Prandtl–Glauert singularity

But as a former physics major, I think those problems happen when underlying models have subtle differences from the real world. In this case, the model assumes infinitely compressible fluid. The model may work out well in some earlier applications. But the model breaks down due to air is not "infinitely compressible" in the real world.

The good thing for mathematics and computations is both are rigorous so they are perfectly well suited for spotting bad assumptions in models. And this is the reason we need well crafted experiments to hold theories against the real world.

They are very different problems.

* Sound Barrier

The air is made of molecules, mostly Nitrogen and Oxygen, lot of them, like 10^23/galon. It’s impossible to keep track of all of them, so you must use approximations, and the approximate versions are too difficult, so you must approximate the approximations, until you get a theory that is simple enough to do the calculations and still it give the correct answer to your problems.

For example, if air is not trapped, then it’s almost incompressible when the speed is < 0,9 the sound speed (perhaps the approximation is good even for 0.99). I.e. for most of the calculations approximating that air is incompressible gives almost the correct result, unless you are very close to the sound speed. Incompressible fluids are lot easier to use in the calculations. (In particular, an incompressible 2D fluid can be modeled with complex analysis, it’s a beautiful approximation.) .So you are happier to get an almost correct result, with a lot less of computations and technical problems.

From the Wikipedia article:

> The Prandtl-Glauert transformation is found by linearizing the potential equations associated with compressible, inviscid flow.

This formula is a good approximation for slow air flux. If you try to apply this to almost Mach 1 problems, you void the guaranty.

* Light speed Barrier

You can combine Special Relativity, Electromagnetism and Quantum Mechanics (well you need a Nobel price to do that :) ) and get one of the most precise Physics Theories. It can be tested with simple systems like a single electron bouncing against a single electron, so you don’t have to make too many approximations. (The equipment is very complex and the calculations are awful, but that’s another kind of approximations.) One of the more precise results is the magnetic moment of a electron. It depends heavily Special Relativity, Electromagnetism and Quantum Mechanics. The theoretical result and the experimental result agree with more than 10 significative figures http://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_momen.... For all practical propose they are equal. The complete calculation involve also the week and strong force, but the theories that model them don’t change Special Relativity.

All the experiments in the LHC use very fast particles and to calculate their properties you must use a lot of corrections of Special Relativity. So the theory is already tested for particles with a speed very close to light speed. It’s very improbable that there will be possible to break the light barrier.

Another problem is that by Special Relativity, if you travel faster than light, someone with the right speed will see you traveling backward in time, and you open a Pandora box of paradox. There are some additional problems with gravity and General Relativity, but they don’t change the main points.

Every Physic Theory be proven wrong by an experiment, so it’s not possible to say that we will never have to modify Special Relativity to allow faster than light travel, but it is very improbable.