On Fri, Jul 22, 2011 at 4:54 PM, Stephen P. King <stephe...@charter.net>wrote: > > > Hi Jason, > > None of those papers address the concern of narratability that I am > considering. In fact they all assume narratability. I am pointing out that > thinking of time as a dimension has a big problem! It only works if all the > events in time are pre-specifiable. This also involves strong determinism > which is ruled out by QM. See > http://plato.stanford.edu/entries/determinism-causal/#StaDetPhyThe for a > general overview >
But the link notes that strong determinism is *not* ruled out by QM: "So goes the story; but like much popular wisdom, it is partly mistaken and/or misleading. Ironically, quantum mechanics is one of the best prospects for a genuinely deterministic theory in modern times! Even more than in the case of GTR and the hole argument, everything hinges on what interpretational and philosophical decisions one adopts. The fundamental law at the heart of non-relativistic QM is the Schrödinger equation. The evolution of a wavefunction describing a physical system under this equation is normally taken to be perfectly deterministic.[7] If one adopts an interpretation of QM according to which that's it—i.e., nothing ever interrupts Schrödinger evolution, and the wavefunctions governed by the equation tell the complete physical story—then quantum mechanics is a perfectly deterministic theory. There are several interpretations that physicists and philosophers have given of QM which go this way. " The many-worlds interpretation, which many on this list are presumably sympathetic to, is an example of a deterministic interpretation of QM. In fact many-worlds advocates often argue that not only is it deterministic, but it's also a purely local interpretation, which doesn't violate Bell's theorem because the theorem makes the assumption that each measurement yields a single unique result, something that wouldn't be true in the many-worlds interpretation. For more on how MWI can be local, see these papers: http://arxiv.org/abs/quant-ph/0103079 http://arxiv.org/abs/quant-ph/0204024 > > The idea that time is a dimension assumes that the events making up the > points of the dimension are not only isomorphic to the positive Reals but > also somehow can freely borrow the well order of the reals. > Not sure what you mean by this, events at a spacelike separation aren't "well-ordered" in time, are they? Only if one event is in the light cone of the other (a timelike or lightlike separation) will all frames agree on the time-ordering, that's just a consequence of the relativity of simultaneity. The block universe idea assumes a unique and global ordering of events, the > actual math of SR and GR do not! > Why do you think the block universe idea assumes a unique ordering? It doesn't, not for pairs of events with a spacelike separation. For such events, the question of which event occurs at a later time depends entirely on what coordinate system you use, with no coordinate system being preferred over any other. Similarly, on a 2D plane the question of which of two points has a greater x-coordinate depends entirely on how you orient your x and y coordinate axes, even if you restrict yourself to Cartesian coordinate systems. And the whole idea of block time is that time is treated as a dimension analogous to space, so it's not surprising that there could be situations where different coordinate systems disagree about which of two events has a greater t-coordinate, with no coordinate system's answer being more "correct" than any other's. > My claim is that the idea that time is a quantity like space only works > in the conceptual sense where we are assuming that all events are chained > together into continuous world lines. > Not really, just as you can have a collection of points on a 2D plane without continuous lines joining them, so you could potentially have a collection of events in spacetime that are causally related but don't have a continuous series of similar events between them. Sort of like if you took vertices on a Feynman diagram to be events, and understood the lines joining them to just express causal relationships, not worldlines. > It is impossible to define a unique Cauchy hyper-surface of initial > (final) data that completely determines all of the world lines in the > space-time block in a way that is consistent with QM. > What specific source are you getting that claim from? I checked the first link you posted after it: > > > http://www.scientificamerican.com/article.cfm?id=was-einstein-wrong-about-relativity > ...but it didn't say anything like that. I'd rather not read through all your links to find the basis for this particular statement, so can you tell me exactly where I should look? > > > When we add to this difficulty the fact that QM does not allow us to > consider all observables as simultaneously definable, because of > non-commutativity and non-distributivity of observables; the idea that > events are representable as pre-specifiable partly ordered sets from the Big > Bang singularity's event horizon into the far distant future falls flat on > its face. > Not sure what you mean by "pre-specifiable", again can you tell me which specific link I should look at to understand what you're saying here? Anyway, the fact that some observables don't commute isn't really a problem for local determinism in the many-worlds interpretation. "Observables" are understood to correspond to a specific set of basis vectors (eigenvectors of the operator for that observable) which can be used to express any quantum state vector as a weighted sum of eigenvectors (the weights are complex amplitudes, and you square these amplitudes to get probabilities of each eigenstate in to the "collapse the wavefunction" version of measurement). The fact that some observables aren't simultaneously definable basically just means that an eigenvector of one observable can't simultaneously be an eigenvector of the other, but if you take the wavefunction as fundamental as in the many-worlds interpretation, this shouldn't be a big deal because there is no longer the concept that the quantum state must "collapse" onto an eigenstate with each measurement. Instead the quantum state vector just evolves deterministically forever, and as the second of the two papers I posted above says, you can break the quantum state down into a set of local field operators at each point in space, whose time-evolution is determined by local differential equations (which I take to mean that nothing outside a point's past light cone affects the value of the field operator at that point). Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
