncluttered by artefacts thought necessary in the past.  The maths is now accepted as a “physical theory” on the grounds that it predicts physical consequences. The sort of thing the theoretical physicist does is to manipulate the maths and make pronouncements which start “This equation implies……”. If they were forced to factor in some form of reality outside of the maths it makes this impossible and an equation on
its own can imply nothing. Such a retrograde step is unthinkable. Theoretical physics is about mathematical formulation, prediction and testing of prediction. A “field” for example can be described mathematically and nature behaves according to the maths. The difficulty Einstein had as to whether a field consisted of some form of ponderable
matter or a state in a medium is circumvented. A field is what the equations describe.

Schrödinger’s. “What is in principle  unobservable should not at all be contained in our conceptual scheme”

Can be translated as – if you can’t observe the state of the cat it it must have all states allowed by the maths. If the maths says both states are possible – then both states exist.

If you can’t measure the position of an electron – it doesn’t have one. If you cannot determine in advance what direction a photon takes from a source S it doesn’t have one and the retrospective measurement i.e. that it arrives at B does not mean that it set out in the direction A-B or that it travelled along the path A-B. The maths says it may set out in
all possible directions – so it does. The many worlds interpretation says that a massive subset of the infinite parallel universes are affected by a single photon as there must be a universe for every feasible point of arrival.

The many worlds interpretation is needed as follows. There is no way of determining in which direction a photon sets out because any attempt to determine it would drastically change it. The direction is therefore “unobservable in principle” so direction cannot be part of the conceptual scheme. The question is why does that particular photon
arrived at B? The only obvious reason is that it it because it set out in the direction A-B and that is not allowed. One is left with the idea that it arrived at B for no reason whatsoever. The many worlds interpretation is a let off. It arrived at B because it has to arrive
at B in one parallel universe and it happens to be this one. The integrity of the maths is preserved, there is not some underlying “cause” which the maths cannot accommodate.

The electron is the most stable of particles and is very well behaved. One never gets half an electron or one with part of its charge missing, or a lighter than usual one. The most precise images we have are produced using and controlling electrons. The point is that if it did have a precise position and velocity we would not be able to determine them for perfectly good physical reasons i.e there is no precise particle with a mass negligible compared to that of an electron which we could use to determine an electrons precise position without disturbing it and this results naturally and physically in Heisenberg’s
uncertainty. One could again have a common sense interpretation that an electron is a precise particle with a precise location and speed and just as our uncertainty about the cat in the common sense interpretation is about knowledge so it is in the case of the electron. Again retrospective measurement supports such a view and again retrospective
measurement is dismissed as invalid.

“On the one hand. a precise  position measurement on the particle P in the domain K yields the  prediction of a very wide range of velocities for P; and on the other hand, when the particle has been detected after a time (delta t) in the spatial domain K’, one can retrospectively ascribe to P a quite sharp value of the  velocity. namely KK’/(delta t),
and also a precise direction of motion. Isn’t it tempting to assert that the particle P actually had the velocity KK’/(delta t), but that quantum theory could not predict it’?
The only option which remains,  is thus to deny that there is anything like a  particle P travelling between K and K`: “Before the second measurement, it is ubiquitous in the cloud (it is not a particle at all)”. Or, in other more provocative words: “You have not found a
particle at K’, you have  produced one there!”. Indeed, if this is so, the location K is not relevant  for the “particle” detected at K’, and there is no reason left to ascribe it  the velocity KK’/(delta t).”
Found in “Schrödinger’s philosophy of quantum mechanics” By Michel Bitbol. The quotes are Schrödinger’s.

Me I believe the cat is either dead or alive and I believe retrospective measurement is a valid aid to understanding. The collapse of the wave function is simply about knowledge. If a coin comes down heads the chances of it coming down tails suddenly vanishes.

Mathematics should be the servant of physics not its master. I agree with Murray that the physicists default was their failure to insist sufficiently strongly in the physical reality of the physical world when faced with a take over by the mathematicians union.

Alfonso