Occam's Razor - What's wrong with your revolutionary new theory?
If it's a simple theory against a complex one then...
... the simple theory is more likely to be correct.
This powerful and insightful rule of thumb should not be ignored, and I am going to give a classic example.
Pioneer is a spacecraft that was launched in 1972. Earth was able to track its progress until communication stopped in 2003.
Newton's laws have thus been tested very thoroughly. The measured and calculated trajectory is very close but there is a very small systematic difference of 8.74±1.33×10−10 m/s2 which has been known as the Pioneer Anomaly.
Complex theories - Equivalence principle
Of the possible explanations, scientists considered an adjustment to our understanding of gravitational physics. (Einstein would take a slap). BUT a complication arises which comes from observation of large celestial bodies that do agree with established theory. To adopt the new idea, we would have to throw away the axiom of equivalence. Doing this would mean that some objects are affected by gravity in a different way to other objects. If that were found to be true, it would have a profound effect on all of physics. It would mean that we could start looking for properties of objects that resisted or enhanced gravity. Ultimately, we might be able to stack these materials or layer them or otherwise engineer them to create a levitating device. If you have a levitating device, then you could make a perpetual motion machine. If you have a perpetual motion machine, then you could create energy from nothing, and that would violate the conservation of energy axiom... and so all of physics comes tumbling.
It's not surprising that this idea was not pursued too vigorously. When your theory breaks long standing axiomatic principles - it's doomed. Of course, you could enhance the theory by making it more complex to avoid breaking these axiomatic principles.
Occam's razor says Nooooo.
The "It can't just be a coincidence" theory
Multiply the Hubble constant by the speed of light, and a number pops out that is numerically equivalent and quite close to the value involved with the anomaly.
I say, "so what" - it's a coincidence. Even though some wacky axiom-stressing new-physics theory creates just such an equation.
It's a common laymens' fallacy that a random stream of numbers cannot produce say, the pattern 1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1 and if it did, then there must be some deep and exciting theory behind it. The truth is, that a proper random stream of numbers MUST produce a sexy looking run like that. The trick is how often, and if each is related or predictable. If related, too frequent, predictable, or even absent, then the stream of random numbers are not necessarily random. And the same base principle applies to measurement and observation.
For a theory to hold water, it needs to be independently repeatable and make predictions and agree with observation and especially strongly demonstrate cause and effect.
You can take a large literary work, like 'War and Peace", analyse it word by word, and create a system (a theory) that makes it look like a hidden message has been installed by the author. In reality, this is an example of backwards-science. It's finding evidence and inventing a crime to fit even though no crime has taken place.
Move to the Dark-side Luke.
Dark matter also got blamed. Dark matter pops up in a lot of new theories about stuff we can't quite explain, like the ratio of mass that is 'out there' to the observable mass. (The rest is dark matter - right?)
But dark-matter explanations bother the equivalence principle too, and so that theory blows out in complexity.
A time-gradient theory
Related to the gravity explanations, and of course General Relativity is an explanation that essentially boils down to a non-uniform time in constant acceleration.
This makes no sense really, and it's a rather complex idea.
Remember Occam's Razor.
Beauty in Mathematics.
Beauty, symmetry (or slightly broken symmetry) and simplicity is universally recognized in many methods of expression. This idea applies to a work of art, a face, a musical rendition, a journey from A to B, and even to a mathematical equation.
The more power a simple explanation has, and the more ways that other theories predict the same explanation, and the closer to symmetry is the theory, then it is no accident that time and again, a theory like that is more likely to be correct than competing complex theories.
I deliberately over-complicated that previous sentence just to make an ironic point.
The boring simple and beautiful explanation.
In early 2011, we began to see mounting evidence that it's simply the emission of heat from the spacecrafts' onboard radioisotope thermoelectric generators that is slowly throwing the craft off course.
It does not invent new physics.
This is the most likely explanation.