Does the notion of an universal clock really contradict special relativity?

Question

Special relativity says that different observers qualify two events as simultaneous based on their velocities. But isn't that a statement about information they can measure rather than about reality? In other words, can we say that there is an universal clock, giving absolute time, but that as observers embedded in the universe, there is no experiment that would allow us to read it?

Answer 1

Can we say that there is an universal clock, giving absolute time, but that as observers embedded in the universe, there is no experiment that would allow us to read it?

We can say that, but for the purposes of physics, a universal clock that cannot be read or observed might as well not exist. I can say that the universe is filled with massless, invisible, undetectable pink unicorns - but that statement is not within the realm of physics.

On the other hand, if the universal clock can be read/observed then it establishes a universally stationary frame of reference (stationary observers are those whose local clocks match the universal clock) which contradicts both special and general relativity.

Answer 2

There is a common confusion about the meaning of the verb observe in relativity. It does not mean what we see i.e. what our eyes tell us. We start with what we see, but then we correct for factors like the time the light took to reach us and the result is the observation. Observation means we assign an event to a point in spacetime $(t, x, y, z)$ where the time $t$ is the time the event happened in our coordinate system, not the time we saw it. There is more on this in The nature of the observer in special relativity.

So when we say that different observers disagree about whether events are simultaneous or not, this does not just mean that the observers saw the events at different times due to the time the light took to reach their eyes. It really does mean the events happened at different times in different frames. That's why there cannot be any universal clock in relativity.

The reason why there is no universal time is because there is no unique way to split up spacetime into time and spatial parts. Suppose we are drawing a coordinate system on the $xy$ plane. There is no unique way to define the $x$ and $y$ axes e.g. we could rotate our axes by any random angle and they would still be a perfectly good way to describe the coordinates on points on the plane.

Now consider the $tx$ plane. Common sense seems to tell us the above argument wouldn't apply because, well, time is special. However special relativity tells us that time is not special, and we can indeed use different $t$ and $x$ axes for our coordinates. Specifically when observers are travelling at different speed their time axes are rotated relative to each other.

For there to be a universal time axis there would need to be a universal speed, in which case the rotation of all other observers' time axes would depend on their speed relative to this universal speed. But no such universal speed exists, and hence no universal time axis exists.

Answer 3

No, you cannot have a universal clock. It is analogous to having a universal up and down axis and a universal spirit-level.