I Can time run backwards in an accelerating frame?

[Gumby The Green]

If the ladder flies through Alice's cabin then the invariant fact of the matter is that Alices cabin will be destroyed.

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.

 

[Gumby The Green]

https://www.imeko.org/publications/tc4-2014/IMEKO-TC4-2014-362.pdf

That is a definition of simultaneity. You could define it also differently.

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.

 

[PeterDonis]

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

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.

the physics in Bob's frame

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.

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?

"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.

I could use a term like "observational frame", like that Wikipedia article does, to specify that it's type #3.

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.

 

[PeterDonis]

What matters here is the relativity of simultaneity, which is determined by relative motion, not convention

Wrong. See below.

as that paper explains

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.

But today is not 1898. Today the way to formulate the laws of physics so they "look as simple as possible" is to formulate them as tensor equations, i.e., in a way that is independent of (and does not even require) any choice of frame or simultaneity convention or any other convention.

Also, you conveniently forgot to include the full paragraph in which the quote from Poincare that you gave a part of appears. Here it is including what you left out:

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].

In other words, your claim that Poincare had somehow found a way to define "simultaneity" as something other than a convention, or that the paper you linked to has, is wrong. And so is your claim that Poincare was somehow talking about relativity of simultaneity: that wasn't even a concept in 1898 (since it didn't get introduced until Einstein's 1905 SR papers).

 

[Dale]

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?

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 physics in Bob’s frame only cares about the invariants.

But isn't it just implied that that's the case when someone speaks of the frame as belonging to an observer?

Definitely not! You can still assign a meaning to “Bob’s frame” even if Bob has no clocks or ruler’s with him.

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."

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”.

More importantly for this thread, for the non-invariant based approaches, it isn’t clear how to apply Poincare’s comment to a non-inertial observer. The radar coordinates follow the same rules as Einstein synchronization for inertial frames, so there is a decent argument that Poincare’s recommendation leads towards radar coordinates. Of course, there is also a decent argument that Poincare’s recommendation rejects non-inertial frames completely.

 

[PeterDonis]

After moderator review, the thread will remain closed. The OP's question has been sufficiently answered. Thanks to all who participated.