Why in the world would Einstein suggest....

When accelerating, the time at the ceiling will move at a different rate than the time at the floor, all part of the non inertial state.

(1) an observer stationed on the ceiling measures the light on the ceiling to be travelling with speed c, (2) an observer stationed on the floor measures the light on the floor to be travelling at c, but (3) within the bounds of how well the speed can be defined (discussed below, in the General Relativity section), a "global" observer can say that ceiling light does travel faster than floor light.

The Minkowski diagram would show how it plays that part.

"Geometry predicates nothing about relations of real things, but only geometry together with the purport of physical laws can do so... The idea of the measuring rod and the idea of the clock coordinated with it in the theory of relativity do not find their exact correspondence in the real world." (Einstein, 1921)

Are you arguing that the math is wrong?

The Minkowski diagram would show how it plays that part.

The math predicts that clocks traveling at a faster speed will slow down. The physics confirms the math

So, you are arguing that before Einstein published his theory of relativity we already knew that clocks slowed down when they moved faster.

... So, you are arguing that before Einstein published his theory of relativity we already knew that clocks slowed down when they moved faster.

Both would see the other clock as moving slower. Both would be correct.

Well, there you go, Parados. Now you are creating the "paradox." But it aint a paradox, it's merely a flat contradiction.

It's impossible for each clock to be running slower than the other.

No, it isn't a paradox. They are different frames of reference.

[Hayes says]: "Precisely because Einstein's theory is inconsistent, its supporters have drawn on contradictory principles in a way that greatly expanded their apparent ability to explain the universe. Most crazes die out when it becomes obvious that they were overblown. The amazing thing about Einstein's theory of relativity is that it has kept going. It is built on contradictions, but these very contradictions means that almost anything ‘proves' that it is right. It is a bit like a theory where you say 1 + 1 = 2, but also that 1+ 1 = 3."

In Einstein's theory, there is a definition of simultaneity that employs light signals going back and forth (cf. The definition of "now"). However, simultaneity thus defined is relative. Observers that are in motion relative to each other (and that employ Einstein's definition of simultaneity) will generally end up with different results: events that one observer judges to be simultaneous will not necessarily be simultaneous for the other.

This insight allows relativity to escape the apparent contradiction that one and the same clock is both slower and faster than another clock. When I come to the conclusion that the clocks in the other space-station are slower, I rely on my own concept of simultaneity for the comparison. The other observer, coming to the conclusion that my clocks run slower, relies on his own concept of simultaneity. (A simple geometric analogy to this is explored in the spotlight topic Time dilation on the road.)

Hold on, I hear you say, how can both clocks run slow? Surely that's impossible? Puzzling, but not impossible. Let's suppose that they synchronise clocks when they pass each other. What happens when they compare time later? Now remember that their relative speed is a substantial fraction of the speed of light. Consequently, when Zoe looks at Jasper's clock, the light will take a while to reach her eyes. So she will see the time that the clock read when the light that she is seeing reflected off Jasper's clock. (Think of astronomers looking at very distant galaxies: they emitted the light we see when they and the universe was much younger than it is now.) So distant observes can't just use the time that they see on the clock, they have to correct this for the time of transmission of light (or radio etc) that is used to send the local time.

This synchronisation effect is important enough to need another page on its own, because it is tempting to try to use this symmetry to create a paradox that would disprove relativity. See the twin paradox for an explanation.

Since that procedure yields different judgments of simultaneity for different frames of reference, there is no longer an absolute fact as to whether two events are simultaneous; that judgment can vary from frame to frame.

ONLY ONE could possibly be objectively correct when making this claim.

Now remember that their relative speed is a substantial fraction of the speed of light. Consequently, when Zoe looks at Jasper's clock, the light will take a while to reach her eyes. So she will see the time that the clock read when the light that she is seeing reflected off Jasper's clock.

In Einstein's theory, there is a definition of simultaneity that...

Since that procedure yields different judgments of simultaneity for different frames of reference, there is no longer an absolute fact as to whether two events are simultaneous; that judgment can vary from frame to frame.

each hear a pitch different than middle C because of the Doppler effect. They are clearly hearing a sound. You are arguing they are hearing an incorrect sound. They just have a different reference compared to the speaker. It doesn't make their sound wrong.