Spin Time Questions

[confused2]

Is it an either/or situation? Evidence for one, is evidence for the other? If so, the sleight of hand [frame-dependent] bit takes matter off the table…hmm, matter doesn’t matter. Am I right?

"This is an example of the Lorentz-Fitzgerald contraction, in which a moving length is contracted by a factor of the square root of 1 minus V squared over C squared along the direction of its motion when it’s moving with a speed V relative to an observer. This is just the same factor as in the Einstein time dilatation. The experiment that we’ve done can be interrupted as showing that moving clocks run slow or that moving lengths are contracted."

https://youtu.be/tbsdrHlLfVQ?si=99q_1wdgJbHdnaEQ&t=2069

My interpretation is that if we sit on a muon (meson) we see length contraction (34:21 "Mt. Washington appears to be only 700 feet high") alternatively we can watch muons (mesons) going past while sitting on Mt. Washington and their clocks run slow by a factor of 9. You get one or the other but not both at the same time for a given observer. [edit .. the clock at the top of Mt. Wash. must be running slow wrt the muon clock so on second thoughts you can get both at once .. er .. I think so, anyway]

There's a sleight of hand in the setup. In the Washington setup you have (implied) a clock at the top and a clock at the bottom separated by 6,000 feet - the separation 'does things' (matters).

Imagine Bob Muon jumps on a train leaving Alice Muon on the platform. Bob gets off at the first (next) station he comes to - the station clocks aren't moving with respect to Alice so by the station clocks Bob is now younger than Alice. If he jumps on a train back to Alice he ends up twice as 'younger' as when he jumped off at the first station.

Does that make any sense?

Edit .. I see Kornee has posted while I was drinking thinking - back in the day when Mr Homm was around there were poles and barns - personally I'm happy to stop at muons and the twin paradox.

[Secular Sanity]

Funny, but at this point, I’m thinking that drinking is essential when thinking about special relativity. Maybe it has something to do with relativity of simultaneity. When is wine time on your side of the pond?

If the string snaps, why don’t all objects tear apart when they accelerate? The explanation is that one part is pulled or pushed, and then the intermolecular forces transmit that information of the acceleration to other parts of the object.

But to keep it together the rigid body must transmit information instantaneously, wouldn’t you think? This would violate the speed of light, right? 

https://www.youtube-nocookie.com/embed/kU8TEcie4hY

Say I've made three clones: Arthur, Bernard, and Charles. Arthur and Bernard's rockets are connected by a string exactly the length of the gap between them. If both rockets begin accelerating at exactly the same moment, at exactly the same rate, then what happens to the string? To be clear, all observers should agree on whether or not the string snaps. Observers can disagree about when events occur, how far apart they are, and even sometimes their order. But they must all agree on which events occur.
Since Charles is stationary, he would observe relativistic length contraction. The rockets contract in length, but the string can't because it's attached to the rockets. Therefore, the string snaps under the stress.
So, paradox solved? Bingo Bango? Not so fast. We haven't considered the other two observers yet. From the point of view of Arthur and Bernard, the string should be stationary. That means no length contraction, which means no snapping of the string. And there is our contradiction, our paradox. The string can't be both broken and unbroken. All observers must agree on which events occur. The string either snaps for everyone or it doesn't... for everyone.
Charles represents what we call an "inertial frame of reference." For special relativity, "inertial" just means stationary or moving steadily. In a space time diagram, those are always straight paths. This means we can trust our conclusions about what Charles sees. He observes length contraction, so the string snaps.
Since we know all observers must agree on which events occur, we know Arthur and Bernard will also see the string snap, but why? They don't observe the length contraction, so what's the cause of the snap?
It has to do with the distance between the rockets. It changes.
When we first described the scenario, we said the rockets must begin accelerating at the same moment and must have the same acceleration rate.
At the beginning, everyone is stationary relative to each other, so they're all in the same frame of reference. Having the rockets start at the same moment isn't the problem. It's the acceleration rate that's the problem. There's only one observer that measures those rates to be the same and that is Charles. Since they accelerate at the same rate, their paths have the same shape. The rockets maintain a steady distance from each other while contracting in length. But the string is attached to both ships, so it can't contract even though it's trying to. The extra tension makes it snap.
It also snaps for Arthur and Bernard, but for an entirely different reason: because their rockets move apart. You always measure length or distance parallel with your own space axis. Hence these distance measurements Charles made from his own frame of reference. But Bernard's axes change over time. If his space axis changes, then how he measures distance also changes. Bernard sees Arthur accelerate too quickly, which pulls on the string making it snap. Arthur sees something similar. In his frame, Bernard is lagging. He’s accelerating too slowly, which pulls on the string making it snap. ↓

https://www.youtube-nocookie.com/embed/PO4a2zO8zW8

So, in one case they’re saying that the rockets contract, but the string length remains the same for a stationary observer. Therefore, the string snaps when the rockets shrink. And in the other case, the string remains the same, but the distance between the rockets change because one accelerates faster than the other.

Argh! This is horseshit. Die you friggin muons…just die already!

[confused2]

Pro tip: closing one eye makes it much easier to read what is on the screen.