Credibility Gap of Exact Prediction from Theory

Precession of Mercury 0.001 degrees per century.

Suppose you have a theory about a complex physical system, like our Solar system or atom physics or global climate,  which you want to sell to the World by showing that it gives predictions in exact agreement with observations. Not in fair agreement with observation, but exact agreement. 

Then you have a problem because observation is subject to error and you cannot expect that your theory about a complex system, which is not known in detail, can be in exact agreement with observations subject to error. This problem can be handled if the observation is known to you before you make your "prediction" from theory, in which case you can fix your model parameters and computation so that your theoretical model appears to agree exactly with observation. Not only in fair agreement, but in exact agreement. But this would not be real theoretical science, just data fitting.

So you should be cautious when you meet predictions from theory which exactly agree with observations (which cannot be exact), and ask yourself if the exact agreement is the result of a posteriori data fitting, or if the prediction was made without prior knowledge of the observation.

Here is a key example: As seen from Earth the precession of Mercury's orbit is measured to be 5600 arc seconds per century (one arc second=1/3600 degrees). Newtonian gravity, taking into account all the effects from the other planets and the Sun predicts a precession of 5557 arc seconds per century. There is a (very small discrepancy) of 43 seconds of arc per century. Newtonian gravity thus showed to be in very good agreement with observation for the complex System system not known in exact detail.  

When Einstein came up with his General Theory of Relativity GR as an improvement of Newtonian gravity, he made a simple computation which exactly delivered the missing 43 arc seconds. Exactly. Einstein then started from the Newtonian prediction of 5557 and added a contribution from GR by a back-of-the-envelope computation and arrived at exactly the missing 43 arc seconds. Einstein did not compute 5600 by applying GR to the complex Solar system, which is impossible because GR is so complicated, but used GR only to make a simple adjustment of Newtonian gravity doing the main job of predicting 5557. 

In any case Einstein managed to sell that GR predicts/computes the precession of Mercury in exact agreement with observation, which Newtonian gravity does not, and so GR has to replace Newtonian gravity. This has become the fundamental pillar of modern physics. Convincing?

The story is the same with Einstein's GR prediction of the aberration of light in exact agreement with  Eddington's 1919 Solar Eclipse observation. 

Another key example is the prediction of the fine structure constant of Quantum ElectroDynamics QED in exact agreement with measurement (up to 0.000000001), used to claim that QED is the most accurate physical theory even more precise than Quantum Mechanics, which is always in exact agreement with observation, although computations in both cases are exceedingly difficult even for simple systems.   

But the gravitational constant is not known better than 0.0003 and there is no theoretical prediction, unless it boils down to data-fitting.