Jesse, Once again, for the nth time, you are making statements about CLOCK time simultaneity with which I agree. That has nothing to do with the same present moment of p-time.
Edgar On Thursday, February 6, 2014 12:15:16 PM UTC-5, jessem wrote: > > > > On Thu, Feb 6, 2014 at 9:38 AM, Edgar L. Owen <[email protected]<javascript:> > > wrote: > > Jesse, > > OK, let's see if I understand your coordinate spacetime model the same way > you do. > > Start with an empty space with no matter or energy. > > [But this is impossible in my theory since the presence of matter/energy > is what creates space in my model so make that a space filled with a thin > homogeneous distribution of matter. This is irrelevant to the discussion, > just a note.] > > This space will be flat, locally at least. [On cosmological scales it will > be curved but we can ignore that for now....] > > Now assume this is a 2D space to make things simpler. > > Now drop an arbitrary orthogonal coordinate grid on this space. > > Next place a clock and a light source at each grid intersection. The clock > and light source will be synchronized and the light source will emit a > pulse of light at every second the clock ticks. > > Note that, in this flat homogeneous space with no acceleration or relative > motion, all grid clocks will tick in unison, and all light sources will > pulse in unison, across the entire surface. In this flat space there is > clearly a common universal present moment, and a simultaneous clock time > reading across the whole space. > > > > You can add a "common universal present moment" in as an untestable > metaphysical assumption if you like, but that certainly isn't "clear" just > from the physical details of the scenario you're describing. The coordinate > grid just provides *a* definition of simultaneity, but there's no guarantee > it would agree with that of a metaphysical absolute present! > > To see why, imagine you have two different coordinate grids in this flat > space, each moving at constant velocity relative to the other (you can > imagine the clocks and rulers are made of some ghostly material that allows > the clocks and rulers of one grid to pass right through the clocks and > rulers of the other without disturbing them). In that case, if clocks > within each grid are synchronized using the Einstein synchronization > convention, then the two grids will actually disagree about > simultaneity--if events A and B are assigned the same time coordinate by > local clocks of grid #1 that are at the same point in spacetime as A and B, > then they will be assigned *different* time coordinates by local clocks of > grid #2 that are at the same point in spacetime as A and B. Even if p-time > simultaneity exists then only one of the grid's definitions of simultaneity > could agree with it, and it could easily be that neither of them do. > > A while ago I drew up some diagrams showing a pair of 1D ruler/clock > coordinate systems moving alongside each other, illustrating how in each > system's own frame their own clocks were synchronized, but the other > system's were out-of-sync: > > http://www.jessemazer.com/images/RulerAFrame.gif > > http://www.jessemazer.com/images/RulerBFrame.gif > > as well as a diagram showing that both frames agree about which events > locally coincide at the same point in spacetime: > > http://www.jessemazer.com/images/MatchingClocks.gif > > > > > > > Now represent this flat 2D space by an elastic rubber sheet with the > coordinate grid drawn on it, and the clocks ticking and light sources > pulsing every second with the ticks. > > As you noted, the time distance between any two points will be simply the > distance that light travels between them, the time it takes for light to > travel from one point to another on somebody's clock, which in this flat > universe will be the same for all clocks. > > > Now add a large mass to this model. This mass will not be a spherical ball > placed on the rubber sheet but the presence of a mass inside a grid cell(s) > of the sheet and the effect of that mass is to dilate the rubber sheet at > that point. That dilation will cause a bulge in the sheet around the mass, > a curvature in space. > > > In relativity those "rubber sheet" diagrams ('embedding diagrams' which > 'embed' a curved 2D surface in our ordinary 3D space so we can visualize > the curvature) already presuppose you have made some (arbitrary, > clock-dependent) choice about how to define simultaneity, and then are > looking at the curvature of a 2D slice of space (a fixed value of one of > the spatial coordinates) within a particular simultaneity surface (a fixed > value of the time coordinate). Choose a different definition of > simultaneity and you get a different picture of curved space at any > instant. > > Phenomena associated with gravity are more fundamentally understood in > terms of *spacetime* being curved, not space. In a spherically symmetric > spacetime the curvature only depends on the radial coordinate, so you can > draw a different sort of 2D "rubber sheet" which has the radial coordinate > as one dimension and the time dimension as the other, and then instead of > imagining embedding the curved 2D surface in 3D Euclidean, you imagine > embedding it in a Minkowski spacetime with 2 spatial dimensions and 1 time > dimension. Now imagine some observers in this larger Minkowski spacetime > whose worldlines are chosen so that they stay on the curved surface at all > times. Then you can use ordinary SR in the 2D+1 Minkowski time to calculate > the proper time along these worldlines, then this will exactly match the > proper times for observers moving radially along the same paths in the > original curved spacetime. If you want to see an example with > illustrations, here's one involving a "Kruskal black hole": > http://arxiv.org/abs/gr-qc/9806123 > > (If you do look over that paper, you may also want some background on the > Kruskal black hole spacetime, which is the "maximal extension" of the > Schwarzschild black hole spacetime, and which also includes a "white hole > interior region" separate from the "black hole interior region", and two > disconnected regions "outside" the event horizon. If so, see this > discussion of the Kruskal-Szekeres coordinate system which is one of the > simplest ways to visualize this spacetime: > http://en.wikipedia.org/wiki/Kruskal–Szekeres_coordinates ) > > > > > Now this model incorporates my STc Principle because, for an observer at > any point, time always passes at c on his own clock, and thus he > continually travels forward in time at the speed of light according to his > own clock. > > > > Not sure what you mean by "time always passes at c on his own clock". Are > you still talking again about the fact that the magnitude of the 4-velocity > is always c? But that isn't directly measurable with your own clock, it > involves taking the derivatives of coordinate positions and time in some > inertial frame with respect to your clock time. What's more, the derivation > assumes we are using an inertial coordinate system, I don't think it would > in general work in a non-inertial coordinate system in curved spacetime > where the relation between the proper time interval dtau and coordinate > intervals dt, dx, dy, and dz may be different, determined by the metric. In > general, any coordinate system that covers a non-infinitesimal region of > curved spacetime cannot be an inertial one. > > > > However now, with the dilation curving the space around the mass, the time > distance along the dilation slopes will be longer because it takes light > longer to traverse a slope than a flat area of the rubber sheet because > space is curved there. The space dilation causes a corresponding time > dilation. > > Thus, from the perspective of an observer in a flat area, time will be > gravitationally dilated around the space curvature slopes caused by a mass. > And conversely for an observer in a gravity well clocks in a flat area will > appear to run faster because light crosses the grids faster in the flat > areas. We might say (light Brent) that proper time actually runs slower in > a gravitational well, though it still runs at the same proper time rate c > on the clock of an observer in that gravity well. It's only when clocks are > compared that the difference is observable. > > > > It's only meaningful to talk about proper time "running slower" relative > to some definition of simultaneity--if you have a definition of > simultaneity such that at one moment clock A reads 0 and clock B reads 10, > and at later moment clock A reads 20 and clock B reads 15, you can say > clock B is "running slower" relative to this definition. But of course in > relativity all choices of simultaneity conventions are arbitrary. Even if > there is an absolute truth about p-time simultaneity, as I understand it > you are now saying there's no way to determine it experimentally, so I > don't see how you could rule out the possibility that p-time simultaneity > would work in a way that clocks in gravity wells could at least sometimes > run faster than clocks outside of them, since there are certainly valid > simultaneity conventions in relativity where this could be true. > > Also, as I understood him, Brent was saying that fundamentally > gravitationally time dilation should be understood in terms of the geometry > of paths through curved spacetime, without any need to talk about some > clocks "running slower" than others. That would be illustrated in the sort > of spacetime embedding diagram I discussed above--the different proper > times of observers with different paths through curved spacetime is > formally identical to the different proper times of observers whose paths > are confined to a particular curved 2D surface in a 3D flat spacetime (2 > space dimensions and one time dimension), so if you agree the different > proper times for paths in flat spacetime can be understood in terms of the > geometry of paths rather than any absolute slowing, the same should apply > in curved spacetime. > > > > > Now this is an effect that both observers agree upon when they compare > each other's clocks to their own. So the clocks in a curved space gravity > well do actually run slower relative to those in flat space when they are > compared even though both observers always see their own clocks run at c. > > Please note again that from our God-like overview, that there IS a common > present moment because from this external perspective time continually > passes at the speed of light through ALL points on the surface. > > > Only because you have *defined* your picture of a God-like overview in > terms of a sort of imaginary movie which shows things moving around on a 2D > spatial surface. But again, for exactly the same spacetime with exactly the > same paths followed by observers, you could slice it up into spatial > sections in many different ways, resulting in many different movies of this > type which would disagree about which pairs of events happened in the same > frame. It may be that only one possible definition of coordinate > simultaneity would agree with p-time simultaneity, but this would be a > purely metaphysical assumption with no physically observable consequences. > So if you are actually trying to *demonstrate* the truth of p-time, rather > than just describe how you believe things really work without attempting to > prove these beliefs, then this picture is of no help. > > > 2. By expanding the rubber sheet model into the surface of a balloon, we > have my model of cosmological geometry. In that model the surface of the > balloon corresponds to the 3 dimensions of space in the present moment, > with past time as the radial dimension back to the center which corresponds > to the big bang where time started. > > > > Do you still have localized depressions in this rubber sheet where there > are local concentrations of matter like stars and galaxies? If so would the > bottom of the well somehow be closer in time to the Big Bang than a point > far from the well, since the radius would be smaller at that point in an > embedding surface? If so I'm not clear on what each surface is supposed to > represent (it can't be a single simultaneous moment in p-time if some > points on a single surface are at times closer to the Big Bang than > others), but if not it seems that the time of a given event is not really > determined by its radius in an embedding surface. > > > > > > 3. In this model we take the continuing passage of time at the speed of > light at all points on the surface to continually inflate that balloon. As > the balloon is inflated through p-time the universe continually computes > its current state as the present moment extends through p-time. > > 4. All relativistic clock time effects are effects that occur on the > rubber sheet surface of this balloon WITHIN the present moment of p-time. > They are computations which the passage of p-time drives (supplies > processor cycles for) to compute clock times and everything else that > makes up the current state of the universe. > > This is how I use the model, but it's peripheral to the current discussion > so we can ignore it for now and get back to the coordinate time model under > discussion.] > > > OK, now note that since this rubber sheet model incorporates the STc > notion at every grid point, that we should be able to use Epstein diagrams > to analyze relativistic cases by attaching them to any objects, moving or > still in this model. > > Once we have the same understanding of the model we can try to see how > that might work with some specific cases. > > Does this model [ignoring my peripheral comments in square quotes] express > what you mean by coordinate time? > > > Coordinate time really just means the local reading on a clock in the > grid, I don't see what the extra elements of your picture (which depends on > assuming a particular definition of global simultaneity so we can picture > what all the clocks read at a single moment) add to that. > > > > > > I think it pretty much does because it specifies what is meant by your "a > same point in spacetime". Isn't that simply the local clock time of any > x,y,z coordinate on a clock that never leaves that point, assuming that is > not a point that moves, but that is fixed in space i.e. a fixed > intersection of the arbitrary (coordinate time) grid? > > > There is no need to make any assumption about whether or not the > coordinate clocks are "moving" relative to the choice of how to define > "fixed points in space", which in relativity would depend entirely on one's > choice of reference frame (an object remaining at a fixed point in space in > one frame will be moving through different points in space in ano > ... -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. 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