Naked Science Forum
On the Lighter Side => New Theories => Topic started by: MikeFontenot on 11/04/2021 01:05:01
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Einstein, in his special relativity, DID fully address simultaneity-at-a-distance according to a perpetually-inertial person (the "PIP"). According to the PIP (she), a distant person who may be accelerating in any way he chooses (the AP), is at each instant ageing slower than the PIP by the well-known gamma factor (which is a function only of the his speed v relative to her, according to her, at that instant). So by integrating those relative ageing rates, the PIP can determine the current age of the AP at each instant of her life. She can thus produce a plot of his age (on the vertical axis), versus her age (on the horizontal axis) ... I call that "the age correspondence diagram" (the ACD), according to her (the PIP).
But as far as I know, Einstein never addressed the question of simultaneity-at-a-distance, according to the person who sometimes accelerates (the AP). How does the AP produce the ACD that gives the distant person's (the PIP's) age at each instant in the life of the AP? And why did Einstein never address the question?
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But as far as I know, Einstein never addressed the question of simultaneity-at-a-distance, according to the person who sometimes accelerates (the AP).
That's because according to Einstein, simultaneity is an abstract relation dependent on an abstract coordinate system of choice, and not dependent on a worldline as you are always trying to fit it. Some coordinate systems define a unique foliation of Minkowski spacetime and some do not. Actual spacetime, which is not Minkowskian, is not in its entirety foliated by any known coordinate system, so the coordinate system of choice is only going to relate a subset of events, not all of them.
This is a serious problem for presentism which posits an objective ordering of all spacetime events, and yet cannot define a coordinate system that meets this criteria.
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But as far as I know, Einstein never addressed the question of simultaneity-at-a-distance, according to the person who sometimes accelerates.
I'm now thinking that Einstein DID address the question of simultaneity-at-a-distance, according to a person who sometimes accelerates. I remember that Einstein predicted that for two clocks stationary in a gravitational field, the clock higher in the field (farther from the source of the field) will run faster than the clock lower in the field. He got this result long before he published his paper on his GR theory (and long before he arrived at his GR theory). He got it by solving an SR problem, and then invoking his "principle of equivalence" between acceleration and gravitation.
The SR problem he solved was for a rocket, not in the presence of any gravitation field, with a clock at the front and a clock at the back, that is undergoing a constant acceleration. He determined that the clock in front will run faster than the clock at the back. So he DID determine what an accelerating observer at the rear of the rocket will conclude about the current time at the front of the rocket.
I've heard that Einstein wrote a paper in 1907 (2 years after his SR paper, and 8 years before his GR paper) that may have discussed the above result. I'm currently trying to find that 1907 paper (translated into English, of course). I'd like to know if he used CMIF (co-moving inertial frame) simultaneity in getting his result, and whether he made any assumptions in justifying that choice.
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I'm now thinking that Einstein DID address the question of simultaneity-at-a-distance
Yes; he said it was not defined.
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Hi all
But as far as I know, Einstein never addressed the question of simultaneity-at-a-distance, according to the person who sometimes accelerates.
I'm now thinking that Einstein DID address the question of simultaneity-at-a-distance, according to a person who sometimes accelerates. I remember that Einstein predicted that for two clocks stationary in a gravitational field, the clock higher in the field (farther from the source of the field) will run faster than the clock lower in the field. He got this result long before he published his paper on his GR theory (and long before he arrived at his GR theory). He got it by solving an SR problem, and then invoking his "principle of equivalence" between acceleration and gravitation.
The SR problem he solved was for a rocket, not in the presence of any gravitation field, with a clock at the front and a clock at the back, that is undergoing a constant acceleration. He determined that the clock in front will run faster than the clock at the back. So he DID determine what an accelerating observer at the rear of the rocket will conclude about the current time at the front of the rocket.
I've heard that Einstein wrote a paper in 1907 (2 years after his SR paper, and 8 years before his GR paper) that may have discussed the above result. I'm currently trying to find that 1907 paper (translated into English, of course). I'd like to know if he used CMIF (co-moving inertial frame) simultaneity in getting his result, and whether he made any assumptions in justifying that choice.
So if I follow that logic correctly if the clocks were in sync at departure they would be in sync once they/the rocket came to rest in reality ?.
Given they have undergone the same velocity and gravitational potential is not a factor.
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So if I follow that logic correctly if the clocks were in sync at departure they would be in sync once they/the rocket came to rest in reality ?.
'Come to rest' is dang undefined without frame reference. If the ship is constantly accelerating, then it is gaining speed and not coming to rest. It can cease accelerating and therefore be at rest in its own frame, but the clocks will be very out of sync after that.
Given they have undergone the same velocity and gravitational potential is not a factor.
There's no gravitational potential in the rocket scenario, but the clocks have not been moving at the same velocity relative to any inertial frame since their accelerations were very different.
I'm now thinking that Einstein DID address the question of simultaneity-at-a-distance, according to a person who sometimes accelerates.
Again, according to Einstein, simultaneity at a distance is determined by choice of coordinate system, not by an observer or any other object. Any observer can choose any coordinate system they like, so he asserted no particular coordinate system that necessarily must be used by any particular observer.
The coordinate system of choice often depends on the purpose for which it is being used, and not necessarily on what anybody is doing. So I might use the rotating reference frame of the ground below me when measuring the speed of my car, but I might use frame of the center of Earth to compute an orbit of a satellite, or the frame of the solar system to compute my orbital speed around the sun. Same observer, different frames, all valid.
A Rindler frame might be used to go about my everyday existence on a continuously accelerating ship, but such a frame would be highly inconvenient to use to navigate to my destination.
I remember that Einstein predicted that for two clocks stationary in a gravitational field, the clock higher in the field (farther from the source of the field) will run faster than the clock lower in the field. He got this result long before he published his paper on his GR theory (and long before he arrived at his GR theory). He got it by solving an SR problem, and then invoking his "principle of equivalence" between acceleration and gravitation.
All correct. I notice even that there was no mention of an observer in all that.
The SR problem he solved was for a rocket, not in the presence of any gravitation field, with a clock at the front and a clock at the back, that is undergoing a constant acceleration.
He determined that the clock in front will run faster than the clock at the back. So he DID determine what an accelerating observer at the rear of the rocket will conclude about the current time at the front of the rocket.
Using most coordinate systems, yes, the front one will run faster. Not all coordinate systems. But the one you're probably thinking of is the Rindler coordinates, yes.
I've heard that Einstein wrote a paper in 1907 (2 years after his SR paper, and 8 years before his GR paper) that may have discussed the above result. I'm currently trying to find that 1907 paper (translated into English, of course). I'd like to know if he used CMIF (co-moving inertial frame) simultaneity in getting his result, and whether he made any assumptions in justifying that choice.
Einstein in 1907 obtained equations for what is known as radar-coordinates. At no point did he assert that any particular coordinate system was more correct than another, so long as both events compared are mapped by the coordinate system of choice.
I can think of no coordinate system that orders all spacetime events in the universe, but usually one can be found that allows one to assign a meaningful ordering between a given pair of events. I can think of exceptions to even this, but maybe only because I am unaware of an exotic coordinate system that might include both.
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It seems to me, if I may interject an impertinent and possibly ignorant comment, that "simultaneity" is not ruled by the fact that light travels at a fixed speed.
All it means, is that we can't see two events happening at the same time.
For example, suppose that at this precise moment, when we Earth beings are enjoying communicating with one another by typing on our computers, there is a another lot of intelligent beings in the M.31 Andromeda galaxy, who are simultaneously doing the same thing.
We can't see the Andromeda beings doing it, because the light from M.31 takes over 2 million years to reach us on Earth.
But why should that fact - that we can't see them doing it - mean that they aren't simultaneously doing it?
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But why should that fact - that we can't see them doing it - mean that they aren't simultaneously doing it?
Because "simultaneous" is still a relative statement, even with taking visual lag due to the speed of light into consideration:
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It seems to me, if I may interject an impertinent and possibly ignorant comment, that "simultaneity" is not ruled by the fact that light travels at a fixed speed.
All it means, is that we can't see two events happening at the same time.
Sure we can. We just need to be at location in space that is midway between the spatial locations of each of the events. Problem is, 'spatial location' is again a frame dependent concept since each frame (coordinate system) assigns different coordinates (x,y,z,t) to each event. So a pair of events is only simultaneous relative to a coordinate system that assigns the same t coordinate to both events. Several coordinate systems might do so, but most will not.
Mike F wants to make it about people, but it's not. Per Einstein, it's about the choice of coordinate system, and anybody is free to choose any coordinate system they like.
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Thanks Kryptid for your post#7.
I've watched the video-clip that you very kindly supplied. However I'm not convinced by it.
I still think there's something not quite right about all this. We humans are "visual" beings. Who rely on the visual medium of "light" to sense, and interpret, what happens in the Universe. All our interpretations are therefore dependent on the properties of "light".
And as one of the properties of "light" is that it travels at a fixed speed - this is bound to influence, and perhaps dominate, our ideas about how the Universe operates.
But suppose we weren't "visual" beings. We didn't have eyes. Then light, and its speed, would mean nothing to us.
Suppose we were intelligent creatures who relied entirely on other media, such as sound-waves, or heat-waves Or even - though this is taking a science-fictional viewpoint - an ability to detect gravitational-waves?
Surely then our interpretation of the Universe might be completely different.
I hope you see what I'm driving at - that our fixation on "light" and its invariant speed may be leading us astray.
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All our interpretations are therefore dependent on the properties of "light".
Watch the video again but every time they say "the speed of light" pretend that they said "the speed limit for the universe".
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All it means, is that we can't see two events happening at the same time.
No it doesn’t. It’s not due to the time taken for light to travel, that is a separate effect.
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All it means, is that we can't see two events happening at the same time.
No it doesn’t. It’s not due to the time taken for light to travel, that is a separate effect.
I don't quite follow you. We can only tell if two events happen at the same, by looking at them.
Our "looking" is dependent on light. So what's the "separate effect" that we can employ without using light?
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Mike F wants to make it about people, but it's not. Per Einstein, it's about the choice of coordinate system, and anybody is free to choose any coordinate system they like.
I HAVE chosen a coordinate system. The coordinate system I chose defines the spatial origin to be where the observer who sometimes accelerates is. The purpose of the coordinate system is to allow that observer to determine the spatial position and the current age of any distant person of interest.
But the problem of interest to me is that the concept of simultaneity inherent in that definition is not universally agreed upon ... there are multiple definitions of simultaneity that have been proposed. The most widely used simultaneity method (by far) is CMIF (co-moving inertial frames) simultaneity. It's the simultaneity method that I prefer. But that method leads to the conclusion that certain accelerations by the observer can result in the conclusion that a distant person gets younger (according to the observer), and that is disturbing to many people. The well-known physicist Brian Greene is not so disturbed, and gives the most startling example of negative ageing, in his NOVA presentation, starting at the 22 minute point (involving a VERY distant alien creature on a bicycle):
https://www.pbs.org/wgbh/nova/video/the-fabric-of-the-cosmos-the-illusion-of-time/ (https://www.pbs.org/wgbh/nova/video/the-fabric-of-the-cosmos-the-illusion-of-time/)
Two alternative simultaneity methods, that do NOT produce negative ageing by a distant person, were proposed in two different papers by different authors, some years ago: the Dolby and Gull method, and the Minguizzi method. Both are problematic, in my opinion, because they both violate the principle of causality.
Almost a year ago, I discovered an alternative simultaneity method that doesn't produce negative ageing, and which doesn't violate the principle of causality. I self-published it on "Spam". But I actually prefer the CMIF method, personally, because it is simpler, and I'm not troubled by the negative ageing it predicts.
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Is this not Capitalism in action - profit from Science by selling books.
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All it means, is that we can't see two events happening at the same time.
No it doesn’t. It’s not due to the time taken for light to travel, that is a separate effect.
I don't quite follow you. We can only tell if two events happen at the same, by looking at them.
Our "looking" is dependent on light. So what's the "separate effect" that we can employ without using light?
It doesn't matter what the speed of light is in the train experiment. What is important is the order that you see the flashes in. Since the light from one flash necessarily travels the same speed as the light from the other flash, then the order that you see the flashes in tells you the order that the events occurred in.
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Charles1948 said:
"Is this not Capitalism in action - profit from Science by selling books."
The monograph is 18 pages long. So at $5, that's a cost to the purchaser of about 28 cents per page ... not much more than it would cost you to photocopy it. My royalty, per monograph sold, is 85 cents. Obviously, I didn't do it to get rich. I provided the information for anyone who wants to understand that new alternative simultaneity method, especially those readers who don't like the negative ageing that the CMIF method can produce.
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Charles1948 said:
"Is this not Capitalism in action - profit from Science by selling books."
The monograph is 18 pages long. So at $5, that's a cost to the purchaser of about 28 cents per page ... not much more than it would cost you to photocopy it. My royalty, per monograph sold, is 85 cents. Obviously, I didn't do it to get rich. I provided the information for anyone who wants to understand that new alternative simultaneity method, especially those readers who don't like the negative ageing that the CMIF method can produce.
Thanks Mike. When you refer to "negative ageing" do you mean that the CMIF method makes people get younger.
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All it means, is that we can't see two events happening at the same time.
No it doesn’t. It’s not due to the time taken for light to travel, that is a separate effect.
I don't quite follow you. We can only tell if two events happen at the same, by looking at them.
Our "looking" is dependent on light. So what's the "separate effect" that we can employ without using light?
It doesn't matter what the speed of light is in the train experiment. What is important is the order that you see the flashes in. Since the light from one flash necessarily travels the same speed as the light from the other flash, then the order that you see the flashes in tells you the order that the events occurred in.
Surely not. The order in which you see the flashes, only tells you the order in which you see them.
Not at all when the flashes actually happened.
If two flashes occurred simultaneously, and you were watching from a distance of (say) 1,000,000 miles from one flash, and 10,000,000 miles from the other, you'd see the two flashes as occurring at seemingly different times. Because the light from each flash would take a different time to reach you..
But that's just a product of your different distance from the flashes. Why should the flashes care about the distance you're watching them from.
If the flashes go off together, simultaneously, that's what they do.
How can a distant observer influence what they do?
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Surely not. The order in which you see the flashes, only tells you the order in which you see them.
Not at all when the flashes actually happened.
Then you can do the math. If you know the speed of light, the distances involved and the time at which you saw the flashes, then you can easily determined when the flashes happened.
If two flashes occurred simultaneously, and you were watching from a distance of (say) 1,000,000 miles from one flash, and 10,000,000 miles from the other, you'd see the two flashes as occurring at seemingly different times. Because the light from each flash would take a different time to reach you..
Again, you can do the math to know the relative timing of the events in your reference frame.
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Why this continual resort to individual "reference-frames"?
What have they got to do with physical reality?
I mean, suppose you fell out of an aircraft flying at 20,000 feet..
During the time you were falling, you might think " Hey this great! I'm in my own individual reference-frame! Just me! No more aircraft! I'm independent of it! I can move my legs and arms about freely, without even feeling any gravity! There's only air, seeming to rush past, but I can cope with that!
Hang on though - what's this underneath me approaching fast - it must be the ground. Well sucks to the ground and its reference frame - I'm in my own individual reference fra.........
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Why this continual resort to individual "reference-frames"?
Because that's how relativity works.
What have they got to do with physical reality?
Everything. Times and distances are different for observers in different reference frames.
I mean, suppose you fell out of an aircraft flying at 20,000 feet..
During the time you were falling, you might think " Hey this great! I'm in my own individual reference-frame! Just me! No more aircraft! I'm independent of it! I can move my legs and arms about freely, without even feeling any gravity! There's only air, seeming to rush past, but I can cope with that!
Hang on though - what's this underneath me approaching fast - it must be the ground. Well sucks to the ground and its reference frame - I'm in my own individual reference fra.........
What do you think this is supposed to prove?
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Thanks Mike. When you refer to "negative ageing" do you mean that the CMIF method makes people get younger?
In the CMIF method, if the observer (he) suddenly accelerates in the direction TOWARD the distant person (her), he will conclude that she suddenly gets much older. (That is what the CMIF method says happens during the turnaround in the famous 'twin paradox".) If instead, he suddenly accelerates in the direction AWAY from her, he will conclude that she suddenly gets much younger. In either case, she won't agree that his velocity changes have had ANY effect on her current age. And other observers who aren't accelerating won't think her current age is making any sudden changes.
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Why this continual resort to individual "reference-frames"?
Because that's how relativity works.
What have they got to do with physical reality?
Everything. Times and distances are different for observers in different reference frames.
I mean, suppose you fell out of an aircraft flying at 20,000 feet..
During the time you were falling, you might think " Hey this great! I'm in my own individual reference-frame! Just me! No more aircraft! I'm independent of it! I can move my legs and arms about freely, without even feeling any gravity! There's only air, seeming to rush past, but I can cope with that!
Hang on though - what's this underneath me approaching fast - it must be the ground. Well sucks to the ground and its reference frame - I'm in my own individual reference fra.........
What do you think this is supposed to prove?
Perhaps nothing, except that modern physics is losing touch with reality. Becoming more like an intellectual exercise with no physical verification of its speculations.
I mean, do you really and truly believe that the Higg's Boson and Gravitational Waves have been proved to exist?
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Perhaps nothing, except that modern physics is losing touch with reality.
You're going to need to explain why someone falling towards to ground is supposed to illustrate that.
I mean, do you really and truly believe that the Higg's Boson and Gravitational Waves have been proved to exist?
No, because there is no such thing as proof in science. There is very good evidence for them, however.
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Perhaps nothing, except that modern physics is losing touch with reality.
You're going to need to explain why someone falling towards to ground is supposed to illustrate that.
I mean, do you really and truly believe that the Higg's Boson and Gravitational Waves have been proved to exist?
No, because there is no such thing as proof in science. There is very good evidence for them, however.
The trouble is that the "evidence" for supposed particles like the Higgs Boson, and Gravitational Waves, seems to rely on statistical analysis of "meter readings" and extrapolations from graphical charts.
This is very different from the old days when particle physics employed Bubble Chambers, in which the ionised tracks left by particles could be actually seen and photographed.
These days there are no photographs.
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These days there are no photographs.
The other day, you were complaining that we are still talking about wind power. Today you are complaining that we no longer use old methods.
When you have finished arguing with yourself, let us know who won.
In the mean time, you might want to consider that the half life of the Higgs Boson is about 10^-21 of a second.
Travelling at roughly the speed of light, it would cover a ten billionth of a millimetre or about 1/100 of the diameter of a hydrogen atom before it fell apart.
How, exactly, would you propose to get a picture of that?
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The trouble is that the "evidence" for supposed particles like the Higgs Boson, and Gravitational Waves, seems to rely on statistical analysis of "meter readings" and extrapolations from graphical charts.
In what way is this "trouble"?
Do you not understand it?
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These days there are no photographs.
The other day, you were complaining that we are still talking about wind power. Today you are complaining that we no longer use old methods.
When you have finished arguing with yourself, let us know who won.
In the mean time, you might want to consider that the half life of the Higgs Boson is about 10^-21 of a second.
Travelling at roughly the speed of light, it would cover a ten billionth of a millimetre or about 1/100 of the diameter of a hydrogen atom before it fell apart.
How, exactly, would you propose to get a picture of that?
If I was told that a supposed "particle" couldn't exist long enough to travel across 1/100th the diameter of a hydrogen atom before it fell apart, I would strongly suspect that the "particle" didn't actually exist in the first place.
So I wouldn't waste time trying to take a picture of it.
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The trouble is that the "evidence" for supposed particles like the Higgs Boson, and Gravitational Waves, seems to rely on statistical analysis of "meter readings" and extrapolations from graphical charts.
Maybe next time you get your electric bill, you can send them some mail claiming that they can't conclude that you used any electricity because they are relying on "meter readings". Do you think that will work?
This is very different from the old days when particle physics employed Bubble Chambers, in which the ionised tracks left by particles could be actually seen and photographed.
These days there are no photographs.
So you think no photographs equals no evidence? Right. We might as well let everyone out of prison who wasn't filmed committing the crime...
If I was told that a supposed "particle" couldn't exist long enough to travel across 1/100th the diameter of a hydrogen atom before it fell apart, I would strongly suspect that the "particle" didn't actually exist in the first place.
So I wouldn't waste time trying to take a picture of it.
Good for you. Actual scientists, on the other hand, would know how to infer its existence from the particles it leaves behind.
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Your remark reminds me of something from the " Hitchhiker's Guide to the Galaxy" series of books!
In one of the books, scientists had a small piece of "fairy-cake", whatever that is, subjected to intense scientific examination. With probes inserted into the cake. The readings from the probes, enabled the composition, structure and functioning of the entire Universe to be inferred and deduced.
Is that possible, do you think?
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Is that possible, do you think?
Probably not, but I'd never rule anything out for sure.
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So I wouldn't waste time trying to take a picture of it.
How about you stop wasting our time by posting your nonsense in the main part of the forum.
Feel free to post your ‘theories’ in the appropriate section rather than here, otherwise you might find your ability to post in the main sections limited.
If it were left to you Hertz would have been told to ignore the meter reading and forget that radio waves might be discovered.
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Suppose Marconi had been told, as he probably was, that meter-readings of radio-waves conclusively proved that the waves always travel in straight lines.
Therefore radio-waves couldn't possibly travel across the Atlantic from Europe to America. It's nonsense! Owing to the obvious upward obstruction between the two continents caused by the curvature of the Earth.
But... .Heaviside layer and all that ........you know the rest
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Hi all
now I know there has been a lot of activity and there is certain links I will try to find the time to study, but can we rewind a little So Halc yes I take your point
'Come to rest' is dang undefined without frame reference. If the ship is constantly accelerating, then it is gaining speed and not coming to rest. It can cease accelerating and therefore be at rest in its own frame, but the clocks will be very out of sync after that.
So I will try to set a scenario that is CMIF and is in touch with reality that we all can relate to.
we have a space ship that is stationary in space, away from any gravitational influence, on this ship is two synchronized atomic clocks with two observers.
The distance between the clocks is 19.62 m the ship accelerates at 9.81 ms^-2 for 2 seconds then decelerates at 9.81 ms^-2 for 2 seconds back to zero
So my back of a fag packet calcs are the observer at the back of the ship will see the clock at the front being 1.07 x 10^-15 sec ahead/faster than his at the 2 sec point and being synchronized again at the four second point.
The question that brings to my mind is what are the clocks actual rate ?
I believe it would be reasonable but happy to be corrected, that for the 2 seconds that they both accelerate they would both slow down by the rate we measure time dilation to be here on earth ( aprox 6.95 x 10^-10 sec/sec) and they would both speed up by the same margin for the 2 sec they decelerate,
hence they are actually synchronized throughout in reality due to their inertial reference frame to each other.
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My apologies for the derailment of your topic by others. I will move them into a new topic if requested.
I HAVE chosen a coordinate system.
Great! Then events are perhaps ordered according to that choice of coordinate system, and not according to the chooser of it.
The coordinate system I chose defines the spatial origin to be where the observer who sometimes accelerates is. The purpose of the coordinate system is to allow that observer to determine the spatial position and the current age of any distant person of interest.
For there to be a current age of anybody, there needs to be a current time on the preferred worldline (time 0 presumably). Are you asserting a preferred time as well?
But the problem of interest to me is that the concept of simultaneity inherent in that definition is not universally agreed upon
The one you chose cannot be agreed upon since
1) the universe would need to know the exact path of the worldline upon which the coordinate system is based (which is very difficult if it is always located at location 0, and
2) it is not a true simultaneity method (at least the CMIF one isn’t) because multiple events at the preferred worldline are simultaneous with events sufficiently distant from that worldline. There’s a many-to-one mapping, so nobody not on the worldline can know what time it is according to the method. Somebody could say when your birthdays are even if they don’t occur in order, but they could not say when their own birthdays are.
Such a method is only a one-way simultaneity method, not a coordinate system. Relative to any event at location zero, there is a list of events simultaneous with that event, but it only works one way, so there is no distinct coordinate of events not at spatical location 0.
If the more complicated method avoids this multiple-mapping problem and gives a unique coordinate to every event (not even inertial frames do this in reality, only in Minkowski spacetime which doesn’t correspond to anything real), then the method avoids this one problem, qualifies as a coordinate system, but still has to deal with the first issue.
The most widely used simultaneity method (by far) is CMIF (co-moving inertial frames) simultaneity.
Actually I cannot think of anybody using it in a practical situtation. It’s perhaps used as a teaching aid in class, but not in real situtaions.
The well-known physicist Brian Greene is not so disturbed, and gives the most startling example of negative ageing
The Andromeda ‘paradox’ has been around a long time and I doubt this guy broke that ground.
When you refer to "negative ageing" do you mean that the CMIF method makes people get younger.
A coordinate system that assigns later times to somebody young than to the same person old is just assigning different numbers to a line. It is just an abstract coordinate system and such abstractions have no causal effect on actual events, so no, it doesn’t make anything actually get younger.
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Suppose Marconi had been told, as he probably was, that meter-readings of radio-waves conclusively proved that the waves always travel in straight lines.
Just another reason why you should never use the word "proved" when it comes to science.
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Suppose Marconi had been told, as he probably was, that meter-readings of radio-waves conclusively proved that the waves always travel in straight lines.
I’m quite sure someone did tell him this, but experiment proved otherwise.
However, this is still posting your alternative theory in a post on a different subject, in the main section.
Please take note of my warning, the choice is yours.
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The coordinate system I chose defines the spatial origin to be where the observer who sometimes accelerates is. The purpose of the coordinate system is to allow that observer to determine the spatial position and the current age of any distant person of interest.
For there to be a current age of anybody, there needs to be a current time on the preferred worldline (time 0 presumably). Are you asserting a preferred time as well?
I'll elaborate a little.
My coordinate system's horizontal axis gives each instant in the life of the observer (he) who sometimes accelerates (or at least the portion of his life we are interested in, like the portion that includes his trip away from the home twin). The vertical axis gives the home twin's (her) age, as a function of his age, according to him. I call this diagram "the age correspondence diagram" (ACD). It gives the complete simultaneity-at-a-distance information that he wants about her.
There are (at least) four such diagrams: the one for CMIF simultaneity, the one for the Dolby and Gull Simultaneity, the one for Minguizzi simultaneity, and the one for my newly discovered simultaneity ... I call it "Fontenot's simultaneity". CMIF simultaneity is by far the best known, but it is disliked by some people because it's ACD can have discontinuities ... specifically, her age can instantaneously increase or instantaneously decrease. The other three simultaneity methods have no discontinuities, and no negative ageing.
I actually prefer the CMIF method. The discontinuities and negative ageing don't bother me at all. And they clearly don't bother Brian Greene, either.
It's possible to produce a similar diagram that gives the home twin's distance from the traveler, according to the traveler, at each instant of the traveler's life. It also has discontinuities in the CMIF method. I don't find such a diagram to be very useful or important. I prefer to just keep track of the separation of the twins according to the home twin. I just use a Minkowski diagram, which plots on the vertical axis the position of the traveler according to the home twin, versus the home twin's age on the horizontal axis. That diagram is the basic starting point for all four of the simultaneity methods.
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I'll elaborate a little.
My coordinate system's horizontal axis gives each instant in the life of the observer (he) who sometimes accelerates (or at least the portion of his life we are interested in, like the portion that includes his trip away from the home twin). The vertical axis gives the home twin's (her) age, as a function of his age, according to him.
It isn’t a coordinate system if it doesn’t assign 4 coordinates to every event in the region-of-applicability. I don’t know about you latest proposed method, but CMIF certainly does not qualify as a coordinate system for the reasons above. Ditto with Minguizzi who only assigns coordinates to one other worldline (that of the twin) and only if that twin remains stationary the whole time. Coordinates of other events are not defined.
The other three simultaneity methods have no discontinuities, and no negative ageing.
OK, so maybe one of them qualifies as a choice of coordinate systems. I’m unfamiliar with the others.
I actually prefer the CMIF method.
That’s a perfectly reasonable choice for a simultaneity method. It just doesn’t qualify as a coordinate system.
What does any of this have to do with the title? Einstein was not concerned with assigning relations between specific worldlines. His point was that any coordinate system (or even a non-coordinate method such as you use) is a valid choice. You can assign any age you like to the other worldline relative to an event on yours so long as the remote event chosen as simultaneous is not within the light cones of your event. Einstein would not have suggested a preferred event that is simultaneous, which would have been in contradiction with the lack of ability to determine a preferred frame.
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My coordinate system's horizontal axis gives each instant in the life of the observer (he) who sometimes accelerates (or at least the portion of his life we are interested in, like the portion that includes his trip away from the home twin). The vertical axis gives the home twin's (her) age, as a function of his age, according to him.
It isn’t a coordinate system if it doesn’t assign 4 coordinates to every event in the region-of-applicability.
What I gave above gives the age of the home twin (her) at each instant in the life of the observer (he) who sometimes accelerates. Although I haven't been interested in her distance from him, according to him, both the CMIF method and my method DO provide that information, and the two methods give the same value. For example, if she says that the turnaround point is D lightyears from her, he will say that it is D/gamma lightyears from her.
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What I gave above gives the age of the home twin (her) at each instant in the life of the observer (he) who sometimes accelerates. Although I haven't been interested in her distance from him, according to him, both the CMIF method and my method DO provide that information, and the two methods give the same value. For example, if she says that the turnaround point is D lightyears from her, he will say that it is D/gamma lightyears from her.
The CMIF method and my method give the same answer to the question "What is the distance between the home twin (she) and the traveling twin (he), according to him" ONLY when there is no discontinuity in the CMIF solution. There is no discontinuity in their separation in the most common version of the twin paradox, where he reverses course at the turnaround point, but comes back at the same speed as he used on the outbound leg.
But if he uses a DIFFERENT speed on the return leg than he used on the outbound leg, the CMIF solution gives a discontinuity in their separation when the speed changes (according to him). My method never produces a discontinuity.
For example, suppose his speed on the outbound leg is 0.57735 ly/y (gamma = 1.2247). (That case is advantageous, because the angle of his worldline wrt her worldline (the horizontal axis) is 30 degrees, and can be easily drawn with a 30-60-90 plastic triangle.) Suppose she is 40 years old when he turns around. He is 32.66 years old then. Then suppose his new speed is -0.866 ly/y (gamma = 2.0). When they are reunited, she is 66.67 years old, and he is 46.0 years old.
For the above case, we can plot their separation at each instant of his life, according to him, for both the CMIF method and for my method. I call that diagram the "SAAOD", for "Seperation According to the Accelerated Observer Diagram." Their separation is on the vertical axis, and his age is on the horizontal axis.
The first straight line segment starts at the origin, when he is zero years old, and their separation is zero ly. It slopes upward at a 30 degree angle. It reaches its peak when he is 32.66 years old, and their separation is 18.86 ly.
When he changes his speed to -0.866 ly/y, their separation instantaneously drops to 11.55 ly, according to the CMIF method. Then, from there, their separation declines linearly with a slope -0.866 until their reunion. (That last straight line segment makes an angle of approximately 41 degrees wrt the horizontal axis).
In contrast, in my method their separation doesn't instantaneously change. Instead, it decreases linearly with a slope of -2.047 from its peak at 18.86 until his age reaches 38.85 years old, and their distance reaches 6.188. (That endpoint corresponds to when he receives a light pulse that she sends at his turnaround). Then, at that point, the slope of the line decreases to -0.866 until their reunion. The two methods coincide along that last segment.
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This Veritassium video suggests that Einstein did address simultaneity at a distance, by saying it is impossible to measure, and defining the convention that the speed of light is identical in every direction.
This video was originally posted by wolfekeeper, in this thread: https://www.thenakedscientists.com/forum/index.php?topic=82170.0
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This Veritassium video suggests that Einstein did address simultaneity at a distance, by saying it is impossible to measure, and defining the convention that the speed of light is identical in every direction.
[...]
At about the 15 minute point in the video, the author says that it's possible that in some directions, we're seeing extremely distant galaxies as they were in the distant past, whereas in other directions we're seeing extremely distant galaxies as they are now. It seems to me that that possibility can be discounted because of the fact that what we see in all directions is amazingly uniform, and that seems to contradict our understanding that the universe has greatly changed since the big bang.
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This Veritassium video suggests that Einstein did address simultaneity at a distance, by saying it is impossible to measure, and defining the convention that the speed of light is identical in every direction.
[...]
At about the 15 minute point in the video, the author says that it's possible that in some directions, we're seeing extremely distant galaxies as they were in the distant past, whereas in other directions we're seeing extremely distant galaxies as they are now. It seems to me that that possibility can be discounted because of the fact that what we see in all directions is amazingly uniform, and that seems to contradict our understanding that the universe has greatly changed since the big bang.
Can't the amazingly uniform appearances that we see in all directions, only be ascribed to one of these two theories:
1. The Earth is in a special position, at the centre of an Big Bang-originated Expanding Universe; or:
2. There was no "Big Bang", the Universe has always existed in a Steady State.
I'd put my money on 2, the Steady State theory. It gets round questions like "But happened before the Big Bang"?
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Can't the amazingly uniform appearances that we see in all directions, only be ascribed to one of these two theories:
1. The Earth is in a special position, at the centre of an Big Bang-originated Expanding Universe; or:
2. There was no "Big Bang", the Universe has always existed in a Steady State.
Nope. The Big Bang theory, as is, has no issues explaining cosmic uniformity. It's important to remember that the Big Bang didn't happen at one particular location in space: it happened at all locations in space.
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This Veritassium video suggests that Einstein did address simultaneity at a distance, by saying it is impossible to measure, and defining the convention that the speed of light is identical in every direction.
[...]
At about the 15 minute point in the video, the author says that it's possible that in some directions, we're seeing extremely distant galaxies as they were in the distant past, whereas in other directions we're seeing extremely distant galaxies as they are now. It seems to me that that possibility can be discounted because of the fact that what we see in all directions is amazingly uniform, and that seems to contradict our understanding that the universe has greatly changed since the big bang.
Can't the amazingly uniform appearances that we see in all directions, only be ascribed to one of these two theories:
1. The Earth is in a special position, at the centre of an Big Bang-originated Expanding Universe; or:
2. There was no "Big Bang", the Universe has always existed in a Steady State.
I'd put my money on 2, the Steady State theory. It gets round questions like "But happened before the Big Bang"?
There are (at least) three other options, and I suspect that these options more likely explains what we observe:
3. There are NO special points in the universe (either due to closed geometry or unbounded size), in which case ALL planets (indeed, all points) in the universe would be equally validly the "center" of the universe.
4. There are VERY FEW special points because the universe is finite, but immensely vast, and the earth is deep within a finite region of space that appears uniform, and we are so fat from the edges that our position within the volume is meaningless (ie, basically option three without needing to actually be closed or boundless). As an analogy, I present this single crystal of diamond (https://en.wikipedia.org/wiki/Cullinan_Diamond) which apparently had a mass of 621 g. That means that there are about 3×1025 carbon atoms in a nearly perfect crystalline lattice (every carbon is equivalent to every other carbon except at the very edge, and 99.999% of the atoms are separated from the edge of the crystal by at least 1,000 intervening carbon atoms. Each of those 99.999% carbon atoms could reasonably appear to be the "center" of the crystal when viewed on an atomic scale, and there would be no way for a single carbon atom to "know" where the closest edge was, or even if there is an edge.)
5. There was no big bang. Clearly the universe is NOT in a steady state, so there must be some other explanation. There are several other competing hypotheses, but each has its own host of problems. I am personally intrigued by the idea that our concept of time is very wrong. (this idea is explored somewhat here: https://www.thenakedscientists.com/forum/index.php?topic=73163.msg540694#msg540694)
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And as one of the properties of "light" is that it travels at a fixed speed - this is bound to influence, and perhaps dominate, our ideas about how the Universe operates.
But suppose we weren't "visual" beings. We didn't have eyes. Then light, and its speed, would mean nothing to us.
Suppose we were intelligent creatures who relied entirely on other media, such as sound-waves, or heat-waves Or even - though this is taking a science-fictional viewpoint - an ability to detect gravitational-waves?
Surely then our interpretation of the Universe might be completely different.
I hope you see what I'm driving at - that our fixation on "light" and its invariant speed may be leading us astray.
It's not just the speed of light. It's the speed of any massless particle, and is the unreachable limit of any massive particle. It's not just special because of light. The speed of sound waves depends highly on the medium through which they travel, and they are unlikely to be of much cosmological importance, because sound doesn't really propagate through the vacuum of space.
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Can't the amazingly uniform appearances that we see in all directions, only be ascribed to one of these two theories:
1. The Earth is in a special position, at the centre of a Big Bang-originated Expanding Universe; [...]
[...]
I think the Big Bang is regarded as having occurred "everywhere at once", even though that "everywhere" was infinitesimally small initially. I.e., no location in the current universe is farther from the Big Bang than any other place.
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At about the 15 minute point in the video, the author says that it's possible that in some directions, we're seeing extremely distant galaxies as they were in the distant past, whereas in other directions we're seeing extremely distant galaxies as they are now.
No mention of 'distant galaxies' was made. This is special relativity being discussed, and while it might be meaningfully applied to nearby galaxies, it certainly does not apply to the distant ones, which illustrates that at cosmological scales, the Minkowski metric cannot be applied.
That said, the video mentioned stars 'hundreds of light years distant', and I disagree with little of it despite the often vague wordings and careless switching of implied frame references being done.
It said that we could see Mars as it is 'now', which is false for the same reason that no massive object can move at light speed. But it can be arbitrarily close, so the time between the Mars even and our observation of it could be any arbitrarily small time, but not zero time as they seem to emphasize. We cannot see Mars at it is 'right now'.
It seems to me that that possibility can be discounted because of the fact that what we see in all directions is amazingly uniform
The point of the video was that a difference in the one-way speed of light would have zero effect on what you measure, so discounting the possibility due some measurement seems only to demonstrate that you didn't get that point.
OK, the video was posted first to the thread which was specifically about the ability to measure the one way speed of light, and only posted here because Einstein knew it couldn't be measured and was very careful to define simultaneity by a chosen convention and not by any assertions that there is a way to know the ordering of a pair of events, even relative to a specific frame of reference.
that seems to contradict our understanding that the universe has greatly changed since the big bang.
Special relativity has never been applicable to the universe at large.
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(my post #41)
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In contrast, in my method their separation doesn't instantaneously change [when he changes is velocity from 0.57735 ly/y to -0.866 ly/y]. Instead, it decreases linearly with a slope of -2.047 from its peak at 18.86 until his age reaches 38.85 years old, and their distance reaches 6.188. (That endpoint corresponds to when he receives a light pulse that she sends at his turnaround).
I have just verified that the above segment is indeed a straight line. The verification is similar to what I did for the linearity of the middle segment in the age correspondence diagram (the "ACD"), which I described in Section 8, titled "Pulses Partly in Both Halves of the Minkowski Diagram", of my monograph.
On the Minkowski diagram, first find the vertical line descending from the traveler's (his) worldline at his turnaround point, down to the horizontal axis (her worldline). Mark the half-way point on that vertical line, and call it "point Q". Then draw a light pulse being sent by her, at such a time in her life that the pulse passes through that half-way point, and continues on until it reaches his worldline. Mark that point on his worldline as point R. His age is 35.75 then.
According to her, their separation at the turnaround is 23.094 ly. And according to her, that half-way point is at distance 11.547 ly from her. According to a perpetually-inertial observer traveling at 0.57735 ly/y (with gamma = 1.2247), that distance is 11.547 / 1.2247, or 9.43 ly from her. Similarly, a perpetually-inertial observer traveling at -0.866 ly/y (with gamma = 2.0), concludes that that pulse travels a distance 3.09 ly from point Q until it reaches the traveling twin at point R. So the traveling twin (he) then concludes that the distance between him and her at the instant he receives that pulse is 9.43 + 3.09 = 12.52 ly. If, on the SAAOD (Separation According to the Accelerated Observer Diagram), you plot the separation 12.52 ly when he is 35.75 years old, you will see that it does indeed lie on the midpoint of the previously described straight line.
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I've heard that Einstein wrote a paper in 1907 (2 years after his SR paper, and 8 years before his GR paper) that may have discussed the above result. I'm currently trying to find that 1907 paper (translated into English, of course). I'd like to know if he used CMIF (co-moving inertial frame) simultaneity in getting his result, and whether he made any assumptions in justifying that choice.
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I've heard that Einstein wrote a paper in 1907 (2 years after his SR paper, and 8 years before his GR paper) that may have discussed the above result. I'm currently trying to find that 1907 paper (translated into English, of course). I'd like to know if he used CMIF (co-moving inertial frame) simultaneity in getting his result, and whether he made any assumptions in justifying that choice.
That is a quote from one of MY posts, not from aujlaakaran0, so I don't know what's going on here. I DID find a copy of that 1907 Einstein publication, and have read the part about clocks in the front and rear of a rocket, but I haven't been able to understand it very well. He doesn't appear to be assuming that an accelerating observer always agrees with the perpetually-inertial observer who is momentarily co-located and stationary wrt to himself. But Einstein also is doing the analysis only for an arbitrarily small acceleration.
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In what follows, I refer to the perpetually-inertial twin as "she", and to the twin who instantaneously changes his velocity as "he".
I've worked out an example that shows an instantaneous negative ageing for her, according to him, when CMIF (co-moving inertial frame) simultaneity is used ...i.e., she instantaneously gets YOUNGER according to him, when using the CMIF simultaneity method. And I'll show the results for this example for my simultaneity method, which gives no discontinuities and gives no negative ageing.
First, here's a description of the Minkowski diagram (with time tau on the horizontal axis and separation X on the vertical axis). That always has to be determined first.
The two "twins" in this case aren't really twins ... they are just babies who were born at the same time but 20 lightyears (ly) apart, and with zero relative velocity. This situation continues until they are both 40 years old. We represent this initial situation by drawing a horizontal line on the diagram at the point X = 20 on the vertical axis, extending from tau = 0 to tau = 40. That is the initial segment of his worldline. At the end of that first segment, write 40 immediately above the end of that segment of his worldline to show his age , and vertically below there write 40 immediately below the horizontal axis to show her age.
Then, he instantaneously changes their relative velocity to v = 0.57735 ly/y, and continues that velocity for the rest of their lives. This causes his worldline to slope upward toward the right at a slope of 0.57735 (and an angle wrt the horizontal axis of 30 degrees). Label that point where the second segment of his worldline starts as point T.
Next, draw a 45 degree line starting at the point 40 on the horizontal axis, and sloping upward to the right, representing the worldline of a light pulse that she transmits when she is 40, and that is moving toward him. We then write an equation giving X as a function of tau for that light pulse, and then we write another equation giving X as a function of tau for the upward sloping segment of his worldline. Then, we set those two equations equal (force their X values to be equal). The result gives the value of tau where those two lines intersect ... label that point Q. That point is vertically above the point tau = 87.32 on the horizontal axis. Write that value just below the horizontal axis, vertically below that point of intersection.
We also need to determine their separation according to her (the value of X) when she is 87.32. The answer is 47.32 ly.
Next, we need to plot two lines of simultaneity (LOS's) that show what "Now" is for him. (The LOS's for her are just vertical lines). His LOS's (anywhere for him when his velocity is 0.57735) have slope 1/v = 1/o.57735 = 1.73, and they make an angle of 60 degrees wrt the horizontal axis. The first LOS we need goes through point Q. That line intersects the horizontal axis at the point tau = 60. That is determined by writing the X(tau) equation for that LOS, and solving it when X is set to zero. So this tells us that when he is 78.63 years old, she is 60, according to him.
Next, we need to determine how old she says he is when she is 60. We know that according to her, he ages slower than she does by the factor gamma = 1.2247 (once he has changed his velocity to 0.57735). So according to her, while she ages from 40 to 60, he ages from 40 to 56.33. Mark that age on his worldline.
We also need to determine their separation according to her (the value of X) when she is 60. The answer is 31.55 ly.
Next, we do the same thing for the LOS that goes through the point T where his worldline starts sloping upward. The result is that her age when he changes velocity is 28.45, according to him. He was 40 then.
From the above information, we can draw the Age Correspondence Diagram (the ACD), which is a plot of her age (on the vertical axis), according to him, versus his age (on the horizontal axis).
During the first segment, their relative velocity is zero, so they each agree that they are ageing at the same rate. Therefore the first segment of the ACD is just a line of slope 1, sloping upward to the right, making a 45 degree angle wrt the horizontal axis. This first segment is the same, regardless of whether you are using the CMIF simultaneity method, or my method. Label the end of that segment point T.
In the CMIF method, at point T, when he changes velocity from zero to 0.57735, he says that she instantaneously gets younger by 11.55 years, from 40 to 28.45. So, for the CMIF case, we draw a vertical line downward from point T, of length 11.55 ly. Then, the next (last) segment slopes upward forever at a slope of 1/gamma = 0.8165.
What does the plot look like after the point T in the case of my simultaneity method? It is a straight line between the point T and the point Q. Point Q is where his age is 78.64 and her age is 60. It is a point on the third segment of the CMIF line we determined above. Point Q is where he received the pulse from her, and it is the end of the "Disagreement Interval" (DI) between him and the a perpetually-inertial observer who is co-located and co-moving with him. So, after point Q, the ACD for my method coincides with the CMIF method for the rest of their lives. I.e., after the end of the disagreement interval (DI), the CMIF method and my method agree thereafter in this example.
So, as was claimed, with my method, the ACD has no discontinuities, and no negative ageing (i.e., the ACD plot never slopes downward).
I personally prefer the CMIF method, because of its simplicity, and because I'm not bothered by discontinuities or by negative ageing. But for those people who ARE bothered by those characteristics of the CMIF method (and in my experience, that's a LOT of people), my method offers a safe refuge.
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There is another argument that (according to the CMIF simultaneity method) the home twin's (her) negative ageing must occur, according to the accelerating twin (he). Suppose in the standard twin paradox scenario that he instantaneously changes his velocity at the intended turnaround from v to -v. That causes an instantaneous increase (according to him) in her age, say by +T years. But suppose that he immediately changes his mind, and instantaneously changes his velocity from -v back to +v. The net effect on her age (according to him) of those two back-to-back instantaneous velocity changes is the same as if he never changed his velocity at all: his world line just continues at the constant slope +v, with no turnaround. But that requires that her first instantaneous age change of +T must be canceled by her second instantaneous age change of -T. If negative instantaneous age changes aren't allowed, then positive instantaneous age changes can't be allowed either.
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For a given perpetually-inertial observer (the "home twin", her), there is only one answer to the question, "How old is that distant person right now?", that agrees with her own measurements. The way she can make those measurements was described in detail by Einstein: a collection of equally-spaced clocks are laid out that are stationary with respect to her (and with respect to her perpetually-inertial mother or grandmother), and all those clocks are synchronized via light signals. There is a perpetually-inertial observer at each clock. Those observers keep a record of every person who goes flying past them, recording the time on that person's clock, and what their own clock shows at that instant. They then send that information to the home twin (which she receives after a long delay) . For the case where she and the traveler (he) were born simultaneously when they were momentarily co-located, and were both perpetually inertial with a relative speed of 0.866 ly/yr (giving gamma = 2.0), those measurement results tell her that when she was 80 years old, he was 40 years old. That result is exactly what the time dilation equation (the TDE) told her, long ago. The TDE told her that result immediately, without the long delay that the measurements took. ANY other answer will disagree with what the measurements say. There is only one correct answer to that original question.