It is a common view that relativity requires the Block Universe. See What is time, does it flow, and if so what defines its direction?. But it isn't really true.
Part of the common sense view of time is that it flows. The present is all that exists. The future hasn't happened yet. The past is over and gone.
We think of time as absolute. A time $t_0$ uniquely identifies a slice of space-time. When t0 is now, all events in that slice have their moment of existence. The state of the universe is uniquely specified by $t_0$. All observers agree on this. The flow of time is the progression of the universal state from cause to effect. This is why the flow of time makes sense.
However measurements show the speed of light is constant. This leads to the failure of simultaneity. Robert and Alicia pass each other at relativistic velocity. Both choose coordinate systems that agree they pass at $(x_0,t_0)$. They look at the event Robert sees as $(x_1,t_0)$
Robert says this is having its moment of existence now. Alicia says the same event already happened or hasn't happened yet. This leads to confusion. One event happens at two different times.
The Block Universe is one way around this. If an event exists at two different times, it must not have a momentary existence. It must exist whenever it is time for it to exist in any frame of reference. This preserves the notion that all events in a slice of space-time defined by a time exist at that time. However, it destroys the notion of flowing time. A succession of events do not come into existence and disappear. The whole block of events in all of space-time just statically exists.
Another way is to let go of the notion that simultaneity is absolute. Each object follows a world line where time flows. Each event that object experiences comes into existence at its time and disappears. But there is no universal way of matching up times of separate events. The match up is as motion dependent as matching up the position of separate events.
This does not change what simultaneity is in relativity. The simultaneity of two separate events measured in a particular inertial frame of reference can be inferred. Robert, sitting at $x_0$, can always rely on his clock at $x_0$ to be uniform. He sends out a pulse of light that reflects off an event at $x_1$ and returns. He records the sendoff and return times. The speed of light is constant, so the pulse spends half the time going out and half returning. The reflection is therefore simultaneous with the event Robert experienced at the time halfway between.
The difference between the Block Universe and Flowing Time viewpoints is purely philosophical. They both use the same space-time diagrams, do the same calculations, and arrive at the same answers. One viewpoint regards the space-time diagram as a block of statically existing events. The other regards it as a collection of loosely matched up histories.
Both notions of time are different from the common sense notion. I don't know of any experiment that can distinguish these interpretations of time. Use whichever one makes you the most comfortable.
However, there is one difference. The Block Universe does not include the progression of state from early time to later time. It must be added. There is some question of how to motivate it and explain the direction. The Flow of Time doesn't explain this progression. It is just assumed.
So if you consider how two universes might be different if one has an object that the other does not, it isn't any different if you think bout the block universe or flowing time.
In this case, you are running two different universes. Nothing reconfigures itself.
Likewise you can think about the universe, and what happens if you suddenly add an object.
If you think in terms of the block universe, you must think about the entire history of the universe at once. You see early history without the object. The object appears and consequences spread out at the speed of light. You would see this as events in the light cone after it appears being different from what they would have been if it had not appeared. History outside the light cone would not be rewritten.
"What are these functions supposed to mean" --> world lines.
– ozw1z5rd Jun 04 '21 at 08:48