Naked Science Forum
On the Lighter Side => New Theories => Topic started by: MikeFontenot on 28/10/2023 20:31:00
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[Mod edit: Topic split from https://www.thenakedscientists.com/forum/index.php?topic=86033
Please do not post personal relativity conjecture in the main sections of the forum]
The Twin "Paradox" is very simple to analyze. Here is how to do it:
The home twin is older that the traveling twin at their reunion. The home twin (she) is ALWAYS inertial, so she can immediately compute the traveling twin's (his) current age from the time dilation equation (TDE): she says his current age is equal to her current age, divided by gamma:
gamma = 1 / { sqrt [ 1 - ( v * v ) ] } .
For example, for v = +-0.866 ly/y, gamma = 2.0 .
So SHE says that, during his entire trip, he is always ageing half as fast as she is. So, in the case where he ages by 20 years on each of the two legs of his trip, she says that he is 40 at their reunion, and she is 80. And everyone must agree with that.
But how does HE describe their ages DURING the trip? He obviously has to agree with her about their respective ages at the reunion (because they are standing together right there, motionless, looking at each other). But what does HE say about their two ages at other times during his trip? Everyone DOES agree that he is 20 years old during his turnaround. But what does HE say about her age immediately BEFORE and immediately AFTER his turnaround?
He can also use the time dilation equation (TDE) immediately before his turnaround. From that, he concludes that, since he is 20 years old then, she is 10 years old then.
He also knows that, since he ages 20 years during his return trip, she must age 10 years during his return trip. So, if that were all that happens to her age during his trip (according to him), she would only be 20 years old at their reunion, when he is 40 years old. But she's NOT 20 years old then ... he can see with his own eyes that she is 80 years old then. Somewhere during his trip, she HAD to age an additional 60 years, according to him. WHERE did that extra ageing by her, according to him, occur? There is only one possible place it could have occurred: it HAD to have occurred during his instantaneous turnaround, because during ALL the rest of his trip, he knows she was ageing only half as fast as he was.
For this simplest scenario, that's all you need to know to solve "the paradox". More complicated scenarios require that you know how to COMPUTE her instantaneous age-changing (according to him). There is a simple equation that allows you to do that (and also a graphical technique that you can use to do it), but neither of those is needed for this simplest scenario.
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it HAD to have occurred during his instantaneous turnaround, because during ALL the rest of his trip, he knows she was ageing only half as fast as he was.
If there's an observer at the middle of the journey, what will it see?
Meanwhile, what will be seen by the travelling twins during that meeting point? Will they see the clocks to have the same values as observed by midway observer?
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I (Mike Fontenot) said:
This post of mine was moved to the "Other Theories" section. But it is NOT "another theory" ... it is completely standard Special Relativity, applied to the "Twin Paradox". It is based solely on the time dilation equation (TDE) for inertial observers ... you can't get any more "standard Special Relativity" than that.
(Halc said:)
Perhaps, but you are a known relativity denier and have been told to not post in the main sections.
I am NOT a relativity denier. Your accusation is absurd. You and I just disagree about some aspects of special relativity, especially those involving accelerations. But those don't arise in the current discussion, because the twin paradox involves instantaneous velocity changes, which are much simpler.
Halc says:
You have posted that positive proper acceleration from a stop can cause negative motion, faster than light motion, ships vanishing from existence, etc.
That's a low blow ... now, you're just being nasty. Try to be specific in what you think my erroneous statements are, and give me a chance to explain them more completely.
[...] and you start asserting that somebody's choices has a physical effect on somebody far away, [...].
Tell me, specifically, what you're referring to above. I've never done that.
I said:
He can also use the time dilation equation (TDE) immediately before his turnaround. From that, he concludes that, since he is 20 years old then, she is 10 years old then.
(Halc said:)
"It's such statements that go against SR. SR would never say that any particular event on her worldline is simultaneous with his turnaround event."
That's an absurd thing for you to say. He (the traveling twin) most certainly has a viewpoint. He CAN certainly ask (and answer) the question, "How old is my twin (she), RIGHT NOW, IMMEDIATELY BEFORE MY COURSE REVERSAL? His answer is not HER view of herself, but it is HIS view of her. They disagree, but they are BOTH right. That's just the way special relativity is. You're understanding of special relativity is highly dis-functional.
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This post of mine was moved to the "Other Theories" section.
Final warning. Please confine your replies to the lighter side. The main sections are not for discussing such issues such as your speculative claims. Dup post removed.
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Halc, as soon as a discussion starts to get relevant and productive, you run and hide, and try to make any information that you don't agree with disappear. The time dilation equation (TDE) is one of the most important results in all of special relativity, but you do everything you can do to avoid discussing it. Special relativity says that the TDE specifies what ANY particular inertial observer MUST conclude about the rate of ageing (compared to their own rate of ageing) of anyone moving with respect to them. In particular, it says that the traveling twin (he) MUST use the TDE to determine how much SLOWER the home twin is ageing compared to his own rate of ageing whenever he is inertial. And likewise, SHE must use the TDE to determine how much slower HE is ageing than she is, according to HER, during her entire life (since she is ALWAYS inertial). They each MUST conclude that, whenever they are inertial, the other twin is ageing gamma times slower than their own rate of ageing ... they have no other choice: their own experimental measurements CONFIRM the correctness of the TDE. Whenever SHE is unaccelerated (which is ALL the time), she says he is ageing gamma times slower than she is, and that is a totally REAL conclusion for her. And whenever HE is unaccelerated (which is ALL the time EXCEPT for the one instant where he is reversing his velocity), he MUST conclude that she is ageing gamma times slower than he is. And that is a totally REAL conclusion for him. And for HIM, those results then require that, according to HIM, SHE instantaneously gets older during HIS instantaneous turnaround. That HAS to happen ... otherwise he won't agree with their respective ages at the reunion, and they obviously MUST agree at the reunion (when they are eye-to-eye).
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Halc, as soon as a discussion starts to get relevant and productive, you run and hide, and try to make any information that you don't agree with disappear.
I only moved it (and deleted dup posts). We can discuss it in two weeks (here, not in the main forums) when your vacation is over.
Three straight posts in the wrong place, despite warnings.
The contradictions were heavily discussed here
https://sciforums.com/threads/bell%E2%80%99s-spaceship-paradox-does-the-string-break.165916/
and you ignore them all, and refuse to answer many questions that directly identify the contradictions
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"Run and hide"? That remark is uncalled for. In my experience Halc will answer any reasonable question. On some of the marathon threads that go nowhere useful he may make a few posts and then cease as nothing of any value can be achieved(rightly so in my opinion).
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[Mod edit: Topic split from https://www.thenakedscientists.com/forum/index.php?topic=86033
Please do not post personal relativity conjecture in the main sections of the forum]
The Twin "Paradox" is very simple to analyze. Here is how to do it:
The home twin is older that the traveling twin at their reunion. The home twin (she) is ALWAYS inertial, so she can immediately compute the traveling twin's (his) current age from the time dilation equation (TDE): she says his current age is equal to her current age, divided by gamma:
gamma = 1 / { sqrt [ 1 - ( v * v ) ] } .
For example, for v = +-0.866 ly/y, gamma = 2.0 .
So SHE says that, during his entire trip, he is always ageing half as fast as she is. So, in the case where he ages by 20 years on each of the two legs of his trip, she says that he is 40 at their reunion, and she is 80. And everyone must agree with that.
But how does HE describe their ages DURING the trip? He obviously has to agree with her about their respective ages at the reunion (because they are standing together right there, motionless, looking at each other). But what does HE say about their two ages at other times during his trip? Everyone DOES agree that he is 20 years old during his turnaround. But what does HE say about her age immediately BEFORE and immediately AFTER his turnaround?
He can also use the time dilation equation (TDE) immediately before his turnaround. From that, he concludes that, since he is 20 years old then, she is 10 years old then.
He also knows that, since he ages 20 years during his return trip, she must age 10 years during his return trip. So, if that were all that happens to her age during his trip (according to him), she would only be 20 years old at their reunion, when he is 40 years old. But she's NOT 20 years old then ... he can see with his own eyes that she is 80 years old then. Somewhere during his trip, she HAD to age an additional 60 years, according to him. WHERE did that extra ageing by her, according to him, occur? There is only one possible place it could have occurred: it HAD to have occurred during his instantaneous turnaround, because during ALL the rest of his trip, he knows she was ageing only half as fast as he was.
For this simplest scenario, that's all you need to know to solve "the paradox". More complicated scenarios require that you know how to COMPUTE her instantaneous age-changing (according to him). There is a simple equation that allows you to do that (and also a graphical technique that you can use to do it), but neither of those is needed for this simplest scenario.
Basically, your description is aligned with explanation from videos by Minutephysics, MIT OCW, and Stanford professor. I take it as the position of mainstream physics community.
That's why I started another thread about twin paradox, by eliminating the turn around event. Hopefully we can get a general explanation of how acceleration or frame switching affects time dilation which causes aging difference.