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Theory often affords multiple viewpoints or interpretations of phenomena. Not all of these need provide one with a feeling that they are sensible. For example, we could choose to view the classical trajectory of say a baseball as being “caused” or due to some future position and velocity and by convention simply integrate the equation of motion in time reverse order obtaining what we normally refer to as the initial conditions. That we can do this doesn’t in itself recommend it.
I would like to layout a view of the classic EPR style experiment in which the decay of an S=0 state particle pair is measure by our friends Bob and Alice. My intent in doing so is to address in part what I feel is a common miss use of terms like “cause” and “effect” in regard to Alice and Bob’s measurement choices. It is clear that choice of measurement apparatus in QM very much is effects measurements, it’s the nature of the beast. It is also clear that Bell’s arguments are an important aspect of the phenomena. But, I’m left wondering in what sense does Alice’s measurements effect Bob’s? Well, there is a view point where Alice’s measurements simply are unaffected by Bob’s.
Because QM measurements involve random events beyond our control things are complicated experimentally. No observation in this type of work is comprised of a single event. In this case what is a single event? We define a single event as a measurement on a single entangled pair of particles. This event, say event ##i##, is Alice’s measurement angle, ##\alpha_i## with her up or down result, ##a_i## obtained. Each of these are paired with Bob’s chosen angle, ##\beta_i##, and his up or down result, ##b_i##. We suppose that Alice and Bob dance around wildly choosing measurement angles at random (or not, it matters not) and we let them do so for a very long time. In this time we collect each event outcome on a card. This gives us a set of measurements, ##(\alpha_i,a_i,\beta_i,b_i)## which we put in a big deck. Now, since each event is independent of every other even, we may shuffle the deck freely. No matter how the deck is shuffled we will always have a potential time sequence of event which is completely consistent with QM and whatever Bell has to say. Each time the deck is shuffled we get a physically reasonable potential outcome of an experiment. Now, we could also choose any subset of cards and we will still have a consistent potential time sequence or outcome for an experiment.
Now, I’m going to choose two sequences of events of identical in length, say ##N##, from our much bigger deck. The first is simply the first ##N## cards of the big deck. The second I am going to choose card ##k## such that ##(\alpha_k,a_k)## is the same as Alice’s results for the ##k##-th card in the first deck. What this does is it gives us two experiments in which Alice’s event sequence is identical in both decks. Both of these experiments could happen even though arranging it real time is not possible (well, very very unlikely at best). Both experiment time sequences are completely consistent with QM. At this point I ask; can we really claim that Bob’s measurements have effected Alice’s? How is such a claim made since both Alice’s results are identical between the two time sequences while Bob's are completely different?
Now, Bob certainly does see a dependence on his choice of relative measurement angle to Alice’s. But this is to be expected since all Bob’s measurements depend on Bob’s choices in QM.
I would like to layout a view of the classic EPR style experiment in which the decay of an S=0 state particle pair is measure by our friends Bob and Alice. My intent in doing so is to address in part what I feel is a common miss use of terms like “cause” and “effect” in regard to Alice and Bob’s measurement choices. It is clear that choice of measurement apparatus in QM very much is effects measurements, it’s the nature of the beast. It is also clear that Bell’s arguments are an important aspect of the phenomena. But, I’m left wondering in what sense does Alice’s measurements effect Bob’s? Well, there is a view point where Alice’s measurements simply are unaffected by Bob’s.
Because QM measurements involve random events beyond our control things are complicated experimentally. No observation in this type of work is comprised of a single event. In this case what is a single event? We define a single event as a measurement on a single entangled pair of particles. This event, say event ##i##, is Alice’s measurement angle, ##\alpha_i## with her up or down result, ##a_i## obtained. Each of these are paired with Bob’s chosen angle, ##\beta_i##, and his up or down result, ##b_i##. We suppose that Alice and Bob dance around wildly choosing measurement angles at random (or not, it matters not) and we let them do so for a very long time. In this time we collect each event outcome on a card. This gives us a set of measurements, ##(\alpha_i,a_i,\beta_i,b_i)## which we put in a big deck. Now, since each event is independent of every other even, we may shuffle the deck freely. No matter how the deck is shuffled we will always have a potential time sequence of event which is completely consistent with QM and whatever Bell has to say. Each time the deck is shuffled we get a physically reasonable potential outcome of an experiment. Now, we could also choose any subset of cards and we will still have a consistent potential time sequence or outcome for an experiment.
Now, I’m going to choose two sequences of events of identical in length, say ##N##, from our much bigger deck. The first is simply the first ##N## cards of the big deck. The second I am going to choose card ##k## such that ##(\alpha_k,a_k)## is the same as Alice’s results for the ##k##-th card in the first deck. What this does is it gives us two experiments in which Alice’s event sequence is identical in both decks. Both of these experiments could happen even though arranging it real time is not possible (well, very very unlikely at best). Both experiment time sequences are completely consistent with QM. At this point I ask; can we really claim that Bob’s measurements have effected Alice’s? How is such a claim made since both Alice’s results are identical between the two time sequences while Bob's are completely different?
Now, Bob certainly does see a dependence on his choice of relative measurement angle to Alice’s. But this is to be expected since all Bob’s measurements depend on Bob’s choices in QM.
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