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We are generally not interested in physical theories that cannot be tested with the scientific method. This would seemingly apply even if the theory has other advantages, e.g. simpler, more general, more elegant. Of course the possibility exists that the "correct" theory may not be testable beyond what it is designed to explain, or may contain many untestable consequences. In this case we would be eliminating such a theory a priori. Isn't this a problem?

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    $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – ACuriousMind Aug 26 '20 at 17:57
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may not be testable beyond what it is coming to explain, or may contain many untestable consequences. In this case we would be eliminating such a theory a priori. Isn't this a problem?

That’s all well and good. Until you have a plethora of such “theories” to choose from. Which one do we pick? Which one do we fund?

If it is consistent with current theories and observations, and it can be shown to be equivalent to existing ones, it becomes another formalism. For example, the path integral formalism of quantum mechanics.

The scientific method is stringent on the falsifiability and that’s where it gets its strength from. That’s how we can safely pick one theory over the rest by seeing which theory best predicts what we observe. If we loosen this, then we lose the strength of the scientific method.

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  • $\begingroup$ This sort of wanders around a bit too much. There really isn't such a thing as "most correct." Maybe you were going for "best predicts what we observe" ? $\endgroup$ – Carl Witthoft Aug 26 '20 at 11:52
  • $\begingroup$ @CarlWitthoft yeah that phrase fits better what I wanted to convey. $\endgroup$ – Superfast Jellyfish Aug 26 '20 at 12:04
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This would seemingly apply even if the theory has other advantages, e.g. simpler, more general, (more elegant?)

I beg to differ. If it is simpler or more general, it will be picked up sooner or later as main theory. If it is more elegant but not simpler nor more general, it will not get adopted in practice, but many people will study it just because of its elegance (albeit it seems to me the elegance is in physics equivalent to simplicity and generality, so "more elegant but less simple and general" seems to me as oxymoron). We are also not at the end of scientific investigation and the elegant ideas might prove to be useful for future theories.

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    $\begingroup$ This isn't even correct. $\endgroup$ – Carl Witthoft Aug 26 '20 at 11:53
  • $\begingroup$ @CarlWitthoft which part is not correct? $\endgroup$ – Umaxo Aug 26 '20 at 20:17
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One obvious example of a "simpler, more general, more elegant" theory is that the big bang was initiated by a supernatural being that created the universe for a specific purpose, which we have so far been unable to discover.

In this case we would be eliminating such a theory a priori. Isn't this a problem?

Is it "a problem" if science completely rejects this perhaps true theory and searches for different, but possibly testable, explanations?

Most scientists don't find it a problem to reject the concept of God. Even those that do hold personal religious beliefs tend to keep them separate from their work.

That's how science works, and so far it doesn't seem to be a problem.

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    $\begingroup$ So what is your answer to the question by the OP? $\endgroup$ – Bob Aug 26 '20 at 12:44
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    $\begingroup$ It is still too subtle for me. Plainly, do you think that a physical theory needs to be testable? $\endgroup$ – Bob Aug 26 '20 at 12:55
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    $\begingroup$ I honestly fail to see how this theory is "simpler, more general, more elegant"... Maybe "simpler" is fine, as it is understandable by a 3-years old (it is quite similar to the existence of Santa Claus as a "theory" explaining why they get presents at Christmas). But "more general and more elegant"? $\endgroup$ – Yvan Velenik Aug 26 '20 at 13:47
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    $\begingroup$ @YvanVelenik, it's more general because everything that can't otherwise be explained can be attributed as a "mystery" that we aren't meant to know. And what could be more pleasingly simpler than having a single cause for everything (even more than a GUT). $\endgroup$ – Ray Butterworth Aug 26 '20 at 14:08
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    $\begingroup$ Well, I guess that elegance, like beauty, is in the eye of the beholder ;) . As for general, well I guess that this "theory" explains everything equally poorly (that is, does not actually provide any explanation whatsoever of anything at all, but just reformulates the initial problem in other terms by adding an irrelevant new layer). $\endgroup$ – Yvan Velenik Aug 26 '20 at 14:18
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Theorem. $\;$ A physical theory does not need to be testable.

Proof (by counterexample). $\;$ There has been a strong interest for string theory but it is not testable because of theoretical and mathematical difficulties and because of the extremely high energies needed. $\; \Box$

Proposition. $\;$ String theory is not a mere mathematical theory.

Proof. $\;$ It is testable in principle (although not in practice). $\; \Box$

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    $\begingroup$ String theory as of today, is more of developing mathematical tools rather than trying to explain nature. To quote Maldacena “The problem is that string theory exists in the landscape of theoretical physics. But we still don’t know yet how it connects to nature as a theory of gravity.” More on this: quantamagazine.org/string-theorys-strange-second-life-20160915 $\endgroup$ – Superfast Jellyfish Aug 26 '20 at 8:37
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    $\begingroup$ String theory’s unique predictions haven’t been tested yet. So it does not qualify as a physical theory. It’s a physical hypothesis. $\endgroup$ – Superfast Jellyfish Aug 26 '20 at 8:46
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    $\begingroup$ There's a huge difference in the meaning of "theory" in mathematics versus its usage in science. "Theory" in mathematics means a mathematical body of knowledge. Examples include knot theory, number theory, set theory, ..., and string theory. String theory uses the mathematical meaning of "theory" rather than the scientific meaning. $\endgroup$ – David Hammen Aug 26 '20 at 8:57
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    $\begingroup$ @DavidHammen But string theory is testable in principle (although not in practice). This makes it more than a mathematical theory. $\endgroup$ – Bob Aug 26 '20 at 10:24
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    $\begingroup$ That's not a "theorem." It's a philosophical claim. $\endgroup$ – Carl Witthoft Aug 26 '20 at 11:53

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