Could scientists test a theory of everything?

Question

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.

Answer 1

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.

Answer 2

First, we should establish what a "theory of everything" actually is. I'd describe it as a mathematical model that predicts the behavior of fundamental particles and forces (from there, emergent phenomena can be described by theories more suited to those particular condition). 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", by 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 would 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 two 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 theory predicted the existence of the Z bosons, which mediates the weak force along with the previously-predicted W bosons. All three were discovered in the 1980s.
• Neutral currents, a type of weak interaction, were predicted to exist, and found in 1973.

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.

Answer 3

None of the given answers seem to address the original question of how one might go about searching for evidence for or against such a theory. I am assuming that you mean for the theory to be experimentally tested (as other answers point out: not proved) in the modern world or near future.

Generally, the theory is going to need to do two things to carry weight:

1. Describe correctly all known phenomena.
2. Predict new phenomena which can be experimentally verified.

Another unnecessary but helpful property would be that it appeals to a sense of "naturalness". There is a lot of debate around the topic of naturalness, how one defines it and if it is even a desirable property of physical theories or if chasing after naturalness actually leads us in the wrong direction. There is a nice discussion here. Also it would help the theory to gain acceptance if it makes claims about certain outstanding philosophical problems.

Open Unexplained Observations in Physics

With our current technological capabilities we have probed everything from the structure of hadrons (on the order of $10^{-16}$m) to the everyday normal Newtonian physics (on the order of $10^0$ m) to the structure of galactic superclusters ($10^{24}$ m) to the cosmic microwave background (CMB) (on the order of the radius of the universe around $10^{26}$ m). Our current theories (Quantum field theory for the extremely short scales, General Relativity for the extremely large scales) are quite good at explaining all of the observed phenomena so far, apart from a few things, such as in this list. A few big ones which stand out to me from a phenomenological standpoint (picked by personal preference):

• Dark Energy: What is the source of the accelerating expansion of the universe?
• Dark Matter: There are numerous sources of evidence that there is far more matter in the universe than we can see, which is hypothesized to be a form of matter which does not interact electromagnetically (i.e. with light), and therefore is "dark".
• Black holes: From a theoretical standpoint black holes are a problem, as they are points of infinite curvature. If so-called "naked singularities" exist, our theories would be unable to make any predictions. Do singularities exist or is there some ultra-dense form of matter that we don't know about yet such as quark stars or some other exotic state of matter? See also the cosmic censorship hypothesis.
• Magnetic monopoles: Why are there no magnetic monopoles? If there were even one magnetic monopole it would explain why electric charge is quantized, but no one has ever detected one.
• Why are there three "generations" of fundamental particles (quarks and leptons)? The lightest generation are the up and down quarks, the electron and the neutrino, all of which are quite abundant (protons and neutrons are made of up and down quarks). But there are three generations of these particles, the strange/charm + muon/mu neutrino and the top/bottom + tau/tau neutrino, which have the same properties but have considerably more mass (and are therefore less abundant).
• Why do neutrinos have mass? Neutrinos were originally thought to be massless but experiments show that they have a very small mass (on the order of a million times less than the electron mass). Why this is is not known.

These are just some examples of what a more fundamental theory might be able to explain from the "known phenomena" side of things.

Predictive Power

Now let's look at what might be predicted. In all likelihood a more fundamental theory would predict things which occur at length scales smaller than what has been observed so far. This means new, bigger colliders will have to be built to reach higher energies and thereby smaller length scales. Unfortunately it is thought that a fundamental theory of everything which unifies gravity and quantum field theory would operate at lengthscales on the order of the Planck length, on the order of $10^{-35}$ m, which is way too small to feasibly study directly with colliders. But there may be interesting things happening just below the currently measurable lengthscales which a new theory might predict which could be probed. What might we find there? Note these are pretty much purely hypothetical:

• One possibility is that quarks could actually be composite particles with some internal structure which is too small to currently probe.
• Higher energy particle colliders could also produce heavier particles, potentially revealing some sort of new extremely heavy fundamental particle. It probably wouldn't show up directly (like the Higgs did) but could show up as a resonance in collider experiments. A new fundamental particle (or perhaps microscopic black holes) might appear near the Planck scale, but would be incredibly difficult to detect due to it being so massive (about $10^{19}$ times the proton mass) and decay so quickly (on the order of $10^{-39}$ s). Unfortunately these scales are not really feasibly reachable with colliders, but perhaps if some sort of new technology was invented it could be possible, for example plasma wake acceleration.
• There are some forms of supersymmetry which have so far escaped our detection capability, so extremely heavy super partners are not entirely ruled out yet.
• Could there be a fifth fundamental force which has so far evaded detection? There are plenty of theories which have postulated such a thing. This would involve finding a new force carrier, or observing interactions which are not allowed by the four forces we currently know of.
• If extra dimensions exist they could be discovered in collider experiments from "missing energy" in the outcome of a particle collision experiment (some of that energy escaping into other dimensions).
• At higher energies microscopic black holes could be discovered in collider experiments. It's fairly well accepted that black holes radiate (Hawking radiation). One question is what happens if a black holes radiates all of its mass away until it is about as massive as the fundamental particles? Will it evaporate completely or will it leave behind a black holes remnant, which would act like a massive particle? Such microscopic black holes remnants are one hypothetical form of Weakly Interactive Massive Particles (WIMPs), which could be a candidate for Dark Matter.

Alternatively, what might be predicted that could be measured at the largest scales?

• If the theory predicts multiple universes then it might yield new methods to try to verify their existence. Theories about the multiverse or "bubble universes" and the like could produce detectable signatures in the CMB.
• The theory may provide new insights into gravitational waves, perhaps yielding a new method to verify the existence of the graviton. (This mixes the lengthscales, gravitational waves are detected on extremely long length scales, but their quantum field theoretical particle form (see wave-particle duality) is called the graviton).

Philosophical Quandaries in Physics

From a more philosophical perspective, some outstanding questions (which are related to the "naturalness" issue, also in the Wikipedia list) are:

• From a Quantum Gravity perspective, a huge issue is the so-call problem of time.
• Another unrelated question about time is, if physical laws are time-reversal symmetric, why is there an arrow of time? The answer to this may lie in the CP symmetry breaking of some weak-force interactions. Many explanations have been attempted which generally involve statistics and the second law of thermodynamics (entropy always increases)
• What is the meaning of wave function collapse? What effect does measurement have on the state of a system? See Interpretations of quantum mechanics.
• Why do the physical constants have the values that they do? How many physical constants are there? Are they related and can their value be derived from first principles? Currently they can only be measured experimentally. Why does the universe seem to be fine-tuned for life? If the values of the constants changed slightly things like stars wouldn't form or everything would collapse. See also the Anthropic Principle or see some points here.
• What happened in the earliest times in the universe and what is the ultimate fate of the universe? We can only see back to about 400,000 years after the Big Bang by looking at the CMB. One possibility could be if we could somehow detect the Cosmic neutrino background, which would let us see back to one second after the Big Bang. Or was there a Big Bang at all or was it maybe a Big Bounce?
• Hierarchy problem: Why is gravity so much weaker than the other three forces? If a hydrogen atom (proton + electron) were bound by the gravitational force instead of the electromagnetic force, it would be larger than the size of the universe.
• Can Quantum field theory be put on a rigorous mathematical basis? See for example this series by Urs Schreiber. Related mathematical quandries in physics are discussed here.

Summary

1. Take into consideration what others have said about "falsifiable" vs. "provable". The theory should be falsifiable.
2. The theory must reproduce the verified results of our current fundamental theories.
3. The theory must predict new experimentally verifiable phenomena. Experimentally verifiable is the key here. String theory for example makes predictions that could hypothetically be verified if we build a super collider the size of the galaxy, which is obviously not feasible.
4. To gain acceptance, it would be nice if the theory were also "natural" and "aesthetically pleasing". Especially if it offers a "nicer" or "simpler" or "more intuitive" explanation than currently prevailing theories.
5. To gain acceptance, it would be nice if the theory were able to explain some currently unexplained phenomena.
6. To gain acceptance, it would be nice if the theory is able to explain certain unresolved philosophical or somewhat metaphysical issues. Of course these explanations are not going to hold any traction unless the theory has verifiable predictive power.

Of course one should take into account the words of Max Planck:

A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.

Answer 4

In order to answer the question, we should first look at what value a "theory of everything" would provide.

1. Offer a simpler explanation for things we observe in nature than the existing theories
2. Explain observations observed in nature which are not sufficiently explained by existing theories
3. Make predictions for the outcomes of events which weren't observed yet. "If X happens, then Y should be the outcome"

The first two are mostly of didactic value because they provide a better way to explain to people how the universe works. But they don't create any new insights. They only make existing insights more palatable.

The third is where we have possible applications. If your theory makes new predictions which contradict the predictions of competing theories, then there might be a way to create an experiment to test the theory.

For example, your theory says: "If we put a hamster into a particle accelerator, it should turn into a frog". The competing theory says: "If we put a hamster into a particle accelerator, it should turn into a pigeon". Nobody tried this before. So some scientists decide to try it. The outcome is a featherless, wingless, green amphibian. That means your theory got verified and the competing theory got falsified.

That means something got to be wrong about the competing theory. But hat does not mean your theory is confirmed to be correct. It only was confirmed to be applicable to this specific experiment. Does it work on any hamster or just this one? Does it work on any particle accelerator or only this specific one? Does it work all the time or were we just lucky? And is that animal actually a frog or is it maybe in fact a very frog-like pigeon?

A different experiment might have a different outcome than your theory predicted. That would mean that your theory got falsified just like the previous theory.

When a theory got confirmed by many different experiments performed by many different people in many different circumstances, then people might come to the conclusion that the theory is very likely mostly correct under most conditions and that it might be worth the risk to try building commercial products which work based on that theory.

And then someone's hamster-to-frog-transmuter suddenly creates a rabbit. Now the whole world is in uproar because something got to be wrong about the "theory of everything" and we need a better theory which also explains this new observation and makes a prediction about the circumstances under which this will happen again.

Answer 5

One thing a "theory of everything" must be able to do is explain why previous theories have worked as well as they do.

For example, classical Newtonian mechanics are not fully correct but it is not trivial for someone to figure out where they deviate from reality. The theory of relativity matches Newtonian mechanics at slow speeds, and only starts to deviate when things are moving at a significant fraction of the speed of light.

Deviation from existing theories is also how a "theory of everything" would be tested - as @Secespitus says, a theory providing opportunities to prove it false that don't end up proving it false is how we can gain confidence in the correctness of a theory. For example, the differences in Newtonian mechanics and relativity let us know that we needed to test things moving very and/or things with significant gravity, and when the results matched relativity instead of Newtonian mechanics we gained confidence in the correctness of the theory of relativity.

Right now, quantum field theory and general relativity together are able to explain pretty much everything, but as the Wikipedia page for the Theory of everything states, physicists have determined that there must be a flaw in one or both of those theories. The problem is that "As it turns out, this incompatibility between [the two theories] is apparently only an issue in regions of extremely small scale and high mass, such as those that exist within a black hole or during the beginning stages of the universe (i.e., the moment immediately following the Big Bang)" In other words, it is indeed likely that a theory of everything would be untestable - not because it is unable to make predictions that deviate from quantum field theory and general relativity, but because the deviations would occur at such extreme circumstances that it would be very difficult technologically to produce the circumstances necessary for the deviations to be significant enough to be measurable.

Answer 6

Well, this "Theory of Everything" would have to tick a few boxes to be even considered to be a candidate for a theory of everything:

1. Have Newtonian mechanics as a limiting case (for everyday speeds, distances and masses).
2. Have General Relativity as a limiting case (for large masses and fast speeds).
3. Have the Standard Model of particle physics as a limiting case (for low energies).
4. Have quantum mechanics as a limiting case.

In addition to these limiting cases (which boils down to the statement that it describes everything our current theories describe) it should answer all currently open questions in fundamental physics (otherwise it would not be a theory of everything, by definition):

1. How do neutrinos acquire mass and what is their order (is the electron neutrino the lightest or the heaviest)?
2. Why is there more matter than anti-matter in the universe?
3. What is Dark Matter (or produces an effect like it)?
4. What is Dark Energy (or produces an effect like it)?
5. What happens at a singularity (both in a Black Hole and at the beginning of the universe)?

If it fulfilled all these constraints, people would definitely pay attention to it, even if it was not immediately falsifiable. It should however be theoretically falsifiable (as noted in the other answers).

Answer 7

If the new Theory of Everything makes different predictions about something, those predictions can be empirically tested. One example of how it seems like it would need to: we don’t currently know how to reconcile General Relativity with Quantum Mechanics to get a theory of quantum gravity, so a Theory of Everything would presumably make new, testable predictions about gravity.

If the Theory of Everything only derived the existing Standard Model of physics in a new and elegant way, but made no new predictions, then it’s like the multiple mathematically-equivalent “interpretations” of pieces of modern physics. It would be a purely theoretical discovery. The paper would prove mathematically, not experimentally, that it makes all the same predictions. If it’s significantly easier to do calculations using the new equations, they would be adopted quickly. Whether people accept a theory like that as a more-elegant, “better” explanation would be a matter of personal opinion and social convention. Perhaps all new physicists would be taught it, or perhaps the group of physicists who use it would form a small subculture.

Answer 8

To put the existing answers in practical world-building terms, if the proposed Theory of Everything predicts something unexpected, e.g., a plausible way to build something like an Alcubierre drive that can actually be affordably tested - even if only on an experimental scale - and if the test has been successfully carried out and later reproduced by multiple independent teams, then the theory is likely to be tentatively accepted by the scientific community as being probably true.

You might even choose to have someone other than the creator of the theory, perhaps a rival or sceptic, notice the unexpected prediction; compare this real-world story about a surprising behaviour successfully predicted by the wave theory of light.

As already explained, this isn't a proof, but it would be enough to explain why the theory would be taken very seriously indeed. It would still take some years before the theory entered the undergraduate syllabus as part of the scientific consensus about how the world works, but everybody would know about it and take it seriously.

Your main problem is to find a potential test that isn't too outré for the mood of your story, that preferably doesn't seem too ridiculous to an actual physicist (as many successful stories can attest, this one is optional!) and of course that doesn't interfere with your plot; though you may be able to work around any plot difficulties with the "experimental scale" loophole, e.g., yes, you built a working Alcubierre drive, but only on a microscopic scale; it will take decades or centuries to work out the engineering problems necessary to make an actual FTL starship, or perhaps the theory rules that out altogether.

(Note also that, depending on the nature of your story, you might not actually need to specify what surprising behaviour the theory predicted, just say that it did and that the theory's predictions were experimentally verified.)

Answer 9

There's no intrinsic reason TOEs wouldn't be testable. If you want a story in which a TOE is more readily testable than is the case in real-world 2018, you just need to tweak some of the mundane practicalities that contribute to such difficulty here. Speaking as a physicist, a few examples off the top of my head include:

• The fact that the energy scale at which "new physics" occurs is so many orders of magnitude larger than what our particle accelerators can access. Maybe in your world their design is more powerful, or certain physical ratios are smaller. The Planck length is determined by the strength of gravity, but you wouldn't even necessarily need a smaller gravity-electroweak strength gap, because the compactified dimensions in string theory can be much larger than the Planck length.
• The fact that the TOEs present so many different options we can't narrow down. The string theory landscape is huge, but it's conceivable we could improve our search techniques. Just as Silicon Valley is about a team with a great compression algorithm, your story could feature an efficient landscape-searching algorithm that has shown all options consistent with past observations make certain predictions we can test elsewhere.
• The fact that there's only so much we can measure. TOEs typically correct certain theoretical details of black hole thermodynamics. Can your civilisation measure black hole entropy? They might be spacefaring, or they might have worked out how to make miniature black holes they can study.
• The fact that New Physics ideas have gone so long without turning up. Real data tell us that the proton lifetime, if finite, is much larger than early GUTs* imagined; real data also tell us that supersymmetric partner particle species, if they exist, have much more mass than the "standard" particles we know of. Again, your universe might not have these problems, at least not in the same degree. (* Grand Unification Theories still neglect gravity, but introduce a strong-electroweak unification.)
• The fact that the real world is so much more complicated than early efforts hoped for. Kaluza-Klein might have panned out, if the nuclear forces didn't exist. (Large atoms' stability would then require negatively charged nucleons, but why not? It's your universe.) One downside would be that without radiometric decay you can't date fossils, but you might decide that's a small price to pay in your story.
• Maybe your physicists have just been working at it longer. Every now and then someone proposes a more imaginative (and hopefully more practical) way to test a TOE than "get your accelerator to the Planck energy". Maybe in a century or two something will pan out. Bear in mind the theories are extremely young.

Answer 10

Question: "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?"

Answer:

Of course every decent theory can be tested. It must (1) agree with all experiments, and it must (2) explain what is so far unexplained. At present (2020), the first requirement is that it must agree with particle physics and with general relativity.

There is astonishingly little that is unexplained in physics so far. All issues have been mentioned in the answer by Kai, above. But in fact, the real issues are even fewer. Therefore, the second requirement boils down to explain all the basic constants of physics. There are about 25 of them. The most famous ones are the fine structure constant 1/137.03599.. and the mass of the electron (as fraction of the Planck mass). The cosmological constant ("dark energy") is one of the list. Dark matter - if it exists - should also be explained.

Here are two additional points, not made so far.

A. In a future world, the theory is not made of equations, because equations require space and time to exist. And a good theory of everything explains how space and time arise, and thus explains how equations arise. A good theory of everything thus does not make use of equations, but makes use of other concepts.

B. The theory of everything might turn out not to be useful (as it agrees with present theories), might turn out not to be important (as it agrees with present theories), might turn out not to be valuable (as it might not allow to build new machines). It thus might turn out not to be powerful, in the usual sense of the term: it does not provide power. It is more a kind of intellectual entertainment.