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Quote from: MikeFontenot on 16/04/2021 21:54:06My 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.
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.
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.
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.[...]
Quote from: evan_au on 25/04/2021 10:22:37This 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.
Quote from: MikeFontenot on 25/04/2021 15:53:05Quote from: evan_au on 25/04/2021 10:22:37This 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"?
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.
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; [...][...]
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
that seems to contradict our understanding that the universe has greatly changed since the big bang.
(my post #41)[...]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'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.