md65536

I think it's better to stick to "rubber sheet" instead of blanket, because the latter doesn't suggest as well that stretching is involved. If there's no stretching, there's only extrinsic curvature, and the analogy isn't as good. I think you could probably even demonstrate intrinsic curvature using a stretched rubber sheet without requiring extra dimensions.

Here's a few people you could ask if that's why they used the phrase: "within a certain region of space around it — nothing can escape its gravitational pull. Inside what's known as the black hole's event horizon, not even light itself can escape from a black hole." -- Ethan Siegel https://www.forbes.com/sites/startswithabang/2020/03/24/sorry-stephen-hawking-but-every-black-hole-is-still-growing-not-decaying/ 'Physical objects (those that move at or more slowly than the speed of light) can pass through the “event horizon” that defines the boundary of the black hole, but they never escape back to the outside world. Black holes are therefore black — even light cannot escape — thus the name.' -- Sean Carroll https://www.preposterousuniverse.com/blog/2020/11/26/thanksgiving-15/ "Ultimately, when the star has shrunk to a few tens of kilometers size, its gravity grows so enormous that nothing, not even light, can escape its grip. The star creates a black hole around itself." -- Kip Thorne https://www.its.caltech.edu/~kip/scripts/PubScans/BlackHoles-Thorne-Starmus.pdf Incidentally, I first looked up Misner, Thorne, Wheeler - Gravitation thinking they might have used the phrase there, and they didn't, and I couldn't find a case where Hawking used it either. The older descriptions of black holes introduced them as "collapsed stars", I guess because that was their only expected existence? They introduced them by describing the formation of the horizon, with a lot more to think about than just "nothing can escape (not even light!)". So I can see how that phrase is at least disappointing. However, I couldn't suggest an improvement, and I think simply omitting "even light" would be even less helpful.

I think it's more useful to include it than not to. It's not just aimed at people who expect light to escape from everything, but also those who wouldn't even consider that light might be related at all. That light--specifically--can't escape a black hole is a huge part of an average lay understanding of black holes.

The expectation that light ALWAYS escapes comes from "in my experience" here, not from the statement "Even light cannot escape!" At best the statement acknowledges that it might be expected that light wouldn't escape, not that it must be expected. But that justifies inclusion of "even light". I think it's more likely that someone already expects that light should escape, and the statement corrects that common(?) misconception, rather than that someone doesn't think that light is expected to escape until after reading the statement. This doesn't really matter though. The statements including "even" are correct, and succinct. I think it's a good way to describe black holes. I think it's useful for beginners to understand that BHs involve spacetime curvature, and I think it's unlikely that anyone who already understands is going to be misled by the word "even".

Typically laypeople would think of inability to escape in terms of strong gravity and its effect on masses, so it is reasonable to emphasize that it also applies to light. I don't think the writers needed to worry, "this word might confuse people who already understand this."

The phrase "not even light can escape a black hole" is correct. Do you find it confusing? The statement doesn't imply that light is expected to escape from everything, or that if IT cannot escape then NOTHING can, and I doubt many others have that confusion.

You wrote "I feared as much" but I think you got it close enough to not fear. Here, Genady has drawn the world lines of the different particles, onto the same Minkowski diagram. The diagram, and the coordinates on their grid, represent the measurements for one particular inertial observer (aka. inertial reference frame). You can draw the same worldlines on a Minkowski diagram for a different observer, and the subluminal "time like" world lines will be at different angles. If you make a physical mark at some fixed location in a this particular Minkowski diagram, and extend it through time, you get a vertical line like the Moon's. So this diagram represents the rest frame of the moon. If your mark is at rest, all events at that mark have the same spatial component (but they have different time component), and the spatial distance of the pairs of events you described will be the same in this particular frame's Minkowski coordinates.

Surely you're joking. What do you call the female equivalent of an American?

There are several answers, but why wouldn't "You're Teresa's daughter" be the simplest assumption? It minimizes the number of people and relationships being talked about. "Mother in law" adds an assumption of marriage, which at least is a cultural bias an AI would need to be trained for.

What do you do if there are 2 pirates who want it, and then neither wants it after the adjustment, or vice versa? What if there's 3 pirates on one side and 1 on the other, and you move some treasure and two (or three) pirates move to the other side? How many adjustments will it take to guarantee there are 2 on each side?

Yes, that's right. I'm assuming that if someone wants a share, and someone else takes it, and the former doesn't also get a share that they're satisfied with from that same division of shares, then they're dissatisfied. Like a child saying they wanted the purple-flavour yogurt that their sibling took and the parent opening a new purple-flavour yogurt and trying to argue that it's the same amount... it's hopeless! Only their own judgment can determine if they're satisfied.

What I wrote is ambiguous... The solution I'm working on seems to work, but I'm having trouble proving it:

Nope, I'm wrong again! This is bad reasoning. Lol, this puzzle has broken my brain. Every time you say I'm right I disagree. Every time I realize something I just said was wrong, I forget some other detail and say something else wrong, all the time flipping back and forth between 2 incorrect positions. What I forgot is that is that it doesn't matter if someone is not satisfied with letting some other share be taken, IF they're also taking a share that they're satisfied with at the same time. So it might (should? but I don't want to give any more answers unless I figure it out) be possible to have someone split up the treasure, and have either everyone satisfied with the shares everyone else is taking, OR they're taking a share they're satisfied with. (However, my previous solution still doesn't work, sometimes not fulfilling either condition.)

My answer before isn't good enough. Consider a worst-case scenario: One pirate divides the loot, and the others evaluate. Say each of the other 4 think there is only one share that is less than equal, and that is the only share that they'd be satisfied with someone taking, but also each of the 4 think that a different share is the smallest. Then there is no share that can be kept by anyone, where they all agree on. Therefore I think that no solution that involves the piles being split up, and then allowing one of them to be kept, can work. I think any solution that involves one person splitting up the loot, would require that the shares be adjusted before guaranteeing that they all agree.

Then my previous answer is no good. I guess any pirate is satisfied if they get to divide the treasure, and any pirate is satisfied if they can pick, but obviously the others wouldn't be happy letting someone else pick.

There are a lot of extra assumptions here. 1. the treasure can be divided to any precision. This wouldn't work if the treasure was 3 large diamonds. 2. The one dividing believes they can do so exactly. 3. There is no conflict in choosing who divides and/or who picks. (I guess pirates are more peaceful than children.)

Sure, apologies for veering off-topic but the ideas still relate! If you look at the Doppler factor formula, you'll see why a sign change of v gives a reciprocal factor. Before or while looking at examples, here's a challenge. Using v=+/-0.6c, the Doppler factors are 2 and 0.5 (perhaps opposite of intuition?) and Lorentz factor is 1.25. Given a statement like, "B spends 1 year traveling away while seeing A age 0.5 years. B turns around, and spends 1 year returning during which it sees A age 2 years, for total of A aging 2.5 years to B's 2," can you similarly (with no more math than that) describe what inertial twin A sees? There's no need to calculate distance, delay of light etc. https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html https://hepweb.ucsd.edu/ph110b/110b_notes/node60.html

The relativistic Doppler effect includes time dilation, and it gives a complete solution to the basic twin paradox (hard to hide aging when you can see each other age the entire time). https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

The same thing happens with the relativistic Doppler effect in the twin paradox, with an outbound and return trip at the same speed. If the clocks appear to tick at 0.5x the rate of a local clock on the outbound trip, they'll appear to tick 2x on the inbound trip. Someone once used incorrect intuition to argue on these forums that this shows that the clocks would age the same amount during the trip, thus disproving special relativity.