The discussion centers on the implications of time dilation and simultaneity in the context of the twin paradox, specifically regarding a traveling twin and their observations of stationary observers. The traveling twin perceives the Earth's time as running slower during their journey, with significant leaps during acceleration phases. The conversation raises critical questions about the physical reality of time in different frames, particularly whether the distant observer's time can be perceived as running backwards in the traveler's frame. Key insights include the distinction between coordinate time and proper time, and the role of conventions like Einstein synchronization in defining simultaneity.
PREREQUISITESPhysicists, students of relativity, and anyone interested in the nuances of time perception in different frames of reference, particularly in the context of the twin paradox and accelerated motion.
Well of course I'm assuming that the cabin's front and back door are both open, that the bunk fits through them without touching them or anything else in the cabin, and that the bunk's trajectory allows it to fly through both doors.jbriggs444 said:If the ladder flies through Alice's cabin then the invariant fact of the matter is that Alices cabin will be destroyed.
PeroK said:
I understand the conventionality of simultaneity, but it has no physical consequences and thus isn't relevant here. What matters here is the relativity of simultaneity, which is determined by relative motion, not convention, as that paper explains. And as it quotes Poincare as saying, "The simultaneity of two events should be fixed in such a way that the natural laws become as simple as possible." So while it's technically true that simultaneity can be defined in a way that's slightly different (in a way that's inconsequential) from what I suggested (using the Einstein synchronization convention, thus assuming the isotropy of the one-way speed of light), I think my point stands that it wouldn't make sense to define it any other way.Sagittarius A-Star said:That is a definition of simultaneity. You could define it also differently.
No, that's not the answer. The answer is that the coordinates you are implicitly using are not valid at or beyond the Rindler horizon. So any statements made using them are meaningless. By "meaningless" I don't even mean "frame-dependent". I mean meaningless, as in not well-defined at all. As in "not even wrong" (to use Pauli's phrase). That is what multiple people in this thread have been telling you all along.Gumby The Green said:If the answer is that beyond that distance, i.e., the Rindler horizon, it does begin to run backwards relative to his own in some sense
There is no such thing as "the physics in Bob's frame". There is only "the physics". Physics is independent of any choice of frame. You have been told this all along as well.Gumby The Green said:the physics in Bob's frame
"Will fit inside" as it stands is not an invariant, so it doesn't tell you anything with physical meaning. You would have to specify some particular physical mechanism that detects whether Bob's bunk "fits inside" Alice's cabin, and how it detects that. There are ways to do that that will end up corresponding with what you are calling "the length of Bob's bunk in Alice's frame", but it's not as simple as you appear to imagine.Gumby The Green said:they're the right ones to use if you want to know whether Bob's bunk will fit inside Alice's cabin for a brief moment while it flies through it (like in the ladder paradox), right?
You could, but then you would have to be sure that such an "observational frame" is even possible in whatever scenario you are talking about. For example, there is no "observational frame" that will ever show some distant object's time running backwards relative to yours. So if that was the answer you've been looking for all along in this thread that has now gone on for five pages, there it is. Seems like we could have gotten there a lot quicker.Gumby The Green said:I could use a term like "observational frame", like that Wikipedia article does, to specify that it's type #3.
Wrong. See below.Gumby The Green said:What matters here is the relativity of simultaneity, which is determined by relative motion, not convention
What the paper is saying is that a convention of simultaneity can (and, the paper argues, should) be chosen so that the laws of physics "look as simple as possible". When Poincare wrote the 1898 paper that is referenced in the paper you linked to (and which you quoted from), he believed that the way to do that was to choose what in SR is called an inertial frame (though SR hadn't been discovered yet and physicists were still not fully clear on what was being defined), and use its simultaneity convention, since that made things look the simplest the way the laws of physics were formulated at that time.Gumby The Green said:as that paper explains
Poincare already expressed this concept in 1989 [sic--should be 1898] writing: “The simultaneity of two events should be fixed in such a way that the natural laws become as simple as possible. In other words all these rules, all these definitions are only the result of an implicit convention” [3]. This synchronization is then substantially conventional and is not necessarily related to true properties of physical reality [2,4].
No, the phrase “in Bob’s frame” is extraneous. The principle of relativity guarantees that the same laws of physics apply in all frames. The physicsGumby The Green said:Let me make sure I understand this. You're saying that the physics in Bob's frame doesn't care about the frame-variant length (and only cares about the length that Bob measures), right? In another frame, which measures a different length, that length becomes the one that the physics in that frame care about, right?
Definitely not! You can still assign a meaning to “Bob’s frame” even if Bob has no clocks or ruler’s with him.Gumby The Green said:But isn't it just implied that that's the case when someone speaks of the frame as belonging to an observer?
Poincare didn’t know it at the time but the simplest form is one expressed wholly in terms of invariants. That form is independent of the simultaneity convention or any other feature of the coordinates (besides simply being valid). This is what I mean by “the physics”.Gumby The Green said:And as it quotes Poincare as saying, "The simultaneity of two events should be fixed in such a way that the natural laws become as simple as possible."