- #36
lugita15
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Not directly, but by determining how much the length of someone's ruler has Lorentz contracted, you can calculate their velocity relative to you.GregAshmore said:Can velocity be measured at one time?
Not directly, but by determining how much the length of someone's ruler has Lorentz contracted, you can calculate their velocity relative to you.GregAshmore said:Can velocity be measured at one time?
GregAshmore said:Can velocity be measured at one time?
No, the two rods were made to be identical, each four units long. One never left the lab; the other was set in motion and observed from the lab frame.Hurkyl said:How do you know it's 4 units long? What do you mean by "it's length"?
In your thought experiment, nobody made any claims about the length of a rod
I was talking about measuring length, not velocity. Your reply is rather irrelevant.GregAshmore said:Can velocity be measured at one time?
bobc2 said:Not by us mere mortals. But, some super hyperdimensional guy with the big hyperdimensional view of the 4-dimensional poles can just measure the orientations of the objects in hyperdimensional space and tell you the velocities. Of course the 4-D poles are just static objects and don't have any motion at all, so he just uses the orientations to come up with numbers that are compatible with the inferior impressions of the 3-dimensional mortals.
I disagree. The projected length by itself is not particularly meaningful.DaleSpam said:I was talking about measuring length, not velocity. Your reply is rather irrelevant.
The measurement you describe does not measure the length of the object; it measures the length of the object's projection in another inertial frame. You pointed out earlier in this thread that the projection is analogous to the shadow of a tilted rod. Just as the length of the shadow on the table is not the length of the rod, the projected length in the moving frame is not the length of the rod.DaleSpam said:If you disagree then please expain how a reply about measuring velocity is relevant to a comment about measuring length?
Btw, I sympathize with your position that coordinate length is less meaningful than rest length, I was only pointing out that the way you described measuring length is incorrect. There is nothing different about the process of measuring the length of an object in different frames.
But all lengths are really cross-sections of the 4D world-tube with some plane of simultaneity; the rest length is just "special" in the sense that it's the maximum possible length, and also that in this case the plane of simultaneity is orthogonal to the worldline of any point on the object.GregAshmore said:The measurement you describe does not measure the length of the object; it measures the length of the object's projection in another inertial frame. You pointed out earlier in this thread that the projection is analogous to the shadow of a tilted rod. Just as the length of the shadow on the table is not the length of the rod, the projected length in the moving frame is not the length of the rod.
Why should one rod imply "one length"? Do you think the rod must also have "one velocity" or "one x-coordinate"? I see nothing wrong with saying "length" is an intrinsically frame-dependent quantity and therefore that it has no one "correct" frame-independent value. Of course you are free to define the "true length" as the "rest length", but this is just an arbitrary convention you've invented--one could equally well define the "true length" as "length in the frame where the rod is moving at 0.5c", there's no physical reason compelling us to adopt one definition or the other, it's purely a matter of aesthetic preference which definition we use, if indeed we want to use a silly phrase like "true length". Do you disagree with any of the above? If so, what, and why?GregAshmore said:Suppose we have two observers of the one rod on the lab bench, moving at different speeds relative to the bench. There will, of course, be two distinct measurements of length--yet there is only one rod, with one length.
Here you seem to assume that the rod will be brought to rest on the work bench, in which case of course it's the rest length we'll be interested in, but that doesn't make it the "true length". You could equally well ask, "suppose each observer wants to use the rod in an experiment involving a toy train car moving at 0.5c relative to his lab, which has a length of 1 meter in the observer's frame--will the rod fit in the train car?" In this case it would be "length in the frame where the rod is moving at 0.5c" that would be relevant to each observer.GregAshmore said:To emphasize the point, suppose that each observer is bidding to purchase the rod, for use in his own laboratory. How much room must be cleared for the rod on the observer's bench? That question cannot be answered correctly without taking the velocity into account.
Yes, it does. This is not a matter of debate, it is a matter of definition.GregAshmore said:The measurement you describe does not measure the length of the object
Don't forget that a rod moving in a frame doesn't have just one length if it is rotated in a particular orientation. Its length will be changing between its rest length and its most contracted length.GregAshmore said:Suppose we have two observers of the one rod on the lab bench, moving at different speeds relative to the bench. There will, of course, be two distinct measurements of length--yet there is only one rod, with one length. The only way to resolve the contradiction is for each observer to account for the rod's velocity relative to his frame.
To emphasize the point, suppose that each observer is bidding to purchase the rod, for use in his own laboratory. How much room must be cleared for the rod on the observer's bench? That question cannot be answered correctly without taking the velocity into account.
Definitions should not allow for contradictory statements. The rod is a physical object, with its own length that is unaffected by the relative motion of other objects. If the definition of "length of an object" allows for multiple lengths, the definition is bad.DaleSpam said:Yes, it does. This is not a matter of debate, it is a matter of definition.
Where is the "contradiction" in allowing "length" to be defined in a frame-dependent way? It seems that all you really mean is that it conflicts with your personal aesthetic intuitions about what the word "length" should imply, you haven't stated any more rational objection so far.GregAshmore said:Definitions should not allow for contradictory statements.
Do you think a 3D physical object should have a single 2D "cross-sectional area", or would you agree it has multiple cross-sectional areas depending on the orientation of the 2D plane used to take the cross-section? If you accept multiple "cross-sectional areas" in that case, why can't you accept multiple 3D cross-sections (with different 'lengths' along a given spatial axis, not to mention different spatial volumes) of a rod's 4D world-tube?GregAshmore said:The rod is a physical object, with its own length that is unaffected by the relative motion of other objects. If the definition of "length of an object" allows for multiple lengths, the definition is bad.
ghwellsjr said:Don't forget that a rod moving in a frame doesn't have just one length if it is rotated in a particular orientation. Its length will be changing between its rest length and its most contracted length.
So if the seller of the rod wants to make sure the two bidders observe the same length of the rod they want to purchase (and they're too stupid to make the correct calculation) he can reposition the rod so that its length is perpendicular to both bidders' directions of motion. Problem solved.
I would say, "It's true length."Or he could just tell them its length.
JesseM said:Where is the "contradiction" in allowing "length" to be defined in a frame-dependent way? It seems that all you really mean is that it conflicts with your personal aesthetic intuitions about what the word "length" should imply, you haven't stated any more rational objection so far.
Do you think a 3D physical object should have a single 2D "cross-sectional area", or would you agree it has multiple cross-sectional areas depending on the orientation of the 2D plane used to take the cross-section? If you accept multiple "cross-sectional areas" in that case, why can't you accept multiple 3D cross-sections (with different 'lengths' along a given spatial axis, not to mention different spatial volumes) of a rod's 4D world-tube?
It is not possible to demonstrate that the rod will fit in the car. The rod will smash through the ends of the car because it is moving relative to the car.JesseM said:Here you seem to assume that the rod will be brought to rest on the work bench, in which case of course it's the rest length we'll be interested in, but that doesn't make it the "true length". You could equally well ask, "suppose each observer wants to use the rod in an experiment involving a toy train car moving at 0.5c relative to his lab, which has a length of 1 meter in the observer's frame--will the rod fit in the train car?" In this case it would be "length in the frame where the rod is moving at 0.5c" that would be relevant to each observer.
Not if they use a ruler moving relative to the room to measure it, which is perfectly possible.GregAshmore said:If I place a block of aluminum on the table, everyone in the room will agree on the absolute value of its physical extents, label them however you wish.
An assertion, not an argument. Why are they wrong?GregAshmore said:Therefore, all will agree on the volume of the block. Any observer, moving or not, who measures a different set of extents, and thus a different volume, is wrong.
You misunderstood my scenario, I was suggesting that the rod would be used in an experiment where both the rod and the car would be moving at 0.5c relative to the lab. This is no more arbitrary than your suggestion that the rod be at rest relative to the lab.GregAshmore said:It is not possible to demonstrate that the rod will fit in the car. The rod will smash through the ends of the car because it is moving relative to the car.
I agree, but you seem to believe that a definition is contradictory simply because it is frame-dependent. If you have any physics background then you are already familiar with using quantities that are defined in a frame dependent manner, such as position, velocity, kinetic energy, momentum, and work. Do you wish to get rid of all of these quantities simply because they are frame-dependent? I hope not. Length is no different, it is a very useful quantity despite the fact that it is frame dependent.GregAshmore said:Definitions should not allow for contradictory statements.
If by "own length" you mean "rest length" then I agree.GregAshmore said:The rod is a physical object, with its own length
If the ruler is moving relative to the room, then it is not in the frame of the room.JesseM said:Not if they use a ruler moving relative to the room to measure it, which is perfectly possible.
The assertion is based on the notion--which I think we all agree to be true--that the rod itself is not affected by the motion of other objects. In that case, it seems to me that any claim that the rod has a different length is wrong. However, you are correct in saying that I have not presented a logical argument to support my position. I've been working on that since my last post; I'll have something in a day or two, I think. When I got here this morning, I saw that I am following a line of reasoning which is similar to that presented by GrayGhost, in #53.An assertion, not an argument. Why are they wrong?
While it is not arbitrary, it is a different scenario than the one we are discussing. We are talking about a measuring device in one frame, and the object to be measured in another frame.You misunderstood my scenario, I was suggesting that the rod would be used in an experiment where both the rod and the car would be moving at 0.5c relative to the lab. This is no more arbitrary than your suggestion that the rod be at rest relative to the lab.
I need to think about this more, but I'm not convinced that there is nothing wrong in saying that the length of an object is frame-dependent. The concept is not merely new; it is of a fundamentally different character, because of the relativity of time. I am not contesting the relativity of time, or the result of the length measurement; I am contesting the interpretation of the length measurement.DaleSpam said:I agree, but you seem to believe that a definition is contradictory simply because it is frame-dependent. If you have any physics background then you are already familiar with using quantities that are defined in a frame dependent manner, such as position, velocity, kinetic energy, momentum, and work. Do you wish to get rid of all of these quantities simply because they are frame-dependent? I hope not. Length is no different, it is a very useful quantity despite the fact that it is frame dependent.
The only difference between length and these other frame-variant quantities is that the fact that length is frame-dependent is a new concept. There is nothing wrong or contradictory here, any more than statements about an objects position are wrong or contradictory. You merely have to specify your reference frame when making statements about frame-variant quantities, then your statements are clear and do not lead to contradictions.
I do mean rest length, but I would say that the rest length is the only length. I would also say that the shorter distance measured in another frame is not the length of the rod, but a measure of its ________. (I've been trying for two hours to find a word to put in that blank, without success. I need to study the spacetime diagram some more. I may confirm the concept I have in mind, and find a word to express it. Or, perhaps not. In the meantime, I see that I am on the same track as GrayGhost, in #51.)If by "own length" you mean "rest length" then I agree.
The process of measuring the distance between the front and the back of an object at a given instant in time according to two synchronized clocks results in some number. The scientific community has given that number a name: "length". It is a defined term. You may think that it would have been better to pick a different name, but you need to know and use the standard name anyway. Otherwise you will be unable to communicate your concepts to others who use the standard name.GregAshmore said:I am not contesting the relativity of time, or the result of the length measurement; I am contesting the interpretation of the length measurement.
... I would also say that the shorter distance measured in another frame is not the length of the rod, but a measure of its ________.
JesseM said:But all lengths are really cross-sections of the 4D world-tube with some plane of simultaneity; the rest length is just "special" in the sense that it's the maximum possible length, and also that in this case the plane of simultaneity is orthogonal to the worldline of any point on the object.
Why should one rod imply "one length"? Do you think the rod must also have "one velocity" or "one x-coordinate"? I see nothing wrong with saying "length" is an intrinsically frame-dependent quantity and therefore that it has no one "correct" frame-independent value. Of course you are free to define the "true length" as the "rest length", but this is just an arbitrary convention you've invented--one could equally well define the "true length" as "length in the frame where the rod is moving at 0.5c", there's no physical reason compelling us to adopt one definition or the other, it's purely a matter of aesthetic preference which definition we use, if indeed we want to use a silly phrase like "true length". Do you disagree with any of the above? If so, what, and why?
Here you seem to assume that the rod will be brought to rest on the work bench, in which case of course it's the rest length we'll be interested in, but that doesn't make it the "true length". You could equally well ask, "suppose each observer wants to use the rod in an experiment involving a toy train car moving at 0.5c relative to his lab, which has a length of 1 meter in the observer's frame--will the rod fit in the train car?" In this case it would be "length in the frame where the rod is moving at 0.5c" that would be relevant to each observer.
It's not at rest in the frame of the room--is that what you mean by "in"? A frame is just a coordinate system, so in another sense any object is "in" the region of spacetime covered by those coordinates, regardless of whether the object is at rest in those coordinates. In any case you didn't say anything about an (arbitrary) requirement that all observers in the room use rulers at rest in that room, you just said:GregAshmore said:If the ruler is moving relative to the room, then it is not in the frame of the room.
They won't agree if they use rulers not at rest in that room. You can impose the requirement that each observer use a ruler at rest in the room to measure the aluminum block, but this is just an arbitrary convention you've invented, no less arbitrary than the convention "each observer must use a ruler moving at 0.5c relative to the room to measure the aluminum block". Do you disagree, and think there is some non-arbitrary, non-aesthetic reason why your requirement is the correct one to use?If I place a block of aluminum on the table, everyone in the room will agree on the absolute value of its physical extents, label them however you wish.
But here you are making the implicit assumption that length must be a characteristic of "the rod itself", and not just a characteristic of how the rod looks when described in a particular frame. Do you think velocity or x-coordinate are characteristics of "the rod itself", and therefore the rod can only have one "true" velocity or one "true" x-coordinate? If not, why do you have this strange mental block about seeing "length" the same way you see velocity and x-coordinate? Can you give any rational argument as to why you feel "length" must be such an intrinsic characteristic of the rod, whereas velocity and x-coordinate are not? (assuming you don't think they are--please address this one way or another!)GregAshmore said:The assertion is based on the notion--which I think we all agree to be true--that the rod itself is not affected by the motion of other objects. In that case, it seems to me that any claim that the rod has a different length is wrong.
Do you think a 3D physical object should have a single 2D "cross-sectional area", or would you agree it has multiple cross-sectional areas depending on the orientation of the 2D plane used to take the cross-section? If you accept multiple "cross-sectional areas" in that case, why can't you accept multiple 3D cross-sections (with different 'lengths' along a given spatial axis, not to mention different spatial volumes) of a rod's 4D world-tube?
Why, did I use the word "silly" at some point? I don't remember. Anyway, to me the problem with your use of "contradiction" is not that it's overly confrontational, but just that it suggests you have some actual logical argument in the form of a specific pair of conclusions that follow from the idea that length is frame-dependent, but which end up contradicting each other. That would allow you to do a proof by contradiction to show that there must be a frame-independent notion of length. However, it seems like you don't actually have any sort of specific contradiction in mind, so my objection to your use of that word is just that it's misleading and makes it sound like your argument has more substance than it actually does.GregAshmore said:btw, in an earlier series of posts, I used the word 'contradiction' inappropriately, thus putting the discussion in a confrontational mode. It seems to me that the word 'silly' tends to do the same thing.
In Special Relativity, all objects are in all frames of reference. The whole point of SR is that you define your entire scenario in any arbitrarily selected single frame of reference. So if you choose the lab frame, then rulers moving in that frame aligned along the direction of motion will be length contracted. It is wrong to think that a ruler moving relative to the room is not in the frame of the room.GregAshmore said:If the ruler is moving relative to the room, then it is not in the frame of the room.JesseM said:Not if they use a ruler moving relative to the room to measure it, which is perfectly possible.
I'll try to remember to say "at rest in the same frame" instead of "in the same frame".ghwellsjr said:In Special Relativity, all objects are in all frames of reference. The whole point of SR is that you define your entire scenario in any arbitrarily selected single frame of reference. So if you choose the lab frame, then rulers moving in that frame aligned along the direction of motion will be length contracted. It is wrong to think that a ruler moving relative to the room is not in the frame of the room.
No, I think there is a contradiction because I know that the rod is 4 units long, and the instruments mounted in the moving rod tell me that it is 3.2 units long.You started this post with a diagram showing two identically constructed objects in relative motion from the frame of reference in which one of them, which you called the "lab bench", was at rest, and then you asked the question: "Knowing that the stationary rod is four units long, would we not have to conclude that the instruments on the moving rod are incorrect when they report its length to be 3.2 units?"
Do you see how this question mixes up two different frames of reference? The expression, "Knowing that the stationary rod is four units long" implies that you are using the lab frame because that is the only one in which the lab rod has a length of four units. And the rest of your question implies the "moving" frame because in that one the stationary rod is 3.2 units long. So because you have switched between frames within a single question, you think there is a contradiction.
You say "no", but I don't see any explanation as to why they are not in error. Again, I understand that the instruments are in perfect working order, and that the results will be the same no matter how many times the experiment is conducted. And I understand the reciprocal nature of the phenomenon. I just don't believe that the rod is shorter; I believe that the moving instruments are unable to see the rod properly, due to the nature of light [in brief, c].Your question could have been asked: "In the frame of reference in which the 'moving' rod is at rest, would we not have to conclude that its instruments are incorrect when they report the length of the lab rod to be 3.2 units?" And the answer is no.
Again, we do not disagree on the result of the measurements; we disagree as to whether the results are correct.So the bottom line of what I'm saying here is that if you want to talk about Special Relativity and the lengths that are assigned according to a particular frame of reference, then it is correct to say that one of the rods is length contracted while the other is not. But if you want to talk about what each rod measures of its own length and that of the other one, it doesn't matter which frame you use, they will always measure the same length for their own rod and a shortened length for the moving rod. And all of these definitions of lengths are correct in their own contexts and none are better than the others or more correct.
Rest length and coordinate length it is (or, they are).DaleSpam said:The process of measuring the distance between the front and the back of an object at a given instant in time according to two synchronized clocks results in some number. The scientific community has given that number a name: "length". It is a defined term. You may think that it would have been better to pick a different name, but you need to know and use the standard name anyway. Otherwise you will be unable to communicate your concepts to others who use the standard name.
Luckily, there is another term used by the community to denote the concept that you prefer: "rest length". So, another way to communicate clearly is for you to simply always talk about "rest length". You can also use the term "coordinate length" to refer to "length" as defined above and thereby simply avoid ever using the unqualified term "length" yourself at all. I have tried to adopt a similar stance regarding "mass" and try to always use the qualified terms "invariant mass" or "relativistic mass", rather than ever using the unqualified term "mass".
Light is not at all relevant to Lorentz contraction. If all the light in the universe disappeared tomorrow, so that the "nature of light" no longer mattered, nothing in relativity would be affected. It is true that in order to derive the Lorentz transformations we make use of the postulate that there exists a speed c that is invariant in all reference frames. However, we do not make use of the fact that there is something that actually travels at this speed.GregAshmore said:You say "no", but I don't see any explanation as to why they are not in error. Again, I understand that the instruments are in perfect working order, and that the results will be the same no matter how many times the experiment is conducted. And I understand the reciprocal nature of the phenomenon. I just don't believe that the rod is shorter; I believe that the moving instruments are unable to see the rod properly, due to the nature of light [in brief, c]
Greg, are you aware of the origin of Lorentz contraction? It predated Einstein. It came about because of the null result of the Michelson-Morley Experiment in which a massive slab of marble was believed to be changing its physical dimensions as it was rotated, even though the slab itself was experiencing different speeds at different times of the day and of the seasons.GregAshmore said:No, I think there is a contradiction because I know that the rod is 4 units long, and the instruments mounted in the moving rod tell me that it is 3.2 units long.
I understand that the instruments read as they do because they are in motion with respect to the rod which they are measuring. However, that by itself does not mean that the rod is actually shorter. As I mentioned, I do have a rational alternate explanation, but it will take me a few days to prepare it. I'm working overtime for the next month or so; there won't be much time in the evenings.
You say "no", but I don't see any explanation as to why they are not in error. Again, I understand that the instruments are in perfect working order, and that the results will be the same no matter how many times the experiment is conducted. And I understand the reciprocal nature of the phenomenon. I just don't believe that the rod is shorter; I believe that the moving instruments are unable to see the rod properly, due to the nature of light [in brief, c].
Again, we do not disagree on the result of the measurements; we disagree as to whether the results are correct.
What does "actually shorter" mean? The claim is that it is shorter in the coordinates of a given frame, i.e. the difference between the position coordinate of the front end and the position coordinate of the back end at a single time coordinate is shorter. One could also define this in terms of simultaneous measurements in the observer's frame, for example if the rod is 3.2 meters long in my frame, that means if I have some calipers set to 3.2 meters apart, the back end of the rod will be passing the back caliper simultaneously with the front end of the rod passing the front caliper, according to my frame's definition of simultaneity. But no one is claiming that this definition of simultaneity is "correct" in any absolute sense, in relativity there is no absolute simultaneity and thus we can only talk about length relative to a particular simultaneity convention. The advantage of the convention Einstein came up with for inertial frames is just that the laws of physics appear to be invariant under a transformation from one inertial frame to the next (the equations of all known fundamental laws are Lorentz-invariant), which implies that if you do any experiment and describe the results in terms of the coordinates of the apparatus' rest frame, you'll get the same result regardless of which frame the apparatus happens to be at rest in.GregAshmore said:I understand that the instruments read as they do because they are in motion with respect to the rod which they are measuring. However, that by itself does not mean that the rod is actually shorter.
"In error" with regards to what? You seem to have this quasi-metaphysical notion of the "true value" of various quantities, but in physics all quantities can only be measured relative to a particular choice of measurement procedure (like assigning coordinates in a given frame), it's completely meaningless to say something like "the measurement procedure itself is wrong" unless this is just a matter of definitions (i.e. if the quantity you're interested in is 'rest length' but you measure it with the procedure for moving length, then you've used the 'wrong procedure' given the usual definition of rest length). You can't ask what the true value of "length" is independent of human definitions of what the word "length" means, unless perhaps you believe that God has a "true" definition of the word "length" and if we use a different one then we are objectively wrong.GregAshmore said:You say "no", but I don't see any explanation as to why they are not in error.
See above, you are using metaphysical/theological language again. What does "is shorter" mean, if it doesn't just refer to definitions of "length" used by physicists which are defined in terms of simultaneous measurements of the front and back in a given frame?GregAshmore said:I just don't believe that the rod is shorter
Same as above. "Properly" with respect to what, if not the human definition of "length" in a given frame?GregAshmore said:I believe that the moving instruments are unable to see the rod properly
The only place light might enter into it would be in the definition of simultaneity, but there are other ways to define simultaneity in a given frame that don't make use of light, like the [post=2937771]slow transport method[/post].GregAshmore said:due to the nature of light [in brief, c].
"Correct" with respect to what? Again, there is no place in physics for some metaphysical notion that words have any "true" definition aside from how we choose to define them.GregAshmore said:Again, we do not disagree on the result of the measurements; we disagree as to whether the results are correct.
In special relativity--inertial frames--there is no acceleration, therefore no pushing at the time of the experiment. If the objects under test have been accelerated to bring them into position for the experiment, we can assume for the purposes of discussion that any deformation was elastic. In that case, yes, I would say that the length of a rod at speed is unchanged from its length at rest. It seems to me that the reciprocal nature of length contraction would be violated otherwise--the rod which was not accelerated would see the other rod as even shorter than the amount predicted by the Lorentz transformation.ghwellsjr said:Greg, are you aware of the origin of Lorentz contraction? It predated Einstein. It came about because of the null result of the Michelson-Morley Experiment in which a massive slab of marble was believed to be changing its physical dimensions as it was rotated, even though the slab itself was experiencing different speeds at different times of the day and of the seasons.
You have argued, apparently based on logic or common sense, that an object cannot change its dimensions simply because of the speed by which it is viewed, but what about when the object itself is having its speed changed? Do you insist that when you push on an object, it cannot change its dimensions? Or are you willing to understand how those early scientists employed Lorentz contraction to explain the null result of MMX?
GrayGhost said:GregAshmore,
You ask a question that all relativists have asked at one time or another. Is a moving contracted length real, or merely apparent? I must admit, even relativists debate this matter at length, and in most those cases comes down to an argument of semantics vs theory.
An accelerating body rotates in its orientation within spacetime, yet we do not witness this rotation in the same way we witness the rotation of a pencil in 3-space. The full rotation we do not perceive, but fortunately, we do perceive effects of the rotation. The effects are length contraction and time dilation, relativistic effects that arise with relative motion. This is proof that bodies remain at their proper length (per themselves) even when moving per others, even though rulers moving relatively can never measure it as such. That said, the contractions are real, while at the same time, bodies always remain their proper length per themselves even during acceleration.
To understand why this is the case, you should really be asking ... WHY does a moving body shrink in length, as opposed to ... is the measurement data correct or not? Understand why, and the question generally no longer needs asked. If you are the persistent type, you may save months (or years) by pursuing the former question first. A good understanding of Minkowski illustrations helps immensely ... food for thought.
GrayGhost
GregAshmore said:At an even more basic level, it seems to me that the length contraction proposed by Fitzgerald, and applied by Lorentz, is different than the length contraction of special relativity. The equation of the transformation is the same, of course. However (it seems to me), the contraction of Fitzgerald and Lorentz must be a physical deformation, because the moving rod is absolutely in motion and the resting rod is absolutely at rest. At any rate, my understanding is that Lorentz believed that the deformation was a physical deformation, in the same sense that compression under load is a physical deformation.
GregAshmore said:In contrast, the contraction in special relativity is attributed to a projection of the rod's strip on the x, ct plane onto a line of simultaneity in another frame. Thus (says Born), "the contraction is only a consequence of our way of regarding things and is not a change of a physical reality." However one may interpret these words, it is clear that (for Born, at least) a physical deformation of the rod is not implied by special relativity.
GregAshmore said:Born goes on to say that this view "does away with the notorious controversy as to whether the contraction is "real" or only "apparent". If we slice a cucumber, the slices will be larger the more oblique we cut them. It is meaningless to call the sizes of the various oblique slices "apparent" and call, say, the smallest which we get by slicing perpendicular to the axis the "real" size."
GregAshmore said:I'm not fully satisfied with Born's explanation. When one slices a cucumber at an oblique angle, the resulting surface is spatial, just as the surface resulting from a perpendicular slice is spatial. Not so with a slice across the rod's strip in the x, ct plane; that slice is a combination of distance and time. Time and distance are interrelated, but they are not convertible one to the other. Therefore, it is very likely a mistake to treat the length of that slice as a simple distance--notwithstanding the fact that the slice is parallel to the x-axis in another frame.
You assume that all measurements provide an accurate picture of reality. How does this square with the fact (as reported by Taylor and Wheeler--I didn't work out the math myself) that no matter how fast an object is moving away from us, we will never measure its speed as greater than 0.5c?JesseM said:What does "actually shorter" mean?
...
"In error" with regards to what? You seem to have this quasi-metaphysical notion of the "true value" of various quantities, but in physics all quantities can only be measured relative to a particular choice of measurement procedure...
The equations of special relativity have the form they do because they start with the observed nature of light--its speed is the same for all observers. The nature of light is thus tightly bound to the characteristics of time and space which flow from the equations.The only place light might enter into it would be in the definition of simultaneity, but there are other ways to define simultaneity in a given frame that don't make use of light, like the [post=2937771]slow transport method[/post].
I'll have a look at your sketches after I see how my concept works out. See you in a few days.bobc2 said:I think you have that exactly right, GregAshomre.
This is certainly correct.
I think most any special relativity physicist would agree with Born's characterization.
You've done a nice job of summarizing the situation, but Greg, I think I would not agree with this characterization. However, you probably have some good company among physicists on this point. The thing that is usually cited to bolster your view is that it is common practice to relate the 4th dimension as X4 = ict, where the imaginary number is associated with the 4th dimension. However, I think this is artificially contrived as I'll try to show in the sketches below where I've derived the Lorentz transformation (rotation only) modeling space as strictly 4-dimensional.