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“Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it.”

Excerpt from Stephen Hawking, A Brief History of Time, iBooks.

So does that mean that Theory = Hypothesis?

Qmechanic
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user17755
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    Please read our FAQ on writing good titles. – DanielSank Jul 04 '16 at 05:29
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    Very similar question here: http://physics.stackexchange.com/questions/31068/can-a-scientific-theory-ever-be-absolutely-proven The idea that nothing can be proved in physics isn't a new idea. I don't personally think it's a particularly important idea because to me, it's splitting hairs, but it's arguably true that nothing in physics is ever proven. – userLTK Jul 04 '16 at 05:52
  • Isn't this more a question about English than about Physics? – RemcoGerlich Jul 04 '16 at 11:17
  • Is it useful to link to a question with no answer in response to this question? The linked question is on hold as well. – Mark H Jul 04 '16 at 19:10
  • user17755: "Is a theory the same as a hypothesis?" -- A theory is certainly not the same as a hypothesis. A system of self-evident ("primitive") notions, definitions and axioms subsequently expressed in terms of these notions, and their logical consequences and relations ("theorems") is not the same as just one single proposition which has been expressed through this (self-evident, or subsequently defined) terminology. [contd.] – user12262 Mar 17 '17 at 20:05
  • Moreover, a ("scientific") hypothesis should be a decidable proposition; compatible with at least eventually being asserted either as "true", or else as "false". In contrast, an assertion as "true", or as "false", is neither possible, nor required, of a theory (as a system of notions, definitions, axioms, consequences). Instead, it may be possible to assert that a theory under consideration is "consistent", or instead "inconsistent", "self-contraductory", and thus failing outright as terminology framework for expressing decidable propositions to begin with. [contd.] – user12262 Mar 17 '17 at 20:06
  • Admittedly, as the quote presented in the question shows there are instances of the word "theory" being used less discriminately, more loosely. It stands to wonder, however, whether such use conveys appreciation for systems of self-evident notions, definitions and axioms expressed through them, and their consequences; or provides language for referring to such systems concisely, if not as "theories". – user12262 Mar 17 '17 at 20:06
  • A theory is a mathematical system, a hypothesis the empirical statement that the theory applies in our universe. – Abhimanyu Pallavi Sudhir Apr 29 '19 at 10:34

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The sentence, as it is quoted, seems moot to me.

In fact, it would apply to any logic theory: a logic theory is nothing else that a collection of statements assumed to be true (axioms/hypotheses - the name is not so important), and a collection of logic symbols and rules of inference (also assumed to be true) that codify how you can get new true sentences combining true sentences.

Given that, it is then the role of physics that differs e.g. from the role of mathematics: the former aims to use axioms/hypotheses and rules of inference (sometimes only intuitively) to produce predictions, and to verify these predictions (and in turn hypotheses) by experimental observation; the latter aims to prove non-trivial true statements, using in a rigorous and strict fashion the axioms and rules of inference.

My personal definitions of hypothesis and physical theory would then be the following:

  • An hypothesis is a statement assumed to be true.

  • A physical theory is a logic apparatus built (with a "physical" level of rigour) on hypotheses, that provides a relevant number of testable predictions, that can either support or contradict the physical relevance of the aforementioned hypotheses.

In any case, contrarily to what happens in mathematics, there is no precise and agreed definition of physical theory. However if you also take a look at the ones given in the comments, they have more or less the same spirit as the one above.

yuggib
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    A physical hypothesis is not assumed to be true (one can't usefully assign a truth value to statements that are known to be false from the get-go). It's only assumed to be "close enough". A physical theory is not built on logic but on experimental data. It always ends where the data ends. Beyond there be dragons. – CuriousOne Jul 04 '16 at 08:09
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In a strict true/false sense, every scientific statement is false. For example, the following two statemaents are both false:

  1. The Earth is flat.
  2. The Earth is a sphere.

However, the second statement is much closer to the truth than the first. [1] It is this kind of closeness to truth that distinguishes a scientific hypothesis from a scientific theory. In one sense, both hypotheses and theories are unprovable statements that are backed by limited quantities of evidence. There are many related ways to distinguish between them:

  • Hypotheses have some evidence backing them; theories have a lot.
  • Hypotheses can explain one set of data; theories can explain a wide variety of data.
  • Hypotheses explain all currently known observations and experiments; theories can predict the results of future observations and experiments.

Like anything that interacts with reality, there is uncertainty, interpretation, and shades of grey. Ultimately though, a hard line demarcating hypotheses and theories is not that useful. Just remember that every statement made by a scientist is followed by an unspoken, "but I could be wrong," and you'll be fine.

[1] Isaac Asimov, The Relativity of Wrong: http://chem.tufts.edu/answersinscience/relativityofwrong.htm

Mark H
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I would not agree that a theory is the same as a hypothesis. Rather I would argue that hypotheses are formulated within the framework a theory. Theory refers to the whole body of knowledge, usually driven by observations. The statements of a theory are validated by empirical data. Theory provides names and concepts for the observations so that scientists know what they are talking about. (NB some authors, most famously Quine, would argue that the statements of a theory are all on the same level, but that is not custom in everyday science)

A hypothesis is a mere statement, using the terms of a theory, awaiting experimental (or even theoretical) validation or falsification.

Consider also the encyclopedic definition of the terms:

"A hypothesis [...] is a proposed explanation for a phenomenon." [https://en.wikipedia.org/wiki/Hypothesis]

"A scientific theory is a well-substantiated explanation of some aspect of the natural world that is acquired through the scientific method and repeatedly tested and confirmed through observation and experimentation." [https://en.wikipedia.org/wiki/Scientific_theory]

Hawking's point might have been that the scientific knowledge cannot be proven to be true. In this aspect, science is different from mathematics, metaphysics, and formal logic.

magnon2020
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  • Except that physicists don't follow that definition of "theory". https://physics.stackexchange.com/questions/68599/what-sets-a-law-apart-from-a-rule-or-a-principle – Foo Bar Oct 29 '19 at 18:42