# Graphical Derivation of the CADO Equation

You two seem to be enjoying this!
May the farce be with you.

Yep, you can see the result of the calculations. But you've dodged my question, because you can also see no clock (worldline) ever goes backwards.

Right, time does not go backwards on anyone's own worldline. Back when you were claiming it would be a violation of causality for Charlie to calculate Alice's clock ticking backwards, I tried to reassure you that time would not be going backwards for Alice in her own frame. That was what I was trying to point out.

No, re-ordering events doesn't make time tick backwards or forwards. I've been saying that for pages now. Haven't you been paying attention to anything I said?

I do vaguely remember some post where you said that t=40 coming before t=10 does not represent time going backwards. You do realize that 40 is greater than 10, right?

Obviously, yes. Does your Minkowski diagram have worldlines going back in time?

No, but it has two different planes of simultaneity (grey dashed lines). There is a horizontal one for the ground frame, and a diagonal one for the train frame. When Charlie touches down on the ground, he uses the horizontal one and knows the time in the ground frame at x=0 is t=40. When he jumps back on the train, uses the diagonal and knows time in the ground frame at x=0 is t=10.

I am purposefully using the word "knows" here, because I am also purposefully talking about the "time in the ground frame at x=0". No bomb can change time itself, and I wanted you to see that all your nit picking about bombs was for nothing. You're welcome!

It's okay for t=40 being followed by t=10 in the space-like region, as long as it's in order when the events cross through the light-like line into the time-like region.

I'm glad you are "okay" with it, but how about addressing the concept that 40 is greater than 10. Doesn't that mean something in regards to the whole forwards vs. backwards thing? Hmm?

Nope, as we've established before (after much struggle from you), all large enough accelerations cause this effect.

Not only large accelerations, small ones too. Remember, the distance is also important. You might recall an alien named Bikey who only had to push his bicycle to make his "now slice" shift 200 years to the past on earth.

Oh wait, I forgot, you think Bikey's bike has a huge acceleration. And you also think 200 years to the past is not backwards. Never mind, carry on!

Please point me to the worldline associated to that clock in the Minkowski diagram, and demonstrate how it is going backwards.

Let's see, Alice's worldline is in cyan. Seems to be ticking forwards quite nicely, yes. Indeed, that settles it! Alice's clock is always ticking forwards; I'm glad you finally agree!

Talk about intellectual dishonesty. Time does not go backward on anyone's world line. To see the time going from t=40 to t=10, simply look at the two different intersections of the two different planes of simultaneity with the t axis. But according to you, time going from t=40 to t=10 is not backwards anyway, so don't worry about it.

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You two seem to be enjoying this!
May the farce be with you.
If you're not interested in an actual discussion on the topic, then why did you respond in the first place?

Right, time does not go backwards on anyone's own worldline. Back when you were claiming it would be a violation of causality for Charlie to calculate Alice's clock ticking backwards, I tried to reassure you that time would not be going backwards for Alice in her own frame. That was what I was trying to point out.
Please point me to the post where I said that the result of the calculation in itself constitutes a violation of causality. Also, please stop it with the preferred frame again...

I do vaguely remember some post where you said that t=40 coming before t=10 does not represent time going backwards.
Please point me to that post.

You do realize that 40 is greater than 10, right?
You do realize it's disingenuous of you to make that statement? But then again, throughout this thread intellectual honesty hasn't proven your strong point.

No, but it has two different planes of simultaneity (grey dashed lines). There is a horizontal one for the ground frame, and a diagonal one for the train frame. When Charlie touches down on the ground, he uses the horizontal one and knows the time in the ground frame at x=0 is t=40. When he jumps back on the train, uses the diagonal and knows time in the ground frame at x=0 is t=10.
I am purposefully using the word "knows" here, because I am also purposefully talking about the "time in the ground frame at x=0". No bomb can change time itself,
and I wanted you to see that all your nit picking about bombs was for nothing. You're welcome!
Actually, it wasn't. You're corrected a mistake in your language. That it took you so long isn't on me, though.

I'm glad you are "okay" with it, but how about addressing the concept that 40 is greater than 10.
How about showing some intellectual honesty, instead of continually misrepresenting my position?

Doesn't that mean something in regards to the whole forwards vs. backwards thing? Hmm?
How about you demonstrate that the change from 40 to 10 is physically meaningful? You know, that kinda critical point you've been dodging for many posts now? Remember, even though Charlie calculates this, he never sees this. How do you resolve this conflict?

Not only large accelerations, small ones too. Remember, the distance is also important. You might recall an alien named Bikey who only had to push his bicycle to make his "now slice" shift 200 years to the past on earth.

Oh wait, I forgot, you think Bikey's bike has a huge acceleration. And you also think 200 years to the past is not backwards. Never mind, carry on!
How about you show some intellectual honesty and stop misrepresenting what I said?

Talk about intellectual dishonesty. Time does not go backward on anyone's world line. To see the time going from t=40 to t=10, simply look at the two different intersections of the two different planes of simultaneity with the t axis. But according to you, time going from t=40 to t=10 is not backwards anyway, so don't worry about it.
Indeed! This very paragraph of yours in an excellent example of intellectual dishonesty.

But let me respond to the only bit that's the least intellectually dishonest, lest I be accused of ignoring something relevant.
To see the time going from t=40 to t=10, simply look at the two different intersections of the two different planes of simultaneity with the t axis.
As I've said multiple times before: please demonstrate that this effect (re-ordering events in the space-like region) is physically meaningful.

Please point me to the post where I said that the result of the calculation in itself constitutes a violation of causality.

Post #38:
"I think you've just violated causality. " -NotEinstein

You wrote that in response to a post I made where Charlie calculated Alice's age to go back to 10 after he previously calculated it to be 40.

Also, please stop it with the preferred frame again...

I gave you a Minkowski diagram showing that Charlie calculates Alice's time to go from t=40 to t=10. You pointed out that time on Alice's own worldline does not go backward. So when you do it, it's okay. But when I do it, you accuse me of believing in a preferred frame.

It is t=40, x=0 when Charlie touches down in the ground frame, and t=10, x=0 when Charlie jumps back on the train. Obviously that is not from one single inertial frame, but two frames minimum.

Please point me to that post.

Oh sorry, maybe you never actually said that t=40 coming before t=10 was not time going backward. So you agree that t=40 coming before t=10 is time going backward then?

If you answer "no" in your next post, then the post you are asking me to point to is your next post. But of course you will not answer with a yes or no, so that won't happen.

Actually, it wasn't. You're corrected a mistake in your language. That it took you so long isn't on me, though.

So the whole point of the bombs was just to get me to call it "time" instead of "the time displayed on Alice's clock?" Why didn't you just tell me that you refuse to use common conventions of SR thought experiments, and that you would prefer not to use any clocks at all, because of bombs and such? I would have understood (that you were, um, 'eccentric').

How about you demonstrate that the change from 40 to 10 is physically meaningful? You know, that kinda critical point you've been dodging for many posts now?

I already answered that, and you said it wasn't even an answer. You can look up my previous answer if you want to, because I'm not going to repeat it after that reply.

Remember, even though Charlie calculates this, he never sees this. How do you resolve this conflict?

I don't think there are any inherent 'conflicts' in SR. But since you do, maybe you should write a paper on it, and get it peer reviewed. You could be the next Nobel winner.

But let me respond to the only bit that's the least intellectually dishonest, lest I be accused of ignoring something relevant.

As I've said multiple times before: please demonstrate that this effect (re-ordering events in the space-like region) is physically meaningful.

I already answered that, and you said it wasn't even an answer. You can look up my previous answer if you want to, because I'm not going to repeat it after that reply.

So, we still have time t=40, x=0 coming before time t=10, x=0 (as Charlie jumps from the ground onto the train). And you still have not accepted that is time going backwards. And you say that it is not meaningful. And you say that there is a conflict between that and what Charlie sees. So I think we are done here. You just don't accept SR, that's all.

Post #38:
"I think you've just violated causality. " -NotEinstein

You wrote that in response to a post I made where Charlie calculated Alice's age to go back to 10 after he previously calculated it to be 40.
Ah, so a post from before the distinction between calculations, measurements, and observations, so that's not a proper reflection of my position for the past several pages. Also note the "I think".

I'll be more clear:
Please point me to a relevant post where I said that the result of the calculation in itself constitutes a violation of causality.

I gave you a Minkowski diagram showing that Charlie calculates Alice's time to go from t=40 to t=10. You pointed out that time on Alice's own worldline does not go backward.
And my statement is correct: Alice does not. Follow her worldline; does it go from 40 to 10 at any point? No.

My point is that there's a seeming discrepancy between what's happening in reality (the worldlines in the Minkowski diagram) and the result of Charlie's calculations. A discrepancy that I've solved, but you apparently haven't (yet?). My statement makes clear that you still have a problem to solve; it's staring you right in the face, but you refuse to acknowledge it.

So when you do it, it's okay. But when I do it, you accuse me of believing in a preferred frame.
So me pointing out the sheer silliness of your "preferred frame" nonsense is now a bad thing?

So the jump backwards in time is an effect experienced by a remote observer caused purely due to that observer switching inertial frame, and not due to time ticking backwards where Alice is? I can live with that, yes. It's what I've been getting at for the last several pages. I'm glad you're following along!

It is t=40, x=0 when Charlie touches down in the ground frame, and t=10, x=0 when Charlie jumps back on the train. Obviously that is not from one single inertial frame, but two frames minimum.
Yes, obviously.

Oh sorry, maybe you never actually said that t=40 coming before t=10 was not time going backward. So you agree that t=40 coming before t=10 is time going backward then?
Yes, of course I do; it's pretty much the definition, isn't it? I mean, that's what kicked off this entire discussion.

I answered "yes", because that's the position I obviously always held. So where's that post then?

But of course you will not answer with a yes or no, so that won't happen.
A fine case where you are demonstrably wrong.

So the whole point of the bombs was just to get me to call it "time" instead of "the time displayed on Alice's clock?"
That's what you turned it into, which works too. I was aiming more at the fact that you were calling what Charlie calculated as what happened in reality, mainly when we were still talking about Alice getting onto the train. You muddied that by switching scenario's (which you do a lot mid-conversation).

Why didn't you just tell me that you refuse to use common conventions of SR thought experiments,
Actually, if you actually studied SR more carefully, you wouldn't have gotten confused by this at all. But nuance seems to be a thing strange to you.

and that you would prefer not to use any clocks at all, because of bombs and such?
I don't mind using clocks at all. Take the recent example of the opposite site of the earth. Did the bomb destroy the clock? No. So why are you still going on about the confusion you created for yourself after we cleared that up?

I would have understood (that you were, um, 'eccentric').
I'd rather be "eccentric" than have the level of intellectual dishonesty you've displayed in this thread, thank you very much.

I already answered that, and you said it wasn't even an answer. You can look up my previous answer if you want to, because I'm not going to repeat it after that reply.
So, you're not going to address it then, as you before. How very reasonable of you.

I don't think there are any inherent 'conflicts' in SR.
I agree, so there must be a resolution to it. But can you find it? I've only mentioned it multiple times in this thread so far; I'm not sure that was enough times for you.

But since you do,
And here we go with the intellectual dishonesty again.

maybe you should write a paper on it, and get it peer reviewed. You could be the next Nobel winner.
Not going to happen, as I don't live in your fantasy world.

I already answered that, and you said it wasn't even an answer. You can look up my previous answer if you want to, because I'm not going to repeat it after that reply.
So, you're not going to address it then, as you before. How very reasonable of you.

So, we still have time t=40, x=0 coming before time t=10, x=0 (as Charlie jumps from the ground onto the train).
No we don't. Charlie's calculations have that. But no observer has that. Demonstrate that Charlie's calculations about the order of events actually plays out.

Oh wait, you refuse to address anything related to "physical meaning".

And you still have not accepted that is time going backwards.
And you still haven't read the article about the "arrow of time".

And you say that it is not meaningful.
Only about a dozen times now, yes.

And you say that there is a conflict between that and what Charlie sees.
And you agree with that: you stated yourself that Charlie never sees Alice going backwards in time.

So I think we are done here.
Aw come on, you're so close to actually understanding what's going on!

You just don't accept SR, that's all.
Actually, I fully except SR. I'm just more aware of its nuances.

---

This has been quite fascinating so far. I've never engaged with somebody like you before. You show all the signs of a pseudoscience-peddler (intellectual dishonesty, misrepresentations, lack of detailed knowledge on the subject, failure to address issues brought up, selective quoting, etc.), but you're not actually peddling pseudoscience: you're just peddling an unnuanced view of SR. Very interesting. Thank you for this experience!

I'll be more clear:
Please point me to a relevant post where I said that the result of the calculation in itself constitutes a violation of causality.

Okay, so I think we can agree that the results of Charlie's calculations do not constitute a violation of causality in and of themselves. Please correct me if I am wrong on that.

Now, what about if Charlie takes the result of his calculation from when he is on the ground, and concludes that the current time at x=0 must be t=40 at that moment in reality, and what about if Charlie subsequently takes the result of his calculation from when he jumps back on the train, and concludes that the current time at x=0 must be t=10 at that moment in reality? Do those two conclusions, taken together, violate causality, in your opinion?

And my statement is correct: Alice does not. Follow her worldline; does it go from 40 to 10 at any point? No.

In that case, you should accuse yourself of invoking a preferred frame. At least try be consistent. You accuse me of invoking a preferred frame every time I say that time does not go from 40 to 10 in Alice's own frame.

My point is that there's a seeming discrepancy between what's happening in reality (the worldlines in the Minkowski diagram) and the result of Charlie's calculations. A discrepancy that I've solved, but you apparently haven't (yet?). My statement makes clear that you still have a problem to solve; it's staring you right in the face, but you refuse to acknowledge it.

Well your statement is no different than my statement.

"Follow her worldline; does it go from 40 to 10 at any point? No." = NotEinstein has solved an apparent discrepancy (according to NotEinstein).

"Time does not go from 40 to 10 in Alice's own frame." = Neddy Bate is invoking a preferred frame (according to NotEinstein).

At least try to be consistent.

So me pointing out the sheer silliness of your "preferred frame" nonsense is now a bad thing?

Yes, and it has always been a bad thing, because it is false. I don't claim a preferred frame any more than you do. The difference is that I don't falsely accuse you of it.

So the jump backwards in time is an effect experienced by a remote observer caused purely due to that observer switching inertial frame, and not due to time ticking backwards where Alice is? I can live with that, yes. It's what I've been getting at for the last several pages. I'm glad you're following along!

That is what I have been saying, too. But again, you give only yourself credit for it.

Yes, of course I do; it's pretty much the definition, isn't it? I mean, that's what kicked off this entire discussion.

I answered "yes", because that's the position I obviously always held.

Okay, so when Charlie calculates that t=40 comes before t=10, he is calculating something which meets your definition of "time going backwards," right?

Now, what about if Charlie takes the result of his calculation from when he is on the ground, and concludes that the current time at x=0 must be t=40 at that moment in reality, and what about if Charlie subsequently takes the result of his calculation from when he jumps back on the train, and concludes that the current time at x=0 must be t=10 at that moment in reality? Is he concluding something which meets your definition of "time going backwards"?

Actually, if you actually studied SR more carefully, you wouldn't have gotten confused by this at all. But nuance seems to be a thing strange to you.

I am not confused by any of this. You were the one who thought that you could demonstrate a contradiction in SR by putting a pressure pad under Alice, not realizing that t=10, x=0 and t=40, x=0 are different events. You are also the one who claimed GR would be required to 'supersede' the results of SR. And so on.

I don't mind using clocks at all. Take the recent example of the opposite site of the earth. Did the bomb destroy the clock? No. So why are you still going on about the confusion you created for yourself after we cleared that up?

What? Please tell me you have a typo in there or something.

That posting seems to have the exact opposite meaning from what you were actually saying in that recent example. You were the one saying that I could not know the time on the opposite side of the earth right now, because all the clocks might have been blown up by a bomb. But of course time itself cannot be blown up.

I can know the time on the opposite side of the earth because we have a convention of time zones on earth. Likewise, Charlie can know the time at x=0 because SR has its own convention. Charlie knows without any doubt that t=40, x=0 changed to t=10, x=0 between the time he was on the ground, and when he jumped on the train. That is what SR says.

I agree, so there must be a resolution to it. But can you find it? I've only mentioned it multiple times in this thread so far; I'm not sure that was enough times for you.

Maybe its that time never goes backward on Alice's worldline? Maybe its that no one ever sees Alice's clock run backward? Who knows? But of course, you only give yourself credit for it, whatever it is.

No we don't. Charlie's calculations have that. But no observer has that. Demonstrate that Charlie's calculations about the order of events actually plays out.

I tried, with the DVR's, but you rejected it. Charlie has two videos, one showing t=40 x=0 at the moment he was on the ground, and the other showing t=10 x=0 at the moment after he jumped on the train.

And you agree with that: you stated yourself that Charlie never sees Alice going backwards in time.

He doesn't see it with his eyes, no. But he knows he was on the ground before he jumped back on the train. And he knows he set his two DVRs correctly, based on the distances involved. That's all he has to go by, physically, and it matches the SR calculations. What else is there? Please do tell.

Okay, so I think we can agree that the results of Charlie's calculations do not constitute a violation of causality in and of themselves. Please correct me if I am wrong on that.
Of course. Writing t=40 before t=10 on a piece of paper doesn't violate causality, and I never claimed otherwise.

Now, what about if Charlie takes the result of his calculation from when he is on the ground, and concludes that the current time at x=0 must be t=40 at that moment in reality, and what about if Charlie subsequently takes the result of his calculation from when he jumps back on the train, and concludes that the current time at x=0 must be t=10 at that moment in reality? Do those two conclusions, taken together, violate causality, in your opinion?
No, because his second conclusion "overwrites" his first. Charlie will conclude t=40 at two moments; the first time gets invalidated during his jump back on the train. It's easy to see: we agree there's only one coordinate (x=0, t=40). After his switch of inertial frame, when information (light) of the (x=0, t=40) event finally reaches Charlie, which of this two conclusions turns out to be correct? The second one. His first conclusion never pans out (in any physically meaningful way).

In that case, you should accuse yourself of invoking a preferred frame. At least try be consistent.
Erm, my entire point is that you should be consistent. Why is it OK for you to work in preferred frames, but not for me?

You accuse me of invoking a preferred frame every time I say that time does not go from 40 to 10 in Alice's own frame.
Please point me to a post where I did that.
Well your statement is no different than my statement.

"Follow her worldline; does it go from 40 to 10 at any point? No." = NotEinstein has solved an apparent discrepancy (according to NotEinstein).

"Time does not go from 40 to 10 in Alice's own frame." = Neddy Bate is invoking a preferred frame (according to NotEinstein).

At least try to be consistent.
At least you're consistent with the intellectual dishonesty.

And I see you once again dodge the question asked of you. As I just said, at least you're consistent!

Yes, and it has always been a bad thing, because it is false. I don't claim a preferred frame any more than you do.
You don't explicitly claim, no, but you do use it. Go back to when I asked you about the violation of causality: you'll notice that you were abandoning Charlie's point of view for Alice's quite a lot. You preferred Alice's frame. I pointed that out multiple times to you.

The difference is that I don't falsely accuse you of it.
Incorrect; the accusation isn't false. Thus I'm also not falsely accusing you of it.

That is what I have been saying, too. But again, you give only yourself credit for it.
Notice how I'm using the word "effect", and I'm explicitly putting its experience by the remote user. This crucially means no traveling backwards in time happens; there are no clicks ticking backwards. That's what I've been saying all along.

I give myself credit for the nuance which resolves the conflict I pointed out. You can't honestly claim credit for that, because you can't even see the conflict!

Okay, so when Charlie calculates that t=40 comes before t=10, he is calculating something which meets your definition of "time going backwards," right?
If this calculation bears out in reality. Charlie could also be smart, know a little bit about SR, and realize his switching of inertial frame invalidates the results of his first calculation.

Oh, and I find it funny that you completely ignore that you were wrong with your entire silly "But of course you will not answer with a yes or no, so that won't happen.". See, that's what happens when you put words in other people's mouths: you might be incorrect, and look a bit silly.

Now, what about if Charlie takes the result of his calculation from when he is on the ground, and concludes that the current time at x=0 must be t=40 at that moment in reality, and what about if Charlie subsequently takes the result of his calculation from when he jumps back on the train, and concludes that the current time at x=0 must be t=10 at that moment in reality?
I invite you to demonstrate that the results of Charlie's first calculation still hold after his switch of inertial frame. I'm pretty sure you'll find that even Charlie disagrees with you.

Is he concluding something which meets your definition of "time going backwards"?
Yes. He's quite literally claiming there's a place in the universe where time went from t=40 to t=10, which is time going backwards.

Luckily for us, reality doesn't conform to misinterpretations of calculations.

I am not confused by any of this.

You were the one who thought that you could demonstrate a contradiction in SR
False; I never claimed that. More intellectual dishonesty from you.

by putting a pressure pad under Alice, not realizing that t=10, x=0 and t=40, x=0 are different events.
False; I've always claimed that. More intellectual dishonesty from you.

You are also the one who claimed GR would be required to 'supersede' the results of SR.
And it does. More intellectual dishonesty from you.

And so on.
Yes, this entire thread is turning into more intellectual dishonesty from you.

What? Please tell me you have a typo in there or something.
Typo? I don't see any?

That posting seems to have the exact opposite meaning from what you were actually saying in that recent example.
Sure; because you are constantly misinterpreting my posts, it might seem that way to you. In reality, it's perfectly consistent with it.

You were the one saying that I could not know the time on the opposite side of the earth right now,
Right, because it's invalid to talk about "the time on the opposite side of the earth right now" if there is no "the opposite side of the earth right now".

because all the clocks might have been blown up by a bomb.

But of course time itself cannot be blown up.
True; and I never claimed otherwise. More intellectual dishonesty from you.

I can know the time on the opposite side of the earth because we have a convention of time zones on earth.
No, you don't know. You can conclude what it would be, assuming the opposite side of the earth still exists as you expect it to.

It's fascinating to see you continually get and then un-get the point.

Likewise, Charlie can know the time at x=0 because SR has its own convention.
Sure, but as soon as Charlie makes statement like "Alice's jumps onto the train" without information about it having been able to reach him, he's wrong (or rather: making assumptions).

Charlie knows without any doubt that t=40, x=0 changed to t=10, x=0 between the time he was on the ground, and when he jumped on the train.
Yep. I fully agree. But it's not that time ticked backwards; it's that his second calculation invalidates his first.

That is what SR says.
And I never claimed otherwise.

Maybe its that time never goes backward on Alice's worldline?
There, right there! Do you see it? We were talking about Charlie, and you sneakily switch to Alice. There's your preferred frame for you!

Maybe its that no one ever sees Alice's clock run backward?
So now you're arguing Charlie's calculations are incorrect? I thought we agreed they weren't?

Who knows?
Clearly, you don't, and you seems to struggle to even understand the conflict. But as we've seen progress from you along the way (and several relapses), you might be able to reach a resolution! Just keep on trying; you'll get there!

But of course, you only give yourself credit for it, whatever it is.
Well, I can give you credit for "forcing" me to think this through, certainly. But I can't give you credit for the resolution, because you didn't (directly) help with that at all. Heck, you don't even accept there is a conflict!

I tried, with the DVR's, but you rejected it.
No, I didn't. I just pointed out that the DVR's as observers also don't see any backwards-in-time stuff, and that it only proves Charlie's calculations aren't incorrect. It's not evidence of backwards-in-time ticking clocks, because that's quite literally not on tape!

Charlie has two videos, one showing t=40 x=0 at the moment he was on the ground, and the other showing t=10 x=0 at the moment after he jumped on the train.
And now use your Minkowski diagram: what conclusions about the first DVR's starting moment of recording does Charlie draw?

He doesn't see it with his eyes, no. But he knows he was on the ground before he jumped back on the train. And he knows he set his two DVRs correctly, based on the distances involved. That's all he has to go by, physically, and it matches the SR calculations.
"That's all he has to go by, physically"? You quite literally three sentences before said: "He doesn't see it with his eyes, no.". Direct observation doesn't count as physically relevant?

Oh boy, would I like to see your definition of physical relevance!

What else is there? Please do tell.
Nothing else. You have two pieces of information: the results from Charlie's calculations, and the results from Charlie's observations. One says Alice's clock tick backwards, the other doesn't. I guess outright rejecting direct observational evidence is also a way to resolve the conflict. That actually matches the pseudoscience-peddling profile quite nicely.

If you're not interested in an actual discussion on the topic, then why did you respond in the first place?
Have encountered the CADO equation before and know it's an idea based on a sloppy interpretation of the twin scenario. It's interesting to see if people buy into the idea.

Have encountered the CADO equation before and know it's an idea based on a sloppy interpretation of the twin scenario.
Ooh, interesting! Can you give more details?

It's interesting to see if people buy into the idea.
Well, I haven't bought into it (yet?), because I haven't checked the details. I did encounter sloppy and lacking definitions, but Mike said he'd fix those.

No, because his second conclusion "overwrites" his first. Charlie will conclude t=40 at two moments; the first time gets invalidated during his jump back on the train. It's easy to see: we agree there's only one coordinate (x=0, t=40). After his switch of inertial frame, when information (light) of the (x=0, t=40) event finally reaches Charlie, which of this two conclusions turns out to be correct? The second one. His first conclusion never pans out (in any physically meaningful way).

Thank you, at least this is a some type of explanation. All this time I have been trying to understand how you could think that time at x=0 going from t=40 to t=10 would not be time going backwards. But if the t=10 "overwrites" the t=40 then we can safely leave out the word "backwards" and just deal with the results. I'm tempted to just agree with you and leave it at that, but unfortunately, there is one small aspect of this explanation that bothers me. From further down in your post:

I invite you to demonstrate that the results of Charlie's first calculation still hold after his switch of inertial frame. I'm pretty sure you'll find that even Charlie disagrees with you.

Of course the first result t=40, x=0 would not hold true from the train frame, which is where Charlie is after he jumps on the train. The train frame is where the second result t=10, x=0 holds true.

However, the first result t=40, x=0 does still hold true from the ground frame, even after Charlie jumps back on the train. That is what Charlie demonstrated when he set the ground-DVR to record with a 34.64 year delay, and obtained the broadcast from t=40, x=0.

That happened after Charlie jumped on the train. So your 'overwrite' idea is nice, from Charlie's point of view, but you can't just make the first result go away altogether.

Yes. He's quite literally claiming there's a place in the universe where time went from t=40 to t=10, which is time going backwards.

But you don't believe time goes backwards, so you must not agree with one or the other part of this:

1. Now, what about if Charlie takes the result of his calculation from when he is on the ground, and concludes that the current time at x=0 must be t=40 at that moment in reality,

2. and what about if Charlie subsequently takes the result of his calculation from when he jumps back on the train, and concludes that the current time at x=0 must be t=10 at that moment in reality?

Can't you just waive your magic wand and say that the second result overwrites the first? Or are we back to square one, with time going backwards again?

PS:
I apologize for not addressing every part of all of your posts. I feel like there have been way too many side issues, and our posts have been getting much longer than they need to be. I think that the only issues that we really need to address now are covered in this post.

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Thank you, at least this is a some type of explanation. All this time I have been trying to understand how you could think that time at x=0 going from t=40 to t=10 would not be time going backwards.
And more misrepresentations.

But if the t=10 "overwrites" the t=40 then we can safely leave out the word "backwards" and just deal with the results. I'm tempted to just agree with you and leave it at that, but unfortunately, there is one small aspect of this explanation that bothers me. From further down in your post:

Of course the first result t=40, x=0 would not hold true from the train frame, which is where Charlie is after he jumps on the train. The train frame is where the second result t=10, x=0 holds true.

However, the first result t=40, x=0 does still hold true from the ground frame, even after Charlie jumps back on the train. That is what Charlie demonstrated when he set the ground-DVR to record with a 34.64 year delay, and obtained the broadcast from t=40, x=0.

That happened after Charlie jumped on the train. So your 'overwrite' idea is nice, from Charlie's point of view, but you can't just make the first result go away altogether.
Well, good thing I never claimed that. In fact, I claimed the very opposite! But you'd know that, if you cared to remember.

But you don't believe time goes backwards,
Show me any evidence (measurements, observations) that it ever did. I'm talking actual, empirical data.

I'll wait.

so you must not agree with one or the other part of this:

1. Now, what about if Charlie takes the result of his calculation from when he is on the ground, and concludes that the current time at x=0 must be t=40 at that moment in reality,

2. and what about if Charlie subsequently takes the result of his calculation from when he jumps back on the train, and concludes that the current time at x=0 must be t=10 at that moment in reality?
(I see that this is a copy-paste from your post #207.)

Can't you just waive your magic wand
No, because I don't have any. Do you?

and say that the second result overwrites the first?

Or are we back to square one, with time going backwards again?
I always objected to time going backwards, remember? So perhaps you're back to square one, not me.

I see you've once again skipped over the preferred frame stuff...

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Very interesting behavior. This time you got close to understanding, but then through repeating you own old stuff back at yourself, you managed to veer off-course and went back the way you came. And then you of course projected that failure onto me. It seems you'll do anything (subconsciously?) to avoid resolving the conflict, or admitting the failure to do so is on you.

Huh? Sorry, I don't understand.

NotEinstein said:
I invite you to demonstrate that the results of Charlie's first calculation still hold after his switch of inertial frame. I'm pretty sure you'll find that even Charlie disagrees with you.

Charlie's first calculation still holds true (in the ground frame) even after Charlie switches back to the train frame.

So all I want to know is how you can claim that his second calculation "overwrites" his first calculation?

That is the only thing holding me back from agreeing with your "overwrites" idea.

If two clocks separate and reunite, is there a difference in accumulated time for the clocks?

Making use of the three clock 'twin' scenario, fig.1 shows the physical setup that corresponds to fig.2 a graphical representation of ct vs x.

A sends a (blue) narrow beam of light after B leaves A at .6c Emission occurs at A2, and reaches B at A5. C is moving at .6c toward A in the opposite direction and receives the same clock image at A5. As C passes B, the C-clock is set to the B4 clock time. The C inbound trip is the mirror image of the outbound trip. This scenario avoids accelerated motion and the fictitious 'time jump. Applying time dilation to each segment of the closed course results in the B+C history accumulates less time than the A history.

The clock synch convention with its axis of simultaneity, distorts the time coordinates of events.

If two clocks separate and reunite, is there a difference in accumulated time for the clocks?

Making use of the three clock 'twin' scenario, [...]
[...]
This scenario avoids accelerated motion and the fictitious 'time jump. Applying time dilation to each segment of the closed course results in the B+C history accumulates less time than the A history.
[...]

In the three "twin" scenario (with each "twin" being perpetually inertial), none of the "twins" are surprised about the outcome of the scenario, so there is no apparent paradox to resolve. The original scenario does produce an apparent paradox (when the unwarranted assumption is made that nothing of interest about the two twins' ages can possibly happen in a single instant). That apparent paradox can be resolved only by learning that the instantaneous turnaround of the traveling twin causes the home twin's age to instantaneously increase (according to the traveler) by just the amount needed to eliminate any surprise at the reunion.

nobel prize.

In the three "twin" scenario (with each "twin" being perpetually inertial), none of the "twins" are surprised about the outcome of the scenario, so there is no apparent paradox to resolve. The original scenario does produce an apparent paradox (when the unwarranted assumption is made that nothing of interest about the two twins' ages can possibly happen in a single instant). That apparent paradox can be resolved only by learning that the instantaneous turnaround of the traveling twin causes the home twin's age to instantaneously increase (according to the traveler) by just the amount needed to eliminate any surprise at the reunion.
No one is expecting a surprise.
The discontinuous speed profile at reversal is the problem. The clock synch convention is based on continuous inertial motion, and that does not exist at reversal.
Why develop a theory to correct a mistake?

The discontinuous speed profile at reversal is the problem.

Just replace the discontinuous speed profile (v to -v in zero time) with a continuous speed profile (v to -v in an arbitrarily small amount of time). Now the speed profile is continuous.

The clock synch convention is based on continuous inertial motion, and that does not exist at reversal.

For consistency, we must assume that after the reversal (turn-around), when the speed is once again constant (inertial motion), that the clock synch convention has been re-applied. Otherwise we would be left with multiple clock synch conventions.

Why develop a theory to correct a mistake?

SR was not a developed to correct a mistake, if that is what you mean.

Just replace the discontinuous speed profile (v to -v in zero time) with a continuous speed profile (v to -v in an arbitrarily small amount of time). Now the speed profile is continuous.

For consistency, we must assume that after the reversal (turn-around), when the speed is once again constant (inertial motion), that the clock synch convention has been re-applied. Otherwise we would be left with multiple clock synch conventions.

SR was not a developed to correct a mistake, if that is what you mean.
No one said that. The subject is the CADO concept. What's missing is a continuous curve connecting the outbound and inbound profiles.
That would require a single wandering twin to continuously re-synch the clocks for the duration of the reversal.
The jump is a fictitious, man-made problem resulting from a poorly formed pictorial representation.
Correct the graphics and the missing time issue disappears!