Jesse, I think the basic problem in our discussion, which seems intractable from you answers below, is your basic belief that time doesn't doesn't flow, that there is no such thing as a now in which you or the twins actually exist. From your answers it seems clear that you can't even bring yourself to agree that you are actually some particular age right now, or were at any time in the past. If you don't even believe that I can't see any hope of agreement or having a meaningful discussion.
It's quite clear from all the numerous examples I gave that it is possible to determine a 1:1 correlation between the twin's actual ages in terms of their own clock time readings (what you call their proper times). This is their 'true actual age' because both twins agree on both actual ages and how their clock times correlate. They do this not by OBSERVING the other's age, but by calculating it from knowledge of how relativity works in both their frames. This is the frame independence I point out that is a fundamental (though unstated) assumption of relativity. It is only in this background notion of frame independence that frame DEPENDENCE of relativity makes any sense. But that concept remains beyond you.... But since you can't even bring yourself to admit the twins were actually alive with a particular actual age at every point on their world lines I see no useful way to continue the discussion. Thus the basic disagreement is not really about whether p-time is incompatible with relativity (it isn't) but that p-time is incompatible with block time, which for you seems a matter of faith which you are unable to set aside. Best, Edgar On Wednesday, February 19, 2014 1:30:11 AM UTC-5, jessem wrote: > > > > On Sun, Feb 16, 2014 at 9:40 AM, Edgar L. Owen <[email protected]<javascript:> > > wrote: > >> Jesse, >> >> OK, I'm back... >> >> Let me back up a minute and ask you a couple of general questions with >> respect to establishing which past clock times of different observers were >> simultaneous in p-time.... >> >> The only clocks in this example are the real actual ages of two twins.... >> >> >> 1. Do you agree that each twin always has a real actual age defined as >> how old he actually is (to himself)? >> >> Yes or no? >> > > Yes, in the sense that at each point on his worldline he has an "actual > age" at that point, which is just the proper time between his birth and > that point. But if you're suggesting a unique "true" actual age, as opposed > to just each point having its own actual age, then I would have to change > my answer to no. > > > > >> >> 2. Do you agree that this real actual age corresponds by definition to >> the moment of his actually being alive, to his actual current point in >> time? (As a block universe believer you can just take this as perception or >> perspective rather than actuality if you wish - it won't affect the >> discussion). >> > > >> >> Yes or no? >> > > > If by "perspective" you mean that each point on his worldline takes his > experiences at that point (including his age) to be the "current point in > time", then yes. > > > >> >> >> Now assume a relativistic trip that separates the twins.... >> >> 3. Do you agree that IF, for every point of the trip, we can always >> determine what ACTUAL age of one twin corresponds to the ACTUAL age of the >> other twin, and always in a way that both twins AGREE upon (that is frame >> independent), that those 1:1 correspondences in actual ages, whatever they >> are, must occur at the same actual times? That this would give us a method >> to determine what (possibly different) actual ages occur at the same actual >> p-time moment in which the twins are actually alive with those (possibly >> different) actual ages? >> >> Yes or no? >> > > IF we had a method to determine a unique 1:1 correspondence in ages for > separated twins, then yes, that could reasonably be interpreted as a > demonstration of absolute simultaneity, telling us which ages "occur at the > same actual times". But I don't believe you can find any such method for > determining a unique frame-independent 1:1 correspondence in relativity. > > Since I am answering your questions, are you willing to answer mine? In > the post that you are responding to I requested that you respond to my > questions at > https://groups.google.com/d/msg/everything-list/jFX-wTm_E_Q/xtjSyxxi4awJ, > especially the part at the end about the meaning of "same point in > spacetime" (i.e. whether two events happening at the same space and time > coordinates in a single coordinate system automatically implies that they > satisfy the operational definitions of "same point in spacetime" I had > given, and whether you'd agree that this means they must have happened at > the same moment in p-time). You ignored that request in your response. I'll > even narrow it down to a single question I asked in that post: > > 'If we have some coordinate system where relativity predicts the event of > Alice's clock reading 30 happens at exactly the same space and time > coordinates as the event of Bob's clock reading 40, do you agree or > disagree that this means relativity automatically predicts these two events > would satisfy the various operational meanings of "same point in spacetime" > I gave at > https://groups.google.com/d/msg/everything-list/jFX-wTm_E_Q/AZOhnG04__AJ , > regardless of whether Alice and Bob had synchronized their clocks in the > past or not? Please give me a clear agree/disagree answer to this question' > > For example, say that in some particular coordinate system Alice's > coordinate position x as a function of coordinate time t is x(t)=80, i.e. > she is at rest at position coordinate x=80, and her age T (proper time > since birth) as a function of coordinate time t is T(t)=t+10. Meanwhile > Bob's coordinate position as a function of coordinate time is > x(t)=68+(0.6c)*t, i.e. at t=0 he is at x=68 and he is moving in the > positive x-direction at 0.6c, and his age T' as a function of coordinate > time t is T'(t)=24+0.8*t. Then at t=20 in this coordinate system, they will > both be at position x=80, and Alice's age will be T=20+10=30 while Bob's > will be T'=24+0.8*20=24+16=40. So the question above is asking whether, in > an example like this one, you'd agree that their reaching these ages at the > same space and time coordinates implies they must actually meet at the > "same point in spacetime" when Alice is 30 and Bob is 40, according to the > operational definitions I gave earlier (like the one involving bouncing > light signals back and forth and noting when the time for them to bounce > back approaches zero). > > Jesse > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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