Reflections on Special Relativity, with an inter-disciplinary approach.
Relativity and semantics
Posted May16-12 at 04:01 PM by Saw
Dalespam recently brought up an interesting semantic issue. What is the meaning of “relative” versus “absolute”? I did not have time to intervene in that thread but the subject links well with the musings of this Blog.
Obviously “relative” is what is defined “in relation with” or by comparison with another object, but in the context of Special Relativity this may mean three different things:
(a) That a measurement (of time or space) is made from and hence with regard to a reference frame. This must forcefully happen. The way to measure in an absolute manner does not exist. In this sense, all measurements are relative.
(b) That the outcome of a measurement is affected by the fact that it is made from a reference frame and hence different from frame to frame, that is to say, frame-dependent. This does not always happen. In pre-SR physics, it was admitted that the measurement of the distance travelled by a projectile in a time lapse was frame-dependent but it was also expected that the measurement of the length of an object and of time elements (duration, simultaneity) would be absolute, i.e., frame-independent. In SR, instead, all time and space measurements have been proved to be frame-dependent but they are so in a manner that they make the measurement of the speed of light frame-independent, absolute in this second sense.
(c) That a measurement from a given reference frame is worse than one effected from another frame, which is better, insofar as the former provides less information than the latter.
This is also a common meaning in day-to-day language. A book by Balzac which impressed me many years ago was called À la recherché de l’absolu. The protagonist was a chemist that sought the ultimate and highest discovery and wasted his fortune and his life in that vain attempt. We also talk in this sense about absolute love, the one whose qualities and intensity would make all other emotions look pale and empty… Finally, in the political arena, we use the concept of absolute power, the one that is over-comprehensive and is not balanced by any constraints.
Shifting back to SR, the point of previous posts has been that the aim of the game, when one handles kinematic concepts, is solving problems about causality. Thus an absolute measurement would be one that provided the completest level of information in this respect. In particular, since the problem is “can event A have an influence on event B?”, the absolute answer would be “yes or no, no matter how fast the agent carrying the causal influence may travel, even if it travels at infinite velocity, that is to say, instantaneously”.
In pre-SR physics, it was initially thought that the measurement of simultaneity [in sense b) = all frames get the same value] would also provide that optimal degree of information, in sense c) (such value furnishes knowledge about the causality ability of infinitely fast agents).
Given this, when it was discovered that “light does not take the motion of the source”, it was then thought that a measurement made with a light signal could not achieve that aim; scientists thus assumed that the absolute knowledge would only be possible in a particular frame, the aether frame, the aether being a (non-material…) medium where light would propagate as a disturbance, just like sound does in the air.
However, it was left open the question as to whether a measurement other than with light, being invariant (in as much as time is concerned) in sense b), would still provide full information in sense c). This would enable us to measure what sometimes is called the absolute velocity of light, which is thus named because it would be made out of absolute time measurements, although such velocity would be relative in sense b), since it would forcefully be frame-variant...
At this juncture, I leave aside the thorny issue of the “relative” merits of Lorentz, Poincaré and Einstein. What seems clear for everybody today is that absolute time is not measurable. The only real time is the relative one in sense b) (it is frame-variant) and…
also in sense c) (it does not provide full information). Or not? What do you think? Do you believe that you could have it both ways? Variant measurements [relative in sense b] that are each of them absolute [in sense c), meaning that each of them leads to a different version about what happens and what does not happen in causality terms]…?
Well, that is what some authors suggest, those authors who argue that “faster-than-light travel and time travel” are necessary companions.
Obviously “relative” is what is defined “in relation with” or by comparison with another object, but in the context of Special Relativity this may mean three different things:
(a) That a measurement (of time or space) is made from and hence with regard to a reference frame. This must forcefully happen. The way to measure in an absolute manner does not exist. In this sense, all measurements are relative.
(b) That the outcome of a measurement is affected by the fact that it is made from a reference frame and hence different from frame to frame, that is to say, frame-dependent. This does not always happen. In pre-SR physics, it was admitted that the measurement of the distance travelled by a projectile in a time lapse was frame-dependent but it was also expected that the measurement of the length of an object and of time elements (duration, simultaneity) would be absolute, i.e., frame-independent. In SR, instead, all time and space measurements have been proved to be frame-dependent but they are so in a manner that they make the measurement of the speed of light frame-independent, absolute in this second sense.
(c) That a measurement from a given reference frame is worse than one effected from another frame, which is better, insofar as the former provides less information than the latter.
This is also a common meaning in day-to-day language. A book by Balzac which impressed me many years ago was called À la recherché de l’absolu. The protagonist was a chemist that sought the ultimate and highest discovery and wasted his fortune and his life in that vain attempt. We also talk in this sense about absolute love, the one whose qualities and intensity would make all other emotions look pale and empty… Finally, in the political arena, we use the concept of absolute power, the one that is over-comprehensive and is not balanced by any constraints.
Shifting back to SR, the point of previous posts has been that the aim of the game, when one handles kinematic concepts, is solving problems about causality. Thus an absolute measurement would be one that provided the completest level of information in this respect. In particular, since the problem is “can event A have an influence on event B?”, the absolute answer would be “yes or no, no matter how fast the agent carrying the causal influence may travel, even if it travels at infinite velocity, that is to say, instantaneously”.
In pre-SR physics, it was initially thought that the measurement of simultaneity [in sense b) = all frames get the same value] would also provide that optimal degree of information, in sense c) (such value furnishes knowledge about the causality ability of infinitely fast agents).
Given this, when it was discovered that “light does not take the motion of the source”, it was then thought that a measurement made with a light signal could not achieve that aim; scientists thus assumed that the absolute knowledge would only be possible in a particular frame, the aether frame, the aether being a (non-material…) medium where light would propagate as a disturbance, just like sound does in the air.
However, it was left open the question as to whether a measurement other than with light, being invariant (in as much as time is concerned) in sense b), would still provide full information in sense c). This would enable us to measure what sometimes is called the absolute velocity of light, which is thus named because it would be made out of absolute time measurements, although such velocity would be relative in sense b), since it would forcefully be frame-variant...
At this juncture, I leave aside the thorny issue of the “relative” merits of Lorentz, Poincaré and Einstein. What seems clear for everybody today is that absolute time is not measurable. The only real time is the relative one in sense b) (it is frame-variant) and…
also in sense c) (it does not provide full information). Or not? What do you think? Do you believe that you could have it both ways? Variant measurements [relative in sense b] that are each of them absolute [in sense c), meaning that each of them leads to a different version about what happens and what does not happen in causality terms]…?
Well, that is what some authors suggest, those authors who argue that “faster-than-light travel and time travel” are necessary companions.
Total Comments 8
Comments
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I have thought I should comment my own post to add a clarification. I have implied that the measurement of, for example, simultaneity under SR, which is relative in senses a) and b), must also be relative in sense c), that is to say, it does not provide full knowledge. However, this knowledge gap is totally irrelevant in practical terms. What the relative measurement does not say, in terms of causality, is how event A could affect event B through a faster-than-light agent. But since travelling so fast is impossible for physical reasons such purported lack of knowledge has no consequence. We know all we need to know.Posted May18-12 at 01:17 AM by Saw 
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To my dismay, I left out another important point in my post. I have just said that measurements in SR provide "absolute" knowledge in the sense that they solve all known problems (with just the caveat that problems involving faster-than-light agents are not solved but that is no drama, because they do not exist). I should have added, however, that such measurements are "absolute" (in the above sense) only when they team up, when you make them collaborate through the relativistic equations, thus building the concept of spacetime.
Posted May26-12 at 04:22 AM by Saw
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Hi interesting attempt! It's rather tricky indeed, and I think that you overlooked an important - perhaps even the main - meaning. "Relative" is not exactly the same as "with regard to a reference frame". Take for example the following statement:
"the ray moves relatively to the initial point of k, when measured in the stationary system, with the velocity c-v" (taken from Einstein's first relativity paper). I can't fit any of your options to this rather standard statement.Posted Aug16-12 at 10:12 AM by harrylin
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Hi Harrylin. Thanks for bringing in this point. You are right that this is another meaning and a key one, quite worth being considered. In my discharge, I would say however that it is not so much “standard” use. If I am not mistaken, what Einstein is saying here is that the stationary frame S considers that the K moving frame should measure that the ray of light moves at (c-v) with regard to that K… if only… (I leave this intentionally unfinished; I will come back to it later). I once used this idea in a thread and JesseM (by the way, what happened to him, does anybody know?) scolded me a little, accusing me of using “convoluted” (non-standard) language. In fact, it is challenging to find the right words for this use of the word. “Relative to” meaning “as measured in” frame S the ray of light in question travels at c, full stop. Similarly, “relative to” = “as measured in” frame K that light also travels at c. The (c-v) expression only comes onto the stage when you mix the two frames in a manner that is not very clear. But the issue would well deserve clarification since it puzzles many people, who tend to think that Einstein is contradicting himself when in fact he is not. I believe that the approach that I started above may be a good start for an explanation. In this sense, (c-v) would be the actual measurement that K frame would obtain… if only… its measurement instruments (clocks and rods), standing physically on K, would behave in the same manner as if they were standing on frame S. What do you think?
Posted Sep1-12 at 11:54 AM by Saw
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Hi Saw, I only noticed your reply by chance (I got no notification of this).
Surely Einstein does no such suggestion at all, he specifies a measurement by S and not by K. (c-v) is perfectly clear. See my recent post here: physicsforums.com/showthread.php?p=3992825
All my physics books of my physics courses agree on the first definition - and I'm not very old.
For me, and no doubt for many others, this is standard use. It appears to be still the standard in books like this one (I have an older version): http://www.amazon.com/Physics-Marcel...o+finn+physics. I see that "relative motion" is still introduced before any coordinate system transformation. An edition may also be in your library.Posted Sep22-12 at 06:36 AM by harrylin
Updated Sep23-12 at 05:20 AM by harrylin (typo; link and update) -
PS: In contrast, some physics books confound objects with reference systems. As a result, relative velocity is velocity (compare 1984, Orwell). I consider that poor physics, with the risk of reducing the mental abilities of the student
. So, what is worse, "convoluted" language or "Newspeak"? Sounds like a good title for a blog of my own. 
Posted Sep22-12 at 06:43 AM by harrylin
Updated Sep23-12 at 05:23 AM by harrylin (elaboration) -
Hmm. I do agree that you are raising an interesting semantic issue, much in line with the present blog entry: should this concept be called “relative motion” o “closing speed”. I also agree that it is not a convoluted thing to talk about. But I suggest leaving aside the terminological issue and focusing on what the concept means. You say that Einstein “specifies a measurement by S and not by K.” (Sorry I was discussing based on my recollection of the text and changed the letters. In the original, the “stationary system”, which I call S, is called K and the moving system, what I call K, is referred to as k. But I will stick to my own notation, since you have been kind enough to respect it.) I am not sure that we can really talk about a “measurement” by S… if we agree to define that (and I think we should) as what comes out of instruments at rest in S. What these instruments “measure” is c for light and v for system K. Full stop. That is an empirical truth, an undeniable fact. If a guy in S dares to employ the expression (c-v) is only after “reasoning”, not on the basis of reading measurements. And what is that reasoning based on? If we were speaking in the context of Galilean relativity, the answer would be quite easy: the guy in S is placing himself mentally in system K and guessing, by way of logic, what K should measure. And in Galilean relativity, such guess is correct: (c-v) is what K actually measures. However, unfortunately, in SR the said reasoning does not work. For a photon, the guy in K will measure c, not (c-v). So in what sense does the man in S mean (c-v)? What does it mean, in his jargon? To me, it means what I advanced before: (c-v) is what one would measure from a frame moving like K but armed with clocks and rods working as if at rest in S. Of course, since we are not talking about a real measurement but a deduction, this is a reasoning that can be made by any observer from any frame, but the reasoning does rely on these two assumptions: you would get (c-v) if measuring in K with S instruments. Or did I get it wrong after all?
Posted Sep24-12 at 04:32 PM by Saw
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Hi Saw,
You make it sound as if we have the power to create the meaning of a term ourselves, or as if it is a hypothetical question. However, most terms are already in use. We often have the choice between conflicting existing meanings, and our choice is like a vote that may help keep the meaning that we prefer alive. And I can't follow you when you write "I suggest leaving aside the terminological issue and focusing on what the concept means". What a concept means is a terminological issue.
Now, we can certainly measure what you call "closing speed". Thus you get (c-v) if measuring with "K instruments" an object and a light ray that are moving at velocities v and c "in K". As far as I can tell, Einstein only employed expressions that conform to feasible direct measurements (at least in principle; length contraction is still out of reach). I guess that that is what you mean with "real" measurements.
And how do you call your velocity as indicated by your GPS receiver? Probably your GPS receiver calls that the velocity of your car relative to the road, but it is determined using the ECI frame; and most people would say that GPS "measures" your speed - even your "speed relative to the road". And in order to perform this impressive feat, GPS makes intense use of "c-v" as determined in the ECI frame.Posted Sep25-12 at 02:33 AM by harrylin
Updated Sep27-12 at 02:35 AM by harrylin (more clarification; font; typo)
