Because muons are traveling very fast, near the speed of light, a muon experiences time dilation effects that allow it to travel much farther than the 660 meters that light would travel in 2.2 microseconds, muons actually make it to Earth’s surface and well below because they interact very little with other matter.  That means that the life of a muon is lengthened to about 0.5 milliseconds.  From the muon’s perspective, because Earth is moving at nearly the speed of light, Earth looks like a flat pancake and Earth’s atmosphere is only a few hundred meters; a muon’s life is long enough for it to go through before it decays.  These are logical explanations from their own perspective, the muon’s and Earth’s as to how events unfold.   Both perspectives are assumed to be true, and it is only an issue of reality being relative.  Now let’s introduce a third element to this event.  This element is in the form of a clock, let’s say a pulsar some 1000 light-years away.  Let’s have this pulsar send out a pulse every 0.1 milliseconds.  A real pulsar with a period that short could not be found, but let’s assume that one exists.  Let’s also have the muon have a motion that is perpendicular to the direction of the pulsar, so as to have common Doppler with Earth.  (See animation below)

Muon falling to Earth with 0.1 ms pulsar

Now, from the Earth’s perspective, as the muon falls through the atmosphere, an Earth observer will see 5 pulses from the pulsar, before the moun decays 0.5 ms later.  From the muon’s perspective, as it goes through Earth’s atmosphere, it will also see 5 pulses in its 2.2 μs life.  While Earth is seeing 0.1 ms pulses, the muon will see very short pulses, of only 0.44 μs long.  It is clear the Earth’s clock and the muon’s clock are not running at the same rate.  They are experiencing different time dilations.  And since time dilations are due to their speed, we have to ask:  With respect to what?  Let’s have another muon, 180º from the first on the other side of Earth, also moving near the speed of light and with about the same life as the first.  The second muon’s path will also be as long as the first, and will see about the same number of pulses as the first.  There has to be a speed along the axis formed by the two muons, for which the period of the pulsar will be a maximum.  This leads to the concept of absolute speed.  A rocket moving with constant acceleration along the axis formed by the two muons will also see shorter and shorter periods for the pulsar as it approaches the same frame of reference as one of the two muons.  This is a different type of blue shifting that is neither Doppler nor gravitational.  And also pulsars on all sides perpendicular to the motion will be blue shifted and their apparent position will also change in the direction of motion.

More evidence for absolute speed can be found at particle accelerators.  Consider two decaying particles like a pair of muons (twins).  One muon stays stationary and the other one is traveling near the speed of light inside the accelerator (circular or linear makes no difference).  It is the one moving fast with respect to the accelerator and the rest of the planet the one that experiences a longer life. This is an experimental proof to the twin paradox.  If we consider the motion of Earth around the sun, and the sun’s motion in the galaxy they are all very small compared to the speed of light, we can say we are almost stationary in space. 

Based on this short discussion and for the rest of this paper, it will be assumed that the concept of absolute speed is valid.  This concept is not incompatible with other aspects of Special Relativity, nor does it mean that there are fixed locations in space as will be discussed in later sections.