Graphical Derivation of the CADO Equation

[NotEinstein]

I believe we two are in agreement that actual backwards time travel, from the pov of either of two observers in arbitrary relative motion, never happens. Concluding otherwise via naive interpretation of instantaneous gradients on a space-time diagram is simply unwarranted extrapolation.
Sadly, not only Brian Greene but even Roger Penrose got to take the naive interpretation of such diagrams too seriously. About the only situation they can be considered to be accurately reflecting reality is for the case of uniform relative speed. Introduce any nonuniformity, and all you get from such, if trying to ascertain what's really happening 'now' over 'there', is paradox. Which never occurs in nature actually. Differentials and integrals are related but different animals. It's the closed path integral that unambiguously matters re 'reality'. An exception is the scenario given back in #30. Which though still falls under the case of uniform relative speed.

I think I'm now supposed to like your post because obviously you are right because you agree with me (post #249), then call you brilliant (post #253), and then you have to thank me for calling you that (post #257), all while ignoring any counter arguments, requests for evidence, or issues raised.

 

[Q-reeus]

I think I'm now supposed to like your post because obviously you are right because you agree with me (post #249), then call you brilliant (post #253), and then you have to thank me for calling you that (post #257), all while ignoring any counter arguments, requests for evidence, or issues raised.

A truly magnificent, astute, and insightful summary worthy of unfettered praise! Nothing left to add except - well put indeed!

 

[NotEinstein]

A truly magnificent, astute, and insightful summary worthy of unfettered praise! Nothing left to add except - well put indeed!

<insert shoulder-patting and high-fiving here>

 

[Neddy Bate]

So, to summarise:

NotEinstein and Q-reeus both seem to be in agreement that they think the results of SR are wrong, in a scenario in which flat spacetime is a given premise. Or, if they do think the results are correct, then those results cannot be taken at face value. Something like, "Yes, t=40 x=0 is followed by t=10 x=0, but that does not mean the time went backward, because we can explain it in some other way."

Meanwhile, Mike Fontenot and I both seem to be in agreement that we think the results of SR are correct in flat spacetime. And that those results can be taken at face value. Something like, "If t=40 x=0 is followed by t=10 x=0 then there is no other meaning that we possibly ascribe to this, as it is not our responsibility to change the meanings of variables or coordinates just for the sake of trying to provide some other explanation that suits our sensibilities better."

 

[Q-reeus]

So, to summarise:

NotEinstein and Q-reeus both seem to be in agreement that they think the results of SR are wrong, in a scenario in which flat spacetime is a given premise. Or, if they do think the results are correct, then those results cannot be taken at face value. Something like, "Yes, t=40 x=0 is followed by t=10 x=0, but that does not mean the time went backward, because we can explain it in some other way."

Meanwhile, Mike Fontenot and I both seem to be in agreement that we think the results of SR are correct in flat spacetime. And that those results can be taken at face value. Something like, "If t=40 x=0 is followed by t=10 x=0 then there is no other meaning that we possibly ascribe to this, as it is not our responsibility to change the meanings of variables or coordinates just for the sake of trying to provide some other explanation that suits our sensibilities better."

An unphysical jump in *inferred* age of home twin as determined by traveling twin's reckoning from a Minkowski chart, just after a sudden acceleration, just never happens when Doppler shift method is used. There, it's bleeding obvious all that happens is a jump in the relative aging *rates* (which are always positive). The home twin doesn't observe this changed rate 'instantaneously' as does the traveling twin, but only after a lengthy interval.
And once again - any *inferred* unphysical jump backwards in time for home twin a la Minkowski chart extrapolation, always dissolves/resolves at end of round trip into accumulated relative aging. Never will one have the home twin being younger than at start of round trip. SR.

 

[Neddy Bate]

An unphysical jump in *inferred* age of home twin as determined by traveling twin's reckoning from a Minkowski chart, just after a sudden acceleration, just never happens when Doppler shift method is used. There, it's bleeding obvious all that happens is a jump in the relative aging *rates* (which are always positive). The home twin doesn't observe this changed rate 'instantaneously' as does the traveling twin, but only after a lengthy interval.
And once again - any *inferred* unphysical jump backwards in time for home twin a la Minkowski chart extrapolation, always dissolves/resolves at end of round trip into accumulated relative aging. Never will one have the home twin being younger than at start of round trip. SR.

In standard SR, the relative aging *rates* are considered to be 1/gamma, reciprocally. In other words, for the case of gamma=2, on the outbound leg of the trip, the traveling twin says the stay-home twin's aging rate is 1/2 his own, and on the return leg of the trip the traveling twin says the stay-home twin's aging rate is 1/2 his own as well.

If you consider only these rates, and not the the change in simultaneity at the turn-around point (shown on a Minkowski diagram), then you would have the traveling twin concluding that the stay-home twin's age would be younger than himself upon his return.

Of course we know that is not correct, because the stay-home twin must end up older than the traveling twin in the end. Please consider that when you defer to the Doppler method, your "aging rates" are not 1/gamma, reciprocally, on both legs of the trip. In that way you are deviating from standard SR.

It is true that things would be different if you only consider what the two twins see with their eyes. But that is not what SR equations are meant to describe.

 

[Q-reeus]

In standard SR, the relative aging *rates* are considered to be 1/gamma, reciprocally. In other words, for the case of gamma=2, on the outbound leg of the trip, the traveling twin says the stay-home twin's aging rate is 1/2 his own, and on the return leg of the trip the traveling twin says the stay-home twin's aging rate is 1/2 his own as well....

Wrong. You are confused as to the basics of the Doppler shift analysis. One has net redshifting outbound, and net blueshifting inbound. The latter to a greater degree than the former - despite a common transverse i.e. 'intrinsic' time dilation factor for both legs of 1/gamma. See:
https://en.wikipedia.org/wiki/Twin_paradox#What_it_looks_like:_the_relativistic_Doppler_shift
Back in #91 (not #90 I referenced to earlier) I gave links to a past thread that went into the correct vs incorrect picture. See #24 there for a summary:
http://www.sciforums.com/threads/traveling-toward-a-light-source.160434/page-2#post-3496815

 

[NotEinstein]

NotEinstein and Q-reeus both seem to be in agreement that they think the results of SR are wrong, in a scenario in which flat spacetime is a given premise.

Please stop lying: you know that I believe that the results of SR are not wrong.

Or, if they do think the results are correct, then those results cannot be taken at face value.

False. The results can be taken at face value; you just have to be very carefully in interpreting them correctly.

Something like, "Yes, t=40 x=0 is followed by t=10 x=0, but that does not mean the time went backward, because we can explain it in some other way."

If it can be explain in some other way, then doesn't that indeed mean that time may not have gone backwards?

Meanwhile, Mike Fontenot and I both seem to be in agreement that we think the results of SR are correct in flat spacetime.

So do I.

And that those results can be taken at face value.

So do I.

Something like, "If t=40 x=0 is followed by t=10 x=0 then there is no other meaning that we possibly ascribe to this, as it is not our responsibility to change the meanings of variables or coordinates just for the sake of trying to provide some other explanation that suits our sensibilities better."

That's the entire thing: the conclusion that Alice travelled back in time must mean that you have misinterpreted something, because that's obviously not what SR predicts. It's impressive the lengths you go through to maintain ignorance.

 

[Neddy Bate]

Wrong. You are confused as to the basics of the Doppler shift analysis. One has net redshifting outbound, and net blueshifting inbound. The latter to a greater degree than the former - despite a common transverse i.e. 'intrinsic' time dilation factor for both legs of 1/gamma. See:
https://en.wikipedia.org/wiki/Twin_paradox#What_it_looks_like:_the_relativistic_Doppler_shift
Back in #91 (not #90 I referenced to earlier) I gave links to a past thread that went into the correct vs incorrect picture. See #24 there for a summary:
http://www.sciforums.com/threads/traveling-toward-a-light-source.160434/page-2#post-3496815

SR actual time dilation rates do not depend on whether the relative movement is toward or away. The actual time dilation rates are 1/gamma in both cases. This is basic SR.

You are talking about the Doppler effect, which is only an effect on the receiver's end, not the transmitter's end. When you hear a passing train horn, the pitch sounds higher when the train is approaching you, and then sounds lower pitch after it passes you. From that, you cannot conclude that the pitch of the train's horn is actually changing like that. That has nothing to do with time dilation rates.

You are discussing a different topic. Even NotEinstein has not been arguing that the Doppler effect shows that the aging rates are not really 1/gamma. So you are not even agreeing with him, you are in left field on your own.

 

[Neddy Bate]

Please stop lying: you know that I believe that the results of SR are not wrong.

You literally said, "Which means that if Charlie says that Alice's clock shows t=10, then t=40, and then t=10, he is wrong." Those are the results of SR, and you are literally saying they are wrong.

If it can be explain in some other way, then doesn't that indeed mean that time may not have gone backwards?

Maybe, but no one has done so yet. You came the closest by saying that maybe when t=40 is followed by t=10, the t=10 somehow "overwrites" the t=40. But even if that is somehow the case, you still have t=40 coming before t=10, and so the problem (if it is one) has not really been explained in any other way.

That's the entire thing: the conclusion that Alice travelled back in time must mean that you have misinterpreted something, because that's obviously not what SR predicts. It's impressive the lengths you go through to maintain ignorance.

You do not know that is "obviously not what SR predicts." The variables are all defined beforehand, as follows:

t = the time in the ground frame at location x=0 (which is where we imagine Alice to be stationary in the ground frame)
t' = the time in the train frame at location x'=0 (which is where we imagine Charlie to be stationary in the train frame)

1) Before jumping off the train, Charlie's simultaneity is such that his own t'=20 and Alice's t=10 are both simultaneously happening.

2) After jumping off the train, Charlie's simultaneity is such that his own t'=20 and Alice's t=40 are both simultaneously happening.

3) After jumping on the train, Charlie's simultaneity is such that his own t'=20 and Alice's t=10 are both simultaneously happening.

There is no place at all where the definition of t changes, ever. So t is still the time at location x=0 (which is where we imagine Alice to be stationary in the ground frame) the whole way through 1) 2) and 3). This is what I mean by taking it at face value. There is no need to add some qualifier, such as that Charlie does not see the clock going backwards with his eyes. That is true, and interesting, but does not change the outcome.

 

[Q-reeus]

SR actual time dilation rates do not depend on whether the relative movement is toward or away. The actual time dilation rates are 1/gamma in both cases. This is basic SR.

You are talking about the Doppler effect, which is only an effect on the receiver's end, not the transmitter's end. When you hear a passing train horn, the pitch sounds higher when the train is approaching you, and then sounds lower pitch after it passes you. From that, you cannot conclude that the pitch of the train's horn is actually changing like that. That has nothing to do with time dilation rates.

You are discussing a different topic. Even NotEinstein has not been arguing that the Doppler effect shows that the aging rates are not really 1/gamma. So you are not even agreeing with him, you are in left field on your own.

Unfortunately you still do not understand the conceptual basis for Doppler shift analysis. There is nothing illusory about it. It really does faithfully present the relative aging rates as seen from either twin's proper frame. The explanation for round trip difference lies in the unsymmetric durations of redshift vs blueshift for home twin.
The method is rigorously correct since it relies only on comparing absolute Doppler pulse counts for the two reunited twins.
And I'm not alone - at least whoever authored that piece in the linked Wiki article agrees with me. And of course the same argument is given in many other articles and by various authors who actually understand the subtleties of SR better than some here do.

As for being a different topic, CADO itself has been shown, back in #30, to be less than what's claimed by it's author. Supposed jumps backward in time is the fork discussed here. And Doppler analysis says such unphysical 'backwards time jumps' are what is illusory.

 

[NotEinstein]

You literally said, "Which means that if Charlie says that Alice's clock shows t=10, then t=40, and then t=10, he is wrong." Those are the results of SR, and you are literally saying they are wrong.

Erm, you even agreed to that? We agreed that no observer (including Charlie) ever sees Alice's clock tick/jump backwards.

Maybe, but no one has done so yet. You came the closest by saying that maybe when t=40 is followed by t=10, the t=10 somehow "overwrites" the t=40. But even if that is somehow the case, you still have t=40 coming before t=10, and so the problem (if it is one) has not really been explained in any other way.

Ah, so you agree there is a conflict, and that the only solution you see is travelling back in time, something that clearly isn't accepted as fact in the scientific community.

You do not know that is "obviously not what SR predicts." The variables are all defined beforehand, as follows:

t = the time in the ground frame at location x=0 (which is where we imagine Alice to be stationary in the ground frame)
t' = the time in the train frame at location x'=0 (which is where we imagine Charlie to be stationary in the train frame)

Note that your definitions are missing the frame from which they are to be calculated/measured/observed.

1) Before jumping off the train, Charlie's simultaneity is such that his own t'=20 and Alice's t=10 are both simultaneously happening.

Where t is calculated from Charlie's frame at that moment; call that inertial frame Charlie1.

2) After jumping off the train, Charlie's simultaneity is such that his own t'=20 and Alice's t=40 are both simultaneously happening.

Let's call this frame Charlie2.

3) After jumping on the train, Charlie's simultaneity is such that his own t'=20 and Alice's t=10 are both simultaneously happening.

Let's call this frame Charlie3.

There is no place at all where the definition of t changes, ever.[/QUOTE]
The definition doesn't change, except that it does, due to the fact you've overlooked that you've forgotten to specify the frame. Unfortunately, this oversight in your definition introduces issues, because: Charlie1 != Charlie2, and Charlie2 != Charlie3. If Charlie's jumping is instantaneous, and he spends zero time in Charlie2, then Charlie1 == Charlie3, but otherwise there is a spatial coordinate shift between them.

Now, for any direct comparison of the obtained values of t to be meaningful in any way, the frames need to be the same. You'll notice that indeed when they are, all calculations work out fine. It's only when the inertial frame is switched that issues pop up. Your definition of t contains frame-dependency. Its definition might not change, but its physical meaning certainly does.

So t is still the time at location x=0 (which is where we imagine Alice to be stationary in the ground frame) the whole way through 1) 2) and 3). This is what I mean by taking it at face value.

"The results can be taken at face value; you just have to be very carefully in interpreting them correctly."

There is no need to add some qualifier, such as that Charlie does not see the clock going backwards with his eyes.

Except that it pointed out the conflict.

That is true, and interesting, but does not change the outcome.

True, but no outcome needs to be changed? That was what the "overwrites" word is all about: because Charlie changes to another inertial frame, the previous calculation no longer is applicable to his situation. This is also why the calculation is still correct: it still holds in the frame for which it was calculated (that's what your DVR's demonstrated, although this was never in question). Due to this frame-dependency built into your definition, these effects happen when changing the inertial frame used. But, as can be seen in the Minkowski diagram, these effects do not affect remote reality, nor can they, due to them being superluminal information transfer if that were the case.

 

[Q-reeus]

SR actual time dilation rates do not depend on whether the relative movement is toward or away. The actual time dilation rates are 1/gamma in both cases. This is basic SR....

'Actual' time dilation rates are always relative to a given proper reference frame. Uniform circular motion of traveling twin as per #30. The instantaneous relative motions are always reciprocal, so your argument implies clocks for both traveling twin B and home twin A tick at equal retarded rates 1/gamma, as measured from each other's frame. But it's not so. In fact that retarded rate 1/gamma only applies to B's clock as measured from A's frame. In B's frame, A's measured clock rate is increased by factor gamma.
If you care to work it through, this is entirely consistent with Doppler shift analysis. Whereas you will have a very hard time reconciling what I quoted of you above, with circular motion case.

Regarding the ambulance siren acoustic analogy, yes it's true the changes in pitch do not reflect actual changes in siren rates in either ambulance or stationary observer frames. It's also the case there is an asymmetry in duration of Doppler frequency for analogous outbound/inbound ambulance trip, as registered in stationary observer frame. But there is a fundamental difference - sound has a preferred rest frame, light does not. Which difference shows in that the absolute round-trip Doppler counts are equal in acoustic, ambulance case, but unequal in SR traveling twin case.

 

[Neddy Bate]

Unfortunately you still do not understand the conceptual basis for Doppler shift analysis. There is nothing illusory about it.

From your own link:

Simultaneity in the Doppler shift calculation
It may be difficult to see where simultaneity came into the Doppler shift calculation, and indeed the calculation is often preferred because one does not have to worry about simultaneity. As seen above, the ship twin can convert his received Doppler-shifted rate to a slower rate of the clock of the distant clock for both red and blue images. If he ignores simultaneity, he might say his twin was aging at the reduced rate throughout the journey and therefore should be younger than he is. He is now back to square one, and has to take into account the change in his notion of simultaneity at the turnaround. The rate he can calculate for the image (corrected for Doppler effect) is the rate of the Earth twin's clock at the moment it was sent, not at the moment it was received. Since he receives an unequal number of red and blue shifted images, he should realize that the red and blue shifted emissions were not emitted over equal time periods for the Earth twin, and therefore he must account for simultaneity at a distance.

Underlines added by me. The actual time dilation rate is 1/gamma on both the outward leg, and the inward leg of the journey. We are not talking about a circular journey, this is a straight path outward, a turnaround, and a straight path back.

The Doppler shifted rates do not represent the actual time dilation rates, as they need to be converted as described in your own link. Notice also that your link never says that the Doppler approach supercedes the Minkowski diagrams in any way. The Minkowski diagrams all show the stay-home-twin's time changing when the traveling-twin turns around, the very thing you are denying.

And I'm not alone - at least whoever authored that piece in the linked Wiki article agrees with me.

No they don't, they agree with me. Read your own link again.

 

[Neddy Bate]

Alright I'm getting bored with this, so let's cut to the chase:

Now, for any direct comparison of the obtained values of t to be meaningful in any way, the frames need to be the same.

The solution to the basic twin "paradox" (with a straight journey out, a turnaround, and a straight journey back) must take into consideration that the traveling twin is in a different frame before the turnaround, compared to after the turnaround.

In the twin-paradox-version of the case we've been discussing, the traveling twin calculates that the stay-home twin's time changes from t=10 x=0 to t=70 x=0 during the very brief turnaround.

Part of your argument is that the t=10 and the t=70 cannot even be compared, because they were calculated from different frames. But there would be no resolution to the twin "paradox" if it was forbidden to consider that the t=10 changes to the t=70.

Granted this is not a 'backwards' change in time, but it is still something you have argued cannot be done, on the grounds that the traveling twin calculated the two different times from two different frames. Yet that is the whole reason it is important for them to be compared!

 

[Mike_Fontenot]

It might help to state clearly that even in the idealized instantaneous velocity changes scenarios, we are still really thinking of a progression of events by the traveler: we still say that at the turnaround, the traveler is initially moving away from the home twin, and then is moving toward the home twin. So it might help to realize that the "instantaneous" velocity changes are actually changes that occur over an infinitesimal, but non-zero amount of time.

 

[NotEinstein]

Alright I'm getting bored with this, so let's cut to the chase:

Yeah, let's. Your dancing around the issues has been fun, but all good things must come to an end.

The solution to the basic twin "paradox" (with a straight journey out, a turnaround, and a straight journey back) must take into consideration that the traveling twin is in a different frame before the turnaround, compared to after the turnaround.

In the twin-paradox-version of the case we've been discussing, the traveling twin calculates that the stay-home twin's time changes from t=10 x=0 to t=70 x=0 during the very brief turnaround.

Part of your argument is that the t=10 and the t=70 cannot even be compared, because they were calculated from different frames. But there would be no resolution to the twin "paradox" if it was forbidden to consider that the t=10 changes to the t=70.

Why are you claiming that's forbidden? Please stop making up nonsense.

Granted this is not a 'backwards' change in time, but it is still something you have argued cannot be done,

Point me to the discontinuity in the wordline of Alice in the Minkowski diagram, where her time jumps from t=10 to t=70 without touching any of the times in between (assuming instant turnaround). Can't do it, can you?

And with a very brief (non-instant) turnaround: explain to me how it is possible that her clock's tickrate "suddenly accelerates" instantly due to Charlie making his turnaround many many lightyears away.

The calculations are correct, but the interpretation that Alice jumps forward in time from t=10 to t=70 due to Charlie's turnaround is wrong.

on the grounds that the traveling twin calculated the two different times from two different frames.

If you do that comparison between quantities that are frame-dependent, that results in some effects that are unphysical. (With the risk of you getting confused and side-tracked again: it's quite similar to pseudo-forces, in that regard.) Yet the calculations are correct. That was the entire conflict you refused to see for the longest time.​

Yet that is the whole reason it is important for them to be compared!

Yes, exactly. Now if only you addressed the conflict you just pointed out... Without introducing unproven things such as time travel, obviously. I mean, all the scientists in the field apparently manage that.

 

[NotEinstein]

I think you already agreed that Charlie's t=40 calculation is correct, and his subsequent t=10 calculation is also correct.

Yes, I've done so multiple times. Now that your memory is refreshed, care to actually address what I said?

I think Charlie would be well aware that he changed frames.

In general, yes. But this frame change wasn't incorporated into the first calculation, so if it turns out that's crucial information, his first calculation doesn't apply anymore after his frame switch. It's "overwritten".

That is the only reason he would say that t=40 x=0 was followed by t=10 x=0 in the first place.

Technically correct, but this has not been used in any calculations: all that was used is his change in velocity with respect to Alice.

Of course he could also say that the t=10 overwrites the t=40 but that does not mean the t=40 was wrong in any way.

And I've never claimed otherwise.

So, how about you now address what I said?

In both cases, the t variable represents the time in the ground frame at x=0.

False; this is an incomplete definition. You yourself just called it a frame-dependent quantity; so where's the frame dependence in this description of it?

Let me correct it: the t variable represents the time in the ground frame at x=0, as calculated, measured, or observed by Charlie.

Even if t=10 overwrites t=40, that does not change the fact that t=40 came before t=10.

Please go back and re-read our "overwrites" discussion; you appear to have forgotten about that as well.

No, not at all. It is special relativity which tells us that t=40 came before t=10 in the case of Charlie's acceleration changing his frame.

Then what was your comment about accelerations about?

The question is what it means for Charlie.

No, we're trying to figure out if Alice is travelling back in time, not Charlie. Or are you suggesting a superluminal form of remote time travel, because Charlie's change of frame instantly makes Alice "go back in time".

And if you are arguing that remote things can travel back in time, but those things never experience it themselves, there's no way to send information into the past that way, and it can never be observed or measured, we're back to the "physically meaningfulness" discussion which you previously bailed out on.

Charlie is the one who says t=40 x=0 was followed by t=10 x=0.

Right, Charlie is claiming Alice travelled back in time.

Alice does not accelerate so she never says anything like that.

What? Where does an accelerating Alice come from? Can you please stick to the topic!

I don't think this is news to anyone who understand special relativity.

Perhaps you should re-read that "arrow of time" article. It seems that none of the scientists involved in the mentioned research area's are understanding special relativity...

Again, this is old news.

Yes, you misrepresenting and ignoring my raised issues is old news.

The change in time was also measured by the DVR recordings.

False, you used two DVR's for that, and had to mix footage of two different inertial frames together. That merely demonstrated that the calculations are correct, which was never in dispute.

Also, the DVR's don't measure, they observe.

It certainly helps to keep in mind that Charlie changed frames when he accelerated.

Erm, obviously?

Of course the t=40 x=0 pertained to when he was in the ground frame, and the t=10 x=0 pertained to when he was in the train frame.

​

Yep, and thus they represent calculations done in two different frames.

Things like the distance between Alice and Charlie changing by 17.32 light years in one moment do not happen in an inertial frame, but they do in an accelerating frame.

Helium balloons also don't rise, unless in an atmosphere. Doesn't mean any underlying theory or formula changed.

There are no special precautions taken in SR to deal with accelerations: it already handles them fine.

Earlier in the thread you talked about "pseudo forces" when I mentioned length contraction.

Yeah, because you implicitly argued that forces are frame-independent, which they are not. I was merely correcting your ignorance.

So you must think that pseudo forces acted on the whole ground when Charlie jumps on/off the train.

You are really terrible at attempting to think what I must think, because you got it wrong again. In fact, your statement is entirely incoherent: pseudo forces arise when working with non-inertial frames, such as the Earth. If Charlie's jumping is instantaneously, there are no non-inertial frames to consider. And therefore, no pseudo-forces.

It is Charlie's simultaneity changing.

Right, exactly. Alice never travels back in time; it's all Charlie.

What? I thought you agreed those calculations were correct.

You have again forgotten the whole "overwrites" thing.

You must think SR is wrong then?

No, I don't. I think people needing travel back in time is required to make sense of SR are wrong.

Charlie would say it does,

Right, Charlie's calculations do. Never his observations, never his measurements.

It's only Charlie's actions that cause this, and it only happens for Charlie.

Nothing happens or changes around Alice, whether Charlie does his jumps or not.

There can be no impact around Alice due to Charlie's frame-switching, because superluminal information travel is forbidden in SR.

Charlie has to mix frame-dependent quantities calculated in different frames together to get to his result.

Charlie agrees through measurements that Alice's worldline never goed backwards in time.

not Alice.

And if Charlie understands what his jumps does, neither does Charlie.

Alright let's look at row 24. Charlie is in the ground frame, and he sees the clock at x=0 displaying 5.36. The distance between him and that clock is 34.64. So, if Charlie stays there 34.64 more years, he would see the distant clock say 34.64+5.36=40.

Of course Charlie does not have to wait that long to make that conclusion. It is immediately evident from the 34.64 distance, and the time 5.36 which he sees with his eyes.

Weird, all of a sudden you are using a completely different way to calculate things. Why is that?
​

Case closed.

Congrats, you just closed a case you opened yourself. Now care to actually address what I said?

 

[NotEinstein]

Risking the accusation of an argument from authority, here's Brian Cox on the matter:

And to make it a bit more explicit what he is talking about:
https://www.quora.com/What-exactly-is-Andromeda-paradox-How-is-it-related-to-the-twin-paradox
https://physics.stackexchange.com/q...owski-metric-mean-that-nothing-can-move-backw

Interesting, I remember bringing up these exact points in this thread! Almost looks like I knew what I was talking about... Too bad it seems many of these points were not understood by some of the participants in this thread.

Also interesting is the results when you Google "can you travel back in time". Reading through the news stories and explanatory articles, seems like a lot of scientists are hard at work, using wormholes and exotic matter and whatnot. But, as has been claimed in this thread by some participants, they clearly all don't understand special relativity, because travelling backwards in time is simple: just switch reference frames!

Just like that one time it was claimed in this thread Einstein didn't understand nuthing about general relativity and the Einstein equivalence principle.

 

[NotEinstein]

When I take a step back, and look at this thread as a whole, I notice a couple of things:
1) I started out with some difficulty getting all the nuances and details right. I asked questions as challenges. I realized on my own what was going on, I corrected myself immediately.
2) At least one participant in this thread has been using pretty much all the standard pseudo-scientific techniques, such as ignoring critical issues raised and misrepresenting other people's position.
3) At least one participant has engaged in name calling.
4) Progress of the thread was hindered in several cases by at least one participant forgetting previous discussion.
5) Some of the issues in the thread stemmed from semantics: some terms weren't interpreted in the same way by all parties, and some terms were defined in non-standard ways. This may be due to several participants not having had any formal training in the relevant scientific fields.
6) Various related subjects and terms were brought up that confused some participants. This may also be due to several participants not having had any formal training in the relevant scientific fields.
7) Whatever happens in this thread, the scientists in the field have already done it before. We are not going to discover anything significant new here (with perhaps the sole exception of the CADO-equation). Thus any claims that seem to go against mainstream understanding of SR should initially be treated with suspicion.
8) Many claims have been made by participants, but some participants failed to back up their claims when challenged.
9) In all places where checks were done, my position turned out to be in line with that of the scientists in the field, and in concordance with the literature.
10) … Profit!