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bernhard.rothenstein
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I find in the literature of the subject different names for the length of a moving rod measured by an observer relative to whom it moves. Please let me know if ther is a standard name. Thanks
Fredrik said:I don't know if I've ever heard a name for it. Does it need one? Why not just give the frame a name, e.g. "F", and call it the "length of the rod in frame F"?
Proper length is defined in terms of a pair of events with spacelike separation (it's the distance between them in the frame where they are simultaneous), not a physical object. Of course you can pick two events on either end of the rod which are simultaneous in the frame F where it's moving if you want, and then the proper length between those events will be the same as the length of the rod in frame F, but just saying "proper length" isn't specific enough.bernhard.rothenstein said:Thanks. I think that would be "proper length".
JesseM said:Proper length is defined in terms of a pair of events with spacelike separation (it's the distance between them in the frame where they are simultaneous), not a physical object. Of course you can pick two events on either end of the rod which are simultaneous in the frame F where it's moving if you want, and then the proper length between those events will be the same as the length of the rod in frame F, but just saying "proper length" isn't specific enough.
L and L(0) are both proper lengths. They are the proper lengths of two different spacelike curves. I would call L the "length" and L(0) the "rest length". What I call "length" is just the difference between the spatial coordinates of the rod's endpoints in some frame. What I call "rest length" is just the "length" in the frame where the rod is at rest.bernhard.rothenstein said:I think I was not enough explicit. Consider
L=L(0)/g
g Lorentz factor. If L(0) represents a proper length then what is the name of L?
Fredrik said:L and L(0) are both proper lengths. They are the proper lengths of two different spacelike curves. I would call L the "length" and L(0) the "rest length". What I call "length" is just the difference between the spatial coordinates of the rod's endpoints in some frame. What I call "rest length" is just the "length" in the frame where the rod is at rest.
Note that although "proper length" is a coordinate independent concept, different spacelike curves have different proper lengths, and in this case the frame is what determines what spacelike curve you should be using, so the "proper length of the rod" actually depends on the frame (and is equal to what I just called "length").
Yes, "length", "coordinate length" and "measured length" are clearly the same. Which one you use only depends on what aspect you want to emphasize. (It's like eigenvector/eigenket/eigenstate/eigenfunction in QM). I don't really like the term "apparent length" though. It suggests that Lorentz contraction is an illusion.bernhard.rothenstein said:Then "REST LENGTH" and "LENGTH". I find for the last one "Coordinate length", "Measured length", Apparent length".
Thanks
Isn't it? Taking a picture shows this.Fredrik said:I don't really like the term "apparent length" though. It suggests that Lorentz contraction is an illusion.
Visually it doesn't appear contracted, because of the Penrose-Terrell effect which actually compensates for length contraction (this is just a consequence of the fact that light from parts of the object at different distances from you will take different times to reach you, distorting the visual appearance). But if you measure the length of a rod using local measurements on rulers and clocks which are at rest and synchronized in your frame, you find the rod is shrunk--for example, if the rod is 10 light-seconds long in its own rest frame, and it's moving at 0.6c in your frame, then if at the moment the back end passes the 2-light-second mark on your ruler the clock at that mark reads t=5 seconds, then you'll find that at the moment the front end passes the 10-light-second mark on your ruler the clock at that mark will also read t=5 seconds, so you conclude the two ends are "really" 8-light seconds apart at any given moment in your frame.clem said:Isn't it? Taking a picture shows this.
Taking a picture (snapshot) you can obtain contraction, dilation and no distorsion of the length. The same situation could take place in the case of the radar detection,clem said:Isn't it? Taking a picture shows this.
Fredrik said:I don't really like the term "apparent length" though. It suggests that Lorentz contraction is an illusion.
That depends on your definition of "illusion". It is an experimentally measurable, but coordinate dependent, effect. Personally, I wouldn't call that "illusion" since it is measurable, but I also wouldn't object to someone who doesn't want to call it "real" since it is coordinate dependent. Same with time dilation.clem said:Isn't it? Taking a picture shows this.
clem said:Isn't it? Taking a picture shows this.
clem said:"If you had a large sheet of photgraphic film and array of flash lights timed to go off simulataneously you would capture a length contracted shadow of the passing rod on the film."
You are describing the same illusion as when a rotated stick looks shorter.
The moving stick is just rotated into time and not into space.
No, you cannot pick a distance in the moving F as “proper”.JesseM said:Proper length is defined in terms of a pair of events with spacelike separation (it's the distance between them in the frame where they are simultaneous), not a physical object. Of course you can pick two events on either end of the rod which are simultaneous in the frame F where it's moving if you want, and then the proper length between those events will be the same as the length of the rod in frame F, but just saying "proper length" isn't specific enough.
Both "proper length" and "proper time" are defined in such a way that it doesn't matter what frame you choose to use. If you pick two events along the worldline of an object, then the proper time is simply the time measured between those events by an clock moving along that worldline, you can calculate it in any frame and you'll get the same proper time. Likewise, the "proper length" between two events with a spacelike separation is always defined as the distance between them in the frame where they are simultaneous, so it has nothing to do with what frame you are using.RandallB said:No, you cannot pick a distance in the moving F as “proper”.
By definition that frame cannot correctly define “simultaneous” only the reference frame “A” can define “simultaneous” where “proper” lengths and distances can be defined.
As I've mentioned before, "proper velocity" is a pretty rarely-used term, and the term was invented long after "proper time" and "proper length" so it has no bearing on what the adjective "proper" was supposed to suggest in those earlier terms. "Proper velocity" is unlike proper time and proper length in that it can have different values in different frames.RandallB said:That is why http://en.wikipedia.org/wiki/Proper_velocity" based on a distance traveled measured in “A” divided by the “proper time” on the clock doing the traveling will always be faster than the speed measured in the stationary frame A (where simultaneous is defined as correct). Even giving the appearance of FTL to the traveling clock in some cases.
It's meaningless to talk about "proper time" or "proper distance" independent of a specific choice of two events that you want to measure the proper time between (if they are timelike separated events that lie on some object's worldline) or the proper distance between (if they are spacelike separated events). This is just how "proper time" and "proper distance" are defined, in terms of pairs of events. And once you have specified the two events, then the proper time or proper distance between them is independent of what reference frame you're using.RandallB said:To put "Proper Distance" in the F frame, the F frame Clocks and Rods must be considered stationary (with simultaneous synchronization in the “stationary” POV) and other frames like Frame A would be in motion with “Proper Times” running slower than the F clocks.
I wasn't using frame F for the rod your defining you are. And you defined the "proper length" of the rod in F as it is measured in the F frame. Now you’re saying that "proper length" has nothing to do with the F frame you are using. Which one is right in your view?JesseM said:Likewise, the "proper length" between two events with a spacelike separation is always defined as the distance between them in the frame where they are simultaneous, so it has nothing to do with what frame you are using.
I don’t find anything inconsistent between the “proper” terms as defined in Wiki, with “velocity” coming directly from “proper length” and “proper time” there. I take your comments to mean they have something wrong.As I've mentioned before, "proper velocity" is a pretty rarely-used term, and the term was invented long after "proper time" and "proper length" so it has no bearing on what the adjective "proper" was supposed to suggest in those earlier terms. "Proper velocity" is unlike proper time and proper length in that it can have different values in different frames.
The phrase "proper length of the rod" isn't really meaningful, as I understand the way "proper length" is defined. You can only talk about the "proper length" or "proper distance" between two events, and if you just say "the rod" it's not clear what events on either end of the rod you're referring to. If you specify that you're talking about two events on either end of the rod which are simultaneous in the rod's rest frame, then we can talk about the "proper length" between them (which is the same as the rod's rest length), but you can equally well specify two events on either end of the rod that are simultaneous in some other frame.RandallB said:I wasn't using frame F for the rod your defining you are. And you defined the "proper length" of the rod in F as it is measured in the F frame. Now you’re saying that "proper length" has nothing to do with the F frame you are using. Which one is right in your view?
Do you disagree with this definition?In relativistic physics, proper length is an invariant quantity which is the rod distance between spacelike events in a frame of reference in which the events are simultaneous.
I have no problems with the proper velocity wiki page, but nor do I see them even mentioning the term "proper length" or "proper distance" on that page, so in what way do you think their definition of proper velocity is "coming directly from proper length and proper time"? As far as I can tell they are defining proper velocity in terms of proper time divided by coordinate distance in whatever arbitrary frame you choose to use.RandallB said:I don’t find anything inconsistent between the “proper” terms as defined in Wiki, with “velocity” coming directly from “proper length” and “proper time” there. I take your comments to mean they have something wrong.
In what way do you think my definition different from the definition I quoted above? Since I'm pretty sure I'm using an identical definition, I think you're either misunderstanding my definition, or misunderstanding the definition on the wikipedia page.RandallB said:While your definition of proper length or distance seems to vary randomly by comparison to the Wiki definitions.
The best name for the length of a moving rod measured by a stationary observer is "proper length". This term is commonly used in the field of special relativity to describe the length of an object as measured by an observer who is at rest relative to the object.
"Proper length" is the preferred term because it takes into account the concept of relativity. In special relativity, length measurements are dependent on the relative motion of the observer and the object being measured. The proper length, however, remains constant regardless of the observer's frame of reference.
The proper length is calculated using the Lorentz transformation formula, which takes into account the relative velocity of the moving object and the observer. This formula is a fundamental concept in special relativity and is essential for accurately measuring the proper length of a moving object.
No, the proper length is not necessarily the same as the physical length of the object. The physical length of an object can change depending on the relative motion of the observer, while the proper length remains constant. This is a fundamental aspect of special relativity and is essential for understanding the concept of length contraction.
No, the proper length of an object can never be longer than its physical length. This is because the proper length is calculated based on the relative velocity of the object and the observer, and there is a limit to how fast an object can travel. Therefore, the proper length of an object can only be equal to or shorter than its physical length.