Time and the principle of relativity We know that every moving clock with respect to some clock A, is running slower than A. My question is simple - why it does not contradict the principle of relativity? Why can't we say that the clock which runs faster than any other clock is at absolute rest?
I remember that I've read in some book that its because the process of measuring time (in a moving train for example) is done in unequal conditions, but I didn't quite understand that.
 A: The clock A is running faster than any other clock - from its relative point of view only!
Any clock B in (non accelerated) movement with regard to clock A would say the contrary: that clock A (and any other clock) is moving slower than clock B.
By the way, this contradiction is settled, if clock A starts at clock B and returns to clock B after a travel (including obligatorily acceleration processes) for time control. The travelling clock turns out to have run slower than the other one (but only due to the existence of acceleration processes!)
A: The missing ingredient is that simultaneity is also relative.  For "rest" frame A, fill the universe with clocks synchronized with clock A that are also resting.  For "moving" frame B (say, moving to the right), fill the universe with clocks synchronized with clock B that are moving along.  
Let clock A encounter clock B when t = 0 on both.  Thereafter, clock A receive a stream of B-synched clocks, and when comparing readings (only meaningful when two clocks are at the same location), find these B-clocks slow.  Meanwhile, clock B will encounter a stream of "head-wind" A-synched clocks, and on comparison also find these clocks run slow.
A: Dear Sir: CalTech has a YouTube video on Lorentz transformation -episode #42 (see the link in comment section), which is an excellent and authoritative reference showing that the equations of SR were already known and published by Lorentz. 
Sir Einstein derived them with a set of hypothesis, while Sir Lorentz was struggling to find their meaning in terms of weird behavior of the apparatus studying Ether. 
......An absolute rest means a traditional Galilean space-time, which would be correct for any 'physical' nature of space, which may be hypothetically marked with 'indelible' ink to represent individual coordinate points...... 
The failed experiments to detect hypothetical medium Ether, the Lorentz transformations needed to explain the wierd results of those instruments (perhaps that was even more brilliant and tedious work than Einstein), and derivation of identical results by simple postulates of SR, put to coffin an idea of absolute rest. 
Please note, Sir Einstein did not give any structure to space. He had said something of this kind: a deeper theory (of cosmos) can only come from intuition, but not experiments. Experiments can only confirm or refute a theory.  In saying this, Sir Einstein was telling, something is missing in our understanding regarding the inner mechanics of space. A plethora of theories regarding origin of our cosmos and fundamental forces have assumed 'wierd' things about space. Sir Hawking predicted, one day we may have a theory in which even space is quantized.  Therefore, it does not serve trying to find an absolute rest, until we can understand the inner mechanics of space. ....In a hypothetical  quantum world of space, there should be no absolute rest, 'jumping' of mass from one quanta to other should be an energy-less process, and space would appear to behave identical to every observer.....But, until someone can intuitively build a deeper theory, we should be content that it is useless trying to find an absolute rest, given what mankind has learnt so far. ....Clocks which are moving become slow as the 'clocking events' of all kinds (light doing tick-tok, a mechanical spring clock, or even an atomic clock) get smeared over a longer distance in space due to direction of travel. To the rest observer (at rest to himself), time gets slower in moving tick-tok light clocks, as he is counting a larger number of time intervals needed for light to travel a longer distance as it is stretched or smeared over a longer distance in space....it is amazing to note that even digital and atomic clocks will become slower. It is again telling us something fundamental about matter and space, which is deeply connected to speed of light. I am not a physicist or a teacher by profession. Please understand my limitations in trying to explain a lengthy topic...see the self-learning video I have suggested in comment section. Then, you should be able to understand the meaning of my description  (which is the next level of understanding the fundamentals) correctly.
A: For two observer A and B ,B moving with respect to A with velocity $v$.
After time $ t $ has elapsed in absolute rest frame(reference frame)
Person A will say $ t$ time has elapsed but person B will say time less than $ t $ has elapsed ,from that A will conclude that his clock is moving faster than the clock of B .
And similarly B will think the opposite way that his clock is running slower than than the clock of A.
