zapatos Posted October 14 Posted October 14 38 minutes ago, Genady said: It is shortening of a distance between two spatial points. It happens at any speed and does not depend on what is there between the points. So length contraction is the shortening of distance from the perspective of the moving observer, and the shortening of the moving object from the perspective of an outside observer?
Genady Posted October 14 Posted October 14 52 minutes ago, zapatos said: So length contraction is the shortening of distance from the perspective of the moving observer, and the shortening of the moving object from the perspective of an outside observer? It is the same. Shortening of the moving object is shortening of the distance between two ends of the object, i.e., between two spatial points. In any case, distance between two points in a frame where they move is shorter than distance between them in a frame where they are at rest.
studiot Posted October 14 Posted October 14 1 hour ago, Genady said: It is the same. Shortening of the moving object is shortening of the distance between two ends of the object, i.e., between two spatial points. In any case, distance between two points in a frame where they move is shorter than distance between them in a frame where they are at rest. I preferred your previous statement. Points are not absolute. The distance between two points in a given inertial frame . But these are not necessarily the same two points in a different frame, whatever that means. I know it's difficult to spell out in a few words.
Genady Posted October 14 Posted October 14 2 minutes ago, studiot said: Points are not absolute. Yes, of course. They should be attached to something, e.g., two galaxies.
MigL Posted October 14 Posted October 14 Let me take a shot at simplifying ... An external observer sees the spaceship, moving at close to c , shortened along the direction of travel. But, relativity ! An observer inside the ship sees the universe ( and the external observer ) rushing past him at close to c ; all distances/lengths along the direction of travel are shortened.
studiot Posted October 14 Posted October 14 8 minutes ago, MigL said: Let me take a shot at simplifying ... An external observer sees the spaceship, moving at close to c , shortened along the direction of travel. But, relativity ! An observer inside the ship sees the universe ( and the external observer ) rushing past him at close to c ; all distances/lengths along the direction of travel are shortened. The danger with simplifying is that word 'sees'. 😀
zapatos Posted October 15 Posted October 15 3 hours ago, MigL said: Let me take a shot at simplifying ... An external observer sees the spaceship, moving at close to c , shortened along the direction of travel. But, relativity ! An observer inside the ship sees the universe ( and the external observer ) rushing past him at close to c ; all distances/lengths along the direction of travel are shortened. That is what I was trying to say although obviously not clearly. So both of those observations are due to the same principle of length contraction?
MigL Posted October 15 Posted October 15 Simplistically, yes. Although other effects also play a part.in what an observer 'sees'. 1
Halc Posted October 16 Posted October 16 On 10/14/2024 at 2:13 PM, zapatos said: So length contraction is the shortening of distance from the perspective of the moving observer, and the shortening of the moving object from the perspective of an outside observer? The perspective of any observer is always being at rest. One is always at rest in one's own frame. So length contraction is the contraction of the length of any object moving in that inertial frame. It is an inertial frame thing, and different rules apply to different kinds of frames. On 10/14/2024 at 4:14 PM, studiot said: Points are not absolute. The distance between two points in a given inertial frame . But these are not necessarily the same two points in a different frame, whatever that means. To be as exact as I can, The front and back of some object each traces a worldline through spacetime. Points along these worldlines are events, and events are objective, frame independent. Different inertial frames (coordinate systems) assign different coordinate values (spatial location and time) to each event. In a frame where the object is stationary, all the events on each worldline have the same spatial coordinates but different time coordinates. The difference in the spatial coordinates of those two worldlines is the object's proper length. In a frame where the object is moving, each event is at different spatial coordinates. At any given time in that frame, the spatial coordinate of each worldline corresponding to that particular time differ by less than the proper length of the object. That's length contraction. It is a coordinate effect, but there are ways to manifest it physically. On 10/14/2024 at 6:01 PM, MigL said: An external observer sees There are no external observers. That wording makes it sound like there's an objective, preferred reference frame, which relativity denies (but alternate theories do not). I don't think you meant that and I agree with the post other than that bit. About 'sees', I just has somebody ask what recession velocity is observed in a particular scenario, and it turns out that velocity isn't observed, it is computed. It is entirely frame dependent, and the same observer would 'observe' very different velocities for the same object in his own frame depending on the kind of frame chosen (cosmic frame, inertial, accelerating frame, rotating frame, etc). Each results in a different value for the same observed distant object. 1
zapatos Posted October 16 Posted October 16 32 minutes ago, Halc said: So length contraction is the contraction of the length of any object moving in that inertial frame. This is why I keep getting thrown off. If someone on earth boards a spacecraft and heads for a distant star at a velocity near c, don't they measure the distance between themselves and the star as shorter than what an observer on earth would measure as the distance between the spacecraft and the star? The distance between the spacecraft and the star is not an "object". So what principle tells us why the distance to the star is shortened for the person in the spacecraft? If it is not length contraction, then what is it?
Halc Posted October 16 Posted October 16 40 minutes ago, zapatos said: If someone on earth boards a spacecraft and heads for a distant star at a velocity near c, don't they measure the distance between themselves and the star as shorter than what an observer on earth would measure as the distance between the spacecraft and the star? The velocity near c is relative to the Earth frame. In the ship frame, the ship is stationary and Earth (and presumably some destination object) are moving fast, and yes, assuming the destination object is reasonably stationary relative to Earth, the distance between them in the ship frame is contracted. That is, on the worldlines of the two planets, the events of the respective worldlines of the two planets that are simultaneous (relative to the ship frame) with the ship's midway event, have less spatial separation in the ship frame than do those same two events in the planet frame relative to which those same two events are not simultaneous. A mouthful, but hopefully followable. The Earth observer is computing (not directly measuring) a spatial distance between two different events which happen to be simultaneous in the Earth frame. 49 minutes ago, zapatos said: So what principle tells us why the distance to the star is shortened for the person in the spacecraft? If it is not length contraction, then what is it? Relativity of simultaneity is probably what you're looking for. In the planet frame, the planets are always stationary, and the midway point of the ship journey is a fixed event at a fixed location in space, so it is half the proper separation of the planets, say 2 of the 4 LY separation of the planets. The ship is moving at 0.866c relative to the planets at that event, so the Lorentz factor is 2. The synced clocks on the planets read 0 at departure of the journey, as does the ship clock which makes the whole trip at that ballistic speed, so it takes 2.31 years to get to that midpoint event, and 4.62 years total. The ship clock reads 2.31 at the destination and 1.155 at that halfway event. In Earth frame, the two planet clocks read 2.31 and the ship clock reads 1.155. These three events are simultaneous in the planet frame. Relative to the ship frame, at the ships midway event, the ship is stationary and Earth has been receding for 1.155 years at 0.866c, putting Earth 1 light year behind, the event where the Earth clock reads 0.577. The approaching destination planet is 1 LY away and will reach the stationary ship in 1.155 years. It's clock reads 4.043. So the three simultaneous events in that frame are Earth@0.577, Ship@1.155, Dest@4.043. These are three different events (well, the middle one is the same) as the 3 events simultaneous in the planet frame above. Point is, different frames label different sets of events as simultaneous, which is what relativity of simultaneity is about. Those different events have different spatial separations from each other, and in the ship frame, the two simultaneous planet events are spatially separated by only 2 light years. In that same ship frame, the three events that were simultaneous in the planet frame are no longer simultaneous, and the spatial separation of the two planet events is 8 LY, more than their proper separation. But that's not a length since a length is by definition computed between simultaneous events. 1
studiot Posted October 16 Posted October 16 20 hours ago, Halc said: About 'sees', I just has somebody ask what recession velocity is observed in a particular scenario, and it turns out that velocity isn't observed, it is computed Exactly so. An observer has to reckon things in his own frame. +1 He can't 'see' things at significant distance he has to calculate them, make allowance for the movements of observed events. 18 hours ago, Halc said: Relative to the ship frame, at the ships midway event, the ship is stationary and Earth has been receding for 1.155 years at 0.866c, putting Earth 1 light year behind, the event where the Earth clock reads 0.577. The approaching destination planet is 1 LY away and will reach the stationary ship in 1.155 years. It's clock reads 4.043. So the three simultaneous events in that frame are Earth@0.577, Ship@1.155, Dest@4.043. These are three different events (well, the middle one is the same) as the 3 events simultaneous in the planet frame above. So from the point of view of the ship frame, if the relative velocity between the ship and the departure planet is zero 1) The ship is at the departure planet and the destination planet is 2Ly away. 2) Therefore there is a point in space 1Ly that is halfway between the planets. 3) The ship rapidly accelerates to its cruising velocity and reckons the departure planet to be receeding at this velocity and the destination planet to be approaching also at this velocity. 4) The ship 'sees' the distance between itself and the departure planet growing and the distance between itself and the destination planet decreasing. So what does the ship reckon the distance is to the halfway point between the two planets ? Or have I misunderstood your scenario ?
Halc Posted October 18 Posted October 18 On 10/16/2024 at 7:14 PM, studiot said: He can't 'see' things at significant distance he has to calculate them, make allowance for the movements of observed events. And has to make allowances for whatever frame type has been chosen. There is no one 'actual velocity' of one thing relative to another. On 10/16/2024 at 7:14 PM, studiot said: So from the point of view of the ship frame, if the relative velocity between the ship and the departure planet is zero No, the ship is moving relative to the planet, and thus the departure planet is moving away from the ship. This is using the inertial frames of the planet and the ship respectively, and the scenario is presumed to be a 2LY proper distance between planets, and the ship is ballistic (not accelerating except at beginning and end) at speed 0.866 for a dilation factor of 2. On 10/16/2024 at 7:14 PM, studiot said: 1) The ship is at the departure planet and the destination planet is 2Ly away. 2) Therefore there is a point in space 1Ly that is halfway between the planets. In planet inertial frame, yes. The planets are separated by a proper distance of 2LY, and 1LY is halfway in that frame. On 10/16/2024 at 7:14 PM, studiot said: 3) The ship rapidly accelerates to its cruising velocity and reckons the departure planet to be receeding at this velocity and the destination planet to be approaching also at this velocity. I would use 'speed', but yes. The velocity of the planets relative to the ship is equal but opposite the velocity of the ship relative to either planet. On 10/16/2024 at 7:14 PM, studiot said: 4) The ship 'sees' the distance between itself and the departure planet growing and the distance between itself and the destination planet decreasing. No numbers there, but yes, that's kind of a frame independent fact and nobody has to actually see it for it to be true. On 10/16/2024 at 7:14 PM, studiot said: So what does the ship reckon the distance is to the halfway point between the two planets ? That is a frame dependent question, but since you said 'ship reckon', I can presume a reference to the ship's inertial frame. The ship is stationary in that frame for the whole trip, so the midpoint is the same as all the other points and is just 'here'. So at any time, the spatial distance to the midpoint of the trip is zero. This entire post has answers that are true even in Galilean relativity (except the bit about the dilation factor, which wasn't an answer to any of the questions).
studiot Posted October 18 Posted October 18 (edited) 14 minutes ago, Halc said: No, the ship is moving relative to the planet, and thus the departure planet is moving away from the ship. This is using the inertial frames of the planet and the ship respectively, and the scenario is presumed to be a 2LY proper distance between planets, and the ship is ballistic (not accelerating except at beginning and end) at speed 0.866 for a dilation factor of 2. But you said the ship is stationary in its own frame. So in which frame are the two planets 2Ly apart? The ships frame or the planets frame ? I'm questioning this because it is not as easy as you initially made out to explain this and parts of your explanation seem to me at variance with each other. Edited October 18 by studiot
Halc Posted October 19 Posted October 19 (edited) 9 hours ago, studiot said: But you said the ship is stationary in its own frame. Everything is stationary in its own frame by definition. If it isn't, it's probably because it doesn't have a defined frame. 9 hours ago, studiot said: So in which frame are the two planets 2Ly apart? 9 hours ago, Halc said: scenario is presumed to be a 2LY proper distance between planets I said 'proper distance', which means a distance as measured by rulers moving at the same velocity as at least one of the objects. That works for special relativity In cosmic coordinates (not relevant to this thread), proper distance is usually measured by rulers that are stationary in the cosmological frame, that is, they have zero peculiar velocity. Peculiar velocity is meaningless in special relativity. Short answer, 2LY apart in Planet frame, and since the ship speed is 0.866 relative to that, the planets are 1 LY apart in ship frame and that's not a proper separation. Edited October 19 by Halc
KJW Posted October 19 Posted October 19 The proper distance in spacetime between earth now and Alpha Centauri four years from now is somewhat less than the proper distance in spacetime between earth now and Alpha Centauri now. This is length contraction. Because we are talking about proper distances, this is true in all frames of reference. But note that I am not talking about distances between the same pair of points (events) in spacetime. The distances are different because the intervals are different. This is an important point because in relativity, the different values of a measurement in different frames of reference are always measurements of different things. Different observers in different frames of reference always measure the same value for the same measurement.
studiot Posted October 19 Posted October 19 6 hours ago, Halc said: I said 'proper distance', which means a distance as measured by rulers moving at the same velocity as at least one of the objects. This is why I said it's tricky and also why many authorities these days have veered away from the the categorisation 'proper'. Proper distance is an invariant in all inertial coordinates. You have defined proper length which exists in only one particular inertial system. https://en.wikipedia.org/wiki/Proper_length
Halc Posted October 19 Posted October 19 2 hours ago, studiot said: Proper distance is an invariant in all inertial coordinates. Quite right, and I didn't suggest otherwise. This goes for proper length as well. Length of an object or distance between two objects is very much frame dependent, but proper length and proper distance is not, which is why it was unnecessary for me to provide a frame reference when stating that our two hypothetical planets were separated by a proper distance of 2LY. 9 hours ago, KJW said: The proper distance in spacetime between earth now and Alpha Centauri four years from now is somewhat less than the proper distance in spacetime between earth now and Alpha Centauri now. The former is meaningless. Distance/length is not a measure of spatial difference of a pair of events at different times, else I could meaningfully say that my car is 200 km in length because the front is at home today and the rear of it in the next town tomorrow. Sure, there's a 200 km difference in the spatial coordinates of those two events in the frame of the ground, but it is not in any way the length of the car, proper length or otherwise. 9 hours ago, KJW said: This is length contraction. It is true that the distance between our two planets is frame dependent, and that each frame would compute that distance as a spatial separation between different events, but only if the pair of events have the same time coordinate in the chosen frame, which your description did not. Length contraction is arguably a coordinate effect, but there are examples that demonstrate it to be physical similar to how differential aging demonstrates that linear time dilation is also physical and not just a coordinate effect. 9 hours ago, KJW said: The distances are different because the intervals are different. This seems to not explain things since distance is not a measure of an interval. The interval between two events is frame independent, but the difference in spatial coordinates of two events is not. I think you know that, but your statement seems to imply otherwise, and you meant to say that length of some object measurements in one frame compare different pairs of events than the events compared for a length measurement in another frames.
joigus Posted October 19 Posted October 19 On 10/14/2024 at 6:23 PM, Endy0816 said: For person onboard the ship, the distance between them and their destination is also shortened due to length contraction. Yes, thanks. That's right. I missed that possible interpretation. If I understood correctly most previous arguments, one cannot reach those distances in that sense either, and I agree. That kind of interstellar travel would require humongous energy. And the braking process too. The argument surfaced at the very beginning, although I'm not up to date on the follow-up Q&A.
studiot Posted October 19 Posted October 19 1 hour ago, Halc said: Length of an object or distance between two objects is very much frame dependent, but proper length and proper distance is not, Did you not read the very clear Wiki article I referred to ? Proper length only exists in one frame; it has no meaning in other frames. So it can't be invariant. Proper distance, however is an invariant that exists in all frames.
Halc Posted October 19 Posted October 19 (edited) 1 hour ago, studiot said: Proper length only exists in one frame; it has no meaning in other frames. The wiki article is accurate and says nothing of the kind, saying instead that "proper distance, provides an invariant measure whose value is the same for all observers." meaning it is frame independent. The rest length of an object doesn't change in a frame where it is moving. The length does, but if it's moving, that's not its rest length. The article says that the length and the proper length are the same not only in the rest frame, but in any frame where the motion is perpendicular to the length dimension being measured. I did however make a mistake with my reply to KJW 13 hours ago, KJW said: The proper distance in spacetime between earth now and Alpha Centauri four years from now is somewhat less than the proper distance in spacetime between earth now and Alpha Centauri now. 3 hours ago, Halc said: The former is meaningless. A frame invariant proper distance between two spacelike-separated events is the coordinate separation between those events in any frame where they are simultaneous. The two events mentioned are still spacelike separated and have a proper separation under 2 light years, not just 'somewhat less' than the proper separation between the 2nd pair of events. But I said it was meaningless, which it wasn't. Both pairs of events were ambiguously identified, but I presumed the temporal references were relative to Earth's frame. Edited October 19 by Halc
studiot Posted October 19 Posted October 19 2 hours ago, Halc said: The wiki article is accurate and says nothing of the kind, It says exactly what I wrote in the clearest manner that I have come across. Quote Proper length[1] or rest length[2] is the length of an object in the object's rest frame. Which is true in one frame and one frame only. and Quote A different term, proper distance, provides an invariant measure whose value is the same for all observers. Which is true in all frames and therefore invariant So the Wiki article makes a clear distinction between proper length and proper distance They are not interchangeable.
Halc Posted October 21 Posted October 21 (edited) On 10/19/2024 at 2:49 PM, studiot said: Which is true in one frame and one frame only. There's a trivial formula given on the wiki site to compute the proper length of a moving object. It produces the same answer regardless of choice of frame, which is what is meant by the proper length being frame invariant. Do you dispute this? Does a ship with a 100meter proper length in a frame where it is stationary have a different proper length in a frame where it is moving forward at say 0.8c? If so, what is that different proper length? Clue: In the 2nd frame, it has a coordinate length of 60m. On 10/19/2024 at 2:49 PM, studiot said: So the Wiki article makes a clear distinction between proper length and proper distance They are not interchangeable. Yes, I agree. For instance, Earth and Alpha Centauri are separated by a frame invariant proper distance (only if you presume incorrectly that they have the same velocity, but they're reasonably close), whereas a rigid ship moving (inertially or accelerating) between the two would have a frame invariant proper length. Two spacelike separated events also have a proper distance separation, and with that specification there is no need for the mutually stationary bit since events don't have a defined coordinate velocity, being physical points in spacetime. If two events are timelike separated, then their proper separation is a proper time, not a proper distance. Edited October 21 by Halc
studiot Posted October 21 Posted October 21 (edited) 11 hours ago, Halc said: There's a trivial formula given on the wiki site to compute the proper length of a moving object. It produces the same answer regardless of choice of frame, which is what is meant by the proper length being frame invariant. Do you dispute this? Does a ship with a 100meter proper length in a frame where it is stationary have a different proper length in a frame where it is moving forward at say 0.8c? If so, what is that different proper length? Clue: In the 2nd frame, it has a coordinate length of 60m. The operative word being compute, not measure. You have just told me that the proper length of a ship is 100m. Since this is only defined in the that ships's own inertial frame, where we are agreed it appears at rest, and will be different in any other frame and measured as such by an observer in that frame. For instance Say I have a super duper camera that is equipped with length measuring stadia. From my observatory on a planet, where I am stationary, I monitor the ship's approach and at the instant its centre passes my telescope, I take a photographic mesasurement of the length of the ship. I observe 60 m So in my frame the length of the ship is 60 m. So yes if I am also measuring the ships velocity, in my frame, I will be able to compute that it has a length of 100m in its own frame. So yes I can compute the proper length, but I cannot measure it in my frame. I mentioned a while back that confusion over the difference between length and distance is the reason why the term 'proper' is depracated by some authorities and why Wikipedia says Quote Proper length[1] or rest length[2] is the length of an object in the object's rest frame. The measurement of lengths is more complicated in the theory of relativity than in classical mechanics. In classical mechanics, lengths are measured based on the assumption that the locations of all points involved are measured simultaneously. But in the theory of relativity, the notion of simultaneity is dependent on the observer. A different term, proper distance, provides an invariant measure whose value is the same for all observers. Incidentally in this world of hurry up and short cuts far too many make the mistake of saying The velocity c is invariant. It is most decidedly not. Edited October 21 by studiot
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