PeterDonis said:
Not exact ones, no. Please re-read "all measurements have finite error" again and again until you understand what it means.
If you don't talk about exact positions of the hidden particles in Bohmian mechanics, you can't really talk about Bohmian mechanics at all, since those exact (hidden) particle positions are the key ingredient of BM.
I appreciate your exactness in your replies because it helps to further my understanding, so again, thank you for that. In this case, however, I think we might be talking past each other. My misinterpretation of certain features of BM is a primary factor in this. I don't think we need to talk about the exact position of the particle because I'm talking about the probabilistic predictions of measurement events and the interpretation of
those positions.
PeterDonis said:
In fact, I can turn the question around: why do you think this question is a meaningful question?
Because I think the probabilistic predictions of QM call for interpretation and, in relativity, the location of an event in relation to the past light cone has meaning.
The interpretation I am trying to get at can, perhaps, be broken into two parts:
1) In what sense is it a genuine possibility for a measurement event to occur at any of the predicted,
non-zero, measurement event positions?
2) In what sense
was there a genuine possibility of measuring the system at a measurement event
position which was/is outside the past light cone of the actual measurement event?In considering the question of the possibility of the system being measured at a position outside the past light cone, of the actual measurement, we might consider a macroscopic example, a spaceship say - solely to attempt to demonstrate the idea.
If we don't know where a spaceship is we might make probabilistic predictions as to where we might find it. Eventually, we measure the location of the spaceship (to within some finite error). If we look back at our predictions we will see that some of the probabilistic predictions lie outside the past light cone. How would we interpret this information?
Incomplete
Someone might suggest that the reason we made such probabilistic predictions in the first place is because our information was incomplete. In truth, some of the positions we predicted weren't genuinely possible, given the actual trajectory of the spaceship and the limiting factor of no-FTL travel.
Simple FTL
Someone else might come along and say, actually, the spaceship might be able to travel faster than the speed of light and so there was a genuine possibility of measuring the position of the spaceship somewhere outside the past light cone.
Collapse
Someone else might say, actually, the "spaceship system" is delocalised in space and when we make a measurement it randomly collapses into a single measurement event. This collapse happens instantaneously (FTL) so there was a genuine possibility of measuring the spaceship somewhere outside the past light cone of the actual measurement event.
BM-like*
Someone else might say, actually, our information is incomplete AND the spaceship can also travel FTL. Not only this, but when the spaceship triggers the measurement device it can result in the spaceship being measured at a spacelike separated position. This process occurs instantaneously (FTL). In this case there was a genuine possibility that the spaceship could have been measured at any of the non-zero predicted positions.
Are there other possible interpretations which don't imply either incompleteness, or some form of FTL causal influence?
*This can be modified to make it a more accurate representation. The instantaneous (FTL) causal influence would carry the explanatory power.