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I came across this question on Yahoo! Answers:

Should M-theory read, M-hypothesis?
It being limited evidence for further investigation, perhaps not yet a theory.

I responded thus:

(I realise the words "use" and "usage" are.. ahem.. overused. Please disregard this stylistic concern.)

I believe this use of the word "theory" reflects an overlap in mathematics and theoretical physics.

In mathematics, the word "theory" is used informally to refer to "a self-consistent body of definitions, axioms, theorems, examples, and so on" (reference). Examples of this usage include "field theory" and "group theory".

This differs from the scientific use of the word "theory" to mean "an extensively tested hypothesis".

I believe the use of the word "theory" here is a purposeful reference to the fact that the inventors were interested in laying a mathematical foundation for their model.

Note that "string theory" has the exact same usage. In fact, the usage seems to be quite rampant throughout theoretical physics.

However, that's quite possibly just a way to rationalise what is actually carelessness on the part of scientists using the terms. It may not even fit with the facts; my knowledge of theoretical physics is admittedly slim.

Can anyone give any support for or against my explanation? I found this blog entry wherein commenter James Reed chalks it up to a combination of carelessness and an alternate definition of "theory" as "a model being developed by a theorist" (which is similar to the informal mathematical definition, I think).

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FWIW, I had the exact same thought as you when I read the question to which you responded. I'm not able to back it up historically though. –  aaronasterling Dec 28 '10 at 6:23
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The use of the word seems perfectly consistent with its mathematical usage. M-theory and string theory are elaborate bodies of the axiom-definition-theorem-proof kind. –  ShreevatsaR Dec 28 '10 at 6:34
    
I've deleted my answer since I agree that lay definitions are useless here. (Please see the comments below the deleted answer.) –  Tragicomic Dec 28 '10 at 10:19
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Thanks for the comments, everyone. I lack the privileges to see deleted answers, so I can only guess at what was discussed. It seems this question is technical to the point that the community would not consider an answer up to standards unless it included a hard reference. I'm glad to be part of a site with such high standards. On the other hand, I'm wondering if such a reference even exists! If finding a source poses too great a difficulty, perhaps the question's wording should be relaxed to allow "softer" answers? I'll wait a while in any case. @Trag @Shree @aaron –  Mitch Schwartz Dec 28 '10 at 12:43
    
@Tragicomic, we can't see the comments below the deleted answer. I think you need over 10000 rep to see deleted posts, which excludes the vast majority of SE users. Perhaps instead of deleting it, you could have edited it? –  Marthaª Dec 28 '10 at 15:57

3 Answers 3

The question is: shouldn't M-theory be M-hypothesis, because it isn't proved yet. An implicit assumption in this question is that theory and hypothesis are mutually exclusive terms.

This is not actually how the words are used in science. Consider the case of continental drift. Continental drift was proposed by Wegener in 1912, but not generally accepted until the 1950s, by which time overwhelming evidence supporting it had accumulated. If you look in Google books in the 1930s, you will see books calling it the theory of continental drift and also saying this hypothesis. So continental drift could be both a theory and a hypothesis.

I would say scientists use theory for a coherent collection of related explanations of phenomena (relativity theory, quantum theory, theory of evolution, gene theory of inheritance), whether or not it has been proven by evidence. By this definition, string theory and M-theory count as theories.

Scientists use hypothesis for an explanation of phenomena which has not yet been proven. A hypothesis can, but need not, be an explanation of a set of phenomena that is much too narrow to qualify as a theory. So by this definition, string theory and M-theory are also hypotheses.

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+1 for "I would say scientists use theory for a coherent collection of related explanations of phenomena (relativity theory, quantum theory, theory of evolution, gene theory of inheritance), whether or not it has been proven by evidence. By this definition, string theory and M-theory count as theories." –  Tragicomic May 18 '11 at 12:56
    
Shor, this one was for you really Peter! I appreciate your citing the Wegener case. Milankovic is another one. May be the M-theory, because it is controversial/difficult to prove, attracts such comments. –  Alain Pannetier Φ May 18 '11 at 15:03
    
+1. Things are never really "proven" in science, only tested. –  T.E.D. Apr 25 '12 at 14:31

I started a comment on Peter's answer (who happens to be well placed to appreciate the context of your question) but then I found out that I had too many ideas of my own and decided it appropriate to share them here.

I'd say that there is a lot of overlapping between both definitions (the mathematical and the scientific one).

Note for instance that in mathematics a theory, in the first sense (a self consistent set of axioms, definitions and theorems), can be studied long before it is actually applied usefully in some scientific area.

Examples abound of these cases (e.g. imaginary numbers in 16c. Italy long before electromagnetism or quantum mechanics were discovered). This is arguably the rule rather than the exception.

So that the purely mathematical sense of the word theory is not that far from the scientific acceptation of "hypotheses making predictions waiting to be proven/disproved".

Which leads to the conclusion that a theory cannot wait to be proven to deserve the rank of theory. One might even argue that it stays a theory as long as it is not disproved (after that is is just an abandoned theory ;-).

If scientists were to put theories forward only when they'd have the technical abilities to prove them, we'd be way backwards. Newton would have had to wait for telescopes to be powerful enough to spot planet Neptune and Einstein for atomic clocks to be invented.

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Merriam Webster's defines theory like this:

  • a plausible or scientifically acceptable general principle or body of principles offered to explain phenomena (e.g., the wave theory of light)

  • a body of theorems presenting a concise systematic view of a subject (e.g., theory of equations)

However, it also defines it like this:

  • a hypothesis assumed for the sake of argument or investigation
  • an unproved assumption

I think in the case of the string theory, theory is being used in the first sense of the definition. Calling it the string hypothesis would take away from what we mean to say (make the idea smaller).

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This answer is completely missing the point. In science, theory and hypothesis are not traditionally interchangeable. A theory is equivalent to a theorem in mathematics. It is as close to proven as science can possibly get. General Relativity was a hypothesis until enough of its predictions were verified for most (and now all) serious physicists to accept it as a theory. String "Theory" is nowhere close to being able to make that claim. Lay definitions of those words are entirely besides the point here. –  aaronasterling Dec 28 '10 at 9:37
    
I concur with aaronasterling's last sentence. –  ShreevatsaR Dec 28 '10 at 9:56
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I don't think aaronsterling's points are borne out by history or usage. The high school textbook definitions are as he suggests (though he omits or discounts the status of scientific "law"). However, scientists have for a long time favoured "theory" over "hypothesis" when naming what are in effect overarching hypotheses. Max Planck coined the term "theory of relativity" in 1908, three years after Einstein published his first paper to touch on general relativity--long before any predictions were verified. You cannot discount lay definitions when these are favoured by prominent scientists. –  Jay Jan 8 '11 at 4:43
    
There is a difference between a 'theory' (string theory, quantum theory, etc) and a 'Theory' (Theory of Gravity, Theory of Relativity, Theory of Evolution). –  HorusKol Jan 24 '11 at 1:47
    
@HorusKol: what is the difference between quantum theory and Theory of Relativity (aside from the fact that you've capitalized one and not the other)? I don't see this distinction. –  Peter Shor May 18 '11 at 11:21

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