On 7/23/2011 11:25 PM, Jesse Mazer wrote:

On Sat, Jul 23, 2011 at 8:45 PM, Stephen P. King<stephe...@charter.net <mailto:stephe...@charter.net>> wrote:Hi Jesse, On 7/22/2011 8:03 PM, Jesse Mazer wrote:On Fri, Jul 22, 2011 at 4:54 PM, Stephen P. King <stephe...@charter.net <mailto: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/0204024Umm, did you notice the words "non-relativistic" in the paragraph?I think that's only because they're talking about the Schrodingerequation, but relativistic QM (quantum field theory) also has its owndeterministic evolution, look at the second of the two papers I linkedto which is specifically about relativistic field theory, specificallyat p. 3.Even MWI does not help because in it one is taking constructions that exist in Hilbert space and assuming that they are ordered a priori.Not if you're talking about MWI of quantum field theory, again see thepaper I linked to.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.Sure, let us focus on the space-like surfaces. Does a unique order of them exist? No. This is the foliation problem that I mentioned below.Depends what sort of foliation and what spacetime you're using, if youhave a "globally hyperbolic" spacetime (which excludes certain weirdconditions like closed timelike curves, seehttp://en.wikipedia.org/wiki/Globally_hyperbolic_manifold ) then itshould be possible to introduce a global time function such that thetime parameter increases continuously along every timelike curve, seep. 18 of http://www.uco.es/geometria/documentos/OMuller.pdf forexample. Naturally this time function corresponds to a foliation, witheach hypersurface corresponding to a set of points that all have thesame value of the time parameter. There will be many different suchtime functions and thus many different foliations with differentdefinitions of simultaneity, but for any *specific* set of space-likesurfaces of this nature, it seems to me that a unique order of themdoes exist. As for non globally hyperbolic spacetimes, I think it's anopen question whether they will even be possible in a theory ofquantum gravity (there is much speculation that quantum gravity willrule out the possibility of closed timelike curves, see for exampleKip Thorne's discussion of the "chronology protection conjecture"towards the end of http://plus.maths.org/content/time-travel-allowed ).Also, that situation where "all frames agree on the time-order" assumes that the ordering already exists. I am asking about how it got there in the first place.The choice about which direction along a single timelike curve tolabel as "increasing proper time" and which to label "decreasingproper time" is arbitrary thanks to the time-symmetry of generalrelativity (see http://en.wikipedia.org/wiki/T-symmetry ) but once youhave picked a convention, in a globally hyperbolic spacetime I believethis would uniquely determine the two directions along every othertimelike curve. See the concept of "time-orientability" athttp://en.wikipedia.org/wiki/Causal_structure#Time-orientability andp. 2 of http://arxiv.org/pdf/gr-qc/9704075 which says a globallyhyperbolic manifold is by definition time-orientable: "Here we recall(see e.g. [6, 7]) that a spacetime is said to be globallyhyperbolic if it is time-orientable and has a Cauchy surface – i.e. anachronalspacelike hypersurface which is intersected exactly once by everyinextendiblecausal curve."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.So the block universe does or does not assume a "time dimension"? If it does then that "time dimension" is equivalent to a unique ordering of events such that events are labeled with values in the positive Real numbers, other wise known as the Real line.No, having a "time dimension" does not imply a unique ordering, that'sa non sequitur. It just means there is a clear distinction betweencurves which are "timelike" and those which are "spacelike" (or"lightlike").Consider the famous words of Laplace: "We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes." —Pierre Simon Laplace, /A Philosophical Essay on Probabilities/ This is the block universe idea. Given that we now known, per QM, that the positions, momenta and other observables cannot be simultaneously given for 'all items' in the universe, how can we still think that the universe just exists as a fixed and eternal 3,1 dimensional 'block'?Not sure why you think not being able to assign unique values ofposition and momentum is in any way essential to the block universeidea. In the many-worlds interpretation of relativistic quantum fieldtheory, the local "state" of each point in spacetime wouldn't be aboutposition and momentum, it would be about field operators as discussedon p. 3 of http://arxiv.org/abs/quant-ph/0204024 and as I mentionedthe values of these field operators is said to evolve in a local anddeterministic way. So Laplace's quote would still be valid if you justreplaced his talk of "positions" and "forces" with talk of the valuesof local field operators in the many-worlds interpretation.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.No, that requires that a basis be chosen for that particular Feynmann diagram.I was just imagining something "sort of like" a Feynman diagram, mypoint was to counter your very broad claim that time can't be adimension like space unless events are chained together by continuousworldlines. To counter this claim it would be sufficient to come upwith a toy model of a hypothetical set of physical laws (that need notresemble our own) which involve discrete collections of events inspacetime that aren't connected by continuous worldline, that's what Iwas getting at with the "sort of like" comment. That said, I thinkloop quantum gravity does propose something like a set of discreteevents with causal connections between them, not continuous 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:I was trying to not write a book.... What is a Cauchy surface? http://en.wikipedia.org/wiki/Cauchy_surface "a plane in space-time <http://en.wikipedia.org/wiki/Space-time> which is like an /instant/ of time; its significance is that giving the initial conditions <http://en.wikipedia.org/wiki/Initial_conditions> on this plane determines the future (and the past) uniquely. More precisely, a Cauchy surface <http://en.wikipedia.org/wiki/Hypersurface> is any subset of space-time which is intersected by every non-spacelike <http://en.wikipedia.org/wiki/Spacelike>, inextensible curve <http://en.wikipedia.org/wiki/Curve>, i.e. any causal curve <http://en.wikipedia.org/wiki/Causal_curve>, exactly once." Since we know from QM that the values of the initial conditions are subject to the Uncertainty principleNo, the uncertainty principle doesn't apply to the evolution ofquantum states, it's just about how those quantum states are projectedonto basis vectors of different observables. So if you don't treat"measurements" as randomly collapsing the quantum state onto one ofthe basis vectors of the observable being measured (this is somethingcalled the "Born rule" or "projection postulate", see my post #2 onthe thread at http://www.physicsforums.com/showthread.php?t=490919 ),as MWI advocates do not, there is no conflict with determinism here.Wave functions do not exist 'in' spacetime.As stated at http://arxiv.org/abs/quant-ph/0204024 in quantum fieldtheory you can replace the notion of a wave function with a physicallyequivalent description of a set of local field operators at each pointin spacetime.Additionally, the diffeomorphism invariance (also known as general covariance) of GR does not allow any particular meaning to "a point in space"But you can assign a physical meaning to "a point in spacetime",diffeomorphism invariance is only about the possibility of usingdifferent coordinate systems on the selfsame spacetime geometry., so the idea that 'a time-evolution is determined by local differential equations..." fails because the mapping that one has to use to identify a particular set of field operators with each point of spacetime is not invariant with respect to diffeomorphisms.The value of the field operators might depend on the coordinatesystem, but there is a unique truth about which point in spacetime asdescribed in one coordinate system constitutes the "same event" aswhich point in a different coordinate system, and I presume in the MWIyou could derive some coordinate-invariant facts about what'shappening at a given point using the field operators in whatevercoordinate system you chose, perhaps something like the ratio ofdifferent "Everett copies" of measurement outcomes at that point asdescribed on p. 2 of http://arxiv.org/pdf/quant-ph/0310186This is similar to how in GR, although the value of the curvaturetensor at each point depends on your choice of coordinate system,there is a coordinate-invariant spacetime geometry in the sense thatif you pick a continuous series of points making a curve, allcoordinate systems agree on the "length" of that curve (which can befound using the correct metric equation for each coordinate system).Jesse --

Hi Jesse,

`We seem to be talking past each other. I am thinking about the`

`notion of time as a dimension and its origin and implications. You seem`

`to just assume its existence. I ask "why?".`

Onward! Stephen -- 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.