Spacetime
Spacetime Mechanics
3D Diagrams
Zero Intervals
Proper Time
The Two Towers
Spacetime & Reality
The Two Towers
The Two Towers is a thought experiment that illustrates the problems in interpreting the effects of viewing an event from different spacetime view points.
The west and east Elysian Towers are derelict 1960's tower blocks in the north of England. They are due to be demolished, and charges are rigged so that both towers will fall simultaneously towards each other, making a neat pile of rubble, and no one will get hurt.
And that's what happens, well at least so far as local spectators are concerned. The charges go off simultaneously, the towers fall towards each other, they end up in a neat pile in the middle, and no one gets hurt. Job done.
But according to Special Relativity, the simultaneity of events is dependent on the frame of reference in which it is observed. So, if the change in simultaneity affected what happened, what would be observed on a spaceship from Andromeda that is travelling at near-light velocity in the direction from the west tower eastwards? Would the pilot see the west tower fall before the east tower, spilling rubble beside the east tower and killing some spectators?
Then there is another spaceship from Andromeda travelling past the Earth in the opposite direction, from east to west. Would this pilot see rubble spill out beside the west tower, killing different spectators? Are there three different versions of events? One where all the spectators live on, one where some spectators near the east tower are dead, and another where other spectators near the west tower are dead?
No. That is, of course, nonsense, and is not what Special Relativity predicts. No matter how many spaceships fly in different directions and have different views of it, what happens happens. So how real are the differences in simultaneity?
Conclusions
We raised the question of how real the differences in simultaneity are in the Einstein's Train example, and it is very relevant here. It is apparent that, in reality, the differences in simultaneity have no effect on the outcome.
Furthermore they cannot have any effect, because the relationship between the spaceships flying past and the towers being demolished is space-like. As we mentioned here, space-like relationships cannot have causal relationships. The one event simply cannot affect the other.
Also, although it is true to say that there is a lot of empirical evidence that supports the theory of relativity, that evidence is of differences in the passage of time. Whereas, a difference in simultaneity is a different phenomenon that has never been empirically shown to exist.
So although the idea of a difference in simultaneity is integral to the theory, there is no reason to deduce that they actually exist. They could be, and I suggest are, simply a mathematical anomaly produced by the way that Einstein derived the Special Theory.
