Let’s not dance around what this paradox is. This is the well-known ladder paradox (or barn paradox), and its resolution is precisely the fact that simultaneity is relative. I close the doors simultaneously in my reference frame. Yes, in a manner of speaking, this “looks to be simultaneous to [me]”, but this isn’t a problem. It looks simultaneous in one reference frame, and not simultaneous in a different reference frame.
No shit. At any non-zero speed, the plank can only remain in the barn for a finite amount of time. As this speed increases, the time decreases. What’s your point?
OK. This is a different – but also well-known – paradox, the Ehrenfest paradox. I’m going to change your hexagonal disk back to a circular one, since by your own admission its peculiar geometry is to make visualization easier. The radius of your disk doesn’t shrink, because any point along the circumference moves orthogonally to the radial vector. Since the radius doesn’t shrink, your disk can’t fit into a cylinder of smaller radius.
Yes, the circumference gets smaller by a factor of gamma. Since the circumference is no longer 2πR, we conclude that the disk is not in Euclidean space. Acceleration must warp spacetime.
This comment reveals that you don’t really understand what doing the math actually entails, and makes me suspect that you don’t trust mathematics because you refuse to put in the work to understand mathematics. You don’t need to assign a precise length to the plank – just call it L in the rest frame.
The reasons I harp on you to do the mathematics is the following:
– In a sense, the burden of proof is on you to explain why the paradox fails. Special relativity is a mathematical theory built upon a few axioms about the nature of the physical world. Any contradiction must be mathematical, and once you point out what that contradiction is, you should be able to trace it back to which axioms are in conflict, and thus which we need to get rid of or alter.
– To expand on the previous point, no one said math is easy. It takes a lot of time, something that few people have. Since you are the one who wants to overturn relativity, please do so using mathematics or experimentation. Why am I limiting you to those? Because your paradox leads to contradiction due to common sense. Common sense is often wrong, particularly in physical regimes (such as relativistic or quantum ones) where our brains didn’t evolve, and so we must rely on experimentation and mathematics to navigate these domains.
– Everyone is harping on you to do the math because when you do the math, you understand the problem and the paradox. This is why math textbooks are filled with proofs that are “exercises left for the reader”. You understand physical theories best when you solve problems with them. Similarly, you can’t understand how to paint by simply watching someone paint – you have to get your hands dirty and play around. Arguing by thought experiment is fine, but it only enables you to pose questions (which are frequently ill-proposed because your assumptions aren’t explicit). It does not equip you with the machinery to answer those questions.
So? If I showed up at an academic conference on Islam with a dissertation on a new and radical interpretation of the Koran, but I don’t understand a lick of Arabic, who would take me seriously?
I don’t trust thought experiments because it is very easy to do something with language and without realizing it you have done something that is grammatically and semantically sensible but not physically sensible.
I can do the same thing.
I fail to see what this has to do with anything.
A few things about this paradox
How is she moving relative to me if we always remain the same distance from each other?
Even if we were moving past each other, why is this a problem?
Really? Really? Getting up from a stationary position and moving is not notable acceleration?
But it does! If you curve through space, you’re in an accelerated reference frame!
I’m not sure what you’re getting at here. I have a feeling you’re confused about how infinitesimal quantities can be related, but it seems like the crux of your complaints against special relativity can be encapsulated in this quote of yours:
Are you referring obliquely to Selleri’s argument against special relativity? I’m not sure, but you’ve also made mention of walking around turntables and of trains on circular tracks, so I’d advise you to do some reading on the Sagnac effect, as well as on how different synchronization conventions cause Selleri’s paradox to disappear in the limit of an infinite radius (i.e., linear motion).