13-Rediscussion of the problems in chapter 6
We already discussed in chapter5 that the bright dots on the scintillating screen are not a direct evidence of the existence of pointlike entities and that this process can be interpreted as a transition of the wave function from an spatially extended form to a localized form around the nucleus. We also discussed the difficulties of such a wave only interpretation in chapter6. Let's take a closer look at the arguments mentioned in chapter 6
To problem 2:
That the wave function of n particle is a function of 3n variables doesn’t mean, that we are confronted with an obscure 3n dimensional space, but it means only that the particles are related to each other and that they behave collectively as a whole or that they are entangled. The conclusion we can draw from this fact not that that the wave function can be only a mathematical tool and that it is physically less real. We have no right to demand that microscopic physical reality must have the same properties we are accustomed from observation of macroscopical phenomena.
One can calculate all observable quantities in 3 dimensional space (like for example the total matter density in 3 dimensional ordinary space created by n particles) by integrations over the coordinates in the 3n dimensional configurations space. It means only that the macroscopical variables provide us with approximate , simplified description of the reality that may be sufficient at macroscopical scales but appear to be inappropriate for description of microscopical world. There is no fundamental problem as long as we can deduce macroscopic description from microscopic description.
To problem 3 :
The use of complex valued wave function indicates only that the wave function is made of two entities: A magnitude and a phase. The appearance of imaginary number in the Schrodinger equation indicates only that the effect of Hamiltonian operator is twofold: Taking the time derivative and rotating the phase at p /2 . This fact is described mathematically in the most simple way if one uses complex numbers . It doesn’t mean necessarily that there is somewhere the square root of –1 as part of physical reality. However there is no logical reason, why even this should not be considered as allowed.
These two arguments alone cannot be considered as serious obstacles, that should hinder us to accept the wave function as a real physical entity, because, it is not required that all elements of physical reality correspond to something directly observable. This is so not only for quantum theory. It is the force on an electrical charge, that we measure and not the electric field itself. What is needed is that what the theory predicts agrees with experiment. Nevertheless theories may refer to unobservable elements and we may interpret (although with a certain degree of caution) the agreement of the observation with a theory as an indirect verification of the unobservable deeper reality that is assumed in the model. This is why theories are not just empirical recipes but reflect our insight in nature.
It is surprising that the defenders of Copenhagen interpretation were so "openminded" on one hand to accept the new reality namely the wave-particle duality and the fundamental indeterminacy as a strange surprising new discovered property of nature inevitably to live with, may it be so strange and so hardly understandable, and tried to convince others to stop trying finding "oldfashioned" analogies with macroscopical world . On the other hand they were so "conservative" so that they could see in these 2 pseudoproblems inacceptable obstacles to consider the wave only wiewpoint seriously.
They are far less problematic then the wave- pointlike particle duality or an obscure undefinable self referencing (see chapter 7 ) concept like "measurement" in Copenhagen interpretation. Thus we think there is no evidence why we should accept the existence of a pointlike entity beside the wave function and why we should stop to try to solve problems 1, 4 and 5 from purely wave mechanical point of view.
Lets summarize our standpoint.
1. We have a wave function representing a physical system . For an n partile system the wave function is a function of 3n variables. It is not probability wave but it IS the physical reality par excellence. All the known ordinary 3 dimensional quantities with classical equivalence like the total 3 dimensional charge density created by n particles are determined by the form of the wave function.
2.There seem to be two different event classes namely two different types of time development of the wave function:
2.1 Under certain conditions The wave function evolves deterministically according to the wave equation.(Schrodinger equation or dirac equation)called U process (U from untary evolution )
2.2 Under certain other conditions it makes apparently random transitions. The probability of a particular transition can be calculated from the initial wave function called R process (R from reduction of the wave packet )
This type of random transitions occur partly in interaction with macroscopical systems called measurement apparatus but partly also in purely microsopical process like spontaneous emission or radioactive decay.
From this point of view The only remaining problems of the quantum mechanics are (see chapter 6)
These are not philosophical problems like the wave particle duality or role of observer etc. but scientific problems waiting to be attacked. Lets discuss these problems in this listed order.