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**New Theories / Split: What is my explanation for the differential age of the twin?**

« **on:**28/10/2023 20:31:00 »

[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.

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.