This may be a bad question, but what are the ways that laws are proven? I would expect that some ways would include by proving them mathematically or through experimentation.
My biggest question about this is about proof through experimentation. If one were to prove a law through experimentation, what is deemed a sufficient number of times?
Another question would be how can one prove something like the second law of thermodynamics?
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1$\begingroup$ As to your biggest question: it depends on the subject (psychology vs particle physics, but there few areas of scientific research that require that the likelihood that you observed the data by random chance was more than 0.1% $\endgroup$– user83548Commented Jun 1, 2016 at 2:33
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4$\begingroup$ Nothing in physics is proven, at all. One can only find counterexamples that invalidate hypotheses. $\endgroup$– CuriousOneCommented Jun 1, 2016 at 2:34
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$\begingroup$ If you want to get a better handle on this, you might get something out of studying the concept of the "null hypothesis" in statistics and what it means for science, which is limited to making finite numbers of observations with finite error bars. Basically we are limited to statements like "Our observations show that effect X does not differ by more than $\epsilon$ (which should be a small number) from our hypothesis about it.". No matter how hard we try, we can never make $\epsilon=0$. $\endgroup$– CuriousOneCommented Jun 1, 2016 at 3:29
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$\begingroup$ Thermodynamics is a special case of a limit theory. Because of the atomic structure of matter and and the quantum structure of radiation it only applies exactly for infinitely large systems that are completely homogeneous and that only change in an infinitesimally slow manner. In all other aka "real" cases it only applies as an approximation. $\endgroup$– CuriousOneCommented Jun 1, 2016 at 3:31
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$\begingroup$ This is a question for philosophy talking about logic and perception. My preferred theory (might be outdated) is Kant's theory. If you think deep in this direction, you might wonder why 1+1=2. Think about when and how do you accept this concept. My understanding of law is that, over years, a concept of law forms. And it is never been fatally challenged by any experiment after it forms. $\endgroup$– user115350Commented Jun 1, 2016 at 5:42
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2 Answers
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This is a physics question and answer site.
Laws in physics are a distillation of experimental observations, and a foundation stone in the theories, mathematical models, built up in order to describe data and predict new behaviors. In a very real sense they are the physics axioms that connect mathematical formulae to physical measurements.
History of physics shows that physics laws change, are absorbed in larger and more descriptive mathematical theories.
The observational history of electricity and magnetism is a good example. Observations gave many laws, but the ingenious use of mathematics reduces the initial assumptions/"axioms" to *"there exist electric and magnetic potentials which obey Maxwell's equations"*. What were "laws" before can be derived from the behavior of the equations. Only the Lorenz force remains as an independent "law/axiom" for classical electromagnetism.
My biggest question about this is about proof through experimentation. If one were to prove a law through experimentation, what is deemed a sufficient number of times?
So one cannot "prove" laws, one can check the validity of the theory that has the law as an axiom. If a theoretical prediction is not validated, the whole theoretical construct has to be redefined, the mathematics changed ,and even the law changed.
Take the mathematical model of flat geometry that fits well on city streets. "two parallel lines do not intersect" is an axiom for the mathematics, and the physical observations. Once one goes to large distances, the axiom is falsified because the measurements do not fit the model: spherical geometry is the mathematical model that fits the surface of the earth, and the axioms change.
Another question would be how can one prove something like the second law of thermodynamics?
When a more encompassing theory has been found that fits observations, it is often that what were "laws" from measurements can be derived from the mathematical formulation, for example Amperes law emerges from the Maxwell's equations. In this sense it is "proven", but the wider framework should exist.
Thermodynamics is an emergent theory from an underlying particle level and in this sense, the inevitability of what are observational laws for thermodynamics can be seen to emerge from the statistical behavior of the underlying particle framework, as others have said.
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In reverse order, and to echo CuriousOne's comments, as you know already I'm sure, the second "law" isn't a law, more a general principle regarding the probabilities of the existence of certain quantum states.
My biggest question about this is about proof through experimentation. If one were to prove a law through experimentation, what is deemed a sufficient number of times?
There is nothing else but repeated experimentation, in other words, the standard reply might be that you are testing GR every time you turn on your GPS and you are testing thermodynamic principles each time you start your car engine.
As CuriousOne implies, we can only falisfy our current theories, and we can never cast them in stone. I have seen statements in Cosmology textbooks that say, in effect: "Some of what's in this book is wrong, and if we are really, really lucky, most of it is wrong", as we have so much that still has to be explained by new ideas, such as why the entropy at the start of the universe was so low. Arrow of Time
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$\begingroup$ Who wrote that lovely statement about cosmology? :-) $\endgroup$ Commented Jun 1, 2016 at 8:57
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$\begingroup$ Whoever did obviously learned a lesson from Weinberg who was probably a lot more confident about what he thought he knew about cosmology in the 1970s than we can be today... I can only agree with the statement. $\endgroup$ Commented Jun 1, 2016 at 9:49