Jesse, See my proximate response to Liz who asked the same question. Basically relativity theory gives you the equations for both frames for any relativistic situation. So all you have to do is do the calculations like I've explained to you with nearly a dozen examples.
To the question in your last paragraph. Yes, of course we assume originally synchronized clocks. Remember this is a thought experiment, and that is clearly possible if we assume it's done at rest relative to each other and then magically without acceleration (your instantaneous acceleration, which is also physically impossible, but has the exact same thought effect). So do you agree that given synchronized clocks, A and B in relative motion will still have synchronized clocks in their own frames to each other? I.e., that A will have the same reading on his own clock that B does on his own clock? And do you also agree that when the relative motion magically stops, their clocks will still read the same as each other's, AND they will both be the same age because of that? This is just elementary relativity theory, nothing to do with p-time at all... What it does demonstrate though is that relativity theory itself provides a frame independent way to compare its own relativistic frame dependent views. It has to because that's the only way it can specify both frames from OUTSIDE those frames. This is why relativity itself requires an independent computational background in which it can specify multiple frame dependent views of all relativistic scenarios. That independent computational background is p-time. P-time is the frame independent background in which relativistic frames can be compared. It is what allows the twins to compare their different clock times when they have real and actual different clock times and ages. When they are in different clock times, only if they are in the same actual p-time, as all observes must always be, could they compare their different clock times. It's a simple and absolutely essential necessity, whether you understand that or not, and relativity itself requires and assumes it. If there was not a common frame independent background in which multiple frame views could be specified, relativity theory could not even exist. Edgar On Wednesday, February 12, 2014 12:26:54 AM UTC-5, jessem wrote: > > > > On Tue, Feb 11, 2014 at 9:23 PM, Edgar L. Owen <edga...@att.net<javascript:> > > wrote: > > Jesse, > > Let me clarify my response since I see it's slightly ambiguous. > > First every observer in the universe is ALWAYS at the same point in p-time > ALL the time with all other observers. No exceptions. > > The question is what clock times of various observers correspond to a same > point of p-time? > > The answer is that to find out what t of any observer in any relativistic > frame corresponds to any t' of any other relativistic frame you just pause > the experiment so that all relativistic effects freeze at that instant. > > > Are you just going to completely ignore my point that "at that instant" is > ambiguous unless you already know which event on B's worldline occurs at > the same "instant" in p-time as an event on A's worldline? Again: if you > want to pause B "at the same instant" that A turns 60, but one frame says > that at the instant A turns 60, B is 48, while another frame says at the > instant A turns 60, B is 75, what PHYSICAL PROCEDURE would you suggest to > determine when to "pause" B? (unless of course you acknowledge that p-time > simultaneity can't be determined by any physical procedure, and is just an > unknowable metaphysical truth) Please don't answer "pause B at the same > instant A turns 60" because that's not a physical procedure, just a > statement of faith that there is some objective frame-independent truth > about B's age "at that instant". > > > > > > If all there is is just non-accelerated, non-gravitational relative > motion, you don't even have to pause the experiment. All you have to do is > note that A's clock in his frame will be the same as B's clock in his > frame, for all t and t' values > > > Are you saying that even if A and B are *not* at rest relative to one > another, as long as they are moving inertially free from gravity you still > assume that at a single point in p-time their clocks have the same reading? > Presumably this would only be if they had synchronized their clocks at some > point in the past, like the moment they passed next to each other at the > same point in spacetime? But then see the questions in my other recent post > about whether you even agree that clock readings that happen at the same > point in spacetime must happen at the same p-time... > > Jesse > > > On Tuesday, February 11, 2014 7:46:30 PM UTC-5, jessem wrote: > > > > On Tue, Feb 11, 2014 at 7:08 PM, Edgar L. Owen <edga...@att.net> wrote: > > Jesse, > > Your example does NOT establish any inconsistency. I NEVER said "I'm > pretty sure you've said before that you agree that if SR predicts two > clocks meet at a single point in spacetime, their two readings at that > point must be simultaneous in p-time)." That is NOT true. Only if there is > no relative motion or acceleration is it true. I really wish you could just > get the basics of the theory straight. > > > I thought you agreed on my operational definition of "same point in > spacetime", and that events that satisfied this definition would also occur > at the same point in p-time. I wonder if you actually are correctly > understanding what I say in the quoted sentence, because I find it hard to > believe you would deny it if you understood it correctly. > > Let's say we have two twins moving towards each other at some nonzero > velocity, and they pass right next to each other without either one > accelerating. Relativity can be used to predict their respective ages at > the moment they pass (if we idealize them as pointlike observers, the > "moment they pass" can refer to their worldlines passing through precisely > the same position and time coordinates). To use my usual numbers, > relativity might say that twin A is turning 30 and twin B is turning 40 at > the moment they pass. In terms of my operational definition, if A was > sending a continual stream of light signals to B and seeing how long it > took to receive the reflected signal, the time interval on A's clock > between sending a signal and receiving the reflection would approach zero > as his own age clock approached 30, and the age he would see on B's age > clock in the reflected light would approach 40 as he approached 30. > Likewise, if there was a camera at the point in space they passed, and it > took a photo just as they passed, the photo would show A's age clock > reading 30 and B's age clock reading 40. And if A had a bomb that would > destroy anything in his immediate local vicinity but would leave anything > at a distance from him unharmed, then if A set it to go off when he turned > 30, B would be killed at age 40, but if A set it to go off at any other > age, B would survive unharmed. > > Given that relativity would predict all these things, are you saying these > predictions could all be correct, but that A turning 30 and B turning 40 > would *not* be simultaneous in p-time, not even approximately so? Or are > you actually saying relativity would be *wrong* in the predictions above > when it predicts the event of A turning 30 will have the same x,y,z,t > coordinates as the event of B turning 40? Or did you just misunderstand > what I meant when I said "two clocks meet at a single point in spacetime, > their two readings at that point [A turning 30 and B turning 40 in this > example] must be simultaneous in p-time"? Or would you say "none of the > above"? Please give a clear answer to this question. > > > > > The method is trivially simple. I'll give two approaches: > > > 1. Instantaneously pause all relativistic effects at any time t on A's > clock and read the time t' on B's clock. These clock times are a point when > A and B were/are in the same p-time current moment. > > > > "Instantaneously pause" has no frame-independent meaning in relativity, do > you disagree? If A and B are in relative motion, and unlike my example > above, B is *not* at the same point in spacetime as A when A turns some age > (say 60), then different frames disagree on what age B is "at the same > instant" that B turns 60. So if one frame said B was 48 at the same instant > A turned 50, and another frame said B was 75 at the same instant A turned > 50, then at what age should B's motion relative to A be "paused"? We don't > have an "objective instantaneous pause machine" that can settle the > question empirically, it has to be *our choice* when to subject B to a > sudden acceleration to instantaneously bring him to rest relative to A. > Again, do you disagree? > > Since the whole rest of your explanation depends on this notion of an > "instantaneous pause", I'll await a response to this question before > dealing with the rest of your discussion of your "method". > > Jesse > > > <blockquote style="margin:0 0 0 .8ex;border-left:1px #cc > > ... -- 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.
