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One of the problems with special relativity is the fact that it essentially operates in "empty space", where there are no objects or matter that could serve as fixed reference points. Granted, motion is relative, so does it matter? It does matter if you accelerate a clock to high speed, leave it to travel freely for some time and then compare it's time with your own clock.
The Cosmic microwave background
Some people try to view the cosmic microwave background (CMB) radiation as the "absolute frame of rest". Figure 1 (from NASA's WMAP) shows a false color image of the temperature fluctuations of the CMB, with our relative movement removed. This relative movement is in the order of hundreds of km/s. So is this a rest frame in the sense that we can detect anisotropy in the propagation of light?
Figure 1: 
The CMB as an absolute reference rest frame fails on a number of different levels. The most important one being that as Earth orbits the Sun at a good ±0.01% of the speed of light, we do not observe any change in the speed of light coming from distant binary pulsars from different directions. We just observe a normal Doppler shift in the pulsar periods.
So, how are we to explain the prediction of special relativity that if we could fly at a very high speed to any nearby star and back, the clock on our spacecraft would lose a significant amount of time relative to clocks here on Earth? What makes Earth a "preferred" frame of reference relative to our spacecraft?
The standard explanation is that the spacecraft is in two different inertial reference frames during its journey - outbound and inbound - causing an asymmetry. Further, the craft is accelerated and we are not.(1) Valid as these arguments may be, it's still quite hard to wrap one's head around it. Here's a view that may make it more palatable.
A different view
In free space, every unaccelerated material object may have the same fixed "space-time speed". This means that if we take a spatial speed vector and we add a perpendicular "time vector" to it, the result is the same for all entities, even for photons! That universal constant speed is c, the speed of light, what else?
It works like this: in relativity, the Minkowski metric requires us to multiply time increments by c. In every time increment dt, a stationary object moves a "distance" cdt along its time dimension. Hence its "space-time speed" is cdt/dt = c. Note that we could have multiplied time by any other constant and would also have found a constant "speed of time" - it is just that c seems to be somewhat special...
If we are accelerated, this space-time speed (a scalar) remains constant, but the space-time velocity (a vector) rotates. Relative to the original reference frame, we acquire a spatial component (dx/dt) and a reduced temporal component (cdτ/dt), where τ is called "proper time". Proper time is what clocks measure, whether they move or not.
The two perpendicular speed components (of space and time) always combine in such a way that the constant space-time scalar c is maintained, as in figure 2 below.
Figure 2: 
By simple Pythagoras trigonometry:
(cdτ/dt)2 + (dx/dt)2= c2, [1]
which is easily reduced to the standard time dilation equation of special relativity, in only one space dimension (x) for clarity:
dτ/dt = √(1 – v2/c2), where v = dx/dt. [2]
So, it is effectively a speed vector diagram – a speed in time and a speed in space, making up a speed in space-time. It implies that the more speed (dx/dt) you acquire in the space dimension, the less "speed" (cdτ/dt) you will have in the time dimension.
Speed relative to what?
However, the question remains: speed relative to what? The answer lurks in what you can measure. You can observe that you have been accelerated and you can measure your spatial speed relative to your starting point, say Earth, by checking the Doppler shift of a radio signal beamed from there.
With this knowledge, you can work out by how much your space-time vector has been rotated relative to Earth's. Hence you know that your clock is losing time relative to Earth's. If that radio signal from Earth is time stamped and your navigation system is accurate, you can physically verify that your clock falls behind Earth's clocks.
So, in a way your starting point has become your "absolute frame of reference"! This happens because you have been at rest there and you have knowledge of the space-time vector of that point. Come to "rest" at a different velocity and you "acquire" that space-time vector as another valid "absolute reference frame", if you wish.
In the end, there are an infinite number of possible "absolute reference frames", bringing us full circle to the original question: "is Einstein's special relativity really comprehensible?" You be the judge…
-J
Notes:
(1) We on Earth suffer gravitational time dilation, making our clocks run slower than clocks in free space. However, this effect is much smaller than the time dilation caused by movement at a significant portion of the speed of light.
(2) You can read more on accelerated frames in Linear Acceleration from Relativity 4 Engineers.
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Re: Is Einstein's Special Relativity Really Comprehensible?
