How to be an Inertial Observer?

In summary: The observer must know the distance to the clock to determine its rate.With Minguizzi...There is no distance requirement. The observer only needs to know the relative speed of the observer and the distant clock.
  • #1
Mike_Fontenot
249
17
I think this "elephant-in-the-room" issue is important enough to deserve its own thread. I believe it is at the root of many of the disagreements that repeatedly occur on this forum. So I copied my last posting over from the "The case for True Length = Rest Length" thread. Here is that posting:
Mike_Fontenot said:
[...]
The issue that you (JesseM and GrayGhost) are both "dancing around" (the elephant in the room, really), is this: Whenever a person is NOT accelerating for some segment of his life, WHEN in that segment can he legitimately be considered to be an inertial observer?
[...]

Here's another way to describe that "elephant-in-the-room" issue:

The standard time dilation result of special relativity answers the following question:

"What does an inertial observer conclude about the rate of ticking of some particular distant clock, which is moving at a constant speed relative to the inertial observer?".

The standard answer is:

"The inertial observer will conclude that the distant clock is ticking gamma times slower than his own watch."

But what exactly IS "an inertial observer"? Is it someone who is TEMPORARILY not being accelerated, but who may have accelerated in the past, or who may choose to accelerate in the future? Or is it someone who is PERPETUALLY unaccelerated? If it's the latter, does that mean that each tiny bit of matter making up the observer's body has never accelerated before? Could ANY person meet THAT test?

And, in order to determine the clock rate of the distant clock, does the inertial observer need to know the distance to that clock?

The Dolby& Gull simultaneity, and the Minguizzi simultaneity, answer the above two questions very differently than does my CADO simultaneity.

My CADO simultaneity says that an observer is inertial during any segment of his life in which he is unaccelerated, regardless of the duration of that segment. And my CADO simultaneity says that the tick rate of the distant moving clock does NOT depend on how far away that clock is.

If the observer is NOT perpetually unaccelerated, then both Dolby&Gull and Minguizzi DO require that the distance to the moving clock be specified, before they can determine its tick rate. So anyone who subscribes to either the Dolby&Gull simultaneity, or to the Minguizzi simultaneity (or to ANY simultaneity other than my CADO simultaneity), needs to be clear about the answers to the above two questions, before they can say anything about the tick rate of the distant moving clock. And what they say about that tick rate will often NOT be what the standard time dilation result says.

Mike Fontenot
 
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  • #2
An inertial observer is one which is not accelerating.
It has nothing to do with being an actual `person' or observing `being;' nor does it have any connection with their past, future, thoughts, whims, or aspirations.
 
  • #3
Mike, a question for you:

What is the standard SR answer to the following question:
What does an inertial observer conclude about the speed of some particular distant object, which is moving at a constant speed relative to the inertial observer?​

And a followup question:

What is the standard SR answer to the following question about the same observer and object in the same situation:
What does the distant object conclude about the speed of the inertial observer?​

NOTE: Both the observer and the object have been perpetually inertial.

And finally, what do you think of this question:
Do the observer and the object need to know the distance between them at any particular time in order to answer the first two questions, respectively?​
 
  • #4
Typically an SR problem will deal with some restricted window of space and time rather than all of infinite spacetime (for example, the twin paradox only deals with the window of time from the moment the twins depart to the moment they reunite), so relative to a particular problem, I'd say an "inertial observer" is just an observer who remains inertial throughout the window being considered. You can also make more specific statements about restrictions, like "from time T1 to T2, observer A is moving inertially".
 
  • #5
JesseM said:
Typically an SR problem will deal with some restricted window of space and time rather than all of infinite spacetime (for example, the twin paradox only deals with the window of time from the moment the twins depart to the moment they reunite), so relative to a particular problem, I'd say an "inertial observer" is just an observer who remains inertial throughout the window being considered.
[...]

By the term "inertial observer" in the above, do you mean that the traveler can use the standard time-dilation result to determine the rate of ageing of the home twin, at any instant during his entire trip in which he is unaccelerated (i.e., excluding only the instant at the turnaround)?

Or, are you using the term "inertial observer" ONLY to mean that the traveler is unaccelerated?

With Dolby&Gull simultaneity, the traveler CANNOT use the standard time-dilation result to determine the home twin's rate of ageing for at least some portion of the unaccelerated outbound leg, and he also CANNOT use it for at least some portion of the unaccelerated inbound leg.

With Minguizzi simultaneity, the traveler CAN use the standard time-dilation result for the entire unaccelerated outbound leg, but he CANNOT use it for at least some portion of the unaccelerated inbound leg.

So, if we use the first of the two senses of "inertial observer" above, Dolby& Gull would say that the traveler ISN'T an "inertial observer" for at least some portion of BOTH of the unaccelerated legs. And Minguizzi would say that the traveler ISN'T an "inertial observer" for at least some portion of the unaccelerated inbound leg.

Mike Fontenot
 
  • #6
Can you provide some references for your "Dolby&Gull simultaneity" and "Minguizzi simultaneity"?
 
  • #7
Mike_Fontenot said:
By the term "inertial observer" in the above, do you mean that the traveler can use the standard time-dilation result to determine the rate of ageing of the home twin, at any instant during his entire trip in which he is unaccelerated (i.e., excluding only the instant at the turnaround)?

Or, are you using the term "inertial observer" ONLY to mean that the traveler is unaccelerated?
I mean that the observer is unaccelerated for the entire duration of the window of time that is being considered for the problem. If this is true then he will have a single inertial rest frame throughout the window, and of course the time dilation equation works in any inertial frame.
Mike_Fontenot said:
With Dolby&Gull simultaneity, the traveler CANNOT use the standard time-dilation result to determine the home twin's rate of ageing for at least some portion of the unaccelerated outbound leg, and he also CANNOT use it for at least some portion of the unaccelerated inbound leg.
But according to my use of "inertial observer", the traveler is not an inertial observer in the twin paradox problem because he does change velocity during the window of time being considered (the window which starts with the twins departing and ends with them reuniting). The stay-at-home twin would be an inertial observer in the twin paradox, even if he accelerates some time before the two depart or after they reunite, since those would be events outside the window of time being considered in the twin paradox. And if the stay-at-home twin uses Dolby&Gull simultaneity to determine the time of events on the traveler's worldline, for the duration of the trip away and back it will agree with simultaneity in the inertial frame where the stay-at-home twin is at rest for this period, even if it might disagree for events before the departure or after the reunion, or for events further away than the worldline of the traveling twin (and in any case, I think it's generally implicit in the phrase "inertial observer" that this observer uses the inertial frame where he is at rest when making frame-dependent judgments about simultaneity and so forth).
Mike_Fontenot said:
With Minguizzi simultaneity, the traveler CAN use the standard time-dilation result for the entire unaccelerated outbound leg, but he CANNOT use it for at least some portion of the unaccelerated inbound leg.

So, if we use the first of the two senses of "inertial observer" above, Dolby& Gull would say that the traveler ISN'T an "inertial observer" for at least some portion of BOTH of the unaccelerated legs. And Minguizzi would say that the traveler ISN'T an "inertial observer" for at least some portion of the unaccelerated inbound leg.
Where do you get the idea that either Minguizzi or Dolby&Gull would define the phrase "inertial observer" in terms of these coordinate systems? Are there any quotes from their papers where they use this specific phrase in a way that suggests such a definition?
 
  • #8
JesseM said:
Typically an SR problem will deal with some restricted window of space and time rather than all of infinite spacetime (for example, the twin paradox only deals with the window of time from the moment the twins depart to the moment they reunite), so relative to a particular problem, I'd say an "inertial observer" is just an observer who remains inertial throughout the window being considered.
[...]

OK, so from your last response, I can re-write the above statement this way (so that it is no longer circular):

"so relative to a particular problem, I'd say an 'inertial observer' is just an observer who remains UNACCELERATED throughout the RESTRICTED window being considered."

Your whole concept of "the restricted window being considered" seems very fuzzy and ill-defined to me. Who decides exactly what the "restricted window" is? Why exactly is one candidate window inappropriate, while another candidate is appropriate? Who gets to decide what the restricted window is?

And regardless, the point is still that a proponent of the Dolby&Gull simultaneity, or a proponent of the Miguizzi simultaneity, or a proponent of ANY simultaneity other than my CADO simultaneity, CANNOT talk about using the standard time-dilation result in any particular situation, without first specifying either:

(1) that the observer, including all the atoms and elementary particles that currently make up his body, has never accelerated in the past, and/or never will accelerate in the future, or

(2) that the distance to the clock in question is such that, considering the observer's prior and/or future accelerations, the use of the standard time-dilation result is justified.

I DO recall many of the proponents of the non-CADO simultaneities on this forum often referring to the time-dilation result when discussing various scenarios, but I don't recall ever hearing them discuss the issue of whether or not that result is justified in the given scenario, or specifying the distance to the clock, and how that distance relates to prior and/or past accelerations,or specifying exactly what the "restricted window" IS, and WHY that should BE the "restricted window".

Whenever I've referred to the time-dilation result in my previous postings, I haven't specified those things either. Because with my CADO simultaneity, I don't HAVE to specify them: an observer is justified in using the time-dilation result during the entire duration of ANY segment of his life in which he is unaccelerated, no matter how long or short that segment is. Period. The distance to the clock in question is irrelevant. An observer who can use the time-dilation result for ANY clock can use it for ALL clocks. There are no "restricted windows" to be determined and defined. It's simple.

Mike Fontenot
 
  • #9
zhermes said:
Can you provide some references for your "Dolby&Gull simultaneity" and "Minguizzi simultaneity"?

They're not MY simultaneities. In fact, I'm convinced that they are both fatally flawed. But various other forum members are proponents of them. I gave some links in another thread in this post:

https://www.physicsforums.com/showpost.php?p=3183896&postcount=239 .

Mike Fontenot
 
  • #10
Just a note that this question already arises in Newtonian physics, except there we talk about Galilean inertial observers and Galilean inertial frames. Newton's laws assert that Galilean inertial frames exist, even if no inertial bodies do. Thus, we know that the solar system obeys to very high accuracy Newton's equations in standard form, which requires an inertial frame, even though all the bodies, and the observers involved are undergoing accelerated motion due to their mutual gravitational attraction.
 
  • #11
Mike_Fontenot said:
Your whole concept of "the restricted window being considered" seems very fuzzy and ill-defined to me. Who decides exactly what the "restricted window" is?
I'm talking about the types of problems that appear in books that involve some well-defined beginning and end, beyond which the writer doesn't even tell you what the objects are doing.
Mike_Fontenot said:
And regardless, the point is still that a proponent of the Dolby&Gull simultaneity, or a proponent of the Miguizzi simultaneity, or a proponent of ANY simultaneity other than my CADO simultaneity
No mainstream physicist would be a "proponent" of any version of simultaneity except in the sense that some might be more useful or elegant than others. But everyone understands that in relativity there is no "correct" version of simultaneity, you can use any version you want and you won't be "wrong" although depending on your choices the analysis might be made more or less difficult mathematically.
Mike_Fontenot said:
CANNOT talk about using the standard time-dilation result in any particular situation, without first specifying either:

(1) that the observer, including all the atoms and elementary particles that currently make up his body, has never accelerated in the past, and/or never will accelerate in the future, or

(2) that the distance to the clock in question is such that, considering the observer's prior and/or future accelerations, the use of the standard time-dilation result is justified.

I DO recall many of the proponents of the non-CADO simultaneities on this forum often referring to the time-dilation result when discussing various scenarios
I would bet that you are just misunderstanding what people were arguing--can you name one of the people arguing against you who was a "proponent" of any version of simultaneity whatsoever, or who used the standard time dilation formula in the context of a non-inertial simultaneity convention where (2) didn't hold? When I argue that it's valid to use some non-CADO simultaneity convention for an accelerating observer, I'm certainly not suggesting that such a convention is "correct" while CADO is "wrong", just that they are both equally valid. And if elsewhere in our discussion I refer to the standard formula for time dilation, it's probably just because I'm calculating things from the perspective of an inertial frame, not any sort of non-inertial simultaneity convention like Dolby&Gull or CADO.
 
  • #12
Mike_Fontenot said:
OK, so from your [JesseM's] last response, I can re-write the above statement this way (so that it is no longer circular):

"so relative to a particular problem, I'd say an 'inertial observer' is just an observer who remains UNACCELERATED throughout the RESTRICTED window being considered."

Let's get specific:

The home twin says that the "restricted window being considered" is the entire trip of the traveler (because she is unaccelerated during that window). She is told (by JesseM, and presumably by Dolby&Gull) that she is justified in using the standard time-dilation result, during that entire window, to determine the traveler's ageing (regardless of whether or not she accelerates outside of that window).

But the traveler says that the "restricted window being considered" is his entire OUTBOUND leg (because he is unaccelerated during that window). He is told (by Dolby&Gull) that he is NOT justified in using the standard time-dilation result, during that entire window, to determine the home twin's ageing.

So even though each twin can declare a restricted window, in which he or she is unaccelerated, those two windows are very different: in one, the time-dilation result holds, while in the other, it doesn't.

How can you tell, in advance, whether any given restricted window allows the time dilation result to be used? (Call it a "compliant window", because it is compliant with the time-dilation result). One way is to use Dolby&Gull to determine the other twin's ageing, and check to see if the answer agrees with the standard time-dilation result. But if you have to do that, what's the value in using the time-dilation result at all?

Maybe there is a simper way (for Dolby&Gull simultaneity, or for Minguizzi simultaneity, or for any non-CADO simultaneity) to determine the compliancy of any given restricted window. If so, I suspect it won't be nearly as simple as it is for CADO simultaneity: In CADO simultaneity, ALL restricted windows are compliant: If an observer isn't accelerating, he can use the standard time-dilation result. Period.

The bottom line is that, if you are using any non-CADO simultaneity in a particular scenario, and if you want to make use of the standard time-dilation result in some declared "restricted window", you must establish that the given restricted window is compliant.

Mike Fontenot
 
  • #13
JesseM said:
[...]
When I argue that it's valid to use some non-CADO simultaneity convention for an accelerating observer, I'm certainly not suggesting that such a convention is "correct" while CADO is "wrong", just that they are both equally valid.
[...]

In my previous postings in this thread, I've been arguing that Dolby&Gull simultaneity (and all other non-CADO simultaneities) are much more cumbersome than CADO simultaneity. It IS intriguing to me that many people so abhor the sudden age swings of the home twin, which occur in CADO simultaneity when the traveler accelerates, that they are willing to embrace alternative simultaneities which have such burdensome costs ... anything to get rid of those pesky age swings.

But you (JesseM, and also other members) well know that my most important concern with Dolby&Gull simultaneity (and with all other non-CADO simultaneities) is not that they are cumbersome (even though they are), but rather that they are INVALID. They are invalid because they contradict the traveler's own elementary calculations ... calculations which use only quantities that he determines from his own elementary measurements.

I doubt that JesseM, Fredrik, Dalespam, and some others will ever agree with me on that. But if there are still some undecided forum members out there, they can start with this post:

https://www.physicsforums.com/showpost.php?p=3106767&postcount=38 .

Mike Fontenot
 
  • #14
Mike_Fontenot said:
Let's get specific:

The home twin says that the "restricted window being considered" is the entire trip of the traveler (because she is unaccelerated during that window). She is told (by JesseM, and presumably by Dolby&Gull) that she is justified in using the standard time-dilation result
Sure, you're justified in using it in an inertial coordinate system. Has anyone said anything about an "inertial observer" being justified in using the standard time-dilation result in a non-inertial coordinate system like Dolby&Gull's? Do Dolby&Gull themselves ever say this? In the specific case of Dolby&Gull, that coordinate system will only agree with the inertial one in the "restricted window if we also know that the observer remained inertial in a larger window which includes the sending and receiving of every radar signal that was reflected at any point in spacetime within the original window. As long as the original window is restricted in both time and space, then this larger window only need extend the original one by a finite amount of time.
Mike_Fontenot said:
In my previous postings in this thread, I've been arguing that Dolby&Gull simultaneity (and all other non-CADO simultaneities) are much more cumbersome than CADO simultaneity. It IS intriguing to me that many people so abhor the sudden age swings of the home twin, which occur in CADO simultaneity when the traveler accelerates, that they are willing to embrace alternative simultaneities which have such burdensome costs ... anything to get rid of those pesky age swings.
Again you are obviously misunderstanding the whole point of the argument. No one "objects" to the CADO system or its sudden age swings, they only object to the claim that it is in some sense "more correct" than any other non-inertial coordinate system with a different simultaneity convention, since all non-inertial coordinate systems are OK to use in relativity. It so happens that the alternative coordinate systems people have brought up do have less sudden swings in simultaneity during the acceleration phase of the twin paradox, but one could equally well construct a non-inertial coordinate system where the swing in simultaneity was even larger than in the the CADO system, and this would be another perfectly valid alternative.
Mike_Fontenot said:
But you (JesseM, and also other members) well know that my most important concern with Dolby&Gull simultaneity (and with all other non-CADO simultaneities) is not that they are cumbersome (even though they are), but rather that they are INVALID. They are invalid because they contradict the traveler's own elementary calculations ... calculations which use only quantities that he determines from his own elementary measurements.
And you know that people always ask you to DEFINE WHAT THE HELL YOU MEAN BY "ELEMENTARY CALCULATIONS" (and how calculations about coordinate-based concepts like simultaneity are supposed to follow from 'elementary measurements' when the readings on measuring-instruments are predicted to be the same regardless of your choice of coordinate system), a request you always studiously ignore. Really, if you just keep repeating this claim without support or explanation, and using it to try to make the case that the mainstream view about all non-inertial coordinate systems being equally valid is somehow incorrect, I think I'll just report your posts to the mods as violating physicsforums policies on non-mainstream views.
 
  • #15
Mike_Fontenot said:
I think this "elephant-in-the-room" issue is important
I don't know why you think this is important. It seems rather trivial to me. An inertial frame is, by definition, perpetually inertial. Whether or not you use an inertial frame where some specific observer is at rest for some given period of time doesn't change any of the physics, nor does whether or not you use some non-inertial coordinate system instead.
 
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  • #16
Mike_Fontenot said:
Let's get specific:

The home twin says that the "restricted window being considered" is the entire trip of the traveler (because she is unaccelerated during that window). She is told (by JesseM, and presumably by Dolby&Gull) that she is justified in using the standard time-dilation result, during that entire window, to determine the traveler's ageing (regardless of whether or not she accelerates outside of that window).

But the traveler says that the "restricted window being considered" is his entire OUTBOUND leg (because he is unaccelerated during that window). He is told (by Dolby&Gull) that he is NOT justified in using the standard time-dilation result, during that entire window, to determine the home twin's ageing.

Those are two totally different scenarios. First you have a twins, one which leaves Earth turns around and comes back to earth, other which stays at earth.

Then Scenario two you have a twin on Earth and one in a spaceship moving at a constant velocity with respect to each other.

As for what your actually asking it simply depends on the scenario you are look at. What happens outside that doesn't matter to what you are looking at. You put a scenario together and that's what you look at.
 
  • #17
JesseM said:
[...]
No one "objects" to the CADO system or its sudden age swings, they only object to the claim that it is in some sense "more correct" than any other non-inertial coordinate system with a different simultaneity convention, since all non-inertial coordinate systems are OK to use in relativity.
[...]

If it makes you feel better, you can substitute the phrase "Inconceivably Stupid" for "Invalid". I don't regard the difference between those two terms to be of any importance. Choosing to use any non-CADO simultaneity for the reference frame of an observer who sometimes accelerates is comparable to choosing to use non-Lorentz simultaneity for the reference frame of a perpetually inertial observer.

Mike Fontenot
 
  • #18
Mike_Fontenot said:
If it makes you feel better, you can substitute the phrase "Inconceivably Stupid" for "Invalid". I don't regard the difference between those two terms to be of any importance. Choosing to use any non-CADO simultaneity for the reference frame of an observer who sometimes accelerates is comparable to choosing to use non-Lorentz simultaneity for the reference frame of a perpetually inertial observer.

Mike Fontenot
Do you think there is any practical reason it's "inconceivably stupid", or is this just a sort of aesthetic opinion?
 
  • #19
JesseM said:
Do you think there is any practical reason it's "inconceivably stupid", or is this just a sort of aesthetic opinion?

It is stupid for the same reason that choosing to use non-Lorentz simultaneity for the reference frame of a perpetually inertial observer is stupid.

In the spirit of GR, you are of course free to choose almost any set of coordinates, with very few limitations. If you like, you can choose to wear a wristwatch whose tick rate is based on the current Dow-Jones average. You can also choose to continually hit yourself in the head with a hammer. But either of those choices is stupid, and irrational.

Mike Fontenot
 
  • #20
For specific problems there are many reasons why one might rationally and reasonably use a non-standard coordinate system. Sometimes the standard systems are the stupid ones to use. Your assertion is merely an unfounded generalization.
 
  • #21
Mike_Fontenot said:
It is stupid for the same reason that choosing to use non-Lorentz simultaneity for the reference frame of a perpetually inertial observer is stupid.
And what is that reason, exactly? Is it a practical one, like the difficulty of making calculations in a non-inertial frame? If so I would say it is equally "stupid" to use a non-inertial frame for any calculation in flat spacetime, regardless of whether you're dealing with an accelerating observer or not. But perhaps your reason is more like an aesthetic opinion?
Mike_Fontenot said:
If you like, you can choose to wear a wristwatch whose tick rate is based on the current Dow-Jones average. You can also choose to continually hit yourself in the head with a hammer. But either of those choices is stupid, and irrational.
These cartoonish comparisons don't illuminate your reasoning--why is it "irrational" to use certain coordinate systems? Usually we only say an action is rational or irrational relative to a specific goal, so for example hitting your head with a hammer would be perfectly rational if you had the goal of causing serious head injury to yourself. With what goal in mind would it be irrational to use Dolby-Gull as opposed to CADO, but rational to use CADO as opposed to an inertial frame?
 
  • #22
Response to both JesseM and DaleSpam:

To paraphrase Louis Armstrong's famous response, "If you don't know by now why using non-Lorentz coordinates for the reference frame of a perpetually-inertial observer is stupid, you ain't NEVER going to know".

And if either of you DOES know, then you SHOULD also know the reason that using non-CADO coordinates for the reference frame of an accelerating observer is stupid, because the reason in both the accelerated and perpetually-inertial cases is the same.

Mike Fontenot
 
  • #23
Mike_Fontenot said:
Response to both JesseM and DaleSpam:

To paraphrase Louis Armstrong's famous response, "If you don't know by now why using non-Lorentz coordinates for the reference frame of a perpetually-inertial observer is stupid, you ain't NEVER going to know".
The issue wasn't about using non-Lorentz coordinates for an inertial observer, it was about using non-CADO coordinates with an accelerating observer. Again, if you have an actual coherent reason for considering the non-Lorentz coordinates "stupid" in the first case, like the practicality of doing the calculations, I don't get why it wouldn't be equally "stupid" to use non-Lorentz coordinates for an accelerating observer--isn't it still true that calculations involving an accelerating observer are easier in an inertial frame than in the CADO coordinate system?

But I guess the reference to Armstrong's quote probably means you're tacitly acknowledging there is no practical or rational reason behind your convictions, that it's a completely aesthetic/emotional thing like "knowing" what jazz is. In your mind I guess non-CADO coordinates just "don't mean a thing 'cause they ain't got that swing", and that's all there is to it!
 
  • #24
Mike_Fontenot said:
And if either of you DOES know, then you SHOULD also know the reason that using non-CADO coordinates for the reference frame of an accelerating observer is stupid, because the reason in both the accelerated and perpetually-inertial cases is the same.
another typical non-response. Your opinions and personal preferences are not divinely-mandated.
 

1. What is an inertial observer?

An inertial observer is an observer who is not accelerating and is therefore not experiencing any forces. This allows them to measure motion and make observations without any external influences.

2. How do I become an inertial observer?

To become an inertial observer, you must be in a state of constant motion or at rest with no acceleration. This can be achieved by being in a free-falling elevator or in outer space with no gravitational forces acting on you.

3. What is the significance of being an inertial observer?

Being an inertial observer is significant in the field of physics as it allows for the observation and measurement of motion without any external influences. This is important in understanding the laws of motion and the principles of relativity.

4. Can anyone be an inertial observer?

In theory, anyone can be an inertial observer if they are in a state of constant motion or at rest with no acceleration. However, in practical terms, this is not always possible as there are always some external forces acting on us in our daily lives.

5. What experiments can be done by an inertial observer?

An inertial observer can conduct experiments to study the motion of objects, the effects of gravity on objects, and the principles of relativity. They can also measure the speed of light and the passage of time in different frames of reference.

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