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71

Ever since the time of Newton physics is about observing nature, quantifying observations with measurements and finding a mathematical model that not only describes/maps the measurements but, most important, it is predictive. To attain this, physics uses a rigorous self-consistent mathematical model, imposing extra postulates as axioms to relate the ...


35

@annav's answer already describes well how physical theories work and how they require self-consistency. I'd like to add some comments from a different perspective to that. TL;DR Physical theories have to be self-consistent AND consistent with observation. Mathematical self-consistency Firstly if we treat a physical theory as a mathematical axiom system ...


14

If theories were only used to describe what we already know and observe, maybe they would not need to be self-consistent; they could even just degenerate into big lists of observed phenomena. This is what science looked like in Sumer, 5000 years ago. If we want physical theories to be predictive, they have to be self-consistent in the sense that they have to ...


14

If the only mathematical statements admitted in a physical theory were those having immediate empirical content (i.e. they can be tested by an unambiguous experiment), then you would have a very good case to make. Why? Because the consistency of the world of experience would guarantee the consistency of the mathematical formalism. End of story. In reality, ...


7

Physical theories are not a collection of mathematical axioms, they are attempts at describing nature. Not only that. Physical theories are also supposed to make predictions. This is part of the Scientific Method. One does not expect to predict new phenomena - that can later be veryfied - using a non self-consistent theory. We cannot cheat. Following ...


7

Mathematical theories which are not consistent prove contradictory things (this is just a statement about mathematics and what it means to be inconsistent, not to do with physics in particular). We do not want theories of physics that predict contradictory things. Ideally we don't want theories that make any wrong predictions, but if our theory makes two or ...


7

Physics is the art of compressing our knowledge of the universe. As it happens, whenever we stick two massive bodies near each other (or notice them near each other), they seem to move towards each other. Now, we could simply record the fact that every massive body (individually) is moving towards every other massive body (individually). This is a large ...


3

Theoretical physics is the attempt to describe a system (a subset of nature) using mathematics, making certain assumptions and idealizations if necessary. Put another way, the language of theoretical physics is mathematics. Roughly speaking, you need an axiomatization of the notion of states, observables and a dynamical law. Most physical theories have more ...


2

To put it in a short way: Self-consistency is required because we expect nature to stick to laws that can be described mathematically. Mathematical descriptions by definition have to be self-consistent.


2

A physical theory uses mathematical objects to model physical systems. In broad strokes, the theory consists of (a) rules for how to relate these objects to the initial conditions of an experiment, (b) mathematical claims about properties that the model must have, and (c) a description of how mathematical characteristics of the model lead to testable ...


2

Good question. Is the many-world interpretation with its insistence on self-consistency and conclusions like that gravity must be quantized really preferable to the Copenhagen interpretation, which just stays agnostic on those matters? One advantage of the insistence on self-consistency is that the theory becomes more falsifiable, because it is sufficient to ...



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