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 Originally Posted by wufwugy
So is it true that all string theories so far have not been able to explain the current standard model without also positing things that are known to be false?
Some string theories make predictions that are known to be false. E.g. if it predicted that an electron should have a mass of a star, that would clearly be a poor description. Most make predictions that are unable to be determined as true or false.
 Originally Posted by wufwugy
Or have some created a framework that explains everything but isn't testable so there's no way to know?
As far as I know, no string theory completely overlaps with the Standard Model... they don't even come close.
If there was a string theory that did "explain everything", then it would be of great interest.
 Originally Posted by wufwugy
If not, what's the furthest that a theory has gotten?
I don't really know. Not so far as to reconcile even one chapter of a physics book, much less all the chapters in all the physics books.
I'm not current in the field and people with PhD's in physics are working on these theories. When I do try to read them, I don't get far. I don't really speak the language enough to even figure out which little nibble on the edge of current theory they're attempting to elucidate.
 Originally Posted by wufwugy
Like has there been unity of the four forces but only in an unfalsifiable way?
Not to my knowledge.
 Originally Posted by wufwugy
Or has every unity of the forces done things like posit additional unknown forces?
I really don't know.
 Originally Posted by wufwugy
Related question: is there a way to know if something is true based exclusively on the math? Or is it that math can operate within its own systems, so even a mathematical model that explains every known thing perfectly may still be false?
I'd argue that the qualities of "truth" and "falsehood" only exist in math, and math-like logical systems. Without a rigorous logical framework, the ideas of true and false are meaningless.
Science is never true or false. Science isn't really concerned with truth and falsehood, just an honest account of observation. Which brings up a whole bonanza of questions.
If someone hallucinates something, observing it, does that mean it's "real"?
If something is observed by many... does that make it "real"?
If something is unobserved... can it be "real"?
Is a sense of shared subjective observation indicative of an "objective reality" that is observed?
Science can't even answer simple questions like those... so the idea that it's going to reveal some deeper truth about anything is, I think, off base.
The magic of math is that you can give it a statement and then work some mathemagic and return another statement. Whatever the truth of the input statement is identical to the truth of the output statement.
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