Could scientists test a theory of everything?
I'm ready to reduce a certain amount of scientific rigor for a good story.
In my world, some person invents a theory of everything. Is there a way that scientists would test the theory, to prove that its right, instead of some scrabbled equations?
From my limited understanding, neither string theory nor loop quantum gravity have predictions and operate at such scales that can't be proven or falsified. I think string theory made some predictions such as supersymmetry that were proven wrong by the LHC.
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A common misunderstanding about theories in general is that you can prove them, when in fact you will never be able to prove a theory - you can only ever falsify a theory. There is simply no way to prove that a theory will always apply to every case that it's supposed to be usable for. You can only ever falsify a theory and thereby say that it doesn't work for a specific case and thereby say that it can't possibly encompass all the cases it was supposed to be applicable for, because you have at least one example for which it doesn't work.
This means that no scientist will ever be able to prove that the theory of everything is correct.
They can only conduct experiments to falsify it. And if they can't falsify it then it's good enough to be used until a case comes up where it's falsified, which would mean that they would need to search for a better theory that is also applicable to that case.
As was noted in the comments this is not a complete definition of what a theory is. For example to be a theory you need to be able to check it. The easier it is to theoretically falsify it the better the theory. The logic behind this is that if there are many points you could attack and anyone could attack the theory at any point without a lot of resources then someone will surely be able to find flaws in your system at some point. If your theory still manages to stand and not be falsified despite experiments being easy to do and many experiments being conducted your theory seems to be usable and people will start to accept the theory as a basis for their work.
High attack surface + after long time still not falsified = good theory
This still means that your confidence in the theory is the only thing that can rise and you will never be 100% sure that your theory is correct. You simply can't be sure that a theory is correct. You can only say that it worked for all tested cases and until a case comes up that falsifies the theory you simply assume that it works this way to make your life easier and continue your work.
If there is no way to falsify a theory then you are in the range of pseudo-science and disregard the normal scientific process. A theory that you can't possibly disprove is by definition not a theory. The same applies to arguments like "There was something here that made it work when I did this experiment, but now it's gone and you can't reproduce it, but my experiment was successful so my results are correct." If another person can't reproduce it under the same circumstances it's useless and not done with the necessary scientific rigor. Yes, the experiment could be very costly or difficult, but it has to be possible to repeat an experiment.
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First, I suppose I should define what a "theory of everything" actually is. I'd describe it as a mathematical model that predicts the behavior of any object under any given set of conditions. It should be valid in all situations, and should, experimentally, match previous observations of the universe. Some would argue that such a theory should also be "beautiful", but some definition of the word. Maybe that's true; maybe it's not. At any rate, a theory of everything should explain exactly what it claims to: everything.
Central to the idea of a theory of everything is the idea of unification. There are four fundamental forces in the universe: electromagnetism, the weak nuclear force, the strong nuclear force, and gravity. We believe that a valid theory of everything might explain how all four forces are really just manifestations of a single underlying force; this principle is called unification. At high energies, all four forces should behave the same, as components of this force. We would expect similar results when talking about the particles involved in the theory.
Let's talk about an example, a partial analog to a theory of everything: the electroweak interaction. The electromagnetic and weak nuclear forces were unified successfully by a number of theorists in the mid-20th century. Now, this unification did make some predictions - some of which you might have heard about:
- We need the Higgs boson to explain electroweak symmetry breaking - a way of saying why the forces have carrier particles with different masses (the photon is massless, while the W and Z bosons have mass). The Higgs boson was detected in 2012.
- The W and Z bosons, which mediate the weak force, must exist, as predicted by the theory. These were found in the 1980s.
- Neutral currents, a type of weak interaction, were predicted to exist, and found in 1973, shortly thereafter.
A theory of everything will predict the existence of new particles or new phenomena, typically at high energies, and would take more powerful detectors and colliders to detect them. Obviously, as technology gets better and better, more powerful particle accelerators and colliders will be built. I'm excited in particular about the International Linear Collider and the Future Circular Collider. The Superconducting Super Collider would have been amazing if it had been built, but . . . it was cancelled because of budget issues. The electroweak force provides an excellent example of predictions at high energies being verified - see, as I mentioned before, the discovery of the Higgs boson.
Now, it's also possible that we could find evidence for a particular theory of everything in nature - possibly in astrophysical experiments. To use your mention of supersymmetry (SUSY) as an example, certain superpartners are candidates for dark matter. The study of those in various environments could provide support for SUSY - although it's important to consider that supersymmetry does not imply that string theory is right, and string theory doesn't need supersymmetry. They're just close companions, and each works rather nicely with the other.
If a theory of everything keeps garnering evidence, eventually it might be accepted as generally correct, although as Secespitus pointed out, a theory can never be proven; it can only be supported by more and more evidence. Maybe we find that a theory makes correct predictions for particles with up to 10 TeV of energy, but at 20 TeV, it fails. If we find that that happens, the theory would have to modified - or thrown away.
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