Sunday 19 September 2021

Quantum Debates part II

 Ok I realise in the last post some people will say well what about the collapse of the wavefunction and the violation of the Bell inqualities don't they show that quantum mechanics is weird. I have covered this in many posts before but to save you looking here is a recap 

Let's take the so called collapse of the wavefunction first. This is usually illustrated by the so called cat paradox. If a quantum system can occupy a number of possible states then prior to measurement the sysrem is said to be in a superposition of states and on the usual story this means that when a measurement is made the so called wave function of the system collapses into one of the possible states with a given probability. Those who see the so called wave function as something more than the square root of a probability density function then make the leap to say that the measurement has caused the system to change from it's superposition to a single state. So there is something special about measurement and indeed quantum mechanics via this so called collapse vindicates idealism. So that we create reality by acts of measurement something which is alleged to be part of the Copenhagen interpretation which in fact it isn't. This should really be called the 'California Interpretation' and if it were true would indeed be weird and mysterious and all those who like to link Buddhism or Transcendental meditation with quantum mechanics would be vindicated. 

But this is totally unnecessary, lets take the classical situation for any statistical event if I know the underlying probability density function which summarises all the possiblities and I pick a given sample then I can calculate the probability that that person has a given height or a particular number will turn up if I throw a dice or spin a roulette wheel. Prior to the outcome I did not know what the outcome would be after the outcome I do. Thus the probability density function has 'collapsed' to give the particular outcome but all that is saying is that for classical systems the probability density function summarises all the possible outcomes and after the event has occured the outcome was realised with the given probability. I would argue the same is true of quantum mechanics before a measurement is made I do not know what the result would be but only the total outcomes with a given probability which if I know the appropriate solution to Schrodinger's wave equation I can calculate via the Born rule. Thus the superposition is not a real superposition but just a summary of possible outcomes of a measurement with the appropriate outcomes. The cat is definitely alive or dead before I open the box all I have done is updated my knowledge of the situation before hand. Opening the box hasn't caused the cat to be alive or dead but whether the radioactive poison was released or not. Something you could estimate if you know the half life of the radioactive material. All of this is consistent with quantum mechanics and how it is applied to calculate the probabilities of certain things happening and there is no need to invoke the collapse of the wavefunction to explain this process. 

In contrast to other realist interpretations such as those invoking hidden variables or the Many Worlds interpretaton nothing is added to the formalism. There is no need to invoke many worlds in a desperate attempt to maintain realism. My solution is robustly realist because the entities to which quantum mechanics is applied electrons, atoms and all the various exotic particles and there interactions are seen as real. Once one accepts that the so called wavefunction isn't anything physical but related to the probability density function via the Born rule, then there is no need to agonise whether or not the wave function is a physical object defined in (3N+1)*S space-time-spin dimensions for an N body system it makes no sense as a physical object but as a probability density function it makes a lot of sense. So by sticking to the statistical interpretation of Born then we can retain a fairly robust realism about the entities to which quantum mechanics is applied to and there is no need to worry about any form of idealism or mysticism. 

I'll talk about the Bell inequalities in a later post. But I defy anyone who disagrees with my perspective to show that my position is inconsistent with quantum mechanics. One can never observe a physical superposition of states because by definition any observation would collapse the wavefunction into one of the possible eigenstates. Those who claim otherwise are simply collating the reuslts of various measurements and claiming that this represents a real superposition. 

 

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