Jesse, et al, A Propros of our discussion of determining same past moments of P-time let me now try to present a much deeper insight into P-time, that illustrates and explains that, and see if it makes sense. I will show how relativity itself implicitly assumes and absolutely requires P-time to make sense.
Every relativistic calculation of clock times consists of some equation describing how one clock time varies with respect to another clock time. This mathematical relationship is of the general form dt'/dt = f( ), that the change in one clock time with respect to another is given by some function depending on the two worldlines of those clock times. This general form is true of every clock time calculation in relativity theory. And likewise we can get the total elapsed clock time differences along the worldlines by integrating along them until any dt'/dt = f( ). This establishes a 1:1 relationship between the clock times, t and t', at every point along the worldlines. Now the absolutely critical insight comes from understanding that for a relationship of any kind to even exist it must exist in some moment of time. The very fact of a relationship implicitly assumes some moment of time in which it exists. This is true of all relationships of every type. This is easy to understand when the relationships do not involve clock times. Eg. if we say Bill is taller than John, we implicitly assume that this relationship is true in some moment(s) of time, whether that moment is explicitly stated or not. The exact same thing must also be true of relationships between clock times. There must always be some kind of moment in which dt'/dt = f( ) for that relationship to even make sense or have any meaning at all. Now obviously that moment of time in which a clock time relationship makes sense CANNOT itself be a clock time, but it must be a real moment of some kind of time, and that kind of time is P-time. All relationships of every kind make sense and are meaningful only by existing in a current moment of P-time, which is the common background time to all events and all relationships including clock time relationships. Normally, for non-relativistic relationships, we would assume this moment was some moment of clock time. And this would be correct because NON-relativitistic clock times do map meaningfully to P-time. But for relationships between relativistic clock times we see that the necessary background time cannot be clock time itself because that is what is being compared in that moment of comparison. Thus we must recognize there is another more fundamental type of time we call P-time, the time of the present moment, because only if that is true does a comparison of clock times make sense, or can even take place. This is what I've meant when I've many times said that the twin's different clock times can only be compared and agreed to in a completely separate kind of time that is not clock time. That kind of time is the current present moment of p-time. Thus we must conclude that relativity theory itself REQUIRES a separate common background kind of time for its clock time and other relationships to make sense within . Relativity implicitly assumes an unstated background time in which its clock time differences can be compared and made sense of and become meaningful in. Relativity theory assumes this but never explicitly states it. This is an absolutely necessary assumption for the clock time relationships of relativity theory to make sense. All relativistic events must occur within a common implicitly assumed background P-time to make any sense at all. Relativity MUST recognize this fact, because without it the clock time variations of relativity don't make sense because they cannot be even compared... So because clock times vary in a 1;1 relationships according to dt'/dt = f( ) we can always back establish what different clock times occurred at the same moment of p-time. However since p-time has no dimensional metric we can not assign p-time t values to that point but only describe it in terms of the clock time relationship that occurred. Thus for any two observer clocks, if they know their dt'/dt = f( ) relationship they can always determine what they were doing at the same p-time moments. Now note that for any two relativistic clocks there will always be two equations, because each observer clock will have its own relativistic view of the clock time relationship and these in general will be different. So we will have two equations: dt'/dt = f( ) for observer A, and dt/dt' = g( ) for observer B. But because we have two simultaneous equations in two variables t and t' we should always be able to determine what t and t' occurred in the same current moment of p-time. And thus we can always determine what observer A was doing when observer B was doing x because there will always be a 1:1 relationship between every A clock time t value in A's frame with one and only one B clock time t' value in B's frame. Edgar On Sunday, February 9, 2014 12:05:32 AM UTC-5, jessem wrote: > > > > On Sat, Feb 8, 2014 at 8:07 PM, Edgar L. Owen <[email protected]<javascript:> > > wrote: > > Jesse, > > Consider another simple example: > > A and B in deep space. No gravity. Their clocks, t and t', are > synchronized. They are in the same current p-time moment and whenever t = > t', which is always their clock times confirm they are the same current > p-time as well as the same clock time. > > > When you say "synchronized", do you mean they are synchronized according > to the definition of simultaneity in their mutual rest frame? As I asked > before, if two clocks are at rest relative to one another and > "synchronized" according to the definition of simultaneity in their mutual > rest frame, do you automatically assume this implies they are synchronized > in p-time? If so you are going to run into major problems if you consider > multiple pairs of clocks where each member of a pair is at rest relative to > the other member of the same pair, but different pairs are in motion > relative to another...I will await a clear answer from you on this question > before elaborating on such a scenario, though. > > > > > Now magically they are in non-accelerated relative motion to each such > that each sees the other's clock running half as fast as their own. > > > Physics textbooks often consider examples where there are "instantaneous" > accelerations such that the velocity abruptly changes from one value to > another, with the objects moving inertially both before and after the > "instantaneous" acceleration, is that the same as what you mean by > "magically they are in non-accelerated relative motion"? > > > > > During the duration of the relative motion whenever A reads t = n on his > OWN clock and B reads t'=n on his OWN clock they will be at the same > current moment of p-time. They can use this method later on to know what > they were doing at the same present moment. > > > Even if we assume instantaneous jumps in velocity, there are multiple ways > they could change velocities such that in their new inertial rest frames > after the acceleration, each would say the other's clock is running half as > fast as their own. For example, in the frame where they were previously at > rest, if each one's velocity symmetrically changed from 0 in this frame to > 0.57735c in opposite directions in this frame, then in each one's new rest > frame the other would be moving at 0.866c (since using the relativistic > velocity addition formula at > http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html their > relative velocity would then be (0.57735c + 0.57735c)/(1 + 0.57735^2) which > works out to 0.866c), and a relative velocity of 0.866c corresponds to a > time dilation factor of 0.5. But likewise, in the frame where they were > previously at rest, it could be that one twin would remain at rest in this > frame while the other would jump to a velocity of 0.866c in this frame, and > then it would still be true that in each one's new rest frame the other is > moving at 0.866c. Does your statement above that "whenever A reads t = n on > his OWN clock and B reads t'=n on his OWN clock they will be at the same > current moment of p-time" apply even in the case of asymmetrical changes in > velocity? Are you saying all that matters is that in either one's new > inertial rest frame, the other one's clock is ticking at half the rate of > their own? > > > Jesse > > > > On Saturday, February 8, 2014 5:28:08 PM UTC-5, jessem wrote: > > > > > On Sat, Feb 8, 2014 at 4:01 PM, Edgar L. Owen <[email protected]> wrote: > > Jesse, > > Yes, I think there is always a way to determine if any two events happen > at the same point in p-time or not, provided you know everything about > their relativistic conditions. > > You do this by essentially computing their relativistic cases BACKWARDS to > determine which point in each of their worldlines occurred at the same > p-time. > > Take 2 observers, A and B. > > 1. If there is no relative motion or gravitational/acceleration > differences you know that every point t in A's CLOCK time was in the same > present moment as every point t' in B's CLOCK TIME when t=t'. > > > And what if there *are* gravitational differences, if there are sources of > gravity nearby and they are at different points in space? Gravity is dealt > with using general relativity, and in general relativity there is no > coordinate-indepedent way to define the "relative motion" of observers at > different points in space (see discussion at http://math.ucr.edu/home/ > baez/einstein/node2.html for details). And the only > coordinate-independent definition of "acceleration" is proper acceleration > (what an observer would measure with an accelerometer that shows the > G-forces they are experiencing), but all observers in freefall have zero > proper acceleration, so if you think there is a "gravitational/acceleration > difference" between an observer orbiting far from a black hole and one > falling towards it close to the event horizon, you can't quantify it using > proper time. > > > > > 3. In the case of twins DURING the trip in relative motion we can always > back calculate the relativistic effects to make a statement of the form > "the twins were in the same current moment of p-time when A read his own > clock as A-t and B's clock as B-t, AND B read his own clock as B-t' and > read A's clock as A-t'. In this case A-t will NOT = A-t', and B-t will NOT > = B-t', but they will have specific back calculable t values for every > current p-time during the trip. Thus if we have all the details of that > trip's motion we should always be able to back calculate to determine which > clock times of any two observers occurred in the same current p-time > SIMULTANEITY even when those observers cannot agree on CLOCK time > simultaneity among themselves. > > > HOW would you "back calculate" it though? Even if we set aside my > questions about gravity above and just look at a case involving flat SR > spacetime, your answer gives no details. If you have any procedure in mind, > could you apply it to a simple example? Let's say Alice is sent on a ship > that moves away from Bob on Earth on the day they are both born, and the > ship moves with speed of 0.8c relative to the Earth, towards a planet 12 > light-years away in the Earth's frame. Alice arrives at that planet when > she is 9 years old, and at that point the ship immediately turns around and > heads back towards Earth with a relative speed of 0.6c. Alice experiences > the return journey to take 16 more years, so when she returns to Earth she > is 25 years old, but Bob is 35 years old when they meet. Can you show me > how to back-calculate how old Bob was when he was in the same moment of > p-time as Alice turning 9 and her ship reaching the planet and turning > around? > > > > So since p-time has no metric itself you can't just compare p-time t > values because there are none. You have to back calculate clock times to > determine in what current p-times they occurred. > > So that's how we determine whether any two events occurred a the same > p-times or not. You should always be able to determine that even though you > can assign a p-time t value because there are none because p-time doesn't > have a metric. > > > I have never asked you for a p-time "value", I'm only interested in the > question of which events are simultaneous in p-time. I don't think your > answers so far have made it clear that you have any well-defined procedure > for determining this, see my questions above. > > Jesse > > > > > Edgar > > > > On Friday, February 7, 2014 12:51:32 PM UTC-5, jessem wrote: > > > > > On Fri, Feb 7, 2014 at 12:27 PM, Edgar L. Owen <[email protected]> wrote: > > Jesse, > > Well you just avoid most of my points and logic. > > > Can you itemize the specific points you think I'm avoiding? > > > > But yes, I agree with your operational definition analysis. That is > EXACTLY my point. That what our agreed operational definitions define is a > COMMON PRESENT MOMENT, and NOT a same point in spacetime, because the logic > of it does not support it being in the same point in space, only in the > same point of time > > > Huh? Even if one accepts p-time, that "operational definition" still must > be seen as a merely *approximate* way of defining the same point of p-time, > not exact, just like with "same point in space" > > ... -- 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.
