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Is 100% proof of a theory possible in physics, or all we can do is to see how well it stacks up against observations and then decide if we accept it or not?

If so, isn't there a danger ,however distinct, that all the knowledge that we have acquired is based on a false theory that so far has agreed with all the tested predictions, but one, that has not been tested yet?

For example, the big bang theory seems to accepted by scientists since it agrees with many of its predictions, right? Physicists work on theories that are based on the big bang theory. However, if the big bang was disproved sometime in the future, all the related theories will too. Isn't that possible to happen to one of the theories that we currently take for granted?

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Proofs exist only in mathematics where a theory starts with axioms and theorems are proven with a quod erat demonstrandum .

Physics uses mathematics for modeling, imposing postulates that relate mathematical quantities and functions to measurements and observations. This has been an ongoing progress ever since Newton and Maxwell.

Physicists work on theories that are based on the big bang theory.

They are based on the Big Bang Model within the theory of General Relativity. It has already changed as a model from the time I took a cosmology course in the 1970s .

Quantum mechanics is a theory, Classical mechanics is a theory, Thermodynamics is a theory, Classical electrodynamics is a theory.

There exist continuities in the theories of Physics. Thermodynamics emerges from statistical mechanics. Classical electromagnetic waves emerge from a huge number of photons. General Relativity for low masses becomes Newtonian mechanics etc.

If the observations and experiments are correctly described by a model based on a theory, and a new datum/observation falsifies not only the model but a basic premise/postulate of the theory on which the model is based, as happened with classical theories and the need for quantum mechanics, (black body radiation, the photoelectric effect) the new theory will have a region of validity at the boundaries of which it should agree with the old theory , plus explain the discrepancy and predict new phenomena.

However, if the big bang was disproved sometime in the future, all the related theories will too. Isn't that possible to happen to one of the theories that we currently take for granted?

No, related models will have to change, but the theory of General Relativity will not need to change if the BB is falsified, i.e. there is an observation disagreeing with the predictions of the model. A new model will have to be formulated that will incorporate all the data and observations plus explain the discrepancy that invalidated the BB model. The theory of GR will have to change if observations/data are found in some region of parameters and variables where the postulates are falsified. The prime example is the implicit postulate of continuous values in energy in classical thermodynamics with the quantization needed to explain black body radiation that eventually forced quantum theory to appear. The Bohr atom has as a postulate the quantization, except that it is a model not a theory. In the final theory quantization appears as a consequence of the postulates.

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    $\begingroup$ anna v: Your answer carefully describes and distinguishes the notions "theory" vs. "model"; therefore I find it largely very agreeable. But there's one important exception (i.e. one inconsistency in your otherwise great answer): "If the observations and experiments are correctly described by a model based on a theory," -- ... yes ... "and a new datum/observation falsifies the theory, [...]" -- No: if new/additional observations or (derived) measured values are not correctly described by some particular model then they falsify that model; without affecting the underlying theory. $\endgroup$
    – user12262
    Dec 3 '14 at 23:25
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    $\begingroup$ @user12262 clarified this I hope, as I was really talking of the need for new theories. $\endgroup$
    – anna v
    Dec 4 '14 at 5:01
  • $\begingroup$ anna v: I appreciate your being responsive. Now: "If [...] a new datum/observation falsifies not only the model but a basic premise/postulate of the theory on which the model is based, [...]" -- Yes, this clarifies your answer: it's now more clearly wrong! Because: "a premise is an assumption that something is true.". Therefore any premise belongs to a particular (falsifiable) model, while the applicable theory is (only) concerned with defining the applicable "something" in the first place, regardless of whether that's then held "true", or "false". $\endgroup$
    – user12262
    Dec 4 '14 at 18:35
  • $\begingroup$ @user12262 Well, in my vocabulary premises are implicit postulates for a physical theory, as for example in classical physics all variables identified with measurable quantities are continuous, but it was never an explicit postulate. Postulates are what define a theory as a physical theory . $\endgroup$
    – anna v
    Dec 4 '14 at 19:20
  • $\begingroup$ anna v: "premises [...] for example in classical physics all variables identified with measurable quantities are continuous" -- The definitions of (how to measure) "quantities", i.e. the main contents and objective of any physics-related theory, include the definitions of their range from the outset. Any "new datum/observation" about some defined quantity cannot falsify its defined range. (The reason to reject/replace "classical physics" is rather its, in hindsight, glaring lack of any careful definitions of "how to measure"). $\endgroup$
    – user12262
    Dec 6 '14 at 20:19
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A theory in physics is a way of "joining the dots" (experimentally determined facts) to make a picture. In the past, that picture was almost literally that. It was a sort of "what really happens is..." notion. That has been superseded by theories which are essentially data compression algorithms to give the most economical fit to the data. "What really happens" is relegated to a philosophical irrelevance these days. Of course, the other function of a theory is to make predictions as to what the remaining dots look like and where they can be found. Despite some mumbling complaints, the "what really happens" can still be useful here.

There is in general no way any given theory can be proved to be "the best" or even true. All that can be said is that it is not yet falsified.

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Well, that's the basic essence of science.
Testing theory by observations and experiments. This is also how knowledge goes on, usually first assumptions are wrong or at least partially and proof of a theory to be wrong help to improve the understanding and encourage one to find a better one describing better our universe.

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