On Sunday, February 2, 2014 11:32:26 PM UTC, jessem wrote: > > > > On Sun, Feb 2, 2014 at 5:13 PM, <[email protected] <javascript:>> wrote: > > > On Sunday, February 2, 2014 8:44:07 PM UTC, [email protected] wrote: > > > On Sunday, February 2, 2014 3:45:24 PM UTC, jessem wrote: > > > > > On Sun, Feb 2, 2014 at 7:13 AM, <[email protected]> wrote: > > > Jesse - if the assumption is a fundamental geometry akin to the surface of > a world, and if the speed of light is constant, then you could draw dots > around that world for exact intervals of the speed of light, in which case > the light arrives at each point from each other point at exactly the same > moment....isn't that saying edgar's p-time? > > > > I don't understand what you mean by "dots around the world for exact > intervals of the speed of light"--in terms of a standard spacetime diagram > from SR, what would the dots be? Different events along the path of a > single light ray, or events along the paths of multiple light rays > radiating from some other event, or something else? It is true that the > spacetime "distance" between any two points along a light-like path is > zero, if that's what you mean, but I don't see the connection between this > observation and the idea that the light arrives "at exactly the same > moment", I'm not sure how you're defining that phrase. "Same moment" > normally suggests a judgment about simultaneity, not a judgment about the > proper time along a particular path between events. Also, note that by > means of a zig-zag lightlike path (like that of a light ray bouncing > repeatedly between mirrors), you can connect *any* two points in spacetime > that are within one another's light cones by a path of zero proper > time--for example, there is a path of zero proper time between the > assassination of Julius Caesar and me sitting here typing this. So if you > were to define events "at exactly the same moment" in terms of the > existence of a path of zero proper time connecting the events, you'd have > to say that all events throughout history occurred "at exactly the same > moment" which is pretty clearly not how it works with Edgar's p-time. > > Jesse > > > Hi Jess/Brent - thanks for getting back, > Perhaps I should backtrack to my first reaction reading your post. First > off, I definitely am not at your level on relativity so get ready for one > big pile of steaming ...misconception. I'll do the right thing, and keep it > short. > > I thought that one of the big themes from the principle of equivalence and > relativity via frames, was that there wasn't a complete resolution to the > absolute, non-relativistic conception of what the whole universe is like., > That you can't necessarily talk about a landscape in absolute terms at all. > > > Plenty of things aren't relative in relativity, like the proper time > between two events on a given timelike worldline. As mentioned on the page > at http://www.asa3.org/ASA/education/views/invariance.htm Einstein > actually called his theory an "Invariententheorie" or "theory of > invariance"--the name "relativity" was coined by Max Planck, and Einstein > resisted it because he thought it would lead to the misconception that > "everything is relative". > > > > > I read liz's thread on block time (very helpful thanks Liz) and will be > rephrasing this issue over there at some point too. > > It's funny because this came up for me first because I speculated with > some guys (and dolls) a lot nearer your level than mine - maybe 3/4 years > back - that spacetime had a definite geometry. They came back very firm it > did not. That even between the Earth and the Sun you couldn't look at it > that way. I must say I couldn't accept what they were saying and said so, > because for me, the geometry would be very clear that there was this huge > gravity well oneside, and this relativily tiny one the other (earth). > > But they maintained it wasn't legitimate to think that way and then when I > wouldn't buy but didn't have the expertise to make a case from relativity > knowledge, got the usual dressing down about intuition and how the world > isn't intuitive and all the rest. > > So where do we actually stand? Was their point legitimate but subtly > different to yours - and it's a case of I don't have the knowledge to tell > them apart? > > > > It depends exactly what they meant by "geometry"--are you still in touch > with them so you can ask, or was the discussion online so it could be > reviewed? I have always seen physicists use "spacetime geometry" to refer > to the frame-independent notion of distance along paths in spacetime > (including "geodesic" paths between events, which are local minima of > proper length for spacelike paths, and local maxima of proper time for > timelike paths) which can be calculated using the metric, see for example > http://books.google.com/books?id=sBiWcWwTp5oC&lpg=PP1&pg=PA236 which says > "In the framework of general relativity, the spacetime geometry is defined > by a metric" or > http://books.google.com/books?id=O3puAMw5U3UC&lpg=PP1&pg=PA7 which says > "So in relativity there is just one spacetime geometry defined by the > metric and measured by both clocks and rods and by particle paths." > > More generally, there are two ways to define the "shape" of a curved > surface--either in an "intrinsic" way which only depends on the lengths of > different paths within the surface, as in general relativity and more > generally in differential geometry as a whole, or in an "extrinsic" way > where we situate the surface in a higher-dimensional "embedding space", > like how the 2D surface of a sphere of radius R can be defined as the set > of all points that satisfy x^2 + y^2 + z^2 = R^2 in a 3D Euclidean space > with axes x,y,z (this embedding is an "isometric" one, meaning that if you > calculate lengths of paths on the surface using the embedding space, you > get the same answer as you would using the metric on the surface). The > extrinsic definitions seem to be more general and useful mathematically > (see > https://en.wikipedia.org/wiki/Differential_geometry#Intrinsic_versus_extrinsicfor > a brief discussion), but I think we humans find the "embedding" notion > more intuitive in terms of how we think of the "shape" of a surface. > > It turns out that curved spacetimes can also be "embedded" in an isometric > way, but rather than embedding them in a higher-dimensional Euclidean space > you embed them in a higher-dimensional version of "flat" Minkowski > spacetime from SR. A while ago I came across an interesting post on the > subject at http://www.physicsforums.com/showthread.php?t=290098 saying > that "Chris Clarke* showed that every 4-dimensional spacetime can be > embedded isometically in higher dimensional flat space, and that 90 > dimensions suffices - 87 spacelike and 3 timelike. A particular spacetime > may be embeddable in a flat space that has dimension less than 90, but 90 > guarantees the result for all possible spacetimes." So if you want an > intuitive picture, it's legitimate to think of the "geometry" of spacetime > in terms of spacetime being a curvy 4D surface sitting in some > higher-dimensional flat spacetime. The shape of this curvy surface should > be totally specified by the metric. > > So, the long and short of it is that I think the people you were talking > to were probably just mistaken when they said that spacetime doesn't have a > definite geometry. The one interpretation I can think of is that they were > actually talking about *spatial* geometry, not spacetime geometry--the > geometry of space at a single moment depends on your choice of simultaneity > convention (once you have done that, you define the geometry in terms of > the lengths of all spacelike paths that have all the points along them > confined to a single moment of time), so there isn't really a unique > correct "shape of space". I suppose it might even be possible to choose a > weird simultaneity convention where the gravity well of the Earth was > actually deeper than the gravity well of the Sun, but I don't really know > about that. > > Jesse > Hi Jesse, thanks for this. In terms of clarifying how I mean 'geometry' that could work for both of us, would be to forget what I might mean and instead go to a common standard of extreme naivety that both of us can take away sense from, by using as a go-between. So what I suggested was that most popularized visual metaphor, that starts with the 'mattress indented with the heavy ball', and then becomes the grid-like thing, were the indentation is now an area of distortion recognizable as an indentation, the heavy ball now gone. The picture then completed with a much smaller ball circling around the rim of the bigger indentation. So using that visual metaphor, and acknowledging a large amount of simplification is involved which, goes someway back toward the true theory but starts to get ambiguous and break down beyond a certain level of detail. The question then becomes, with your very detailed level of knowledge, whether among those points of furtherest extent the mattress metaphor can go, there is one that actually renders the very metaphor itself of seeing the much bigger indentation being circled by the much smaller one, as a unified singular view, does not reflect a legitimate single view in relativity? Clearly it does not in terms of frames of reference. There's two things there moving relative to oneanother so there's at least two frames of reference in play. Then there's the principle of equivalence in play between them. So it isn't a legitimate view past a certain level of detail from the metaphor back to the theory at least in that sense. In which case, is there a deeper level of detail than that that says actually there's a definite real landscape sitting beneath the level involving frames and equivalence and, basically therefore beneath and more fundamental than relativity itself? Or, is it more that there are feasible visual presentations in terms of intuition familiar landscape fixtures that do a good job translating the relative nature of the world onto a sort of non-relative canvas? Difference between the two being that the latter, could be very complex and detailed, but would ultimately still be more akin to the mattress metaphor, just at a much more detailed level. Whereas the former would be whole other, more fundamental theory. underlying relativity. Surely? I mean, sure, it represents relativity theory, so relativity is a pre-requisite, but if that landscape as you described it is fundamental in its own right, then that's a more fundamental level. Else if it isn't then it's a metaphor. One way I'd personally start to ask that question would with Einstein and maybe the other guy Hilbert too, thought they were saying at the time, in terms of what was made explicit rather than what was left implicit (i.e. as un-computed consequences) Any idea which way it was? The reason I would always go there first, is because when consequences get computed later on by others, the logic and reasoning can be totally flawless on its own terms, but nevertheless in the interval between the theory originator and the computation of those consequences, there has often been enough time for all kinds of devilish little implicit unrealized assumptions to creep into the background thinking. Such that, there's actually a fairly large number of precedents in the history of science of this kind of flawlessly logical computation of consequences that happens much later on, to have a long day in the sun enjoying a consensus status that finds it no less robust than the core of the original theory, only to be thrown out by subsequent generations after some flaw is uncovered.....as I say in the form of an implicit but unrealized built in assumption. What I'm talking about here is common enough that I'm not going to find it too hard to pull you out an historical example that is both recent enough that you almost certainly lived through it, and for a lot of you here, were also almost certainly part of the generation that had to face it down and throw it out. I should also be able to narrow things right down such that I'm pulling an example from relativity itself. And yep, there is one right there that even I remember, which dominated the consensus until as late as the late 1990's. Namely that because not just matter was created in the Big Bang, but everything, including space and time itself, any talk of there being a 'before' the big bang was hopelessy misconceived, and no truck given to it. It wasn't just relativity in play there but relativity was a big part. And has the logic of that ever been flawed on its own terms? No, and yet it was wrong, and thrown out. Why? Because at some point an implicit unrealized assumption sneaked in, that said something that went way beyond the paygrade any of our theories including relativity either did say, or could say. Namely, that it can be 100% true that everything in this universe, the dimensions, including time itself were created in the moment of the big bang. But all that says is that nothing like a continuation of our dimensionality in our universe existed before the big bang,. What it doesn't, and can't say, is that NO dimensionality or structure could have existed before the big bang. It just can't say that, because there's a huge assumption built in. Yet that dominated for a significant period of time. I think it's a good example because a lot of you were probably among those who had to suffer in silence under that regime, despite intuitively realizing there was just a dab of dogma in play. A lot of you probably had to be part of the big heave-ho effort that taking on, and facing down a major consensus dogma can take. Or else wait for the ringleaders to retire off, and jump into the vacuum and do it that way. Anyway, I hope with all this I've clarified what I'm asking you. Is that landscape sitting beneath relativity, fundamental or is it a metaphor? How do you, yourself, go about the business of distinguishing the one from the other, since if it goes down at certain level of detail, one can very much look like the other. Physicists can very much work to a theme just as you say, of assuming a fundamental landscape underpinning things. That don't mean it ain't a metaphor.
-- 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.
