General Relativity Versus Quantum Theory
My conclusion is:
- in quantum theory, there is no such thing as a complete description of the individual system.
- the attempt to conceive individual systems through quantum theory leads to unnatural theoretical interpretations which become immediately unnecessary if one believes that they refer to ensembles of systems and not to individual systems.
- In that case, the whole “egg-walking” performed in order to avoid the “physically real” becomes superfluous.
But I have a simple psychological reason for shunning quantum theory.
Quantum theory does not describe the individual system (and its development in time) completely. And so we must look elsewhere for a complete description of the individual system. But this means that such descriptions are not within the conceptual scheme of the statistical quantum theory.
Therefore, quantum theory cannot be the basis of theoretical physics.
If a complete physical description were accomplished, quantum theory would just be analogous to the statistical mechanics of classical mechanics.
Quantum theory refers to ensembles of systems and not to individual systems. It will not extend to individual systems.
For me, however, the expectation that the adequate formulation of the universal laws involves the use of all conceptual elements which are necessary for a complete description, is more natural.
Only statistical statements can be obtained out of such an incomplete description,
If we could have a complete description, the laws would likely represent relations among all the conceptual elements which have nothing to do with statistics.
I will elaborate:
- on what a concept is
- that a real concept is metaphysical and is to be rejected
A necessary prerequisite of scientific and pre-scientific thinking is the distinction between:
- “sense-impressions” (and the recollection of such) versus
- mere ideas
There is no such thing as a conceptual definition of this distinction between real and imaginary.
There is no absolute evidence that proves all distinctions between real and imaginary in the same way that we can absolutely distinguish between red and blue.
Yet, we need this absolute distinction in order to be able to overcome solipsism.
My solution is to commit a metaphysical “original sin”.
We regard this absolute distinction as a “way of thinking” which we use to explain our real world. The “sense” and the justification of this absolute distinction lies simply in having this category.
I then represent the sense-impressions as conditioned by an “objective” and by a “subjective” factor.
This conceptual distinction also does not have any logical-philosophical justification.
But if we reject it, then we cannot escape solipsism.
This only requirement for this “way of thinking” is for it to be useful. The objective factor is our perceptions.
Insofar as physical thinking justifies itself, in the more than once indicated sense, by its ability to grasp experiences intellectually, we regard it as “knowledge of the real.”
This “real” in physics is to be taken as a type of program, to which we are, however, not forced to cling a priori.
No one is likely to be inclined to attempt to give up this program within the realm of the “macroscopic”. But the “macroscopic” and the “microscopic” are so inter-related that it appears impracticable to give up this program in the “microscopic” alone.
Nor can I see any occasion anywhere within the observable facts of the quantum-field for doing so, unless, indeed, one clings a priori to the thesis that the description of nature by the statistical scheme of quantum-mechanics is final.
The theoretical attitude that I advocate here is distinct from that of Kant only by the fact that we do not conceive of the “categories” as unalterable (conditioned by the nature of the understanding) but as (in the logical sense) free conventions.
They appear to be a priori only in the same way that thinking without the positing of categories and of concepts in general would be as impossible as is breathing in a vacuum.
It might seem as a mistake to permit ,
as it seems to me to be intended [for example] in
Bohr’s principle of complementarity seems to explain a theoretical description which is directly dependent on the act of observation.
- I have been unable to achieve its precise formulation despite much effort.
I think that such statements or measurements can occur only as special instances which I cannot ascribe any exceptional position above the rest.
The above-mentioned essays by Bohr and Pauli appreciate my efforts in the area of physical statistics and quanta.
They accuse me of “Rigid adherence to classical theory.”
This accusation demands either a defence or the confession of guilt. But I can give neither because they did not define “classical theory”.
The one or the other is, however, being rendered much more difficult because it is by no means immediately clear what is meant by Newton’s theory deserves the name of a classical theory.
Classical theory has been abandoned ever since Maxwell and Hertz showed that:
- the idea of forces at a distance has to be relinquished and
- one cannot manage without the idea of continuous “fields.”
This led to the current belief that continuous fields are the only acceptable basic concepts underlying the theory of the material particles.
This new belief then became “classical”.
But a complete theory has not grown out of it.
Maxwell’s theory of the electric field remained a torso.
- It was unable to set up laws for the behaviour of electric density which makes up an electro-magnetic field.
Analogously, General Relativity gave a field theory of gravitation, but no theory of the field-creating masses.
A field-theory cannot contain any singularities or any parts in space where the field laws are invalid.
Consequently, there is no such thing as a classical field-theory today.
One can, therefore, also not rigidly adhere to it.
Nevertheless, field-theory does exist as a program: “Continuous functions in the four-dimensional [continuum] as basic concepts of the theory.”
Rigid adherence to this program can rightfully be asserted of me. The deeper ground for this lies in the following= The theory of gravitation showed me that the non-linearity of these equations results in the fact that this theory yields interactions among structures (localised things) at all.
But the theoretical search for non-linear equations is hopeless (because of too great variety of possibilities), if one does not use the general principle of relativity (invariance under general continuous co-ordinate-transformations).
In the meantime, however, it does not seem possible to formulate this principle, if one seeks to deviate from the above program. Herein lies a coercion which I cannot evade. This for my justification.
Nevertheless I am forced to weaken this justification by a confession.
If one disregards quantum structure, one can justify the introduction of the gik “operationally” by pointing to the fact that one can hardly doubt the physical reality of the elementary light cone which belongs to a point.
In doing so one implicitly makes use of the existence of an arbitrarily sharp optical signal. Such a signal, however, as regards the quantum facts, involves infinitely high frequencies and energies, and therefore a complete destruction of the field to be determined. That kind of a physical justification for the introduction of the gik falls by the wayside, unless one limits himself to the “macroscopic.”
The application of General Relativity to the “microscopic” can, therefore, be based only on the fact that that tensor is the formally simplest covariant structure which can come under consideration.
Such argumentation, however, carries no weight with anyone who doubts that we have to adhere to the continuum at all.
All honour to his doubt — but where else is there a passable road?