nkpstn said:
Is it possible for a particle to exist according to one reference frame and simultaneously not exist according to another?
The issue you refer to, which is a good one (at least I enjoy it), is in the end just a semantic challenge. Some people are very crafty to choose (and omit) the right words and thus phrase the matter so that it suggests something "crazy, alarming, unbelievable…". Thus they sell more books. But if you take a little time to think of it, you realize that there is nothing abnormal here and you can also choose the right words to settle that.
Whether a particle is created or destroyed is an event. In SR all frames agree on whether an event has happened or not. (Otherwise SR would be a bad theory, because theories are created for predicting events and if they do not, if they give out contradictory versions of reality, that means that they are wrong or misinterpreted.) It is true that different observers (reference frames) attach different time labels to each event, but those labels must be interpreted by those intelligent observers (isolatedly or in conjunction with other readings of their instruments) to infer the same events through the appropriate equations.
Take this example: a moun is created when a cosmic ray hits the atmosphere. At that time, the moun itself and an observer hovering in a spacecraft (at rest with the Earth) sync their clocks. The muon keeps racing towards the ground at close to the speed of light. Finally, before disintegrating, the muon hits the ground. Just before this collision, the muon consults its clock and it is time t1 in its muon-frame. An observer at the ground does the same and it is a little later, say t1+1, in the ground-frame. Please note that the moun's half-life in ground labs is t1-1. Should the ground observer start shouting that, before landing, the muon has ceased to exist "in his frame" and refuse to believe what his instruments show? No, what he does is combining his time measurement (dt = t1+1) with the fact that in his frame the moun has traversed a distance (dx). He does it through the SR's space-time interval formula. Thus he gets the proper time of the muon, which is less than a moun's half-life. Ok, that is why the moun is here, he infers. Conclusions: relativity of simultaneity solves the problem, rather than creating it.
bobc2 said:
In Bill's 3-D world (one cross-section of the 4-D universe) the government somewhere in the galaxy is trying to decide whether to attack earth. In Ruth's 3-D world (a different 3-D cross-section of the 4-D universe) the decision has already been made and the attack is under way.
So what? What is the problem?
I think that, whenever the Andromeda "paradox" is mentioned, one should also mention that there is no problem at all, no paradox. Otherwise it is misleading.
The attack was launched or not. That is an event, so it cannot be controversial in SR.
Let us assume the attack was launched. If that is simultaneous, in Ruth's frame, with her meeting Bill, that means the two events (the meeting and the launch of the attack) are spacelike, so there is no causal influence between them. In other words, if Bill (taking advantage of the fact that in his frame the attack has not yet happened) wanted to prevent it by sending a diplomatic message, the latter would not arrive in time for that purpose, because the distance would be too long for any infra-luminal or even luminal messenger to cover it before the time when the attack would also start according to Bill.
But what determines if the attack was actually launched or not? Well, it is precisely a bunch of situations like this. A bunch of events. Focus on any other situation of this sort that you can imagine and solve it according to these rules. You will realize that the story is the same in all frames.
