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I personally cringe when people talk about scientific theories in the same way we talk about everyday theories.

I was under the impression a scientific theory is similar to a mathematical proof; however a friend of mine disagreed.

He said that you can never be absolutely certain and a scientific theory is still a theory. Just a very well substantiated one. After disagreeing and then looking into it, I think he's right. Even the Wikipedia definition says it's just very accurate but that there is no certainty. Just a closeness to potential certainty.

I then got thinking. Does this mean no matter how advanced we become, we will never become certain of the natural universe and the physics that drives it? Because there will always be something we don't know for certain?

Emilio Pisanty
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Joseph
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    I'm sorry to say, but it has been proven now for over 80 years that it is impossible to prove all true statements.

    http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems

     – AdamRedwine Jul 03 '12 at 11:38
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    @AdamRedwine: I'm not sure how related this is, given that it applies only in certain frameworks and conditations. – Nikolaj-K Jul 03 '12 at 17:31
  • Let me add this very brief comment on terminology: "Theory" in everyday language often is meant as "guess", "hunch", "could be that way". Scientifically speaking, those should be called guesses, educated guesses or hypotheses. A theory in science is a rather exhaustive framework of explaining all currently available data pertaining to a certain subject, as in "theory of electrodynamics", "theory of fluid dynamics" etc.

    Currently, this confusion about what the word "theory" means is most annoying in discussing the "theory of evolution"...

     – Lagerbaer Jul 03 '12 at 19:48

  • We will never become certain of the natural universe and the physics that drives it. Mass of the Universe $\sim3.5\cdot10^{54}$ kg Mass of your brain $\sim 1.5$ kg What do you think, is it possible to squeeze information contained in the latter into the former? To me it is really remarkable that we are able to know at least something.

     – Kostya Jul 03 '12 at 09:15
  • Not 100%. You could always argue that for example, the measurement of the 43 arcseconds per century problem in mercury's perhileon in Newtonian Gravity was actually simply because of quantum fluctuations or something, eventhough repeated observations confirmed it. – Abhimanyu Pallavi Sudhir Jul 02 '13 at 11:08
  • In the language of science, "Theory" means "explanation". A theory can be logically valid, or it can be pure BS. It can be consistent with observed phenomena, or it can be provably wrong. A theory can be elegant or it can be ugly. It can be complete or it can have holes. It can be subtle or it can be obvious, Broadly accepted or controversial, trivial or enormously complicated. A scientific theory can even be true, but if it's an interesting theory, then we'll probably never be able to prove that it's true. – Solomon Slow Aug 10 '15 at 17:24
  • @Joseph, I suspect that the idea of "no absolute proof" tends to make you a bit uncomfortable. In effect, a theory remains "accepted" until the first confirmed evidence that contradicts it. Then, the theory is either modified or abandoned in favor of a better theory. – David White Aug 10 '15 at 18:55

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I basically agree with Argus, though I take a slightly different perspective.

Physicists try to explain the world by constructing mathematical models to approximate it. The phrase mathematical model can sound mysterious, but it just means an equation or equations that predict what's going to happen given some initial conditions. For example Newton's laws of motion are a mathematical model, as is general relativity, quantum mechanics, string theory and so on.

Every mathematical model has a domain in which is a good description of the world, and within that domain we regard the model as effectively exact. Outside that domain we know the model fails. For example Newton's laws describe the motion of ideal particles at speeds well below the speed of light. We know that for higher speeds we need a different model i.e. special relativity, but this fails for high mass/energy densities. To handle high mass/energy densities we need general relativity, and so on.

So we describe the world using a range of theories i.e. mathematical models, and we pick the one that we know works for the situation we are considering. In this sense our theories are always approximate.

However within the domain of our model we are completely certain the model works. If you're sitting at a desk in NASA working out how to send a spaceship to Pluto you can be absolutely confident that the trajectory you calculate will work. You would not be worrying about whether some new and unexplained physics might send your spaceship spiralling into the Sun.

John Rennie
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  • +1 very true each mathematical model describes its perticular are of "application to a high enough degree of accuracy to effectively predict "set" situations. – Argus Jul 01 '12 at 07:13
  • Cheers guys :) interesting read. – Joseph Jul 01 '12 at 17:41
  • "However within the domain of our model we are completely certain the model works" - Can you explain this statement? Is it ment in an absolute sense (justification) or do you interpret "we can" as "it's possible to imagine a world where everyone agrees on this". Or do you mean it as a suggestion, as in "to do it is a good idea, because otherwise you'd worry to much and that's unhealthy". And who is "we" in this sentence? – Nikolaj-K Jul 03 '12 at 17:19
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    Within it's domain Newtonian mechanics has been working perfectly for about 400 years so far. Some may say that this doesn't prove anything, to which I'd reply that they really need to get out more. – John Rennie Jul 03 '12 at 17:23
  • I doesn't prove anything. (This might however lead in a discussion about the term "prove".) – Nikolaj-K Jul 03 '12 at 17:27
  • @JohnRennie First: nice answer, +1. Second: "If you're sitting at a desk in NASA working out how to send a spaceship to Pluto you can be absolutely confident that the trajectory you calculate will work." [emphasis added] That sounds like the kind of thinking that led to this. – OSE Jan 27 '14 at 21:01
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Simple Answer: Nothing is guaranteed 100%. (In life or physics)

Now to the physics part of the question.

Soft-Answer:

Physics uses positivism and observational proof through the scientific process. No observation is 100% accurate there is uncertainty in all measurement but repetition gives less chance for arbitrary results.

Every theory and for that matter laws in physics are observational representations that best allow prediction of future experiments. Positivism can overcome theological and philosophical discrepancies such as what is the human perception of reality. Is real actually real type questions.

The scientific process is an ever evolving representation of acquired knowledge based on rigorous experimental data.

No theory is set in stone so to speak as new results allow for modification and fine tuning of scientific theory.

Argus
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  • Cheers pal. Good writing there. :) do you reckon a super advanced civilization could ever become 100 certain of everything or is there a fundemental issue with that? – Joseph Jul 01 '12 at 06:02
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    That is a tricky question as we are 100 percent certain untilled new date proofs us wrong. Fundamentally there is always an arbitrary uncertainty in any "complex" measuring device so I would have to say technically knowing everything all at once would be extremely difficult if not implausible. To be fair ask me again in 100 thousand years I am sure I will have a better answer. – Argus Jul 01 '12 at 07:17
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You can never be certain of anything, except possibly mathematical theorems. This is the conclusion after long debates on epistemology. The ancient Greek skeptics were of the opinion that knowing the uncertainty of everything will give you peace of mind.

Maurice
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The philosopher David Hume pointed out induction can never be proven. Even if we have some proposed "law" describing everything we know so far, there is no guarantee the next observation will completely violate it. The world might not be what we think it is. There could be some malicious demon messing with our minds.

Dusra Insan
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I'll try to answer this with three points about the scientific method and how "certain" we are of the truth in our theories. Keep in mind that scientists are overly dogmatic about pet theories but we should aspire to transparency about how wrong we might be and distrust everything until the evidence, be it scant or ample, is verified.

First, you can gather quite a lot of insight by listening to Richard Feynman's analogy between discovering the laws of nature and learning the rules of chess through observation of a fraction of the board. In particular, there's the part where he talks about a bishop changing it's colour despite ample observations of this never happening. His overall point is that we're never truly sure but we are always inadvertedly gathering evidence that the theory is right.

Secondly, you should read Isaac Asimov's essay The Relativity of Wrong. His point is that while a theory might be "wrong", sometimes they're very wrong ("the Earth is flat") but sometimes less wrong ("the Earth is a sphere"). In some cases, you can quanitify this. For a contemporary example, cosmologists have settled on $\lambda$CDM as the right model of the Universe. The point isn't that $\lambda$CDM is necessarily the whole story but that, if it isn't, then the evidence we've gathered already implies that the whole story can't be much different.

Finally, let's think back to the superluminal neutrino fanfare. It made big news, with the media painting a picture that made it look like the scientific community needed to revolutionize special relativity (SR). But a lot of scientists responded skeptically, even by offering to eat their shorts. So why the skepticism? Surely that flies against the scientific mantra of doubting authority?

Not quite. There were good reasons to doubt the result and anyone who dismissed those results should've defended their position. It was quickly pointed out that, if neutrinos travelled faster than light, we'd detect supernovae early. Also, I think Glashow and others pointed out that we'd see something like Cerenkov radiation from the neutrinos.

But more importantly, SR is, to me, a theory that is close to being "certain". It was and still is tried and tested extensively and it forms the basis of other theories that are themselves successful. So the odds of SR being "wrong" are outrageously small. We have inadvertedly tested it bazillions of times and it's worked perfectly. And the amount by which it can be wrong is very small. At the time, it could've been like the first time a pawn was queened into a bishop, but, to roll out the cliche, extraordinary claims require extraordinary evidence.

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Warrick
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  • "We have inadvertedly tested it bazillions of times and it's worked perfectly." How does this vary, from say, the Aristotle's (and other ancient) views of gravity that IIRC weren't disproven for a thousand years, even though they are trivial to disprove today. – NPSF3000 Dec 19 '14 at 14:31
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The reason you can not prove things in real life, as apposed to in mathematics, is that you can not check your theory for all variables x and t. For example, you can not test that the theory of gravitation holds everywhere in the universe (it will take an almost infinite amount of experiments). And you especially can not prove that it holds at every moment in time, that is backwards in time or forward. You can only test the theory right now.

Check out Clavius' answer at yahoo answers. It is very good: http://answers.yahoo.com/question/index?qid=20081004094805AAzyeZF

Ron Mexico
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This is a question about philosophy of science and epistemology, so you should expect varying answers with different prespectives.

This is my personal approach to the question.

First let's examine what does it mean to say that a scientific theory is "absolutely proven".

Just as John Rennie pointed out in his answer, a scientific theory is a mathematical model, or another way to put it, a scientific theory consists of a set of axioms which are usually mathematical in nature, and theorems that follow from such set of axioms.

To give you a concrete example, consider Newtonian mechanics, Newton's theory is made up of three axioms: his famous three laws. Add to that the theorems that follow from these axioms, like the work-energy theorem and many others.

Newton's second law is given by: $F=m\dfrac{d^2x}{dt^2}$. To say that Newton's theory is absolutely proven, is tantamout to say that this equation holds true for any arbitrary values(real numbers in this case) of $F,m$ and $x$. The same applies to Newton's first and third law, they should hold for any arbitrary real number.

There is no logically neccessary reason that Newton's second law should hold for all real values. Hence the only way to absolutely prove it, is to test it for all the real values it can take! This is obviously an impossible and insurmountable task to do, and hence it's impossible to absolutely prove a scientific theory.

There's another crucial point to consider, even if you were able to test your theory, for all the values it takes, you have to have gadgets with precision and accuracy of 100%.This is another reason why you cannot prove a theory to be stricly true.

However, There are things in empirical sciences(and mathematics and logic) that you can prove to be absolutely true. You can absolutely prove that assuming Newton's theory implies the work-energy theorem. Or assuming the constancy of speed of light and the principle of relativity impliy relativity of time,space and simultaneity.This is the same as assmuing the axioms of Euclid implies Pythagorean theorem.

To sum up, either in physics or mathematics, You can prove Axiom A implies theorem B, but you cannot stricly prove Axiom A is true, hence you can never absolutely prove a scientific theory is true.

Omar Nagib
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  • Two points:Mathematical theories start from axioms and prove theorems and are self consistently proven. Physics theories require postulates which are not connected to the mathematics axioms necessarily, but are statements which tie up the mathematics to the observables in physics. example: the postulates of quantum mechanics. Without them the wave mechanics differential equations although self consistent , have no physics meaning. In addition a physics theory can only be validated. Even one falsification will require reexamination of the postulates and the region of validity of the theory. – anna v Aug 10 '15 at 18:29
  • @annav I agree with you. – Omar Nagib Aug 10 '15 at 19:10
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No, a physical theory can never be "proven".

There is a classical metaphor to illustrate why, known as the black swan problem or problem of induction.

If in your entire life you have only see white swans, you will formulate the general law (or theory) that all the swans are white. You will then keep seeing only white swans -thousands of them- and think "my theory is great: it has been confirmed by countless observations, and every single observation confirmed it!".

Then, one day, you will se a black swan, and your theory will suddenly, catastrophically fall apart.

With physics, it is exactly the same. No matter how many experiments corroborate your theory: if only a single experiment gives a result different from the one predicted by your theory, then the theory is wrong: it has been falsified.

The problem of induction and of the foundations of scientific theory has been extensively analyzed by the philosopher Karl Popper, who identified falsifiability as the defining characteristic of every scientific theory.

A theory which can never be falsified (proven wrong) is like religion: not scientific. For a statement to be questioned using observation, it needs to be at least theoretically possible that it can come into conflict with observation. For example, "God created the Universe" is not a falsifiable statement because it cannot be falsified with observation.

valerio
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