On Thursday, September 30, 2021 at 1:30:09 PM UTC-7, sep...@yahoo.com wrote:
> Are both twins at rest in F1 in terms of the twins measurements we just discussed
> when their simultaneous times are T1+T2?

You're mixing up F0-times with F1-times. The twins reach rest in F1 simultaneously in terms of F0, but not in terms of F1. We covered this before, remember?

> Or do the twins now say, the accelerations were different and we did not
> reach zero velocity with respect to F1 simultaneously?

It isn't about "what twins say", it's about the objective verifiable facts in terms of any specified system of coordinates. Again, the twins reach rest in F1 at the same F0-time, but not at the same F1-time. You can read this directly off the clocks in the respective standard grids. Is there anything about this that seems unclear to you?

On Thursday, September 30, 2021 at 3:41:30 PM UTC-5, Al Coe wrote:
> On Thursday, September 30, 2021 at 1:30:09 PM UTC-7, sep...@yahoo.com wrote:
> > Are both twins at rest in F1 in terms of the twins measurements we just discussed
> > when their simultaneous times are T1+T2?
> You're mixing up F0-times with F1-times. The twins reach rest in F1 simultaneously in terms of F0, but not in terms of F1. We covered this before, remember?
> > Or do the twins now say, the accelerations were different and we did not
> > reach zero velocity with respect to F1 simultaneously?
> It isn't about "what twins say", it's about the objective verifiable facts in terms of any specified system of coordinates. Again, the twins reach rest in F1 at the same F0-time, but not at the same F1-time. You can read this directly off the clocks in the respective standard grids. Is there anything about this that seems unclear to you?
So again,
What restriction must the twin use when he uses the mirror to start two events simultaneously when he is in an inertial reference frame? You keep saying its not what the twins say so its not clear to me when the twin can use that method to create two simultaneous events when he is not accelerating. Please clarify.
David Seppala
Bastrop TX

On Thursday, September 30, 2021 at 2:26:05 PM UTC-7, sep...@yahoo.com wrote:
> What restriction must the twin use when he uses the mirror to start two
> events simultaneously when he is in an inertial reference frame?

The answer hasn't changed since the last time this was asked and answered (or the time before that, or the time before that...). Again, the mirror procedure you described obviously only works when the twins are both at rest in the same frame throughout the process. For example, if the left hand twin initiates the mirror process as soon as he is at rest in F1, he will be initiating the process at at F1-time that is substantially later than the F1-time when the right hand twin reached rest in F1. That's the extra dwell time that you overlooked, remember?

> You keep saying its not what the twins say so its not clear to me when the
> twin can use that method to create two simultaneous events when he is not
> accelerating. Please clarify.

The reason I say it's not about "what twins say" is because a twin is not a coordinate system, nor does a twin uniquely even imply a specific coordinate system. In fact, even if you limit yourself to coordinate systems in which the twin is (momentarily) at rest, this still doesn't uniquely identify a coordinate system, because there are infinitely many different coordinate systems in which a twin is at rest at any given moment, and hence it doesn't uniquely identify a simultaneity. "Simultaneous" means at the same value of the time coordinate, which depends on the system of coordinates. So it is meaningless to talk about "what a twins says". You need to state the facts in terms of some definite system of measure.

Now does anything I've said remain unclear to you?

On Thursday, September 30, 2021 at 4:43:10 PM UTC-5, Al Coe wrote:
> On Thursday, September 30, 2021 at 2:26:05 PM UTC-7, sep...@yahoo.com wrote:
> > What restriction must the twin use when he uses the mirror to start two
> > events simultaneously when he is in an inertial reference frame?
> The answer hasn't changed since the last time this was asked and answered (or the time before that, or the time before that...). Again, the mirror procedure you described obviously only works when the twins are both at rest in the same frame throughout the process. For example, if the left hand twin initiates the mirror process as soon as he is at rest in F1, he will be initiating the process at at F1-time that is substantially later than the F1-time when the right hand twin reached rest in F1. That's the extra dwell time that you overlooked, remember?
> > You keep saying its not what the twins say so its not clear to me when the
> > twin can use that method to create two simultaneous events when he is not
> > accelerating. Please clarify.
> The reason I say it's not about "what twins say" is because a twin is not a coordinate system, nor does a twin uniquely even imply a specific coordinate system. In fact, even if you limit yourself to coordinate systems in which the twin is (momentarily) at rest, this still doesn't uniquely identify a coordinate system, because there are infinitely many different coordinate systems in which a twin is at rest at any given moment, and hence it doesn't uniquely identify a simultaneity. "Simultaneous" means at the same value of the time coordinate, which depends on the system of coordinates. So it is meaningless to talk about "what a twins says". You need to state the facts in terms of some definite system of measure.
>
> Now does anything I've said remain unclear to you?
If two twins are at rest and separated a distance L along the x-axis in F0, and they both accelerate simultaneously parallel to the y-axis of F0 in an identical manner as measured by observers in F0, and they land simultaneously as measured in F0 in inertial reference frame F1 that has a velocity V with respect to F0 along the x-axis, are the twins the same age after they land? If not, what caused one twin to age more than the other twin?
Thanks,
David Seppala
Bastrop TX

On Thursday, September 30, 2021 at 3:58:38 PM UTC-7, sep...@yahoo.com wrote:
> If two twins are at rest and separated a distance L along the x-axis in F0, and they
> both accelerate simultaneously parallel to the y-axis of F0 in an identical manner as
> measured by observers in F0, and they land simultaneously as measured in F0 in
> inertial reference frame F1 that has a velocity V with respect to F0 along the x-axis...

Huh? You said they are moving in the y direction, and then you say they "land" in a system of coordinates that is moving in the x direction. Do you mean they abruptly accelerate in the x direction so that they are at rest in terms of F1, or just moving in the y' direction in terms of F0? If I didn't know better, I'd think you were trying to replicate your idiotic "landing on a rotating planet" stuipidity.

> are the twins the same age after they land?

In terms of what system of coordinates? You see, even before they "landed", the proper ages of the twins are the same at constant t of some systems of coordinates and not of others, and this continues to be true after they land. What you are overlooking is the relativity of simultaneity. Remember?

On Thursday, September 30, 2021 at 3:58:38 PM UTC-7, sep...@yahoo.com wrote:
> If two twins are at rest and separated a distance L along the x-axis in F0, and they
> both accelerate simultaneously parallel to the y-axis of F0 in an identical manner as
> measured by observers in F0, and they land simultaneously as measured in F0 in
> inertial reference frame F1 that has a velocity V with respect to F0 along the x-axis...

Huh? You said they are moving in the y direction, and then you say they "land" in a system of coordinates that is moving in the x direction. Do you perhaps mean they abruptly accelerate in the x direction so that they are at rest in terms of F1, or just moving in the y' direction in terms of F1? If I didn't know better, I'd think you were trying to replicate your idiotic "landing on a rotating planet" stupidity. What rhetorical purpose does the motion in the y direction serve? The simple fact, which you been told hundreds of times, is that two separate events that are simultaneous in terms of one system of inertial coordinates are not simultaneous in terms of another that is moving along the axis of separation.

> are the twins the same age after they land?

In terms of what system of coordinates? You see, even before they "landed", the proper ages of the twins are the same at equal time coordinates of some systems of coordinates and not of others, and this continues to be true after they land. What you are overlooking is the relativity of inertial simultaneity. Remember?

Special Relativity: 838 .... Barnpole Dave: 0

On Friday, October 1, 2021 at 2:23:16 AM UTC-5, Al Coe wrote:
> On Thursday, September 30, 2021 at 3:58:38 PM UTC-7, sep...@yahoo.com wrote:
> > If two twins are at rest and separated a distance L along the x-axis in F0, and they
> > both accelerate simultaneously parallel to the y-axis of F0 in an identical manner as
> > measured by observers in F0, and they land simultaneously as measured in F0 in
> > inertial reference frame F1 that has a velocity V with respect to F0 along the x-axis...
>
> Huh? You said they are moving in the y direction, and then you say they "land" in a system of coordinates that is moving in the x direction. Do you perhaps mean they abruptly accelerate in the x direction so that they are at rest in terms of F1, or just moving in the y' direction in terms of F1? If I didn't know better, I'd think you were trying to replicate your idiotic "landing on a rotating planet" stupidity. What rhetorical purpose does the motion in the y direction serve? The simple fact, which you been told hundreds of times, is that two separate events that are simultaneous in terms of one system of inertial coordinates are not simultaneous in terms of another that is moving along the axis of separation.
> > are the twins the same age after they land?
> In terms of what system of coordinates? You see, even before they "landed", the proper ages of the twins are the same at equal time coordinates of some systems of coordinates and not of others, and this continues to be true after they land. What you are overlooking is the relativity of inertial simultaneity. Remember?
>
> Special Relativity: 838 .... Barnpole Dave: 0

I understand that when the two twins have zero velocity with respect to F1, after being in F0, their clocks show different times. And I understand if they both start moving toward each other with identical motions in F1 based on the identical times shown on their clocks when they are at rest in F1 they will have equal times when they meet at the midway point. What I don't follow is if the twins don't know anything about F1 and are asleep from the journey from F0 to F1, and wake up when they have zero velocity wrt to F1, and they determine they are a distance L' apart, and a twin wants to send a birthday greeting to the other twin using a light signal so that it arrives precisely on the other twins birthday, it is impossible for the twin to do so because he doesn't know whether F1 was moving in the positive or negative direction relative to F0. So the twin might send either an early birthday greeting or a belated birthday greeting so now he has only a 50-50 chance of getting it right.
David Seppala
Bastrop TX

On Friday, October 1, 2021 at 6:13:47 AM UTC-7, sep...@yahoo.com wrote:
> I understand that when the two twins have zero velocity with respect to F1, after being
> in F0, their clocks show different times.

No, that is not an accurate statement. Here's a correct statement: Two clocks that show the same times at equal values of the time coordinate of F0 do not show equal times at equal values of the time coordinate of F1, and vice versa.

> And I understand if they both start moving toward each other with identical
> motions in F1 based on the identical times shown on their clocks when they
> are at rest in F1 they will have equal times when they meet at the midway point.

You contradict yourself. In the previous sentence, you acknowledged that the clocks do not read the same at equal values of the F1 time coordinate, but in this sentence you say the clocks show identical times in terms of F1. Again, since you have stipulated that the clocks to begin moving toward each other simultaneously in terms of F1, they do not show the same readings when they initiate their respective accelerations. The right-hand clock must dwell for a period of time after reaching rest in F1 before initiating his final acceleration. Remember? I gave you the explicit coordinates for all these events.

> What I don't follow is if the twins don't know anything about F1 and are asleep
> from the journey from F0 to F1...

The twins aren't a significant part of the scenario, because you have not specified any re-setting of the clocks. Hence the clocks show the same elapsed time as the twins. Also, please note that the twins do not stop aging when asleep.

> and wake up when they have zero velocity wrt to F1, and they determine they are a distance
> L' apart, and a twin wants to send a birthday greeting to the other twin using a light signal so
> that it arrives precisely on the other twin's birthday, it is impossible for the twin to do so
> because he doesn't know whether F1 was moving in the positive or negative direction
> relative to F0.

So, you fail to understand why lack of knowledge as to the past motions of your twin (or the other clock) correspond to lack of knowledge as to the proper age of the twin (or reading of his clock). You see, given that the laws of physics are Lorentz invariant, it follows that the elapsed time for a twin or a clock between two specified events depends on the path that is taken between those events. Hence, if you know the age (or clock reading) at some initial event, but you don't know the path that has been taken by the twin (or clock) to reach some specified later event, you do not know the age or the clock reading at that later event (without checking). You tell me that you "don't follow" this. Do you mean you simply don't understand it, or you think it entails some logical inconsistency, or you understand it and realize that it does not entail any logical inconsistency but you think it is not empirically correct? If it's the first or second, you are just failing at math, and if it's the third, you just need to acquaint yourself with the empirical facts. Understand?

Special Relativity: 839 .... Barnpole Dave: 0

On Friday, 1 October 2021 at 18:03:52 UTC+2, Al Coe wrote:

> So, you fail to understand why lack of knowledge as to the past motions of your twin (or the other clock) correspond to lack of knowledge as to the proper age of the twin (or reading of his clock). You see, given that the laws of physics are Lorentz invariant, it follows that the elapsed time for a twin or a clock between two specified events depends on the path that is taken between those events. Hence, if you know the age (or clock reading) at some initial event, but you don't know the path that has been taken by the twin (or clock) to reach some specified later event, you do not know the age or the clock reading at that later event (without checking). You tell me that you "don't follow" this. Do you mean you simply don't understand it, or you think it entails some logical inconsistency, or you understand it and realize that it does not entail any logical inconsistency but you think it is not empirically correct? If it's the first or second, you are just failing at math, and if it's the third, you just need to acquaint yourself with the empirical facts. Understand?
>
> Special Relativity: 839 .... Barnpole Dave: 0

In the meantime in the real world, however, the clocks of GPS keep
indicating t'=t, just like all serious clocks always did.

Twin's separate equally.
Should they not share the same clock by that relative equality?
What about length contraction?
What can take away space?
Where is proof that distance leaves?
You don't have measurements...
You are just making it up.

Mitchell Raemsch