Then strictly by what you say, shouldn't that should be a symmetric situation? Why is the outcome different?Mister T said:
Is there anything other than acceleration that would cause something to be non-inertial?robphy said:
Like I said in the OP, it's not so much whether the website is wrong or right, I just want to analyze the exact difference between the 2 thought experiments. I also wanted to revisit the topic about whether or not acceleration plays a role, if not the only role, in the twin paradox.FactChecker said:
Just out of curiosity, is the website's spacetime diagram wrong for the space traveler in the rest frame?robphy said:
student34 said:
A non-zero acceleration anywhere along a worldline segmentstudent34 said:
In Minkowski spacetime. a non-inertial traveler's diagram is not a complete map of spacetime.student34 said:
Yes, but we are putting in the path-lengths to show what happened. I am trying to figure out the exact reason for the difference between the two diagrams.robphy said:
I guess then it comes down to whether or not non-inertial is defined only by acceleration?
They are symmetric. The right hand one doesn't correspond to any meaningful analysis, obviously so because the clock ticks on the black worldline are wrong in the upper half.student34 said:
Becasuse, as @Ibix said directly above, the second scenario posits an assumption (the Earthbound character turns around, i.e. accelerates) that has no basis in reality and thus is a bogus analysis of anything meaningful.student34 said:
I don't think I explained what I really wanted to in the OP. Whether or not the diagrams make any sense, I would like to really analyze what breaks the symmetry between the two scenarios.Ibix said:
Nothing breaks the symmetry. Were we not clear? They ARE symmetrical, it's just that one represents reality and one does not.student34 said:
Specify exactly what you think the two scenarios are. Who feels proper acceleration in each case? How long does each twin coast between meetings and/or accelerations?student34 said:
I would like to know why one does not represent reality. Why does the scenario on the right turn into the image that robphy posted (since the image in the OP is not really correct) on the right side of the screen in post #4. Why aren't they symmetrical diagrams? Is it only because of non-inertial frame/acceleration, or are there other reasons?phinds said:
This looks very interesting. I am going to learn exactly what it means.robphy said:
But on the other thread called "Sabine on GR", there were advisors here that did not believe acceleration was the only reason.phinds said:
You are conflating different things.student34 said:
You don't seem to be addressing what you quoted from what I wrote. Instead, I feel like you are going into a semantic argument.Ibix said:
I do not understand how it is wrong to attribute acceleration to time dilation. Does a non-inertial imply acceleration? If so, then what you say in your 3rd paragraph seems to contradict that acceleration does not cause time dilation.Ibix said:
Because time dilation is an effect between inertial clocks. Acceleration does not come into it. And differential aging (what Sabine was calling "real time dilation") depends on path length, not acceleration. As I told you in the Sabine and GR thread, in fact.student34 said:
Because the diagram on the right is not a diagram of an inertial frame. In fact it's not even a diagram of a non-inertial frame. It's just something the website author waved their hands and drew to look like a mirror image of the diagram on the left, without even asking the question whether that mirror image diagram represents any actual valid coordinate chart. It doesn't.student34 said:
Okay, this is interesting. I looked for exact definitions of non-inertial, and all I could find is that acceleration implied non-inertial. What else can be considered non-inertial that the twin would experience? Whatever this is, if it exists, will help narrow down the difference that I am looking for.Ibix said:
Because the website author just made it up. They didn't use physics to produce it.student34 said:
Non-inertial frame. The fact that an object, in this case the traveling twin, has nonzero proper acceleration does not mean you have to use a non-inertial frame to describe their motion. Conversely, the fact that an object, in this case the stay at home twin, is inertial all the time does not mean you have to use an inertial frame to describe their motion.student34 said:
The twin paradox is a thought experiment in special relativity where one twin travels at high speeds while the other remains on Earth. When the traveling twin returns, they will have aged slower than the twin who stayed on Earth, leading to a perceived paradox.
The twin paradox is based on the principles of special relativity, which state that time is relative and can be affected by factors such as speed and gravity. In this scenario, the traveling twin experiences time dilation due to their high speed, causing them to age slower than the twin on Earth.
While the twin paradox is a thought experiment, it is based on real scientific principles and has been tested through experiments with atomic clocks. These experiments have confirmed the effects of time dilation and the validity of the twin paradox.
The twin paradox is not a true paradox, as it can be resolved by taking into account the different frames of reference for the traveling twin and the stationary twin. Both twins experience time passing normally from their own perspective, but their different frames of reference lead to a perceived difference in aging.
While the twin paradox is often used as a thought experiment, there are real-life examples of time dilation and the effects of special relativity. For example, astronauts on the International Space Station experience time dilation due to their high speeds, causing them to age slightly slower than people on Earth.