On Tue, Feb 25, 2014 at 8:57 AM, Edgar L. Owen <[email protected]> wrote:
> Jesse, > > Here is a clearer, unambiguous and more general way to define p-time > simultaneity in terms of proper times. Let me know what you think. I'll > also address your latest questions in separate replies....... > > > Drop an arbitrary coordinate system onto an arbitrary space. Place a clock > at each grid intersection. I don't think we even have to worry about those > clocks being synchronized initially. (We do assume only that physical > processes, including the rate of time, follow the same relativistic laws at > all locations.) Place a stationary observer with each clock just for > terminological convenience. We don't really need this coordinate clock > system but I include it to address your concerns. > > Each clock will display the coordinate time of its grid intersection, > which will also be the proper time of the stationary observer at that > location. > > These grid clocks will run at different rates depending on the > gravitational potentials of their grid locations. > > Do you agree? > I agree you can construct an arbitrary non-inertial coordinate system in this way. As I said before in the second half of my post at https://groups.google.com/d/msg/everything-list/jFX-wTm_E_Q/SX19ccLeij0J(starting with the paragraph that begins "Not a well-defined assumption."), I think the only two ways to compare the "rates" of clocks at different locations are by 1) picking an arbitrary coordinate system and looking at how fast each clock ticks relative to coordinate time in that system, or 2) restricting yourself to talking about purely visual rates of one clock as seen by an observer at a different position, with the visual signals timed against his own clock. If you think there is any more objective notion of clocks having different "rates" which can be compared with one another, then I disagree. > > > Now also introduce an arbitrary number of observers either stationary, or > moving relative to this grid, each with its own proper time clock, some > accelerating, some with just constant relative motion. > > This model covers all possible types of relativistic time effects > (disregarding black holes and other types of horizons for the moment). > > Do you agree? > I basically agree, although I would also specify that you can have more than one coordinate grid covering the same region of spacetime (imagine them as being able to pass through one another without obstruction), since some of the mathematics of relativity deals with coordinate transformations from one system to another, like the Lorentz transformation that deals with how the coordinates of different inertial frames map to one another. > > It is possible for all observers in this space to have knowledge of the > relativistic conditions of all other observers as well as themselves. In > other words they can know the equations governing how any observer would > view any other observer. > > Do you agree? > "How any observer would view any other observer" seems ill-defined, again the only way I can think of for observers to have "views" of one another is either 1) associate a coordinate system with a particular observer--often one where they are at rest and coordinate time matches their own proper time along their worldline--and examine the coordinate-dependent behavior of other observers in this coordinate system, and 2) just consider what a given observer sees visually about other observers using light signals, including the proper times that he receives different signals. If you're talking about 1), note that although in SPECIAL relativity physicists often adopt the linguistic convention that a given inertial observer's "view" or "perspective" is taken as a shorthand for how things work in their own inertial rest frame, in general relativity there is no similar convention for assigning meaning to a word like "view", and you have an infinite variety of possible non-inertial coordinate systems that could be used by a given observer (even if you restrict yourself to coordinate systems where that observer is at rest and coordinate time matches proper time along their worldline)., So, I would agree only if you are either using "view" to refer purely to what each observer sees visually, or if you mean that we SPECIFY a particular coordinate system that should be used by a given observer to define his "view". If you don't mean either of those things, then I don't think this is a well-defined statement in relativity. > > > Thus it is possible for all observers to know the RATES of all proper > clocks in this system, and all observers will agree on all those proper > clock rates. > > E.g. all observers would agree that the proper clock in a certain gravity > would be running at 1/2 the rate as clocks in no gravity. All observers > would agree that the proper clock rates of all observers in inertial motion > would be running at the same rate. And all observers would agree that the > proper clock of an observer with a specific acceleration close to the speed > of light would have a proper clock rate half that of a non-accelerating > observer. > > Do you agree? > No, under neither of my definitions above--associating a coordinate system with each observer to call his "view", or using "view" to refer to what he sees visually--would it be true that different observers would generally agree about the ratio between the "rates" of clocks in different parts of space. For example, observer A might be associated with a coordinate system where observer B's clock is ticking 3 times as fast (relative to coordinate time) as observer A's clock at two particular points on each clock's worldline, but observer B might be associated with a different coordinate system where observer B's clock is only ticking 2 times as fast (relative to coordinate time) as observer A's clock at the same two points on each clock's worldline. Likewise, if we are talking about visual rates, those too can be non-reciprocal. Since this point seems to be essential to the rest of your argument, I don't think I need to respond to the rest of your "do you agree?" questions until I see if you disagree with my points above (and if you do, please tell me if you think my statements are incorrect in relativity itself, or if you agree that in relativity these are the only ways to compare the "rates" of clocks at different positions but you think there is some alternate procedure for doing it that physicists haven't noticed). Jesse -- 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.
