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I note the question "Time and space – a subject of metaphysics?" might be very near to my question, and maybe the answer is there somewhere. In that case I - as an amateur - would be grateful for a simplified answer.

I posted a thought earlier on physics.SE (No 272653) where I speculated that Newton might have considered bent space (but with classical time) so that Newton´s ball would spin fine in a curved surface.

I now would like to take that thought a little further and think about the question: might we not alternatively consider – with impunity - the bent space-time in the theory of relativity being in the category of initial concepts on which theories is built, rather than being a theory in itself in Popper’s sense?

I am assuming we disaggregate the initial concepts time and space from the formulas applicable to physical bodies entitled to both time and location.

I believe such a question might fit better in this forum.

  • It is ahrd to imagine that such abstract concepts like time and space can be considered "theory-free" (assuming that we can have theory free concepts...). – Mauro ALLEGRANZA Dec 4 '17 at 13:21
  • @Mauro ALLEGRANZA I mainly considered theories here in Popper's sense. It may be impossible to interprete time and space in such a way that they might be falsified. I admit they are part of a system that do contain theories. – Mikael Jensen Dec 4 '17 at 13:55
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    I think you better explain what " theories in Popper's sense" are. Is it the Tarski-Popper convention under which any set of sentences closed under consequence is a "theory"? Also, there is no such thing as falsifying concepts, it is theories (in the usual sense) that are falsified. How do you propose to "disaggregate" concepts from theories they feature in? – Conifold Dec 4 '17 at 19:30
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    Maybe it's the whole idea of theories in the Popper sense that must be abandoned. What you say about space and time could be said about the conceptual structure of theories in general, given that it is models with context-specific additional hypotheses that are confronted to experience. – Quentin Ruyant Dec 4 '17 at 19:39
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    Agree with Mauro here. Time and space simply are theoretical concepts and there's no getting around it. . – PeterJ Dec 5 '17 at 13:34
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The interpretation of a curved spacetime in General Relativity is a consequence of the theory rather than the theory itself.

The form of the theory is based on a number of postulates:

  1. the constancy of c i.e. special relativity
  2. the Equivalence Principle i.e gravity is (almost) indistinguishable from inertial acceleration
  3. the dynamics must match Newton at low energies and speeds i.e. reflects observation

Now, it is possible to add curvature as a new postulate. However, you can't remove any of the other 3 and still end up with General Relativity (without cheating). As such, it would be redundant to include it.

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