There is no explanation. (this is why it is a postulate).
Not answering a direct question is a mistake. People do not want an answer that says "just because it is so".
My answer was long and I apologize for that but you won't find this explanation in any of your wrote textbooks (... thats a challenge folks... go and find it). This detail is required so people understand the circumstances and also the motivation behind Relativity. If you do not analyze this concept then you will not understand why Relativity works and you begin to accept things "just because they are so" as Trout is saying. You can accept what Trout says on the basis of "authority"... what I offer is "understanding" on the basis of a real knowledge... your knowledge. The difference is this is harder at first but the "gain is worth the pain". You will truly "understand" a concept that other take on "authority" handed down by "the high priesthood of science".
I don't believe anything people tell me about anything in science unless I have first tried to understand it. It is far safer than "blind acceptance" and "blind acceptance" is not necessary in science since experiment can confirm the validity. Science has the "Scientific Method" where you can know for yourselves and not simply because someone tells you to believe and remain silent. It is "very important" for people to actually "know" why things are the way they are and not some other way. "Scientific Democracy" in the hands of "true believers" is a very dangerous thing, you end up with "mobs" of "collective foolishness". If you have gone all your lives "not truly knowing anything" then I am saddened because you have missed out on a "great joy". I am willing to accept the "flack" from those who will not try or can't make a sufficient effort to gain this tiny foothold on a deep wisdom. If only one of you succeed then I am very happy for you... honestly... you have done something of great personal achievement. Millions and even billions on this Earth "know" Relativity but only a handful "understand" Relativity. You could be one of those few rare individuals who one day will make a real difference. You need to choose...
I will try and put this "proof" a different way. Movement relative to a background is easy to explain... movement without a background is not so easy to explain and that is what this "essay" is all about. What it shows is a bullet, sound and light have a common methodology in their analysis. The difference is sound needs a medium for "transmission" while a bullet does not need a medium for "transmission" and this is analogous to light which does not need a medium for transmission either. However the "rub" is sound and light share a common basis... wave motion.
This explanation relies on the notions everybody uses to justify "phenomena" such as "absolute motion". The loss of this "absoluteness" means the loss of a medium or any way to view the light at any other speed than the speed of light. This assertion must be shown not simply "asserted" so that you can all understand. The velocity of a bullet, the velocity of sound, and the velocity of light have more facts in common than usually recognized. Sound will always propagate away from all sources at the speed of sound (in the medium) regardless of the motion of the source. If "air" is stationary sound will always be received by all stationary observers at the speed of sound regardless of the state of motion of that source. Movement of the source relative to the "air" does not change the velocity at which sound is "launched". Sound always expands away from the point in space at which it was "formed" at the speed of sound in the still air. This is because sound can't be "pushed or pulled" or made to go faster or slower in still air. This is exactly the same situation as for another kind of wave motion ... light. The speed of approach of sound in still air can be altered if the observer "moves with a velocity" relative to the still air in which the sound is moving as a wave. This can cause sound to "approach or recede" at a speed greater than or less than the nominal velocity of sound in still air. If a "wind" blows in your face the sound is "carried with the moving air" to you at a speed apparently faster than sound in the still air. This is simply because sound is a wave motion moving in a medium... the stationary air. The observer can move relative to "the stationary air"... the air is always stationary if you move along with it of if it is "still", thus air always has a
preferred frame of reference... the still air. The argument now revolves around this point... why does this not happen for light? Why is there no "preferred frame of reference" for light?
Contrast this with a bullet which when fired out the back of a moving "bullet train"... if the speed of the bullet and the train have matching but opposing velocity ... even in the vacuum of space (lets say in free fall)... the bullet will go "nowhere".... it does not "propagate"... it does not need to propagate like a wave... it is a projectile. While the gun travels away from the bullet at the speed of a bullet (in the bullet train), the bullet itself is "motionless" relative to the observer in the still air (and would normally fall to the ground). On the other hand... Sound must
always propagate in a medium regardless of the speed of the source. That is the difference. Sound "projected" out the back of a train moving at the speed of sound and does not cause sound to "stop its motion" like the bullet... it continues to propagate through the air at the speed of sound. It cannot pick up any speed from the train at all... it cannot be "pushed or pulled", it propagates at the speed of sound as if on the surface of an expanding sphere in the "still air".
So Sound (unlike a projectile)
propagates through the
medium at the speed of sound relative to all "stationary observers" (meaning observes whose state of motion has the air stationary with respect to them). Sound in such circumstances will always be "heard" at the speed of sound by all "stationary observers" but the pitch is altered depending on the velocity of the source. This is just the influence of lineal translation of the source "stretching our or compressing together" the successive wavefronts of the vibration of the sound source.
In the case of light it does not behave like the bullet since it is like sound ... it is a wave not a projectile. Light can never be "arrested" in motion like the bullet was. The single and only difference in the analysis is sound can move through a medium and the observers can be in motion relative to that medium too and thus the reception of sound can be at a velocity other than the speed of sound in still air (plus or minus the relative velocity of the observer "through" the still air). The still air is the absolute state of motion (rest frame or frame of reference) to which everything is referenced.
Light does not need a medium to propagate and in a vacuum is received by
all observers in a constant state of motion in any direction
as if they were entirely motionless in a "fictitious medium"... the aether. This observer velocity only appears to alter the relative velocity between the source and the observer but is totally ineffective at altering the velocity between the observer and the proposed aether.. So this motion is exactly equivalent to changing the velocity of the source while the observer considers itself always at rest... or visa versa.. it is absolutely identical.
If the observer can't move relative to the "aether medium" no matter how he moves at constant velocity, then the observer can't "observe" light arriving at a velocity of light "plus the relative velocity that the observer has relative to the medium". The subtlety is nothing the observer does can cause this differential "aether breeze" (motion through the stationary aether) to "blow on their faces" which would bring the light to them faster or retard the light from arriving "on time" depending on the observers direction of motion. The light always arrives at the exact speed of light.... a universal constant and an experimental fact.
It is as if all our experiments are in deep space far away from all external references and we do not know who is at rest and who is moving. Is the source moving towards us or are we moving towards the source? All we appear to know is the source-observer distance is shortening and all our experiments confirm this surprising fact. It is surprising because we expect that "aether wind in our face" and it appears not to "blow" no matter what. Furthermore it appears that it does not make any perceivable difference if we should propose that there is no aether at all. If the aether wind can't "blow" the light will always arrive at the same speed since we appear to always be "at rest" with respect to the expanding shells of the waves.
This "explains" the question... "Why Light Has Constant Speed W.r.t Any Observer". Every observer no matter what his or her motion is relative to the source "appears to remain at rest". It is demonstrating a "principle" regarding this aether (a material substance needed for the propagation of light in a similar way air is for sound). This hypothetical aether is
always at rest relative to any constantly moving observer (or source) regardless of where we are or in what direction or
relative velocity he should move with (up to but not including the speed of light). Using Occam's Razor there is no proof that any "substance" like an aether follows us all around to cause light to have no added motion relative to all observers. Not only that what could this "special mechanism" for the material aether be to hide this absolute motion from us? Neither light from a lightbulb in your room nor light from a distant star that is moving at a vast speed relative to us or even light from our own Sun around which our planet revolves.... no relative motion of an all pervading aether could be found. Now you can understand why the light always approaches at the speed of light and naturally is emitted at the speed of light as well. And more importantly why there is no absolute frame of reference or aether.
Now "postulate" why this is not true! No mere winging please... complaining that you simply don't like it. Think about this like a "true scientist" and find that deep level of satisfaction that comes to you when you really understand something in a way that only a scientist can feel.
Cheers
PS: Some background additional material...
PhysOrg: "Relativity" Speaking