Jesse, So we agree on my first two points. And yes, I agree you can have as many arbitrary coordinate systems as you like but that adds nothing to the discussion.
I accept your criticism of my third point which was not worded tightly enough. I'll reword it... What I mean here is that all observers can know how relativity works both for them, and for all other observers. In other words they can know exactly what equations any observer A uses to calculate the observables of any other observer B, in particular the equation A uses to calculate the clock time of B relative to A's own proper time clock. This is standard relativity theory assumed in all relativity examples. it follows for any observer who knows relativity theory. With that revision do you now agree? As for your last comments where you disagree. I do NOT mean observationally, I mean computationally via his knowledge of relativity theory. You inconveniently snipped the examples where I made clear what I meant by this and did not respond. Here they are again: 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. Note I'm talking here only of RATES, not of proper TIME clock readings. We will get to that. E.g. IF THEY UNDERSTAND RELATIVITY, then all observers would agree that the PROPER clock in a certain gravity would be running at 1/2 the rate as PROPER 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 1/2 that of a non-accelerating observer. Do you agree? This is just using standard relativity theory to deduce what PROPER time rates would result in what observational clock time rates of other clocks for any observer. It's done all the time in pretty much any relativity example. If you don't agree I can lead you through any number of examples to demonstrate how it works, but on second thought I've already done that for a number of examples, so you still may not get it. Let me try one example though to make it clear... Take twins A and B. 1. They are initially at the same spacetime point (by your definition). They synchronize their clocks. 2. They BOTH embark on what I will call a symmetric relativistic trip. By symmetric I mean that their worldlines are exact reflections of each other. Their velocities, accelerations, and gravitational encounters, whatever they are, will be exactly symmetric so that their worldlines will be exact reflections of each other. 3. Still with symmetric worldlines they again meet up at the same spacetime point (your definition). 4. Because their trips were symmetric their clocks will read exactly the same because their relativistic histories will be equivalent in their effects on their clocks. Do you agree? Again, this is standard relativity theory. 5. Thus because their relativistic histories were exactly symmetric their proper times must have been exactly in synch from the beginning to the end of the trip. They cannot OBSERVE this but they they both KNOW it is true because they both understand how relativity works. They both know that equivalent relativistic effects cause equivalent PROPER clock time rates. Do you agree? Again standard relativity theory... Edgar On Tuesday, February 25, 2014 10:52:26 AM UTC-5, jessem wrote: > > > > On Tue, Feb 25, 2014 at 8:57 AM, Edgar L. Owen <edga...@att.net<javascript:> > > 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 > ... -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
