# Constancy of c - second postulate

by mangaroosh
Tags: constancy, postulate
P: 359
 Quote by harrylin The original (and more pure or fundamental) definitions are the standard meter and kg as well as the solar day. For convenience (increased precision) impure (indirect) definitions are used nowadays. For theoretical discussions it is often better to stick to the pure definitions in order to avoid circular arguments as well as discrepancies with the definitions that were used for the formulation of the theory; however this should of course be clarified at the start. Atomic clocks as used by NIST are at rest on the earth, and corrected for such things as altitude, pressure, temperature,... Thanks to a lucky fact of the shape of the earth, it is not necessary to make a correction for the rotational speed: the clock slowdown due to rotation speed is compensated by the rate increase due to the higher potential from the bulging of the earth as a result of that same rotation.
When you say the pure definitions, do you mean things like the metre being defined in terms of the meridian (was it?) of the earth?

It seems, although not expressly stated, that measurements expressed in those units tacitly assume the earth centred reference frame as the rest frame; as you mention atomic clocks are at rest on earth, and the "pure" definitions would have been relative to the earth centred rest frame too.
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P: 15,610
 Quote by mangaroosh the measurement of the path length of light in a vacuum first has to be measured using the existing standard.
No, it doesn't. The current standard stands on its own. There is no need to do any measurements using previous standards in order to implement the current standard.

 Quote by mangaroosh It could probably easily be cleared up though by asking if the clocks flown in planes in the Hafele-Keating experiment can be said to have measured the proper second. I presume the answer has to be no, because if they did they wouldn't have had net losses or gains.
The correct answer is "yes, the clocks flown in planes in the Hafele-Keating experiment measured proper seconds". Proper time is defined as the time measured by a clock, and identified with the spacetime interval in both special and general relativity. It has nothing to do with the Earth centered reference frame, except coincidentally for clocks which happen to be at rest in the Earth centered reference frame.
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P: 15,610
 Quote by mangaroosh Just on that point, and this is somewhere I might lack clarity, but if someone uses a slower clock and a smaller ruler (than similar instruments at rest on earth) and if they measure the speed of light to be 300,000 km/s with those instruments, would it not mean that the speed of light in both frames is actually different;
What you say would be correct except that you are forgetting the relativity of simultaneity. The Lorentz transform is not just length contraction and time dilation, but it also includes the relativity of simultaneity. You cannot just ignore it and get correct conclusions.
P: 359
 Quote by DaleSpam No, it doesn't. The current standard stands on its own. There is no need to do any measurements using previous standards in order to implement the current standard.
The previous standard, however, forms the basis for the current standard. Again, the path length of light in a vacuum had to be measured using the existing standard, before the path length of light in a vacuum could be used as the standard. This would be so right the way back the line, and so the implications would be the same.

 Quote by DaleSpam The correct answer is "yes, the clocks flown in planes in the Hafele-Keating experiment measured proper seconds". Proper time is defined as the time measured by a clock, and identified with the spacetime interval in both special and general relativity. It has nothing to do with the Earth centered reference frame, except coincidentally for clocks which happen to be at rest in the Earth centered reference frame.
The seconds measured by the clocks in the Hafele-Keating experiment did not measure seconds equal to that of the clock at rest on earth, so both cannot be said to have measured proper seconds, because that would mean that proper seconds are different in each reference frame. That would infer that a measurement of 300,000 km/s in one reference frame is materially different to that in another.

 Quote by DaleSpam What you say would be correct except that you are forgetting the relativity of simultaneity. The Lorentz transform is not just length contraction and time dilation, but it also includes the relativity of simultaneity. You cannot just ignore it and get correct conclusions.
Forgive me for copying and pasting someone else's response [on another forum] to this point; I'd effectively just be saying the same thing anyway - the emphases are the other persons.

 ROS is a subsidiary shorthand way of using distance contraction and time dilation and is not a separate stand-alone component of SR. ROS is a SUBSTITUTE for distance contraction and/or time dilation. It is NOT an additional function.
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P: 15,610
 Quote by mangaroosh Again, the path length of light in a vacuum had to be measured using the existing standard, before the path length of light in a vacuum could be used as the standard.
This is not true. By historical accident the previous standard was measured before the current standard was, but there is no reason that it had to have happened that way. Back in Romer's day, in 1676, long before the BIPM ever made the first meter standard, someone could have defined a unit of length based on the distance light travels in 1/299792458 second and named it the meter.

 Quote by mangaroosh The seconds measured by the clocks in the Hafele-Keating experiment did not measure seconds equal to that of the clock at rest on earth, so both cannot be said to have measured proper seconds, because that would mean that proper seconds are different in each reference frame.
Proper time is frame invariant but path dependent. The different clocks in the HK experiment measured different amounts of proper time because they took different paths. See: http://en.wikipedia.org/wiki/Proper_time

Please read the wikipedia article to begin. It is clear that you have some misunderstanding of what proper time is, and it is one of the most important concepts of relativity. If you have any questions, I would be glad to clarify.

 Quote by mangaroosh ROS is a subsidiary shorthand way of using distance contraction and time dilation and is not a separate stand-alone component of SR. ROS is a SUBSTITUTE for distance contraction and/or time dilation. It is NOT an additional function.
Completely incorrect. I can easily come up with a coordinate transformation which has length contraction and time dilation, but not relativity of simultaneity. Likewise, I can easily come up a coordinate transform which does not have length contraction nor time dilation but does have the relativity of simultaneity.

They are three separate features of the Lorentz transform, and all three are required. You cannot simply use length contraction and time dilation and assume that relativity of simultaneity is somehow autmoatically included.
P: 3,179
 Quote by mangaroosh That's not so much to do with the equations themselves, but rather the interpretation of them isn't it? Isn't is possible that the measurements which lead to the derivation of the equations could carry certain tacit assumptions with them?
That's always possible; however both postulates were based on a long history of measurements and successful theories that were based on each.
 Is RoS a result of time dilation and Lorentz contractions?
In a certain way, but it's also the result of a human choice. Thanks to time dilation and Lorentz contraction the PoR applies to all laws of nature; consequently no absolute simultaneity can be established. Thus we can freely choose to make a relativity of simultaneity, as is the custom. Alternatively one could define for example the centre of the universe as in rest, and synchronize our clocks accordingly.
 Just on that point, and this is somewhere I might lack clarity, but if someone uses a slower clock and a smaller ruler (than similar instruments at rest on earth) and if they measure the speed of light to be 300,000 km/s with those instruments, would it not mean that the speed of light in both frames is actually different; because it would mean that the light in the reference frame moving relative to the earth actually took longer than a second to travel a distance shorter than 300,000 km?
You forgot the RoS, and according to the PoR we can't determine what is actually true for such cases. Instead, we can only operationally define such things as "speed of light" without any metaphysical meaning as to what "really" occurs. That is the basic message of the introduction of Einstein's 1905 paper.
However, necessarily the velocity of a light ray relative to both frames as measured with an independent reference system is indeed different. As a matter of fact, that velocity (also called "closing velocity" in modern jargon) is equal to the vector subtraction (c-v).
 The uni-directional speed of light is, essentially, an untestable assumption though isn't it? If it was abandoned, because it is untestable, and replaced with the notion that the round trip speed of light is the same for all observers,would that affect any of the conclusions drawn from experiments?
That would change nothing as you can easily understand by you re-reading my 1907 citation of the second postulate.

Effectively Einstein assumed that when setting up a reference system we can make the one-way speed equal to the round trip speed which is postulated (as a law of physics) to be constant (everywhere and in all directions, independent of the motion of the source); and we postulate also that all laws of physics must be valid for all inertial reference systems. Combining those two postulates, we find that the round trip speed must be the same constant in all inertial reference systems, and we can make the one-way speed equal to the measured two-way speed by convenient clock synchronization. That is important to keep the laws of physics free from unnecessary complexity.
 I came across this abstract when looking up the Fizeau experiment, but unfortunately I can't find the full paper [without having to pay for it]: American Journal of physics Are you familiar with the paper by any chance?
Sorry no, but it's likely irrelevant: it is well known that such tests are too imprecise to distinguish between the Galilean transformation and the Lorentz transformation. Much more relevant are the introductions of the papers to which I gave you the links and which explain why ballistic light theory was disproved before the end of the 19th century.
P: 3,179
 Quote by mangaroosh When you say the pure definitions, do you mean things like the metre being defined in terms of the meridian (was it?) of the earth? It seems, although not expressly stated, that measurements expressed in those units tacitly assume the earth centred reference frame as the rest frame; as you mention atomic clocks are at rest on earth, and the "pure" definitions would have been relative to the earth centred rest frame too.
With "pure" I simply meant a definition that is not derived from other definitions by means of assumptions - for example the standard kg in Paris I call "pure". However, it is not at rest in the ECI frame; for that you would have to measure something at for example the North Pole.
P: 359
@George - just wondering if you had a chance to read this post by any chance; I had a few questions on the analogy you used.

 Quote by mangaroosh It's not so much concern that measurements of the speed of light don't use "the [official] second", I'm just wondering if the Maxwell's equations implicitly state that the speed of light is relative to a clock at rest on earth. Because, a sundial is effectively just a means of breaking the daylight period into smaller segments; it effectively just breaks the "arc" of the sun, over a particular location on earth, into hours and minutes, doesn't it? So any measurement, expressed in the units measured by a sundial, could be read as a function of the movement of the sun relative to a an object at rest on earth. If that object were in motion relative to the earth, then the units would be different. The same could be said for measurements expressed in the units measured by observatories plotting the apparent motion of the fixed stars. Equally so, for an atomic clock at rest on earth, but perhaps even a more precise expression of it's location may be necessary. Thanks, I think this analogy might be helpful. This is more for myself, but I think we can imagine a plane shaped like a plus sign; such that, if the RC planes were both to start from the tail of the plane, and one of the planes turned at the intersection where the wings are, flew out to the end of the wing and then flew the distance to the end of the opposite wing, it would fly the same distance as the other RC plane flying out to the nose of the plane, returning to the midsection turning, and flying to the end of the same wing as the other RC plane; where the the detector determines if they arrived at the same time. Staying with that analogy; what if the RC planes were of such a design (let's say they are made of massless particles) that there would be no wind resistance, they wouldn't need to assume that the plane's length had shortened, would they? Also, if the length of time it took, for both RC planes to complete their respective trips, wasn't actually measured, rather the simple observation of whether they arrived simultaneously, or not was used; could they then conclude, when the planes arrive simultaneously, that someone on the ground would measure the speed of the RC planes to be the same as that measured by a person on the plane? I replied to the part above before [re-]reading this part, so take no notice of the repetition; if the RC planes were designed [from massless particles, say] such that wind resistance wasn't a factor. I try not to learn about relativity from someone who finds fault with Einstein, I generally try to learn about it from people like yourself - who are generous enough to take the time to answer posts; but I try not to accept things simply on the basis that someone says such and such is the case. With regard to the MMX, I think what the author suggests is effectively a ballistic-like (not necessarily a ballistic) explanation for the MMX results; namely that the wavelength of the light reflected from the mirrors [in the interferometer] is the same, and so, no fringe shift would be expected. But that would be circular reasoning wouldn't it, because both clocks use light; if he were to use a very precise mechanical clock, say, even though the light was traveling at speed c, he would measure a slower speed in his reference frame, with the other clock, wouldn't he; is that how experiments would measure the speed of light? That is one thing that I have trouble getting my head around as well, because it seems that according to relativity that both observers can assume that they are at rest in the one and only ether frame; it does seem like both observers are treated as being at absolute rest, from their own perspectives.
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P: 4,178
 Quote by mangaroosh @George - just wondering if you had a chance to read this post by any chance; I had a few questions on the analogy you used.
Yes, I read your post and was impressed by your level of understanding. I've said before, you seem to understand a lot about relativity. Am I right?
P: 359
 Quote by ghwellsjr Yes, I read your post and was impressed by your level of understanding. I've said before, you seem to understand a lot about relativity. Am I right?
Thanks George, I think I've got a half decent understanding of certain concepts, but obviously far from a full understanding. Based on that understanding though, Einsteinian relativity doesn't seem to sit well with me, so I'm hoping that through discussing it in depth I'll either confirm my bias or resolve those issues.

Just referring back to the RC plane analogy, with the planes that don't experience wind resistance, if the RC planes making their journey across the "big" plane in flight were to arrive simultaneously at the detector, I don't think we would conclude that length contraction and/or time dilation occurred, would we?

Also could we conclude that a person on the ground would measure the same speed of the planes as the RC operators? I think based on our previous discussions, that we couldn't; I'm just trying to figure out, what a reasonable conclusion would be from that scenario?

Also, just wondering if you had any thoughts on the issue of the moving observer measuring the speed of light; we mentioned that he would measure the speed to be c if he used a light clock, but if he were to use a mechanical clock, for example, an infinitely precise pendulum clock, then he would measure a speed different to c. I'm wondering if there are any issues that mean we couldn't use such an idealised pendulum clock? Is the fact that it wouldn't work in an inertial reference frame in deep space sufficient reason to exclude it?

Also, just on the point of being at absolute rest in the ether frame, this is something which also doesn't sit too well with me; I often hear that Lorentzian relativity contains the superfluous assumption of an undetectable, absolute rest frame, but Einsteinian relativity seems to include the assumption that reference frames are at rest in that rest frame, which doesn't seem to be any less of an assumption - to my mind it seems more objectionable.
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 Quote by mangaroosh Thanks George, I think I've got a half decent understanding of certain concepts, but obviously far from a full understanding. Based on that understanding though, Einsteinian relativity doesn't seem to sit well with me, so I'm hoping that through discussing it in depth I'll either confirm my bias or resolve those issues. Just referring back to the RC plane analogy, with the planes that don't experience wind resistance, if the RC planes making their journey across the "big" plane in flight were to arrive simultaneously at the detector, I don't think we would conclude that length contraction and/or time dilation occurred, would we?
Planes that don't experience wind resistance are not a part of my analogy and you shouldn't be introducing them into the discussion.
 Quote by mangaroosh Also could we conclude that a person on the ground would measure the same speed of the planes as the RC operators? I think based on our previous discussions, that we couldn't; I'm just trying to figure out, what a reasonable conclusion would be from that scenario?
I covered the situation where the measurement was made while stationary on the ground. You shouldn't be asking about this again.
 Quote by mangaroosh Also, just wondering if you had any thoughts on the issue of the moving observer measuring the speed of light; we mentioned that he would measure the speed to be c if he used a light clock, but if he were to use a mechanical clock, for example, an infinitely precise pendulum clock, then he would measure a speed different to c. I'm wondering if there are any issues that mean we couldn't use such an idealised pendulum clock? Is the fact that it wouldn't work in an inertial reference frame in deep space sufficient reason to exclude it?
It's not just in deep space but at different altitudes on earth. Note 7 of Einstein's 1905 paper says:
 Not a pendulum-clock, which is physically a system to which the Earth belongs. This case had to be excluded.
You shouldn't be bringing this up. Isn't it obvious that if you want to use a mechanical clock, it must be one that is not going to be influenced by environmental factors? You could use a mechanical clock that has a balance wheel in it, the type that Einstein says to use.
 Quote by mangaroosh Also, just on the point of being at absolute rest in the ether frame, this is something which also doesn't sit too well with me; I often hear that Lorentzian relativity contains the superfluous assumption of an undetectable, absolute rest frame, but Einsteinian relativity seems to include the assumption that reference frames are at rest in that rest frame, which doesn't seem to be any less of an assumption - to my mind it seems more objectionable.
Why do you object to any assumption that doesn't conflict with experimental evidence? You are free to adopt ether Lorentzian relativity or Einsteinian relativity (or both) since they both comport with reality identically (they both stand or fall together) but to argue that one should be excluded because it "doesn't sit too well with me" or because "to my mind it seems more objectionable" is the height of arrogance.
P: 359
 Quote by ghwellsjr Planes that don't experience wind resistance are not a part of my analogy and you shouldn't be introducing them into the discussion.
Apologies, I was trying to get a better understanding of the MMX without the notion of an ether wind.

 Quote by ghwellsjr I covered the situation where the measurement was made while stationary on the ground. You shouldn't be asking about this again.
Apologies, I thought they were different questions

 Quote by ghwellsjr It's not just in deep space but at different altitudes on earth. Note 7 of Einstein's 1905 paper says: You shouldn't be bringing this up. Isn't it obvious that if you want to use a mechanical clock, it must be one that is not going to be influenced by environmental factors? You could use a mechanical clock that has a balance wheel in it, the type that Einstein says to use.
In the scenario of the moving train, where the slower relative [to the train carriage] speed of light would be offset by the slower ticking light clock, would the use of such a mechanical clock to measure the speed of light lead to the observer measuring a slower speed.

 Quote by ghwellsjr Why do you object to any assumption that doesn't conflict with experimental evidence? You are free to adopt ether Lorentzian relativity or Einsteinian relativity (or both) since they both comport with reality identically (they both stand or fall together) but to argue that one should be excluded because it "doesn't sit too well with me" or because "to my mind it seems more objectionable" is the height of arrogance.
I don't think it's a matter of arrogance, rather a matter of reason.

The objection to Lorentzian relativity, that usually seems to get cited as the reason for preferring Einsteinian relativity, is the fact that it doesn't have the undetectable, absolute rest frame; while Einsteinian relativity appears to treat each reference frames as though they are that absolute rest frame - that doesn't appear to be too different from my own reasoning.

However, that I find it more objectionable is not necessarily a conscientious preference for one over the other, rather that from trying to develop an understanding of both theories, the process of assimiltation of information has lead, for some reason, to Einsteinian relativity not sitting well; that could be, in part, due to the reasons that are given for preferring Einsteinian relativity over Lorentzian.

EDIT: also possibly because it seems like the superfluous assumption [of an absolute rest frame] that seems to make Lorentzian relativity less attractive, could probably be done away with, within the context of Lorentzian relativity.
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P: 4,178
 Quote by mangaroosh In the scenario of the moving train, where the slower relative [to the train carriage] speed of light would be offset by the slower ticking light clock, would the use of such a mechanical clock to measure the speed of light lead to the observer measuring a slower speed.
Now if that were the case, then there would be an experiment that would violate the Principle of Relativity in different Frames of Reference. You can rest assured that any type of accurate clock that isn't influence by environment factors will give identical results.
 Quote by mangaroosh I don't think it's a matter of arrogance, rather a matter of reason. The objection to Lorentzian relativity, that usually seems to get cited as the reason for preferring Einsteinian relativity, is the fact that it doesn't have the undetectable, absolute rest frame; while Einsteinian relativity appears to treat each reference frames as though they are that absolute rest frame - that doesn't appear to be too different from my own reasoning. However, that I find it more objectionable is not necessarily a conscientious preference for one over the other, rather that from trying to develop an understanding of both theories, the process of assimiltation of information has lead, for some reason, to Einsteinian relativity not sitting well; that could be, in part, due to the reasons that are given for preferring Einsteinian relativity over Lorentzian. EDIT: also possibly because it seems like the superfluous assumption [of an absolute rest frame] that seems to make Lorentzian relativity less attractive, could probably be done away with, within the context of Lorentzian relativity.
It sounds like you don't like either one!!

You said earlier, "I think I've got a half decent understanding of certain concepts, but obviously far from a full understanding". Could you please itemize those concepts that you feel you half-way understand?
P: 359
 Quote by ghwellsjr Now if that were the case, then there would be an experiment that would violate the Principle of Relativity in different Frames of Reference. You can rest assured that any type of accurate clock that isn't influence by environment factors will give identical results.
Is there an experiment which would reveal such a violation of the PoR, given that many such experiments don't actually measure the speed of light in terms of distance/time?

I try to picutre the MMX in such a scenario, but wonder if it would reveal that the light was traveling slower relative to the carriage, because the light would still be traveling at an actual speed of c.

 Quote by ghwellsjr It sounds like you don't like either one!!
sorry, I meant less attractive for proponents of Einsteinian relativity (to generalise and sterotype )

 Quote by ghwellsjr You said earlier, "I think I've got a half decent understanding of certain concepts, but obviously far from a full understanding". Could you please itemize those concepts that you feel you half-way understand?
I haven't tried to itemise them before, so I'm not sure if I'll label them correctly. I suppose whatever concepts you reckoned I had a good understanding of; I'm not sure what the concepts are apart from some generic terms, because my understanding is based on discussions with those more knowledgeable, on the topic, than myself, and the specific concepts might not always be named, or I might not recognise them as specific concepts.

The obvious ones would be:
- Time dilation
- Length contraction
- RoS (although that might be disputable - my level of understanding that is)
- the constancy of the speed of light
- twin paradox
- reference frames
- clock synchronisation
- Principle of Relativity
- Equivalence principle
P: 3,179
 Quote by mangaroosh Thanks George, I think I've got a half decent understanding of certain concepts, but obviously far from a full understanding. Based on that understanding though, Einsteinian relativity doesn't seem to sit well with me, so I'm hoping that through discussing it in depth I'll either confirm my bias or resolve those issues. [..]
There are quite different things called "Einsteinian relativity": his philosophy and his theories of physics, and those are often mixed up - although his philosophy is perhaps not well understood and it certainly changed over time.

For example, Ives was a physicist who claimed to reject SR - until he apparently realised that what he rejected was not really the theory itself but a popular interpretation of the theory which he deemed inconsistent. In one of his later papers he even re-derived SR, using other postulates (Maxwell + conservation laws). That could be instructive.
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P: 4,178
 Quote by mangaroosh Is there an experiment which would reveal such a violation of the PoR, given that many such experiments don't actually measure the speed of light in terms of distance/time?
There are plenty of experiments that confirm PoR, Einstein's first postulate. There are plenty of experiments that confirm the round-trip speed of light is equal to c.
There are no experiments that violate Einstein's second postulate because they cannot measure the one-way speed of light.
The purpose of this forum is to learn relativity, not to try to find ways to disprove it.
Quote by mangaroosh
 Quote by ghwellsjr You said earlier, "I think I've got a half decent understanding of certain concepts, but obviously far from a full understanding". Could you please itemize those concepts that you feel you half-way understand?
I haven't tried to itemise them before, so I'm not sure if I'll label them correctly. I suppose whatever concepts you reckoned I had a good understanding of; I'm not sure what the concepts are apart from some generic terms, because my understanding is based on discussions with those more knowledgeable, on the topic, than myself, and the specific concepts might not always be named, or I might not recognise them as specific concepts.

The obvious ones would be:
- Time dilation
- Length contraction
- RoS (although that might be disputable - my level of understanding that is)
- the constancy of the speed of light
- twin paradox
- reference frames
- clock synchronisation
- Principle of Relativity
- Equivalence principle
Can you tell me what the meaning of "event" is in the context of Special Relativity?
P: 359
 Quote by ghwellsjr There are plenty of experiments that confirm PoR, Einstein's first postulate. There are plenty of experiments that confirm the round-trip speed of light is equal to c. There are no experiments that violate Einstein's second postulate because they cannot measure the one-way speed of light. The purpose of this forum is to learn relativity, not to try to find ways to disprove it.
Surely a good way to learn it is to subject it to critical questioning without any bias as to the outcome?

 Quote by ghwellsjr Can you tell me what the meaning of "event" is in the context of Special Relativity?
I probably can't give the exact definition, and my terminology may not be exact, but roughly I think it refers to anything that to which 3 spatial and a temporal co-ordinate can be assigned in a given frame of reference; for example, the striking of a pole by lightning can be assigned 4 co-ordinates (the point of impact that is - another location on the pole would have a different spatial co-ordinate - and possibly temporal depending on the size of the pole).

These co-ordinates can then be mathmatically transformed to give the co-ordinates of the same event from the perspective of a different reference frame.
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P: 15,610
 Quote by mangaroosh Surely a good way to learn it is to subject it to critical questioning without any bias as to the outcome?
There is no such thing as "without any bias". SR goes against both our hard-wired nervous system and against our Newtonian training. Every student is biased against SR (including myself).

The best way to learn it is:
1) do homework problems so that you understand how it actually works (i.e. so that you don't mistakenly think that SR claims something it does not)
2) read the experimental evidence for and against it

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