Einstein’s theory requires synchronization of clocks of both frames before one departs from another for the derivation time dilation/ Lorenz transformation.

And that synchronisation holds only at that moment. While there is relative motion those clocks will go out of sync.

As such when you describe an event happening at a particular time you need to say what time reference you are using.

But regardless, you can set any arbitrary time to be time 0, for any reference frame.

it was explained clearly in accordance with Einstien relativity when both observers have light clocks. Here again

No it wasn't, as you continue to pretend time is absolute, ignoring the relativity of time and simultaneity.

You also ignore the change in reference frame when Oa stops.

How about the occurrence of events when two bolts of light strike the longitudinal sides of the oncoming train relative to the stationary observer who stands in the middle of railway tracks. Both lights strike at the same time for both inside and outside observers.

No, they don't.

That is a key point you keep on ignoring.

The order of events is relative.

If you have 2 events, A & B, occur simultaneously for 1 particular reference frame, then there exists another reference frame where A occurs before B, and there is exists another reference frame where B occurs before A.

The order of events is relative.

Ingoing that wont change it.

There are lots of paradoxes based upon this strange behavior.

For Example?

Well one based upon ignoring the relative order of events is a train going through a tunnel.

Say there is a train with a proper length of 100 m, and a tunnel with a proper length of 90 m.

This tunnel also has a door on the entrance and exit.

If the train passes through the tunnel at 50% of the speed of light, is it possible for both doors to be closed at once?

Well according to the stationary observer outside, length contraction reduces the length of the train to ~87 m, meaning it will fit in the tunnel and both doors can be closed at once.

But according to the train, the tunnel has had its length contract to ~78 m, so it definitely can't fit.

So there is an apparent paradox because it appears that from one view it should fit and from the other it shouldn't.

This paradox is resolved by the relative ordering of events.

To the stationary observer, they see the train entirely in the tunnel, with the entry door closing and then the exit door opening a short time later. Notice the order of events, entry door closes then exit door opens.

To someone on the train, they see the exit of the tunnel open before the train is entirely in the tunnel. Only after they exit the tunnel does the entry door close behind them. Again notice the order of events, the exit door opens before the entry door closes.

The order of the events changes due to the relative motion of the reference frame.

If you had someone going backwards on the train at the appropriate speed then the exit door would open at the same time as the entry door closes.

As time, and the ordering of events, is relative there is no problem.

There only falsely appears to be a problem when you ignore that relativity and pretend the order of events should be the same in all reference frames.

This is also known as the ladder paradox, and uses a ladder in a garage.

An extension of it is to ask what happens if the doors remain closed.

To the observer at rest, the train fits in the tunnel, with both doors closed, so you should be able to stop it and keep the doors closed and keep the ladder inside.

But from the trains point of view, it was never able to fit.

This is resolved by considering how acceleration happens.

If you want the train to stop in an instant, then that doesn't just apply to all reference frames, again, because of the relativity of simultaneity.

If you have it stop instantly for the observer at rest, then in the inertial reference frame where the train is momentarily at rest the front must stop before the back, which causes the train to be crushed/compressed.

A similar paradox to that instead uses 2 accelerating spaceships.

An observer at rest observes 2 spaceships, which are currently at rest, separated by some long distance, with a string tied between them.

Then, in this frame, both spacecraft start accelerating at the same time. What happens?

A very naive approach is to just treat the 2 spacecraft and string as a single object, and say the length is contracted and nothing much happens.

But in reality, the distance between these 2 spacecraft was defined by the initial separation. The 2 spacecraft accelerating together will keep that distance between them. In order for that distance to shrink, the lead spacecraft would need to accelerate at a slower rate.

But the string is a physical object, and its length would contract. This should cause the string to snap.

But from a naive view of the reference frame of the spacecraft, both accelerate at the same time, and thus should remain the same distance apart, so the string should remain connected.

But this is also wrong.

This is now akin to gravity, as you have an accelerating reference frame. In this accelerating reference frame, time passes differently for the 2 ships.

The simplest way to analyse it is by using a inertial reference frame momentarily comoving with one of the ships.

In this reference frame, the lead ship will have started to accelerate first, and the second ship will accelerate some time after. This means the distance between the 2 ahs increased, and the string breaks.

Again, it only appears to be a problem because the relative order of events is ignored. When it is properly analysed, there is no problem.