# Can time run backwards in an accelerating frame?

• I
• Gumby The Green
In summary, the conversation is discussing the concept of time dilation in the context of the twin paradox. The Earthbound twin experiences slower time during each leg of the journey, but catches up with the traveling twin due to the leap forward in time during the turnaround. The same applies for a distant observer, but to a greater extent. The main question is whether there is a single correct way to track time in both frames, and the answer is that time tracking is frame independent. Conventions such as Einstein synchronization may be used, but are not physically significant. The relativity of simultaneity is also discussed, with the suggestion that it is the same as the conventionality of simultaneity. However, this conflicts with previous studies and the conversation
ergospherical said:
I bet you a tenner that they would observe no such thing :)
We're going to hijack this thread if we continue the discussion - but if I drop an object of mass ##m## into a black hole of mass ##M## we will end up with a black hole of mass ##M+m## in fairly short order.

Sure, but not in fairly short order (or at all) according to the guy watching the in-fall from infinity. It’s the same reason that distant observers can never actually see the formation of an event horizon of a collapsing star.

ergospherical said:
Sure, but not in fairly short order (or at all) according to the guy watching the in-fall from infinity. It’s the same reason that distant observers can never actually see the formation of an event horizon of a collapsing star.
The OP's point, however, is that unless an observer sees an event it doesn't take place. Because there is only one valid coordinate system that the observer is allowed to use. This is the issue being challenged.

Gumby The Green said:
If light from two equidistant events reaches my eyes at the same time, I say those events are simultaneous for me. How would it make sense for me to judge simultaneity any other way?

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

Gumby The Green said:
a rod has different lengths in different frames
No, different observers in different states of motion relative to the rod measure different invariants that, because of unfortunate limitations in ordinary language as compared to precise math, they both refer to as "length" of the rod. But nothing about the rod itself changes. All that changes is which invariant each observer measures.

Gumby The Green said:
a charged particle produces different magnetic fields in different frames.
No, a charged particle's field has different effects on another charged particle depending on the second particle's state of motion relative to the first. In other words, the effect of the first particle's field on the second particle is an invariant that depends on the invariant inner product of the 4-velocities of the two particles. And this invariant can be computed in any frame you like.

Gumby The Green said:
the relativistic Doppler shift includes the effect of time dilation, which depends on the frame.
No. As I've already said, you have this backwards. The relativistic Doppler shift is the invariant, and depends, like the charged particle effect above, on the invariant inner product of the 4-velocities of the emitter and the observer. (Actually, it's only that simple in flat spacetime; in curved spacetime you have to do a more complicated invariant computation for the shift. But it's still an invariant.) And you can compute that in any frame you like.

The "time dilation" is derived from the Doppler shift by allowing for "light travel time"--but the "light travel time" computation is not an invariant, it depends on your choice of frame, and the final result it gives you, "time dilation", is also not an invariant, it depends on your choice of frame. But that doesn't mean Doppler shift is frame-dependent; it means you are looking at everything backwards, as I've already said.

Gumby The Green said:
it turns out that the magnitudes of these effects that are measured by an observer equate to their magnitude in the frame that treats that observer as stationary.
There might not be any such unique frame that treats the observer as stationary. This has already been pointed out to you many times in this thread.

In any case, once more you are looking at things backwards. Invariants are the same in any frame. But among the invariants that are the same in any frame, some will be invariants that include the 4-velocity of an observer. Obviously which invariant is relevant to a particular observer will depend on that particular observer's 4-velocity, and changing observers means changing which invariant you look at. This doesn't make any invariant frame-dependent; it means that which invariant you care about will depend on which observer you care about. None of this requires any choice of frame. The choice of frame is a convenience for calculation. It is not necessary for any physics.

Gumby The Green said:
So wouldn't it make sense to say that's the frame of that observer?
No, because there is no requirement that an observer always adopt a frame in which they are at rest. What frame do you use when planning a trip to the grocery store? A frame in which you are at rest? Or a frame in which the Earth is at rest?

Gumby The Green said:
wouldn't it make sense to say that those effects—as well as the claim that that observer is stationary and everything else is moving—are true and physical in that frame and for that observer?
It never makes sense to say that any quantity which is not an invariant is "true and physical". But it might make perfect sense to care about different invariants depending on which observer you are considering. No observer can say that they are stationary and everything else is moving in any absolute sense; no such statement can be "true and physical". But an observer can perfectly well say that they observe light signals from some source as having a particular Doppler shift (assuming they know the required properties of the source to be able to measure the Doppler shift), and (in flat spacetime) they can perfectly well attribute this Doppler shift to the relative velocity between them and the source. (In curved spacetime, as I've said, the computation has to be more complicated, because there is no invariant notion of "relative velocity" between spatially separated objects in curved spacetime. But there are more complicated invariants that correspond reasonably well to our intuitive notion of "Doppler shift".)

Gumby The Green said:
Wikipedia is not a valid reference. Find a textbook or peer-reviewed paper that takes the viewpoint you are advocating, and then we can talk.

vanhees71
Gumby The Green said:
why does there appear to be unanimity to the contrary here?
It should be noted that the term "reference frame" is ambiguous. We have had some previous threads on this, which I can't find right now, but basically, there are at least three distinct concepts that can be referred to by the term "reference frame":

(1) A coordinate chart. (In many SR discussions, "inertial frame" means a particular kind of coordinate chart on flat spacetime, the one implied when the Minkowski metric is written as ##ds^2 = - dt^2 + dx^2 + dy^2 + dz^2##.)

(2) A tetrad field. This is a more technical concept, but if you think of the four orthonormal coordinate basis vectors of an SR "inertial frame", in the sense described just above, i.e., the unit vectors in the ##t##, ##x##, ##y##, and ##z## directions at every point, that is an example of a tetrad field. The general definition is an assignment of a tetrad--a set of four orthonormal vectors, one timelike and three spacelike--to every point in some region of spacetime.

(3) A physical apparatus for making measurements of time and length. In the simplest case, this will be a clock and a set of three mutually perpendicular rulers that are all at rest relative to the clock. Or, more comprehensively, a family of such clock-ruler setups spread at fixed intervals throughout your laboratory, all at rest relative to each other.

There are, of course, obvious correspondences between these definitions. For example, given a tetrad field covering a region of spacetime, one can always define a coordinate chart covering the same region. (The reverse is not necessarily true.) And given a clock-ruler setup of the kind described above in your laboratory, one can always define a tetrad field covering the region of spacetime corresponding to the "world tube" of the laboratory. So in some particular cases, such as the kinds of cases Einstein considered in his initial papers on SR, you can have a "reference frame" that defines all three of the above things at once, and in correspondence with each other (for example, Einstein's clock-and-ruler vision of an "inertial frame" in SR).

Because of such correspondences, one can, in some particular situations, get away with using the term "reference frame" without specifying which of the three above meanings is intended. But that is still a bad habit, and can easily bite you when you find yourself using the same term to mean different things which now no longer have a well-defined relationship with each other. Or when two people are using the same term to mean different things and are talking past each other.

And, of course, of the three things above, note that only #3 is an actual physical thing. The other two are mathematical abstractions. So if you're going to make claims about what is "true and physical", it's very important to be careful about how you use terms like "reference frame", which can refer both to things that are "true and physical" and things that aren't.

Gumby The Green and vanhees71
Gumby The Green said:
Relative motion causes relativistic effects that can include measurable physical effects that differ depending on the frame. For example, a rod has different lengths in different frames
This is a subtle point that I wish to discuss a bit further.

Let's say that Bob, in a spaceship, is building a new bunk for his cabin. Bob measures the length of his cabin and the length of the bunk he is building.

Bob's measurement of the length of the bunk is invariant, as all measurements must be. Other invariant facts include Bob's measurement of the length of the cabin and whether or not the bunk will fit in the cabin. The relevant law of physics is that if Bob's measurement of the length of the bunk is smaller than Bob's measurement of the length of the cabin then the bunk will fit in the cabin. All frames will agree on Bob's actual measurements and whether or not it fits. Those are physical invariants.

The length of the bunk is frame-variant. In other words, all frames will agree on what number Bob obtains with his measurement device. Not all frames will agree that that number is the length. But the physics doesn't care about the frame-variant length. If some frame finds that, due to different orientations of the cabin and the bunk during its construction, the frame-variant length of the bunk is larger than the frame-variant length of the cabin, it will still fit if the invariant law says it will fit. Conversely, if some frame finds that the frame variant length of the bunk is smaller than the frame-variant length of the cabin, it will still not fit if the invariant law says it will not fit.

So the "measurable physical effect" is the actual number that Bob measures on his device. That is an invariant and it does not differ depending on the frame. The judgement about whether or not that number is the length does differ depending the frame, so it is a bit less "physical". Sometimes these less physical quantities, the frame-variant ones, are still super-useful, so you shouldn't hesitate to use them as needed. But it is important to pay attention to the context of a discussion so that you can pay attention to what quantities are invariant and which are not, and recognize that the invariant ones are the ones that drive physics.

nasu, vanhees71, Gumby The Green and 3 others
Dale said:
The judgement about whether or not that number is the length does differ depending the frame
Not that this judgment might be about other invariants, such as the invariant that Alice, who is moving relative to Bob, calls the "length" of the bunk, based on her measurements of the bunk (obviously done by a different process from Bob's). And if, as you say, the orientations of bunk and cabin were different during construction, Alice might have yet another invariant that she calls the "length" of the cabin, based on her measurements of that, and this invariant might be less than Alice's "length of the bunk" invariant. Alice's invariants are perfectly good invariants; they're just the wrong ones to look at if you want to know whether Bob's bunk will fit inside Bob's cabin.

vanhees71 and Dale
PeterDonis said:
Not that this judgment might be about other invariants, such as the invariant that Alice, who is moving relative to Bob, calls the "length" of the bunk, based on her measurements of the bunk (obviously done by a different process from Bob's). And if, as you say, the orientations of bunk and cabin were different during construction, Alice might have yet another invariant that she calls the "length" of the cabin, based on her measurements of that, and this invariant might be less than Alice's "length of the bunk" invariant. Alice's invariants are perfectly good invariants; they're just the wrong ones to look at if you want to know whether Bob's bunk will fit inside Bob's cabin.
Yes, Alice and Bob will both agree about the value that the other person will get when doing the respective measurements. Both measurements are invariants, as they must be. Their disagreement is only in the labeling of that measurement as “length”. They each believe that their own number is the length and that the other number is not the length. And both agree which invariants determine if it fits.

vanhees71
Gumby The Green said:
The only thing I care about here is what's true in the frame of the traveling twin, i.e., what clock times for the stationary observers does he conclude are simultaneous to his at each point during his journey?
When the traveling twin is accelerating, he is changing any frame that he used to synchronize his clocks at a distance to maintain a constant speed of light. Whatever method he is using, the assumption that the speed of light is constant forces him to keep adjusting his "synchronized" clocks. He is the last one who can claim that the Earth's clocks ran backward.

PS. With the amazing sensitivity of current clocks and experiments, your hypothesis would be apparent in many of today's experiments.

vanhees71
FactChecker said:
He is the last one who can claim that the Earth's clocks ran backward...

PS. With the amazing sensitivity of current clocks and experiments, your hypothesis would be apparent in many of today's experiments.
I don't think you've understood what I was arguing for. I was saying that during his acceleration away from the Earth and the distant observer—who is farther away from him than the Earth is—he would believe that the time of that distant observer runs backwards relative to his own. But note that I'm not reasserting that hypothesis here (since I've promised to not do that yet). I'm just clarifying it and refuting what I see as a straw man of it...

To make it a little more clear, let's say that there's another observer who's only slightly farther from him than the Earth and let's say that the acceleration is finite. In this case, he would perceive that observer's time as slowing down relative to his own due to "gravitational" time dilation during his acceleration. The farther away that observer is, the slower the traveler will perceive her time to be. The question I've posed is essentially this: As we increase the distance between these two people, what happens when the observer's rate of time in the traveler's frame can't decrease any further?

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, it would happen behind the horizon and thus he would have no way to directly measure it in real time (he could only measure the effects of it after he stops accelerating, which would be combined with the forward leaps in time he perceived to produce an end result that would be equal to any other mundane calculation of differential aging in an inertial frame). So no, the backwards time flow itself couldn't be directly measured by any experiment.

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Dale
Dale said:
Bob's measurement of the length of the bunk is invariant, as all measurements must be.

The length of the bunk is frame-variant. In other words, all frames will agree on what number Bob obtains with his measurement device. Not all frames will agree that that number is the length.
This aligns with what I understand. It sounds similar to the concept of proper time. I was tempted to call it "proper length" but then realized that there's a subtle distinction: proper length is the length measured in the rod's rest frame, but you're saying that the measured length of the rod in any frame is invariant, which makes sense to me.

Dale said:
But the physics doesn't care about the frame-variant length.

So the "measurable physical effect" is the actual number that Bob measures on his device.
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?

Dale said:
Their disagreement is only in the labeling of that measurement as “length”. They each believe that their own number is the length and that the other number is not the length.
If they have disagreements on what the rod's length is, doesn't that effectively mean that they each occupy a particular frame (the frame whose length calculation aligns with what they measure)?

PeterDonis said:
Alice's invariants are perfectly good invariants; they're just the wrong ones to look at if you want to know whether Bob's bunk will fit inside Bob's cabin.
True but 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?

Dale
Gumby The Green said:
True but 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?
If the ladder flies through Alice's cabin then the invariant fact of the matter is that Alices cabin will be destroyed.

The ladder will not be in a very usable condition either.

However, if Alice opens her front and back windows at the right times, the ladder can pass through successfully whether it fits or not.

PeterDonis said:
Because of such correspondences, one can, in some particular situations, get away with using the term "reference frame" without specifying which of the three above meanings is intended. But that is still a bad habit, and can easily bite you...

And, of course, of the three things above, note that only #3 is an actual physical thing. The other two are mathematical abstractions.
I see. Well I could use a term like "observational frame", like that Wikipedia article does, to specify that it's type #3. But isn't it just implied that that's the case when someone speaks of the frame as belonging to an observer?

jbriggs444 said:
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.

Dale
PeroK said:
Sagittarius A-Star said:
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.

PeroK and weirdoguy
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
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:
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.

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?
"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:
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.

Gumby The Green said:
What matters here is the relativity of simultaneity, which is determined by relative motion, not convention
Wrong. See below.

Gumby The Green said:
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).

PeroK
Gumby 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?
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.

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?
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:
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.

Last edited:
vanhees71
After moderator review, the thread will remain closed. The OP's question has been sufficiently answered. Thanks to all who participated.

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