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Before Einstein, scientists believed that all physical laws to be discovered were already discovered. Of course, that was proven wrong.

If we somehow manage to come up with the Theory Of Everything that even explains dark matter and dark energy, can we know if the TOE is all there is?

If we cannot know that there is nothing beyond the TOE, it might be presumptuous to call it TOE, like scientists did before Einstein. But since scientific method is inductive, I think it is impossible to know for certainty. (And hence the name, theory.)

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    $\begingroup$ Yes, it impossible to know anything for absolutely certain. Is there a physics question here? $\endgroup$
    – ACuriousMind
    Commented Jul 4, 2015 at 9:40
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    $\begingroup$ I think this is primarily opinion based. $\endgroup$
    – Gonenc
    Commented Jul 4, 2015 at 10:47
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    $\begingroup$ @gonenc I disagree. The question is essentially asking whether the completeness claims of a TOE are falsifiable. That's not opinion-based. $\endgroup$
    – lemon
    Commented Jul 4, 2015 at 10:57
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    $\begingroup$ @lemon: I think the question is asking whether we will be able know if a ToE can be extended in the future. $\endgroup$
    – Gonenc
    Commented Jul 4, 2015 at 11:12
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    $\begingroup$ Yes - we can know with certainty that we can never know with certainty :-). [[If you can get anyone to explain, without legerdemain, how either of the two possible 'explanations' for the universe can be possible [always has been, came into being from genuinely genuinely genuinely nothing] OR what an alternative is, then the above certainty may be in doubt. Until then ... :-) ]]. $\endgroup$ Commented Jul 4, 2015 at 11:18

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Thermodynamics, electromagnetism, and classical mechanics were the "TOE" of physics at the time of Lord Kelvin. They remained a "TOE" until new phenomena were discovered, which could not be explained by their theories, such as the photoelectric effect, the energy quantization of photons, the atomic spectra, and many others.

In the same way, a TOE which would unify quantum mechanics and general relativity, describe dark matter etc, will remain a TOE until new phenomena will be discovered, which will contradict the TOE, or simply cannot be described in its framework.

One can say that a TOE is a TOE until some unexplained experimental phenomena falsify the TOE.

EDIT: There is also one other consideration. The term "theory of everything" in its current meaning is misleading, because it is not a theory of "everything" in the strict sense. There are physical phenomena that are not addressed by the TOE. For example, chaos dynamics, non-equilibrium thermodynamics, solid state physics, biology and many others. Proponents of a TOE argue that such theory would explain in principle all known phenomena, including chemistry, biology, etc. This is logically correct, but practically useless. Of course chemistry and biology are "in principle" already explained by the physical laws currently known. But practically, nobody has been able to reduce Darwin evolutionary theory to quantum mechanics. There are physical phenomena that are simply beyond the scope of a TOE.

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    $\begingroup$ Saying that a TOE doesn't explain all phenomena because nobody has reduced evolution or other theory to quantum mechanics is an arthropodic view. Just because we can't show it, doesn't mean it isn't logically implied. $\endgroup$ Commented Jul 4, 2015 at 13:40
  • $\begingroup$ You are right, chemistry and biology can be logically reduced to quantum mechanics, but this reduction is completely useless at the end of the day. We will still need the theory of evolution to describe biology. One will still need emergent theories build up on the fundamental theory. All I want to say is that a TOE can be fundamental, but not exhaustive of all physical phenomena. $\endgroup$
    – sintetico
    Commented Jul 4, 2015 at 13:44
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    $\begingroup$ It is exhaustive of all physical phenomena, it's just that we can't exhaust it, and emergent theories are easier. $\endgroup$ Commented Jul 4, 2015 at 13:46
  • $\begingroup$ it is exhaustive but it cannot be exhausted! Interesting. In which way emergent theories are easier? In which sense chaos dynamics is easy? Anyway, I stress that we agree on the fact that emergent theories cannot contradict fundamental theories, and can "in principle" logically deduced from the latter. $\endgroup$
    – sintetico
    Commented Jul 4, 2015 at 13:48
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    $\begingroup$ I never said it cannot be exhausted, I said we cannot exhaust it. Chaos dynamics isn't easy for us, just easier for us then deriving it from a TOE. $\endgroup$ Commented Jul 4, 2015 at 13:50
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can we know if the TOE is all there is?

One of the main principles of science is falsifiability. All scientific theories are falsifiable. A theory may explain all we currently know but we always have the hope and expectation that our knowledge may expand. We must not know if things we don't yet know will also conform to current theories. That is an essential principle.

And hence the name, theory

Many people misunderstand this word and the way it is used in science. Some lay people might say "evolution is only a theory" or "gravity is only a theory" in a dismissive way as if to suggest that theories are no more than uneducated guesses.

The way I understand the progression of ideas, along a path of increasing certainty, is as follows

  • Conjecture: An educated guess of the form "perhaps X occurs because of Y" where X and Y might be complicated.

  • Hypothesis: A more fully worked-out idea, often one that can be expressed mathematically, is capable of making new predictions about the universe and which is therefore testable.

  • Theory: A hypothesis which has been subjected to very extensive testing to try and find circumstances in which it can be falsified.

So, in science, a theory is a pretty substantial thing.

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    $\begingroup$ Layman also regard laws as more substantial than theories when really they are not: a law is just a rule of thumb; a theory explains. So, e=mc^2 could be thought of as a law (the law of mass energy equivalence). Special relativity, from which it is derived, is far more substantial. It's perfectly understandable that people should think that, given the words used, and its a pity. In a way, it's good that we've stopped using the word 'law' for the new science but that it still exists for the old gives the impression that the old was more correct and certain than the new. $\endgroup$
    – Avon
    Commented Jul 4, 2015 at 13:33
  • $\begingroup$ This, especially the first part, might have been a good answer about 50 years ago, $\endgroup$
    – innisfree
    Commented Jul 4, 2015 at 14:05
  • $\begingroup$ Your falsificationism (i.e. strictly deductive) answer contradicts the OP's assertion "scientific method is inductive". You haven't addressed that at all. $\endgroup$
    – innisfree
    Commented Jul 4, 2015 at 14:08
  • $\begingroup$ +1 for the elaboration on the misuse/misunderstanding of the word "theory". $\endgroup$
    – Gonenc
    Commented Jul 4, 2015 at 17:03
  • $\begingroup$ @innisfree Since when did being falsifiable mean a conclusion was reached deductively? Red is correct about scientific conclusions needing to be falsifiable and OP is right about science being inductive. These do not contradict. $\endgroup$
    – reirab
    Commented Jul 5, 2015 at 4:06
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Here's an answer from a slightly different, more philosophical perspective.

Physical laws are not "laws" that describe and embody some absolute truth. The entire endeavor of physics is to find mathematical descriptions that match our observation of how reality behaves, and allow us to make predictions about future observations.

A "law" is just the best current description, and is always subject to revision, adjustment, or even being completely discarded if some future observation doesn't match its predictions. In fact the most important advances in physics usually come from such discrepancies. As various people have said, physics revolutions usually start with some one saying "Hmmm... that's unexpected...". For example, the orbit of Mercury not matching Newtonian predictions.

So the answer has to be, a priori, that we cannot ever discover ALL physical laws. Even if we reach a point where we're not discovering ANY discrepancies, there will always be realms of precision we cannot measure, or avenues of research we haven't thought of. Heisenberg and Godel conspire to ensure that we can never know everything.

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If we somehow manage to come up with the TOE that even explains dark matter and dark energy, can we know if the TOE is all there is?

Take the current favorite candidate for a theory of everything, a string theory to be decided in some future while we are still alive. It will model all of particle physics, quantize gravity all in one mathematical structure.

If it succeeds it will be the current TOE, and since it has all these dimensions there is a probability that new experiments, not thinkable presently, will be proposed from this TOE to try and falsify it. History of of physics tells us that the probability is high that at some values of coordinates, energies, ..., it may not hold up, showing that it is not really a theory of everything, but the last mathematical model in a long row of models modeling nature.

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  • $\begingroup$ The opening sentence in e.g. wiki about a TOE - "A theory of everything (ToE) or final theory, ultimate theory, or master theory is a hypothetical single, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe" - suggests that a TOE is not simply an effective theory that describes phenomena in a particular domain, but, well, a theory of everything... $\endgroup$
    – innisfree
    Commented Jul 4, 2015 at 16:18
  • $\begingroup$ @innisfree I an talking about a candidate TOE, at the moment the only viable one I see, will be a particular string theory. I argue that TOEs are effective theories, i.e. mathematical models of nature, up until they are falsified. Our experience is that they end by being falsified, and we will not know until it is. Maybe if it is continually validated for 500 years one might consider it the last, but even so a probability will exist that it will be falsified for some part of phase space not explored experimentally till then. $\endgroup$
    – anna v
    Commented Jul 4, 2015 at 18:32
  • $\begingroup$ "effective theories, i.e. mathematical models of nature, up until they are falsified" - are you sure that's what "effective theory" is conventionally taken to mean? as far as i'm aware, an effective theory is a theory valid in a particular (e.g. energy) domain $\endgroup$
    – innisfree
    Commented Jul 4, 2015 at 20:47

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