Genady

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.

In my quoted description, 'down' is direction of gravitational acceleration.

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.

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.

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.

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.

Another one: Trudeau says unidentified object was shot down over northern Canada | CNN Politics

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.

I don't see an inconsistency. Could you elaborate? What do you mean, "making a completely symmetrical travel"? Which "contradictory results" are observed?

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.

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.

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.

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.

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.

Half a cube. The southern hemisphere would still be a hemisphere.

A useful mental trick to qualitatively answer questions is exaggeration. Imagine the sticking out part as large as possible, e.g., the bases of the corners located at the equator, and the height equals the planet radius, so the center of the flat area is on the North Pole, and the northern hemisphere is almost entirely inside. The answers become quite clear, I think.

This is incorrect. Anything, true or false, can be derived from a false statement. See the truth table and the second dot here:

No, we do not.

I have a question that actually belongs to the psychology rather than relativity forum: Why do you even bother? IOW, why to feed the troll?

Several comments in this thread related the duty of care to the future of their children, grandchildren, etc. What about people who don't have children to care about? Do they just ignore the issues?

You see what I mean? I am from these people. In spite of the similarities in shape. There are also other categories that I am very different from.

DISAGREE!!! Not 'ultimately the same'. Rather, somewhat similar. Mostly, similar in shape, like the snowflakes. Unlike the snowflakes, we are very different inside. I trust what it says about us as much as I trust what it says about the origins of Earth, the origins of life, historical events, etc. *I don't open links without good reason.

OK, got it. However, if we all means every person, then I don't think this ("We all have a price for turning a blind eye") is correct. I don't know about this. I don't understand the grammar of this sentence. Sorry.

Ahh, I got the pun.

How can I know what the arguments are?