2014-02-06 Edgar L. Owen <[email protected]>: > 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. >
Once again, for the nth time, there is absolutely no need of p-time for that. It's so obvious, are you blind not to see... (no, no that's not some blatant obvious plagiarism) Quentin > > 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]> 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. > For more options, visit https://groups.google.com/groups/opt_out. > -- All those moments will be lost in time, like tears in rain. 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