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What do you think would happen if they are both accelerated equally in magnitude, but in opposite direction?

I'll assume there is an inertial frame, F, with respect to which both people can be considered to have equal and opposite accelerations at all times, t, using the co-ordinates of frame F. The situation is then perfectly symmetric for the two people

The good news: There will always be a frame of reference where you can consider the people to have equal and opposite motions.

Example 1: The Hafele-Keating experiment discussed earlier / maybe in some vaguely related thread. The clocks on the aeroplane showed a positive/negative time difference compared to the clock that stayed on earth depending on whether the aeroplane flew eastward or westward. The frame in which the earth clock was at rest was not an inertial frame, if it had been then eastward or westward travel would have made no difference.

. F|xyz E|xyZ |xy z |xy z |xy z D|xY z C|x y Z |x y z B|x Yz |x yz |x yz A|xYZ--+------------ |

I don't know. Where is the inertial frame? You need to provide more information.

I have to assume some things. I'll assume there is an inertial frame, F, with respect to which both people can be considered to have equal and opposite accelerations at all times, t, using the co-ordinates of frame F. The situation is then perfectly symmetric for the two people, there is no dependance on which direction the people went in. So the proper time elapsed for each person will be identical and if their clocks were synchronised at the start then they remain synchronised when they finally meet up again.

The situation is perfectly symmetric only if F is the inertial frame in which the two of them are initially stationary.

I'll assume there is an inertial frame, F, with respect to which both people can be considered to have equal and opposite accelerations motion at all times, t, using the co-ordinates of frame F. The situation is then perfectly symmetric for the two people, there is no dependance on which direction the people went in.....

traveling twin can also have valid observation, and eventually get the same conclusion as the staying twin. He only need to take relativity of simultaneity into account. We don't just say that his observation is invalid, whatever it is, only because he changes his frame of reference.

We only need to explain how much his changes of reference frame affect his calculated age of the other twin.So far, I haven't produced my own explanation for the twin paradox. I only cited various sources which I thought interesting or plausible, and then explored their implications, and found out how far they can be extrapolated until they break down and give nonsensical or clearly wrong results.

Quote from: hamdani yusuf on 14/01/2024 07:43:29We only need to explain how much his changes of reference frame affect his calculated age of the other twin.So far, I haven't produced my own explanation for the twin paradox. I only cited various sources which I thought interesting or plausible, and then explored their implications, and found out how far they can be extrapolated until they break down and give nonsensical or clearly wrong results.Still not able to figure out why the twin paradox isn't actually a paradox?

We can also change the speed of one twin to make the situation no longer perfectly symmetrical. They go to the opposite direction in the same amount of time, say 4 years, then go back home. If your previous explanation is valid, it should also give the correct results in the slightly different situations.

If you think you can, please let us know. Let's start with this.

Let's start with this.

both travelling twins always move at speed 0.999c

Let's make a simpler case.

But according to the first travelling twin, the second travelling twin moves relative to him for half of the journey, which should produce time dilation.

...traveling twin(s) can also have valid observation, and eventually get the same conclusion as the staying twin. He only need to take relativity of simultaneity into account.

according to the first travelling twin, the second travelling twin moves relative to him for half of the journey,

Quote from: hamdani yusuf on 15/01/2024 16:26:12Let's make a simpler case. That isn't a simpler case. The most simple case is a one way trip to another star or point in space.The scenario is not important anyway since you will never figure out what is going on, you never reach a conclusion, you just go round and round and get more confused as your thread goes on.

Quote from: Halc on 12/01/2024 14:20:50Bad idea to reference your common sense or intuitions when discussing relativity that you obviously don't understand. Here's what understanding means.QuoteGregory Chaitin propounds a view that comprehension is a kind of data compression.[19] In his essay "The Limits of Reason", he argues that understanding something means being able to figure out a simple set of rules that explains it. For example, we understand why day and night exist because we have a simple model?the rotation of the earth?that explains a tremendous amount of data?changes in brightness, temperature, and atmospheric composition of the earth. We have compressed a large amount of information by using a simple model that predicts it. Similarly, we understand the number 0.33333... by thinking of it as one-third. The first way of representing the number requires five concepts ("0", "decimal point", "3", "infinity", "infinity of 3"); but the second way can produce all the data of the first representation, but uses only three concepts ("1", "division", "3"). Chaitin argues that comprehension is this ability to compress data. This perspective on comprehension forms the foundation of some models of intelligent agents, as in Nello Cristianini's book "The shortcut", where it is used to explain that machines can understand the world in fundamentally non-human ways.https://en.wikipedia.org/wiki/Understanding#As_a_model

Bad idea to reference your common sense or intuitions when discussing relativity that you obviously don't understand.

Gregory Chaitin propounds a view that comprehension is a kind of data compression.[19] In his essay "The Limits of Reason", he argues that understanding something means being able to figure out a simple set of rules that explains it. For example, we understand why day and night exist because we have a simple model?the rotation of the earth?that explains a tremendous amount of data?changes in brightness, temperature, and atmospheric composition of the earth. We have compressed a large amount of information by using a simple model that predicts it. Similarly, we understand the number 0.33333... by thinking of it as one-third. The first way of representing the number requires five concepts ("0", "decimal point", "3", "infinity", "infinity of 3"); but the second way can produce all the data of the first representation, but uses only three concepts ("1", "division", "3"). Chaitin argues that comprehension is this ability to compress data. This perspective on comprehension forms the foundation of some models of intelligent agents, as in Nello Cristianini's book "The shortcut", where it is used to explain that machines can understand the world in fundamentally non-human ways.https://en.wikipedia.org/wiki/Understanding#As_a_model

Similarly, we understand the number 0.33333... by thinking of it as one-third.

Quote from: hamdani yusuf on 15/01/2024 16:26:12 both travelling twins always move at speed 0.999c Not true. The fundamental error of almost everyone who talks about a paradox is to forget that a change of velocity is an acceleration. Even if you could have instantaneous acceleration, "go there at c and come back at c" is two different velocities.

Quote from: hamdani yusuf on 16/01/2024 02:13:00Similarly, we understand the number 0.33333... by thinking of it as one-third. So how do we "understand" 1.414213......, 3.141459..... 2.71828..... or any other irrational number?

I'll let competing ideas compete, and let the best idea win. They don't have to be perfect, but I'll stick to the best one for the time being.