The fuss is about something subtle, quite askew to the issues you mention. The fuss is about the definition of time itself. In order for you to understand that, you have to comprehend the meaning of the idea behind "relativity". The fundamental concept behind relativity was around long before Einstein: the idea is that the "laws" of physics are independent of the coordinate system of the observer. For example, to a sailor on a ship, a stone dropped from the crows nest falls straight down to the deck but to an observer at rest watching the ship sail by, the stone is seen as falling in a parabola. This difference exists because the rest observer and the sailor are using different coordinate systems to describe the motion of the same stone.
Newton showed us how to convert the laws of physics between different coordinate systems moving with respect to one another. He did not call it "Newton's theory of relativity" because he did not think of it as a theory: he thought it was "true", but it was a theory none the less. This is the old velocity addition rule which almost everyone picks up on by the time they are 10 years old. If a kid on a truck moving 50 mph throws a ball in the same direction the truck is moving at 30 mph, someone standing on the road will see the ball moving at 80 mph.
That "fact" was experimentally proved false over a hundred years ago; but there are a lot of people out there who still think it is true. There are a bunch of kooks who simply cannot comprehend the fact that Newton's concept of relativity is just WRONG!!! They spend all their time arguing (from insupportable positions by the way) that Einstein is wrong!! Now, as soon as I say "Einstein is wrong", everyone immediately classifies me as one of those kooks and no one educated enough to understand what I have to say can be moved to listen to a word of it (due to the volume of nuts in the world). The current academic position is "Einstein cannot possibly be wrong"!!!
The moment I begin to present an argument based on a specific well specified coordinate system, they all assume that I am putting forth an "absolute time" argument and begin laying out all the standard retorts to that argument, paying not the slightest attention to what I am saying. I assert that there is nothing anywhere in modern physics which denies one the possibility of analyzing any given phenomena from the perspective of a specific observer. In fact anyone familiar with physics will find it impossible to solve any dynamics problem without resorting to analyzing the phenomena from the perspective of a specific observer (often from the perspective of several different specific observers). So it is indeed the "Einstein is wrong" part which blocks everyone from paying any attention to what I say.
So, if I think the concept of time is confused, it behooves me to clarify exactly where I believe the problem resides. I think it was Newton, with his unprecedented success, who created the confusion.
To begin with, the concept of time has been around long before the invention of clocks. The very fundamental characteristic of time is that it divides our universe (the reality within which all conceivable experiments are performed) into two distinctly different realms: the past and the future! It is an experimental fact supported by observations extending back to before written history that "nothing can be done to change the past" and that "no one knows exactly what the future will turn out to be". The power and dependability of this single idea (that the past and the future are fundamentally different realms) is the central reason for the very existence of the concept. To forget this fact is to overlook a very important phenomena fundamental to any scientific analysis of anything.
Even prior to the invention of writing, it was evident to our ancestors that the motion of the sun provided a useable reference to the division discussed above. This brought forth the idea of a clock, a device which could track and label the present (the boundary between the past and the future). When Newton showed that the future mechanical motion of objects could be predicted from the past motion via some very simple mathematical relations, time (as a numerical parameter) became a very important scientific concept and the refinement of clocks to ever finer precision was insured.
In fact, this precision became so important that we actually moved to the position that "clocks define time"; totally losing sight of the fact that the central issue of time was the division of the past (that which cannot be changed) from the future (that which science is trying to predict). We had become so sure of Newton's mechanical picture of the universe that it was taken as obvious that time could be numerically labeled and that the future was a direct, calculable consequence of the past. (God does not play dice!) As a result, science forgot the underlying purpose of the concept. The need to maintain the separation of the two realms vanished from scientific thought: an issue unimportant to modern science (at least before quantum was thought up)!
In science, attention is focused on new ideas, not on the old concepts which are presumed to be clear and consistent; how else could Newton's error (that all clocks could be set to read the same) have stood for three hundred years? Do you think everyone who studied physics during that 300 year period was stupid? The power of the parameter t in the mathematics of physics is so omnipresent that every scientist today just presumes he knows exactly what he is talking about and doesn't think about the matter at all. Time??? that is the measurement I get from my clock!!! I say, that if one takes a moment to think about the issue, it is absolutely obvious that the reading on the clock cannot possibly be used to define time (not the variable t we use in our physics anyway)!
Just as an aside, let me point out that there is a conflict between relativity and quantum mechanics. I find it rather funny that most of the high powered minds attribute the problem to quantum mechanics (they are trying to find a representation of quantum gravity by quantizing the general theory of relativity). Absolutely every competent physicist on earth simply presumes no errors could possibly exist in Einstein's relativity. They are so blinded by their prejudice that they cannot see an error which, once seen cannot be ignored.
So I say "clocks do not measure time" and everyone just barfs all over me! Well, if I don't think clocks measure time, what do I think they are measuring? I say clocks measure what Einstein calls "proper time". Now all the scientists say, "well proper time is time in the rest frame of the clock" - they see my complaint as spurious and they go back to whatever they were doing - conversation over.
But there is a problem there; a problem they all utterly refuse to even look at. The issue is that clocks absolutely always measure proper time along their space time path! No competent physicist will argue with that, they simply see it as unimportant. Again, argument is over and by this time they are convinced that I just think I am right and will not listen to their well defended position.
But I say it is very important from a very fundamental perspective! Clocks directly measure the path length of their trajectory in Einstein's geometry. Now "clocks" are very important parts of modern physics. Any conceivable entity which has internal structure which changes in time can perform the service of a clock so there are very few entities studied in physics which are not clocks. It follows that their internal structure performs a measure of the path length of their trajectory. And this is "ALWAYS" true, even in accelerating frames!
But, is the path length of their trajectory the same as time? Well of course not and no physicist would claim such a ridiculous thing. Therefore, I say clocks do not measure time! Instead, they measure path length in Einstein's geometry.
Now this brings me to my earlier comment, "Einstein is wrong!" He uses a geometry which casts time as one of his coordinates and then, in that geometry, clocks measure the path lengths of trajectories. Oh sure, as long as one uses a particular clock who's trajectory is a straight line, conversion between what the clock reads and time is trivial (special relativity - no acceleration) but suppose all your clocks are accelerating in various ways. Now life gets difficult (the problem is called general relativity).
Most experimental scientists go to the world and take measurements. Then they try to find relationships between those measurements which they can call "laws". In searching for those relationships, they generally plot the data taken in their experiments in some geometry (chosen for its convenience). What kind of results would you expect if the experimentalist decided to plot one of his "measurements" as trajectory path length in his geometry.
What I am saying is very trivial. I am saying simply that Einstein is using the wrong geometry. He should be using a geometry which has, as its coordinates, the things the scientist measures. When one goes to do that, some subtle things happen. One of the first things which happens is that relativistic effects fall directly out of quantum mechanics and the conflict between quantum and relativity utterly vanishes. That alone seems to me to justify looking at the issue carefully.
Now, if I could ever make contact with someone who could follow my work, maybe the world would learn something.
Have fun -- Dick