Schrödinger’s cat or shut up and calculate!

I have been recently reading through Meera Nanda’s article, “Intellectual Treason”.  I have prepared a general reply to that article which will be posted eventually in TMJ. Here I want to discuss a specific philosophical issue raised by Nanda.  The specific philosophical issue was raised by Nanda, probably inadvertently, in the following question:


Can we not say that modern science provides us a closer, a more approximate representation of nature which is more adequately supported by reason and logic?


Does modern science provide us a representation of nature? The question is a hotly contested one in Quantum Mechanics but also in General Relativity both of which were proposed in the twentieth century.


It is probably better and easier to start with General Relativity. Newtonian mechanics explains the planetary rotation around the Sun as due to a gravitational force between the planets and the Sun. This force, F, depends on the solar and planetary masses, M and m, respectively and on the distance between the Sun and the planets, R. The exact relationship is given by F=k(Mm)/(r2).  K is the gravitational constant. This simple equation explained most of the planetary motion and is widely used even nowadays in a variety of fields. Einstein, however, over turned the Newtonian paradigm in 1915 by introducing his General Relativity theory. According to Einstein there is no such thing as a gravitational force and planets rotate round the Sun due to the Sun distorting the local spacetime.  The success of the Newtonian Mechanics is due to the fact that the Newtonian force equation very closely matches the General Relativity equation for weak gravity. So it is clear that Newtonian mechanics is certainly not a representation of nature. Is Einstein’s General Relativity a representation of Nature, i.e., is spacetime really there in nature?


The question of representation is even more convoluted in Quantum Mechanics. I will discuss 2 examples here to make my point:


Example 1

According to non-relativistic Quantum Mechanics all fundamental particle like electrons, protons, quarks, atoms and molecules can be represented by wavefunctions which reside in a special mathematical space called Hilbert space. Hilbert space is a unitary, complex linear vector space. All the operators which represent Quantum Mechanical observables like energy and momentum operate on the wavefunctions in the Hilbert space. This approach has yielded good agreement with all experiments at least in theory. This raises the question as to whether the wavefunctions of the particles are representations of the particles or are the particles themselves. To understand the problem, think of human beings. We are made of electrons, protons, atoms etc. If the fundamental particles reside in the Hilbert space then we who are made up of these particles should also be residing in this Hilbert space. Have any of you seen a Hilbert space? After all if we are residing in it we should have seen it. So where is it? So is the wavefunction of an electron a representation of an electron?


Example 2

Another famous example that shows up the problems of interpretation of modern science is called the Schrödinger’s cat problem.  This is a gedanken (thought) experiment first suggested by Schrödinger. Imagine a box in which a cat is kept. The box also contains a vial of poison gas. The vial can be opened by a machine. The machine is designed in such a way that it can randomly open the vial in which case the box will be filled with the poison gas in a given time or it will not open the vial in which case the cat will live. So if you are an experimenter then you will set up the experiment with the cat and the poison vial in the box and cover the box with some cloth and then leave the room for say 1 hour. What will you see after one hour? What does Quantum Mechanics say? It says that the wave function, WF, of the entire set up will be a linear superposition:


WF= (a1)(cat alive)(poison vial closed) + (a2)(cat dead)(poison vial open).


A1 and a2 are two coefficients. Quantum Mechanics says that the WF will change with time according to some equation. The implication is that the cat will be both dead and alive at the same time as long as no one is watching the cat. What happens if you go back into the room and lift the cloth and look at the cat? The Copenhagen school of Quantum Mechanics (Niels Bohr) says that you will see either a dead cat or a living cat. You will never see a cat both living and dead at the same time!  If that is true then can you say that WF is a representation of the cat and the vial? If you ask the Copenhagen school of the meaning of  this WF then it will answer, “Shut up and calculate”. According to the Copenhagen school the 2 branches of WF (branch 1=(cat alive)(poison vial closed) and branch 2=(cat dead)(poison vial open)) collapse to just one branch when an observer watches. When an observer is not watching then the cat is both alive and dead at the same time.


The interpretation of WF gets even more bizarre if you insist that the WF is indeed a representation of the cat and the vial. This bizarre interpretation is known as the Many Worlds interpretation of Everett. Everett says that the Copenhagen school is playing a dirty trick when it arbitrarily throws out one of the branches while insisting that the mathematics of Quantum Mechanics is correct. Everett says that it is true that in our universe only one branch is seen; either the cat is alive (branch 1) or the cat is found dead (branch 2). No one sees a cat that is both alive and dead. That does not mean that the 2 branches collapse as is claimed by Bohr’s Copenhagen school. Everett says what happens is that the branch that we do not see in our universe happens in a parallel universe. Thus if we see a dead cat here then a clone of that cat will be happily mewing in a parallel universe!


So what do you think? Is modern science providing us with a representation of nature as suggested by Meera Nanda?

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