A model of (and for) physical theories

In the following we propose a model of physical theories as a linguistic construction--that is: using (formal) language--consisting of the following parts:

a specific mathematical theory,
observational statements about a chosen part of nature, and
a set of rules relating these observations to the mathematics and vice versa.

When we speak of our model as a metatheory, we simply mean that it talks about physical theories.

The model presented below was devised by the German theoretical physicist Günther Ludwig. Later, it has been extensively analyzed and refined by Joachim Schröter, also a theoretical physicist from Germany.

The linguistic components of a physical theory

A physical theory sets out from a domain of known factual observations. These are expressed as (formal) statements about entities and relevant mutual relationships. These will serve as observational inputs to the theory. While physicists select and construct them in view of the (new) physical theory they wish to describe, these input statements are formulated about entities and their relationships, both of which one can state without the help of this new or subsequent theory. They form the theory's Domain or Initial Domain .

The engine which brings each physical theory to life, is a Mathematical Theory . This is itself a formal language construct. Following Ludwig, we require this mathematical part to be formulated in the shape of a Bourbaki-Edwards species of structure theory. This means we will work with certain sets that carry an appropriate mathematical structure. This structure is itself defined by axioms: claims which we impose on these sets and their elements, and which they are required to fulfill. Though often treated without full rigor, this is common practice in mathematics.

The Domain specifies a list of entities, each one formally represented by a letter, and a list of formal relational sentences about these entities. This observational language is not a part of the formal language of the Mathematical Theory. So if we want to link the mathematics to our observations as physicits intend to, we need a mechanism to translate back and forth between the two. This is accomplished by a set of meta-rules called the Mapping Principles of the physical theory being considered. }}.^{[notes 1]}

From a good physical theory, we expect that it will tell us new things about some part of nature. It should go beyond the Initial Domain. These claims about reality generated by our Physical Theory are its Scope or Range ^[1]..^{[notes 2]}

Notes

^{[notes 2]} ^{[notes 1]}

^ ^a ^b In a hierarchy of physical theories such as quantum mechanics.
^ ^a ^b Named spacetime models.

Short references

^ Schmidt 2002, p. section 4.2.

References

Schröter, Joachim (1988), "An Axiomatic Basis of Space-Time Theory. Part I: Construction of a Causal Space with Coordinates.", Reports on Mathematical Physics, 26 (3): 303–333, doi:10.1016/0034-4877(88)90012-2

Schröter, Joachim (1992), "An Axiomatic Basis of Space-Time Theory. Part II: Construction of a C⁰ Manifold.", Reports on Mathematical Physics, 31 (31): 5–27, doi:10.1016/0034-4877(92)90003-J {{citation}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

[ST-ATEST-1] In a hierarchy of physical theories such as quantum mechanics.

[ST-primitives-3] Named spacetime models.

[FOOTNOTESchmidt2002section_4.2-2] Schmidt 2002, p. section 4.2.

[notes 1]

[1]

[notes 2]