This comes down to some semantics here. The clocks ARE all ticking off time at the same rate: just put the all the clocks stationary next to each other. However, observers will observe the clocks ticking at different rates if the clocks are moving at different speeds with respect to the observer. And different observers will also observe different rates with respect to other observers if they are moving relative to those other observers. A single clock can have many different rates simultaneously if many different observers moving at different speeds are observing that clock. All observers will observe the same rate of ticking of clocks that are stationary to them and that rate is the same rate as any other set of clocks that are stationary to any other observer. In this sense there IS a universal time: the rate of “my” clock (a clock stationary to me) has exactly the same as the rate of “your” clock (a clock stationary to you).

Is a clock measuring the passage of time or is it defining the passage of time? Note we never observe directly “the passage of time”, we only observe clocks that tick. Sometimes the clocks tick faster sometimes slower. It is an assumption that we make of physical reality that the quantity of “time” between two subsequent ticks of a clock is always the same. What we see is that motion (of observers with respect to clocks) affects the rate of ticking they see on the clocks. It is perhaps somewhat misleading or at least incomplete to say that “motion affects the passage of time” it would be more accurate to state that “motion affects the passage of time as seen by a particular observer moving with respect to the clocks being observed”.

“Time itself is running slower on the moving clock” -> an observer watching a clock moving with respect to the observer will observe the clock ticking at a slower rate than a clock that is stationary with respect to the observer.

“A clock that is in motion will tick off time at a slower rate” ->A clock that is in motion with respect to an observer will be observed (by that observer) to run at a lower rate.

Is a clock measuring the passage of time or is it defining the passage of time? Note we never observe directly “the passage of time”, we only observe clocks that tick. Sometimes the clocks tick faster sometimes slower. It is an assumption that we make of physical reality that the quantity of “time” between two subsequent ticks of a clock is always the same. What we see is that motion (of observers with respect to clocks) affects the rate of ticking they see on the clocks. It is perhaps somewhat misleading or at least incomplete to say that “motion affects the passage of time” it would be more accurate to state that “motion affects the passage of time as seen by a particular observer moving with respect to the clocks being observed”.

“Time itself is running slower on the moving clock” -> an observer watching a clock moving with respect to the observer will observe the clock ticking at a slower rate than a clock that is stationary with respect to the observer.

Is a clock measuring the passage of time or is it defining the passage of time? Note we never observe directly “the passage of time”, we only observe clocks that tick. Sometimes the clocks tick faster sometimes slower. It is an assumption that we make of physical reality that the quantity of “time” between two subsequent ticks is always the same.

And if the carriage is just 10m long then the time difference is 5s.

Note that signalling via light has to be part of the observation process to get this effect. You can set up different schemas where everyone both on and off the train agrees. For example, supposing the presidents sit 10m from each other, set up two poles at a 10m distance from each other on the platform (assume the distance from the pole to the president is practically zero). When each president passes their respective pole they sign. Individuals situated on the platform next to the poles will register exactly the same time as individuals on the train who are standing next to the president.

Note that signalling via light has to be part of the observation process to get this effect. You can set up different schemas where everyone both on and off the train agrees. For example, supposing the presidents sit 10m from each other, set up two poles at a 10m distance from each other on the platform (assume the distance from the pole to the president is practically zero). When each president passes their respective pole they sign. Individuals situated on the platform next to the poles will register exactly the same time as individuals on the train who are standing next to the president.

Thanks for posting this link. Indeed, Einstein very much states that an ethereal concept is required however we cannot ascribe any concept of motion to it. The concept of motion has no meaning in space – or in an ether concept – as I already conjectured in my previous reply. Motion is an object based construct.