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Again point well missed, who are you to say what they believe in is nonsense, that seems arrogant to me, is what you believe truer? In the words of Jimmy Carr "there are two types of idiot in this question, those who believe the bible is litterally true and those who believe religion has no value".

No. I simply disagree with it. (I don't give negative points) I don't need your permission to feel sorry for someone. We don't. You do. Repeatedly, and I don't need your permission to find that characterization annoying. And he was entirely irrelevant to the topis. If intellectually challenged people are happy believing nonsense or making useless gestures, nobody's trying to stop them. But that doesn't change the fact that Nietzsche didn't predict a second coming and was hostile to religion generally. It's not hard to believe whatever your father says when you're 4 years old. Most people don't get disillusioned with their parents' religion until age 10 or 12. Some just keep waving at cars till they die, and that's all right too.

I do appreciate everyone answering this question, I honestly had no idea I was opening such a can of worms! While I am aware of Relativity and how frames of reference worked I was genuinely unaware of how fundamental the idea of reference frames was in this scenario. Thank you very much for answering my question in detail, while I am sure I am stilling missing much of the concept due to not speaking mathematics I am much closer than I was to understanding.

OK, that's two negs for two reasonable post's, are you offended or insulted by my conjecture? What makes you think I want people to feel sorry for him? These arguments are really very weak indeed. I merely provided context that I think lends credence to my premise, his early life was steeped in a belief in the god of his father's teaching, which he was entirely happy with until his fathers very painful death. My point is, sigh 🙄, the village idiot is perfectly content with his lot, he doesn't even care that we call him the village idiot; which is a really neat fit with the madman parable I mentioned earlier in this thread and whomsoever Jesus actually was, which is also an irrelevance to my premise; someone inspired the book and it seems was inspired by who many thought was an equivalent of 'the village idiot' or <insert idiom here>.

OK, I got it. Now I get your point about the importance of (centripetal) acceleration. Clever. Correct. Still, if frame-dragging is present (and significant), the clocks at rest in the dragged frame would be the fastest ... while rotating (with respect to distant stars) and having(?) centripetal acceleration ... You understood exactly what I intended to convey. Thank you!

A few grams?

The end might produce a few grams of actual matter in a brief burst of radiation. "Explode" makes it sound bigger than a wink. The vast majority of the original mass radiates away as massless particles, mostly photons and gravitons, neither of which is a building material for stars.

for the differential aging in the twins' paradox, not the acceleration, nor the frame change. Yes, when the orbiting twin turns his gaze around, he will appear to be approaching instead of receding. So the redshifted view of the tower clock will change to blue shift, the difference being purely Doppler effect in both directions. The dilation is due to speed, and speed isn't affected by where anybody is looking, so the dilation is unchanged at the far side of the planet. Yes, there is acceleration, but all of it orthogonal to motion, so since the 'twins' are at the same potential, the dilation is constant for the entire orbit. It is objective. The orbiting twin will be younger when the meet again, just like the one that goes out and back to the distant star. To do this in special relativity, the planet can have no mass, and the 'orbiting' twin would need to curve his path via say a string tied to the center of Earth to get him to curve is path like that. Rockets also works, but the engineer in me hates to waste fuel when there's a better way.

The station isn't necessary. All that is needed is a frame reference. One can say that each rocket is moving at .9999c relative to frame arbitrary abstract inertial frame S which happens to have nothing stationary in it. The lack of a stationary object in S would make it difficult for any rocket guy to directly measure that speed, but it can still be computed. A frame is, after all, an abstraction, not a physical thing. So if X is moving west relative to S at 0.9999c and Y is moving east relative to S at 0.9999c, then X is moving at about 0.999999995c relative to Y and V-V. (.9999 + .9999)/(1 + 0.9999*0.9999) = 0.999999995 In that case the velocity of the two respective departure points relative to each other needs to be specified. Without that, there is no way to compare the rocket speeds relative to each other since there can be no common frame. Usually, in the absence of an explicitly specified frame, an observer on any object (a rocket say judges his own speed to be zero.

It's simply that velocity always has to be stated relative to something in order to have any meaning. 2 cars in adjoining lanes on a motorway may be travelling at 5mph relative to each other but at 75 and 80mph relative to a policeman by the side of a road with a speed camera, and at 20 and 25mph relative to a truck which it itself travelling at 55mph relative to said policeman. The problem is we unthinkingly assume "the ground" is our reference frame in daily speech, treating it a bit as if it were an absolute frame of reference, when in reality there is no such thing. (This should however be a bit more obvious in space.) So you can't say you have a spacecraft "travelling at 0.999% of c" without saying with respect to what. Hence I proposed a space station to provide a reference, so that these speeds have a meaning.

Yes Bach seems to be a great inflexion point in the evolution of Western music. All the pros play Bach, even rock musicians. I remember once talking to a Thai pianist, playing jazzy hotel stuff in a hotel bar in Bangkok. My colleague asked him what music he played for pleasure at home and he replied "Bach". I tried to persuade him to play some for me, as he was taking requests, but he said the hotel management wouldn't like it (!) and I could not convince him. I also recall once listening to an organ performance of the Art of Fugue in my room in Oxford, when a fellow chemist came in who was a jazz clarinettist (He had been a member of the Kent Youth Orchestra before coming up). One of the weirder fugues was playing and he couldn't make it what it was. He thought it sounded so edgy it must be some c.20th composer - Messiaen or something. He was amazed when I told him. But if you liked what I posted, this (opening chorus, 1st 7 mins) is another of my all time favourites as a choral singer, from Part V of the Christmas Oratorio (apologies if I've posted this one before at some point): You have to click the "watch on YouTube" link to see it. This is also in 3/4. My impression is Bach does not often use that time signature and when he does, he often thinks it's time for some gaiety. In the video you can actually see the musicians enjoying it. They are making eye contact with each other and smiling.

Just to link it up for Moontanman, the bits I bolded above are worked examples (reverse order) of what I described in the 3rd post:

It was, because otherwise one rocket's relative speed to the other one is equal and opposite to the converse, no matter what relativity principle you use (Galilean or Einsteinian). It's exactly as Swansont said with 0.5, 0.5, giving 0.8 (in units of c) It's perhaps an illuminating exercise to do it with 0.99999 and 0.99999. It gives (0.99999+0.99999)/(1+0.99999*0.99999) = 0.9999999999 (in units of c) which is practically just c. But, and here's what interesting, with small velocities as compared to c. 0.00001, 0.00001, it gives (0.00001+0.00001)/(1+0.00001*0.00001)=0.00002000000000 which is so close to the simple addition of velocities that nobody could tell the difference. That's why our intuition tells us velocities are additive.

Fantastic indeed. Thank you. The Suite muffled by the voices was great for setting the mood. I've long felt that all music gravitates towards Bach... or emanates from it. Or something like that. I feel that music before Bach is a preamble to Bach. And music after Bach is a corollary to Bach. Even atonal music seems like an attempt to break the shackles of Bach while still doing music. Like 'how little Bach can one get without making just noise?' I'm very partial about Bach, you see. I'm very Bach-centred. So thank you.

RIP Dickey Betts

It's always about who is measuring what relative to what.

Thank you, exactly what I was wondering but I didn't realize the station was necessary.

For Moontanman: in the above, that 0.5c is as measured by the space station, and each rocket to the station; and the 0.8c is as measured by each rocket to the other rocket. For the space station, the closing speed of the rockets (which is not the speed of either rocket) is c.

If two rockets each approached the space station at 0.5c, from opposite directions, they would be approaching each other at 0.8c (.5 + .5)/(1 + 0.5*0.5) (Galilean addition would give you c)

If you don't summon any other observer, then it's 0.99999c relative to each other, as Swansont and others said or implied, and/or/thus I'm missing the point. / / 🤷‍♂️

Just come across this Flashmob video from Lausanne, in the course of revising the bass line in my favourite chorus from Bach's St. John Passion: The cellist plays part of one of Bach's Cello Suites and ends on a (baroque pitch) G, from which the basses can get the C they need to start the fugue. The conductor pretends to be a waiter delivering beer to the next table, until the moment arrives. They sing it very well, especially given the acoustics of a busy restaurant. Pretty cool, I thought. This chorus is in 3/4, with real JSB swing, syncopation and drive. Fantastic music.

Impartial observer... not what I had in mind, I was just thinking of the two rockets approaching each other and how they would see each other. The relative speeds of the cars was what I was getting at, I really didn't realize I wasn't being clear on that. I understand there is no track to measure anything by in relativity.

No, you've got it, that's the point. You obviously don't add the velocities, as you would in classical dynamics.

I think you really need to get clear on the difference between measuring closing speed (which is the speed of a gap, a nothing), and the speed of a thing. And it depends a lot on who is observing. Say the fastest car in the World can do 500 km/h. Stick two of them on a track facing each other and run them, at top speed. The gap between (from the point of view of the track) them is decreasing at 1000 km/h. Hang on! That's faster than the car can go! But that 1000 km/h isn't the speed of either car according to the track. Sure, if the track considers it from the point of view of one of the cars, then the other is getting closer at 1000 km/h, but that reference point is moving according to the track. It's an illusion, if you like. Relativistic addition comes in (in this scenario) when you consider the point of view from one of the cars. Each car can consider itself as still, and the other car moving towards it. But note that the track is also moving towards it! The track is moving towards each car at 500 k/h, and the other car is moving towards it at 500 km/h relative to the track. And that's where you cannot (at relativistic speeds where it starts to matter) just add the 500 and 500. Each car will consider the other car approaching at 999.99999 km/h. The track considers the closing speed as 1000 km/h, and the cars consider the other is approaching at 999.99999 km/h. These are different numbers.

Moon, I think you're trying to think of an "impartial" observer who's sitting on some dock of the aeronautical bay, so to speak, and watches both approaching each other at 0.99999c. Then they would see each other approaching at higher than that, but never c or higher. You must run the Einstein velocity transformation formulas that to see how much. The relative speed from their POV would indeed be closer to c than that 0.9999c (or however many pieces of c she/he sees them from the dock. If you actually run the calculations, you'd find, I don't know, something like 0.999999999999999999999999999999c relative to each other (you actually must run the calculation if you want to know how many 9 digits closer to c). I think you're implicitly thinking of this "impartial observer" but failing to say so, and causing some amount of understandable confusion. Is that so? Does that help?