Misconceptions in Relativity

The Pioneer Anomaly is probably not gravitational in origin. This is because we can test the semi-major axis of Neptune and Uranus extremely pricisely. If there was a gravitational origin to the anomaly then it would have an affect on the axis of the two planets.More details here:
http://arxiv.org/abs/gr-qc/0608127I should mention that these tests are model independant, that is they don't assume any theory of gravity in particular in order to carry out the observations.This paper is from 2006, as of 2009 the Pioneer Anomaly is consider to be almost certainly not of gravitational origin.Edited by Son Goku, : Repeated phrasing removed.

Smooth Operator, it is unrealistic to think that time dilation is due to some slowing down of a clock's internal mechanisms.
There is time dilation due to relative motion and gravitational time dilation, both of these produce different effects so they could not really come from the same clock based mechanism.Also think of particles which have been observed to have their time dilate. They are too simple to have internal workings which could slow down.

No, although these effects are fundamentally different to how relativistic time dilation occurs. Particularly for special relativistic time dilation where the body isn't really interacting with anything. Hopefully the examples below will help. I think Rrhain dealt with this quite well, so I'll instead concentrate on the next statement. Well first of all, the particles are actually moving extremely fast with respect to us, so they aren't slowed down. The point is that particles moving at huge velocities live longer from our point of view.
Now you could say maybe high speeds has a physical effect on the decay rate of a particle, however this is easy to refute using Galilean relativity, which I will assume you accept. Galilean relativity says that if you are moving inertially then you can't tell you are moving. So these incredibly fast particles in their own reference frame are stationary. Since any physical effect on their decay rate would have to be real in all frames, well then the slowing down of their decay rate would be true in their own rest frame. So what about the particles which aren't moving fast with respect to us? Well they are at rest in our frame, so from the above analysis they should also have their decay rate slowed down.
However they don't, only particles moving fast with respect to us have their clocks slowed down. This refutes the possibility that the decay rate is being affected by a speed based mechanism.

It's a little hard to reject Galilean relativity, since you can prove it by stepping on to a boat. Are you saying that there is some way to tell when an inertial body is moving?
This is very odd, since even in normal intuition people are aware that you don't "feel" motion if it is "steady".
Rejecting Galilean relativity is a bit silly. If you do reject it, then by what method do you detect inertial motion? Let us make this very simple, if special relativity is wrong how come it agrees with every experiment that has tested it?
(Yes, there have been countless tests of relativity.)In your response to cavediver: It must be said that it also takes into account relativistic calculations.

Well Quantum field theory is tested in particle accelerators. It's major experimental success occured in the tests performed on it in the 70s, 80s and early 90s. For instance its predictions of the W and Z bosons, as well as various decay rates and scattering for quarks.The best evidence for General Relativity is the binary pulsar system PSR B1913+16 and studying what is called its periapsis precessions.

There is no real evidence that inertial motion can be detected. All experiments designed to test if it can be detected have continuously ruled it out to a higher and higher degree and there is no experimental evidence of the aether. For the trajectories of the particles in the magnetic fields, as well as their trajectories around the accelerator. Also for the dynamics of the magnetic fields themselves.