Superphysics
The Philosophy of General Relativity
7 minutes • 1473 words
Table of contents
Relativity
How does my theory of relativity relate to philosophy?
Reichenbach has precise deductions and sharp assertions.
Robertson’s lucid discussion also is interesting mainly from the standpoint of general epistemology, although it limits itself to the narrower theme of “the theory of relativity and geometry.”
Is Reichenbach’s assertion true?
I answer with Pilate’s famous question: “What is truth?” Is a geometry — looked at from the physical point of view — verifiable or not?
Yes, provided that the empirically given solid body realises the concept of “distance.” Poincare says and consequently is condemned by Reichenbach.
No. The bodies are not rigid. Consequently, they cannot embody geometric intervals. Therefore, the theorems of geometry are not verifiable.
Bodies cannot be immediately adduced for the “real definition” of the space. Nevertheless, this real definition can be achieved by taking the thermal volume-dependence, elasticity, electro- and magnetostriction, etc., into consideration. This is demonstrated by classical physics.
In gaining the real definition improved by yourself you have made use of physical laws, the formulation of which presupposes (in this case) Euclidean geometry.
The verification, of which you have spoken, refers, therefore, not merely to geometry but to the entire system of physical laws which constitute its foundation.
An examination of geometry by itself is consequently not thinkable.
Why should it consequently not be entirely up to me to choose geometry according to my own convenience (i.e., Euclidean) and to fit the remaining (in the usual sense “physical”) laws to this choice in such manner that there can arise no contradiction of the whole with experience?
I replace Poincare with a non-positivist because Poincare does not want me putting words in his mouth
But the objective meaning of length and physical distances has not led to complications. We can thus use the concept of the measurable length, as rigid measuring-rods. It is impossible for Einstein to create the theory of general relativity without the objective meaning of length.
Against Poincare’s suggestion, the important thing is the greatest possible simplicity of all of physics, inclusive of geometry. This is why we must reject his suggestion to adhere to Euclidean geometry.
If distance is be a legitimate concept, how then is it with your basic principle (meaning = verifiability)?
Do you not have to reach the point where you must deny the meaning of geometrical concepts and theorems and to acknowledge meaning only within the completely developed theory of relativity (which, however, does not yet exist at all as a finished product)?
Do you not have to admit that, in your sense of the word, no “meaning” can be attributed to the individual concepts and assertions of a physical theory at all, and to the entire system only insofar as it makes what is given in experience “intelligible?”
Why do the individual concepts which occur in a theory require any specific Justification anyway, if they are only indispensable within the framework of the logical structure of the theory, and the theory only in its entirety validates itself?
It seems to me, moreover, that you have not at all done justice to the really significant philosophical achievement of Kant.
From Hume, Kant had learned that there are concepts (as, for example, that of causal connection), which play a dominating role in our thinking, and which, nevertheless, can not be deduced by means of a logical process from the empirically given (a fact which several empiricists recognise, it is true, but seem always again to forget).
What justifies the use of such concepts?
Thinking is necessary in order to understand the empirically given, and concepts and “categories” are necessary as indispensable elements of thinking. If he had remained satisfied with this type of an answer, he would have avoided scepticism and you would not have been able to find fault with him.
You are misled by the erroneous opinion, difficult to avoid in your time — that Euclidean geometry is necessary to thinking and offers assured (i.e., not dependent on sensory experience) knowledge on objects.
From this easily understandable error, you concluded the existence of synthetic judgments a priori*, which are produced by the reason alone, and which, consequently, can lay claim to absolute validity.
Superphysics Note
I think your censure is directed less against Kant himself than against those who today still adhere to the errors of “synthetic judgments a priori.”
The above is closely related to Bridgman’s essay. In order to be able to consider a logical system as physical theory, it is not necessary to demand that all of its assertions can be independently interpreted and “tested” “operationally;” de facto this has never yet been achieved by any theory and can not at all be achieved.
In order to be able to consider a theory as a physical theory it is only necessary that it implies empirically testable assertions in general.
This formulation is insofar entirely unprecise as “testability” is a quality which refers not merely to the assertion itself but also to the co-ordination of concepts, contained in it, with experience. But it is probably hardly necessary for me to enter upon a discussion of this ticklish problem, inasmuch as it is not likely that there exist any essential differences of opinion at this point.
Margenau’s essay says that my position contains features of rationalism and extreme empiricism. It’s correct.
This remark is entirely correct. From whence comes this fluctuation? A logical conceptual system is physics insofar as its concepts and assertions are necessarily brought into relationship with the world of experiences.
Whoever desires to set up such a system will find a dangerous obstacle in arbitrary choice (embarras de richesse). This is why he seeks to connect his concepts as directly and necessarily as possible with the world of experience.
In this case, his attitude is empirical.
This path is often fruitful, but it is always open to doubt, because the specific concept and the individual assertion can, after all, assert something confronted by the empirically given only in connection with the entire system.
He then recognises that there exists no logical path from the empirically given to that conceptual world. His attitude becomes then more nearly rationalistic, because he recognises the logical independence of the system. The danger in this attitude lies in the fact that in the search for the system one can lose every contact with the world of experience. A wavering between these extremes appears to me unavoidable.
I did not grow up in the Kantian tradition, but I found what is truly valuable in Kant’s doctrine: “The real is not given to us, but put to us (aufgegeben) (by way of a riddle).”
It means that we have a conceptual construction for grasping the inter-personal. The authority of this construction is purely in its validation. This conceptual construction refers precisely to the “real” (by definition). Every further question on the “nature of the real” appears empty.
I am not convinced by Margenau’s Section 4.
It is clear that every magnitude and every assertion of a theory lays claim to “objective meaning” (within the framework of the theory).
A problem arises only when we ascribe group-characteristics to a theory, i.e., if we assume or postulate that the same physical situation admits of several ways of description, each of which is to be viewed as equally justified. For in this case we obviously cannot ascribe complete objective meaning (for example the x-component of the velocity of a particle or its x-coordinates) to the individual (not eliminable) magnitudes.
In this case, which has always existed in physics, we have to limit ourselves to ascribing objective meaning to the general laws of the theory, i.e., we have to demand that these laws are valid for every description of the system which is recognised as justified by the group.
It is, therefore, not true that “objectivity” presupposes a group-characteristic, but that the group-characteristic forces a refinement of the concept of objectivity. The positing of group characteristics is heuristically so important for theory, because this characteristic always considerably limits the variety of the mathematically meaningful laws.
Now there follows a claim that the group-characteristics determine that the laws must have the form of differential equations; I can not at all see this.
Then Margenau insists that the laws expressed by way of the differential equations (especially the partial ones) are “least specific.” Upon what does he base this contention? If they could be proved to be correct, it is true that the attempt to ground physics upon differential equations would then turn out to be hopeless.
We are, however, far from being able to judge whether differential laws of the type to be considered have any solutions at all which are everywhere singularity-free; and, if so, whether there are too many such solutions.
