" As I see it, this thread is revolving around two semantic concerns:
1. What is the meaning of "real" (length, time, etc.)?
2. What is the meaning of "apparent" (length, time, etc.)?
Arguing, correctly in my opinion, from the perspective of a
sophisticated practitioner of physics, John Denker argues
persuasively that "real" should be essentially synonymous with what
is commonly called "proper," that the "real lengths" of rods and the
"real rates" of clocks are their "proper" lengths and rates. Thus,
moving clocks do NOT "run slow" and moving lengths do NOT "contract."
When we say that they do, we are talking only about "appearances." "
Is the speed of a moving car a real characteristic of the process or not?
If to be real means to be proper, then what is its proper speed? Zero, as measured in its rest frame?
Then why does the car smash into smitherenes if it (God forbid!) crashes into a concrete wall? Only because the wall runs into it? But, again, the wall's motion is not real either, because its proper speed is also zero.
Will you say that the crash itself was not real because of this?
If you do not like the example with the speed as I use it here to make it more vivid, you can recast the discussion in more rigorous terms of relativistic energy E and momentum P suggested by Bob Sciamanda, but the question I ask will not disappear.
There is still a big confusion between real and absolute (or invariant, for that matter). Many people think that what is not absolute, but "merely" relative, is thereby not real.
I use the word "real" here in the conventional sense as something that can be verified by many independent observers using identical experimental equipment, as opposed to illusory or apparent (possibly distorted by some masking effect, like, for instance, the rate of approaching ticking clock distorted by the Doppler effect, in which case the corresponding corrections for all distortions could and should be made).
Of course, a property thus defined can be real and relative at the same time. Just because it is not proper (or absolute, or invariant - call it as you wish) for observers in another RF, does not make it unreal.
The size, momentum, relativistic energy, rate of temporal evolution of a moving object, - are all its real characteristics, even though they may be numerically different for different observers. This is one of the most important aspects of the principle of relativity (here I mean even broader relativity than Einstein's - the relativity of 3-velocity had been known centuries before.)