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Everything posted by Genady
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No, turning of C does not affect B. B just observes C moving with different velocities and calculates the total effect. However, turning of B affects B and its observations. The same in the classical scenario, with A staying on Earth and B going out and returning. Turning of B does not affect A. It does affect B and its observations. We would have to consider the turning of C and its effect on the C observations, if we described the scenario in the C frame.
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I'd like to recognize my cultural bias, as much as possible. Where should I look?
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Yes, you are. I picked some specific numbers for illustration. If you go through the math of Lorentz transformations, you'll find that it works out the same for any velocity. Nowhere I considered the twins' velocities as the same as the signals' velocities. I assume that the signals are light. The twins' velocities are whatever they are.
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No, the acceleration is not 0. The air in the wind moves with the constant velocity before it gets to the wall. At this time, its acceleration is 0. But when it hits the wall, the air cannot continue moving as before because it cannot go through the wall. It starts slowing down before it hits the wall, because of the air in front of it, and eventually it stops moving toward the wall. So, its velocity changes during this time. Change in velocity per time is acceleration.
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It is the same point all the way, i.e., the starting point in the full process, the source point of the signals, and the meeting point at the end. IOW, the observer A.
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No. Two eyes allow to estimate a distance to an object in 3 dimensions, 2 dimensions, 4 dimensions, etc. You have a triangle with the known length of one side and two angles. From these, the brain computes the distance.
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If B takes a picture of himself with a timestamp, say, 3, by his clock, and C takes a picture of himself with the same timestamp, 3, by his clock, then when they compare the pictures, they will look the same. The same at any timestamp.
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They were moving toward each other. The OP wanted to avoid acceleration and instead to "synchronize" their clocks by a signal from the middle point.
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No. C did not age more than B. C started his clock before B. That's why by the time B starts his clock C has already 5 on his.
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Here it is step-by-step, in the B frame. 1. Signal goes out from the middle point in both directions. 2. One signal reaches C. C starts his clock. 3. Another signal reaches B. B starts his clock. At this moment in the B frame, B's clock shows 0 while C's clock already shows 5. 4. It takes 10 units from then for B to reach the crossing point. B observes that C's clock advances 5 units during this time. 5. At the crossing point, B's clock shows 10. C's clock also shows 10, because it was on 5 when B started his clock, and it advanced by 5 since then.
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No. When they meet, the age of B, since receiving his signal, is 10. The age of C, since receiving his signal, is 5+5=10. 10=10.
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In my quoted description, 'down' is direction of gravitational acceleration.
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No. In the last scenario, after B receives his signal, B ages by 10 while he observes C aging only by 5. The point is that when B receives his signal, C is already 5 in the B frame, because in this frame C received the signal before B.
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If a synchronizing signal is sent from a point in the middle in the two directions, then, in the B frame, it will reach C before it reaches B, because C moves toward B in twice the speed with which the middle point moves toward B. Thus, by the time the signal reaches B, the C clock will be already on 5. Then by the time they meet, the B clock advances 10, while the C clock advances 5, which makes them equal, 10.
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One way to see it is to consider that when B turns around, he experiences an acceleration. This acceleration affects his clock similarly to a gravitational field. A clock in gravitational field runs slower than the clock which is not. Thus, during the turning around the clock of B will advance little compared to the clock of C. In my example, this makes C to age 10 years more than B while B is turning. There are other ways to analyze this situation, without involving gravity. In any case, after turning around B is in a different inertial frame than he was before, and this difference makes for the extra difference in their ages.
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Let's see it from the frame of B observing C. By the time they reach the turning points, B aged 10 while C aged 5. After B turns, let's say almost momentarily, B will still be 10, but he will observe C being 15. By the time they reach the crossing point, B is 20, and C is 20. The C will find all the same symmetrically.
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Another one: Trudeau says unidentified object was shot down over northern Canada | CNN Politics
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OK. Got it. There will not be a contradiction, because at the crossing point, i.e., when they meet again, they will be at exactly the same age.
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I don't see an inconsistency. Could you elaborate? What do you mean, "making a completely symmetrical travel"? Which "contradictory results" are observed?
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Yes, he will feel like going down slope to the center and then up slope again. This is because our vestibular system detects gravity as a direction down. It is not very different from your ball example.
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If they measure a shortest distance from one corner to another on the diagonal, they'll find that the line of the shortest distance goes along the surface, touching the surface all the way. Thus, the surface is flat, not slopped. Another way is by drawing a large triangle on the top surface and measuring its angles. If the surface is slopped inward, the sum of the angles will be less than 180o. If the sum is 180o, the surface is flat. They will find that it is in fact 180o. Not slopped.
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The ball will behave like you describe, right. But the light rays will keep going straight and along the surface. So, if they just look at the structure, or make geometrical measurements, they will see that the top is flat. It would not be slopped toward the center.
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They will see the same as from outside, but close-up. The walls will stick out from the ground at an angle, tilted backwards. The top surface will look flat. BTW, people on Earth can easily see its curvature by getting up to mountains, or by watching a ship disappearing behind the horizon, for example. I live on an island and the next island is about 60 km away. It is behind the horizon and not visible from the shore. But when I climb to our highest elevation, in a good weather, I see the island appearing into the view.
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Can we care about and act for the Earth as a whole rather than about and for the people, current or future? Like, if I see a beautiful painting getting destroyed by a flood, I'd want to save the painting because it is so beautiful, not necessarily because of the future generations that might see it.