I miss this thread. Wish James was around, just to try (and no doubt fail) to come to the same page on this finally. Would be fun.
He had me convinced. Always presented interesting challenges, pushing the threshold of disagreement into the minutest details.
What’s your take on the op?
I’m not sure anymore.
Do you want to work it out together?
Possibly… but restarting the thread I agree with you that Phyllo is right in the first response.
“You can either set the triggers so the flash is simultaneous in the train frame of reference or you can set the triggers so that the flash is simultaneous in the station frame of reference. But you can’t do both."
Do you now think there is more to it than this?
No, not really. Could be fun to draw a space time diagram anyway though.
I’ve read a lot of James words over the last few days - other threads he made about relativity, not this one. He was always insistent that, if he were clever enough and careful enough, he could make a pair of clocks synchronised in all frames. “If I treat these two clocks identically, they should stay identical”.
Really, the rest of the so called “paradox” was superfluous - this was actually the center of his disagreement with relativity. The ability to synchronize clocks in one reference frame and keep them synchronized in all reference frames, via “equal treatment”.
There were other confusions as well though. I think it took some time to convince him about the train being length contracted in the station frame, for example. Drawing a space-time diagram could have cleared that up I think.
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In another thread, he tries to develop some clever way of making clocks synchronised in both frames of reference. In this thread, he tries to develop some clever way of making sure the train is the same length in both frames of reference.
All of the stopped clock paradoxes are really this, at heart. They are James attempt at proving relativity is wrong by trying to cleverly circumvent relativity, via his “equal state + equal treatment = equal result” statement.
He says relativity can’t disagree with that, but you @Jakob , when you were fixed cross, noted that in fact relativity CAN disagree with that, even MUST. If you’ve treated both ends of the train equally in the station frame of reference, then you’ve treated them unequally in the frame of reference going 0.5c, the reference frame the train will be in by the time it’s coming to the station.
Now his answer to that was, “the 0.5c reference frame doesn’t exist yet”, which is… imo a misunderstanding. All reference frames “exist” all the time. But even so, let’s just grant him that for a minute.
If you’ve begun to accelerate the frame, then at the very least he must admit that the train is now in a reference frame it wasn’t in before, even if infinitesimally. So if you’ve begun acceleration of both ends of the train equally in the original frame, then already - even if infinitesimally - this new frame of reference the train finds itself in, if it looks to past events to ask the question, “when did the train start accelerating?”, will have to conclude that the front and back began accelerating at an infinitesimally different time.
And as the train continues to accelerate, those infinitesimals add up. I’m not sure what the calculus is there - it is calculus, I’m sure, as we’re adding up an infinite series of infinitesimals - but they add up, and they would show unambiguously that, no matter how clever James thought he was being, the final reference frame for the train and the original reference frame for the train cannot agree that all acceleration was done equally and simultaneously on both ends of it.
James endeavour was, “can I construct a situation within relativity cleverly enough to override relativity?” THAT’S the paradox he thought he found.
Interestingly, James isn’t the first person to think of accelerating an object like this. In fact it has a paragraph on wikipedia
Another example is Bell’s spaceship paradox: If the endpoints of a body are accelerated with constant proper accelerations in rectilinear direction, then the leading endpoint must have a lower proper acceleration in order to leave the proper length constant so that Born rigidity is satisfied. It will also exhibit an increasing Lorentz contraction in an external inertial frame, that is, in the external frame the endpoints of the body are not accelerating simultaneously. However, if a different acceleration profile is chosen by which the endpoints of the body are simultaneously accelerated with same proper acceleration as seen in the external inertial frame, its Born rigidity will be broken, because constant length in the external frame implies increasing proper length in a comoving frame due to relativity of simultaneity. In this case, a fragile thread spanned between two rockets will experience stresses (which are called Herglotz–Dewan–Beran stresses[8]) and will consequently break.
Bolded paragraph is what James is trying to do.
I found a beautiful little online tool to help with visualizing lorentz transofmrations
source code here:
If you input x coordinates in terms of light-seconds, and t coordinates as seconds, everything kinda just makes sense.
Here’s another, even better one - the prevous one is a bit buggy, but with a bit of playing I figured out how to make this one work really well:
It bugs out a bit when you try to zoom out though which isn’t nice.
Sad but true I’m afraid.
He was working to validate or flesh out his affectance ontology. I sparred with him using my ontology, asserting that every bit of matter, energy or affectance must be relative to itself before being able to be relative to another point, which it can only be incompletely. This at least corresponds to Relativity.
I ran across these Intro to Philosophy notes from Fall 2002. I was connecting the dots weird way back then lol.
Function=Value
“Function” (Value) “Ontology”…
Can you tie that in to this thread?
No, I don’t mean that. Affectance is barely brought up in this thread
Why would an entirely different person chime in on you sharing your class notes here? How is he supposed to know why you decided to share your notes?
I was responding to Jakob.
Plus the entirely new person deals with planetary orbits and masses & stuff.
I don’t think this post is a reply to Jacob
oh really? intriguing! What do you think it is?