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Ontological concepts(?)/ Special relativity.

  1. Feb 25, 2010 #1
    I have written this to test my understanding of some of the concepts involved with Special Relativity. Any comments, corrections; agreement or disagreement; will be gratefully received:

    1.Every IFoR can be considered to be stationary. An observer positioned within one would certainly say that it is.
    2.An IFoR has no forces acting upon it; Physical laws and therefore the existing conditions are the same/identical/unchanging between IFoRs
    3.The coordinates that obtain within an IFoR, and that are perceived by an observer within an IFoR, are measured in Proper units.
    4.Each body can have only one existence.
    5.Each and every inertial body that exists in space possesses innate(ontological?) dimensions .
    6.Those innate dimensions are those measured within that body's own frame of reference.
    7.Measurements made from any other body, or frame of reference, are made under different conditions using different coordinates
    8.So a single body that exists alone in space is not moving and possesses innate dimensions, due to its composition and structure.
    9.If a 2nd body were to be present, at rest relevant to the 1st then it, too, would use the same coordinates and measure the same dimensions.
    10.But if that 2nd body were to have a constant velocity, relative to the 1st, then it* would use a different set of coordinates to measure the dimensions of the 1st body. These coordinates and measurements being related by the Lorentz transformations.
    11.The 2nd body's measurements are just as real to the 2nd body as the 1st body's are to her but does this mean that the 1st body has changed dimension, or that it has developed a new existence with different dimensions? I think not.
    12.The different measurements taken by the 2nd body are due to the different conditions under which they are measured. i.e. the relative velocity of the two bodies.
    13.For any two IFoRs, with whatever relative velocity, a third can be imagined that is permanently mid-way between the first two, and this 3rd one would have an equal but opposite relative velocity with each of those first two.
    14.Any measurement taken by the third of, let us say, one second, from the 1st body and transformed into the 3rd body's coordinates, would be equal to the similar measurement taken from the 2nd body and transformed into the 3rd body's coordinate, because the transformations would be made using equal relative velocities.
    15.Consequently we can say that the proper** seconds measured in each of the first two bodies are equal as measured by an independent observer.
    16.The same process can be applied to any two IFoRs.
    17.Therefore Proper time in any IFoR is exactly equal to proper time in any other IFoR as measured/transformed/calculated by an independent observer.





    * I realise that this is anthropomorphising the bodies, so let us consider that they may be astronauts
    ** see 3. above.

    I just hope I am getting some of this right, now

    Grimble
     
  2. jcsd
  3. Feb 25, 2010 #2

    JesseM

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    Agreed that physical laws are the same in different IFoRs, but I think it's a bit confusing to say no forces are acting on it--an IFoR is really just a coordinate system for labeling arbitrary events with space and time coordinates, how could a coordinate system have forces acting on it? Of course an IFoR can be physically realized using a system of measuring-rods and clocks which are all at rest in that frame, so that the coordinates of an event are based on the measuring-rod-marking and clock-reading that were right next to the event as it happened, so in that case it's true that these clocks and measuring-rods should be ones that aren't being acted on by any forces.
    That's a little too broad, if I'm in a given IFoR and I measure an object which is moving in this frame to have a given length L, it wouldn't be right to call that the object's proper length, since proper length refers to an object's length in its own rest frame. Likewise for an inertial clock the proper time between events on its worldline is always equal to the coordinate time between those events in the clock's own rest frame, and as I mentioned on the other thread proper time can also be generalized to non-inertial clocks, it just means the time that elapses on the clock itself.
    The terminology here sounds a bit more philosophical than physical...physical definitions should just be stated in terms of things that can be measured, I think. I don't know how you'd define "innate/ontological" in these terms, for example.
    You can certainly define "innate" to mean measurements in an object's own rest frame, but if you're suggesting that in some ontological sense these measurements reflect "reality" more than others that seems like a philosophical conclusion I'm not sure I'd agree with. Consider a spatial analogy--in a given 3D cartesian coordinate system, we could define the "cross-sectional area" of a 3D cylinder as the area of the 2D intersection of the cylinder with the xy plane. Obviously this means that for any given cylinder, our judgment about the cross-sectional area will depend on how the xyz axes are oriented relative to the cylinder's own axis. But would you say that somehow the cross-sectional area in the coordinate system where the z axis is parallel to the cylinder's axis is more "innate" or "real" than any other coordinate system's definition? Well, volume of an object in its own rest frame in SR is basically similar, it's just the 3D intersection between the object's world-tube and the xyz plane in a 4D coordinate system where the t axis happens to be parallel to the worldline of the object's center, I don't really think this is any more innate to the object than any other coordinate system's definition of volume. In both cases the problem is that the 3D volume of a 4D world-tube, or the 2D cross-sectional area of a 3D cylinder, are inherently dependent on the angle you choose to slice up the higher-dimensional object into lower-dimensional cross-sections. On the other hand the 3D volume of a 3D cylinder is truly coordinate-independent, and similarly I think you could define some notion of 4D "volume" in spacetime.
     
  4. Feb 25, 2010 #3

    Fredrik

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    1. Yes.
    2. A coordinate system is just a function that assigns four numbers to each event, so you should be talking about "an object with constant spatial coordinates in this frame" or something like that. But yes, there are no forces on such an object. This is because we define these objects to be "not accelerating". Acceleration is defined as a measure of how much the curve that represents the objects motion deviates from being a geodesic (i.e. having constant velocity in all inertial frames).
    3. You can use any units you want, but it's convenient to set c=1.
    4. Not sure what that means, but you should think of spacetime as an abstract set of points, and the motion of an object as represented by a set of curves in spacetime. A point particle is by definition an object that only needs one such curve. (Note that I didn't mention coordinates, which are just functions that assign four numbers to each of those points).
    5. Not sure what that would mean. The curves that represent its motion fill up a region of spacetime. If you connect two points on two different curves by a new curve, that curve will have some properties that have nothing to do with coordinates.
    6. "Its own frame of reference" defines a "preferred" set of curves: The ones that are parallel to some axis.
    7. That other body will "prefer" a different set of curves.
    8. If it's a single point particle, the whole theory becomes meaningless. If it's an extended object, we can at least talk about how the component parts move relative to each other.
    9. Assuming that the method we use to associate a coordinate system with the motion and spatial orientation of an extended object is the usual clock synchronization procedure than yes.
    10. Yes. (Assuming that we're still in Minkowski spacetime, and what I said in 9).
    11. It does not.
    12. The "different conditions" will make them measure coordinate independent properties of different curves.
    13. Yes.
    14. The third measures one second from the first's body? I don't know that means.
    15. I don't know what you mean by "proper seconds".
    16. Yes. (I'm not sure what process you're referring to, but anything that can be done to one inertial frame can be done to any other).
    17. I haven't been able to follow your reasoning, but proper time is a property of a curve. If that curve is parallel to the time axis of some inertial frame, then it can be calculated by an inertial observer that has a non-zero velocity in that frame. He just measures the proper time of a curve that's parallel to his time axis and applies the time dilation formula to the result. (The endpoints of that curve must be simultaneous in his frame with the endpoints of the other curve).
     
  5. Feb 25, 2010 #4

    Saw

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    Grimble, just a broad comment: I somehow sympathize with your will to find something that is "innate", "real" or "ontological" ("absolute"?), but I don't think you can find it, precisely, in dimensions. Dimensions are the outcome of measurements, physical operations carried out with physical instruments and hence affected by environmental circumstances. Thus forcefully their magnitudes are contingent upon those physical conditions, i.e. relative. This comment also applies to "proper" dimensions, i.e. those measured in the rest frame of the measured object, like proper time or rest length. You cannot say that the latter are less relative than those obtained in other frames. If you want to establish a hierarchy between the two sets, you must look at the purpose for which you measure, at the reason for which intellect creates the concept. This purpose is nothing but making predictions about what will happen and what will not. And in this respect, that is what SR means (I think), all measurements are equally valid: they all do the trick and so thay are all equivalent. You could claim, however, that proper time is a more direct route to learn what happens in the rest frame where it is measured. For example, if you want to predict if a muon created at the upper atmosphere will reach the ground and you happen to know proper trip time in its frame, you already have the answer, whereas measuring from the ground-frame you need two values, trip time as measured by non-colocal clocks and distance travelled. But that is all. All values are functional, regardless the frame where they are obtained.
     
  6. Feb 26, 2010 #5
    `

    Thank you Jesse, that was just the sort of response I was hoping for!

    I have re-written the first few points to try and accomodate your input. Thank you.

    In the following points I am defining every body as having its own frame of reference, so please read IFoR as meaning 'body and its associated IFoR whose origin is the same as that Body's origin.'

    1.Every IFoR can be considered to be stationary. An observer positioned within one would certainly say that it is.
    2.An IFoR has no forces acting upon it; Physical laws and therefore the existing conditions are the same/identical/unchanging between IFoRs
    3.The coordinates that obtain within an IFoR, and that are perceived by an observer, who is stationary within that same IFoR and adjacent to that frame's clock, are measured in Proper units.
    4.Each body has an existence and possesses properties. These properties (dimensions and duration) are innate to that body.
    5.They may be measured differently by different observers, according to the conditions under which they are measured. i.e. the measurements of a body will vary depending upon how and by whom it is measured, but those innate properties will exist unchanged.
    6.Measurements made from any other body, or frame of reference, are made under different conditions using different coordinates which would affect the resulting measurements.
    (I am not saying one would be preferred, only that they will be different)
    7.So a single body that exists alone in space is not moving and possesses innate dimensions, due to its composition and structure.
     
  7. Feb 26, 2010 #6
    Thank you Saw, I certainly see what you mean in the first part of your reply: magnitude would be a much better term to use than dimension.

    I suppose that what I am trying to say is that there must be some way of looking at a body that perceives its magnitudes 'locally', without any 'distortions' caused by the conditions , or, therefore, the coordinates, under which it is measured.
    When a moving body is measured by a 'remote' observer, its coordinates are a function of the relative velocity of the two bodies, and must therefore change if that relative velocity changes.
    But the moving body, itself (and any local observer situated in that body) could be completely unaware of the remote observer and changing relative velocity and would continue unchanged. It is the remote observer's observations/measurements that change,
    because the conditions under which they are measured have changed.

    So I would say that there is a real difference between the two sets of coordinates/measurements: that is that any change that occurs to the local observer's measurements would have to be seen also in the remote observer's measurements; but changes to the remote observer's measurements wouldn't necessarily be reflected in changes to the local observer's measurements. (If it were only the relative velocity that changed due to a change in the motion of the remote observer.)
     
  8. Feb 26, 2010 #7

    JesseM

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    Re: `

    I think you may be getting hung up on the notion that a frame of reference represents the perspective of a particular "body" or observer. There's no physical reason why a given observer should use their rest frame to do calculations, this is really just a matter of convention, so we can use the shorthand of what a given observer "measures" or "sees" instead of spelling out that we are talking about what the coordinate distances and times are in that observer's inertial rest frame. But reference frames are just coordinate systems, in reality there is no physical reason an actual human observer couldn't use a coordinate system where they are not at rest to perform calculations. In terms of your point #7, there's no reason we can't still talk about what would be true in a frame where the lone body in space was moving, even if this frame did not represent the rest frame of any physical observer...again, frames are just abstract coordinate systems, not physical things which "cease to exist" if there is no one around at rest in that frame.
     
  9. Feb 26, 2010 #8
    Re: `

    Maybe, but the reason I refer to observer's in frames, rather than what would be the perspective from that frame, is that I was accused of 'anthropomorphising' frames.

    So would it be preferable to substitute 'how and from where it is measured' for 'how and by whom it is measured'?
     
  10. Feb 26, 2010 #9

    JesseM

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    Re: `

    As I remember, that accusation was specifically related to your talk of how one frame "viewed" another frame or something along those lines, which doesn't make much sense if we just understand frames as coordinate systems. Talking about the "perspective" of an individual frame is fine, because that's just understood as a shorthand for how that coordinate system defines coordinate times, coordinate distances, coordinate velocities and so forth. So you can certainly talk about how these things are defined in a coordinate system that doesn't happen to correspond to the rest frame of any physical object in the region of spacetime you're considering.
     
  11. Feb 26, 2010 #10

    Saw

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    That is true. If I am lying on the ground, the fact that my length has ten thousand values in ten thousand different frames does not mean that I am stretching and compressing every time that those diverging values are either measured by the corresponding observer, if that happens, or (as JesseM points out) simply used in a formula by a single person who mentally takes the perspective of any of those frames. But that fact (fortunately, I don’t experience any twitching in my body) doesn’t make the value of my length in my rest frame more real or more innate or more ontological than the others.

    If physical measurements actually take place, what they reflect is the reality of the measurement itself. I have, for example, sent a light pulse from my feet to the top of my head, counted the time for the round trip and divided by two. You have done the same, with regard to my body, from a train moving wrt the ground. We get different values. Is mine more “real” than yours? No, they were both obtained analogously, through the same physical procedure, under different circumstances, and they are both functional. On this basis both you and I can predict if I can enter a house without hitting my head. It would be more dramatic if you held that, in your frame, I have a fewer number of atoms than in mine. But it seems that SR doesn’t mean that. We only disagree in terms of "length", which is just a concept, an abstraction created for a purpose, i.e. predicting what will happen and in that we don’t disagree. If you still feel uncomfortable because we are using the same term with discrepant values, just change that: call my value rest length and yours coordinate length and I will agree that I have coordinate length X’ in your frame and you’ll agree that I have rest length X in my frame.

    And if physical measurements are not taking place right now…

    I fully agree. Paraphrasing, a frame is an abstract idea, an idealized point with a given inertial motion, even if there is no physical object and no physical observer at rest with it. For example, I can mentally take the perspective of the frame of the center of mass the two-body system, even if I am actually sitting on the Earth, which is (or, if you prefer, co-moves with) an accelerated frame, and make successful calculations. But I am sure that you agree that for this purpose I must use in my equations values that have been measured somewhere by somebody, by applying, if appropriate, the relevant transformations. Physical measurements and their physical circumstances are always there, at the root of the reasoning process.

    What I mean by this is that your point, which is true, does not invalidate Grimble’s point that values are relative because, ultimately, they are obtained under different physical conditions... Well, in the end, what I am always doing is coming back to the idea that reality is not relative, only concepts are. That’s a little boring, even for me, so let us leave it like that. :smile:
     
  12. Mar 2, 2010 #11
    Oh dear! This all becomes so complicated. It is so difficult to describe something in terms such that the reader understands the writer's point.

    Let me try again in simple terms...

    1.let the abstract 'body' refer to spacecraft.
    2.Each spacecraft contains an observer and it is that observer who 'sees' for that body
    3.When referring to a body's IFoR it is that at whose origin that body is located.
    4.Coordinate time is that which is passing within that IFoR.
    5.By subjective measurements I refer to those made directly using rulers and clocks that exist within the observer's IFoR
    6.By objective measurements I refer to those made using rulers and clocks that exist within the observed IFoR

    Any lone body in space may be considered to be stationary.
    It may be alternatively be considered to be moving with respect to some hypothetical frame of reference.
    This lone body A has no forces acting upon it and its frame of reference is therefore an IFoR.
    This body, being a rigid body has spatial magnitudes.

    A second body B exists at rest relative to A.
    A may be considered to exist in B's IFoR and B may be considered to exist in A's IFoR.
    Therefore both will agree, on the subjective and objective measurements, of the other's spatial magnitudes and passage of time.

    Now if B were not at rest with respect to A but was moving at a constant relative velocity v then each may still be considered to be within the other's IFoR but would be a moving body in it.

    Now the subjective measurements being measured within the observer's IFoR would be unchanged for the two observer's but their objective measurements would changed.

    The objective measurements would be related to the subjective measurements by the Lorentz transformation equations.

    A & B would still exist just as they did when they were at rest with one another.
    The only changes would be to the objective measurements, those being changed as a function of their relative velocity.

    I see an analogy here with looking at a fish underwater. The Kingfisher has to make allowance for the distortion caused by the refraction of the light as it dives. What it sees and 'measures' from its branch above the stream is real to it yet it knows that it has to calculate the 'transformation' from the water's surface.

    So the only changes here are the apparent changes to the objective measurements caused by the change of conditions under which they are measured.

    Time does not pass differently at all, it is how it is seen to pass, that changes. The subjective and objective measurements are not measuring the same thing, because what they are measuring changes according to the conditions under which they are measured and the Lorentz transformation relates one measurement to the other.

    So are we talking about how a remote observer witnesses the transformation of the measurements taken in the observed frame of reference. Converting them into their objective values, as seen from that observer's frame of reference?

    The remote observer may then take objective measurements and, by applying the Lorentz factor, transform them back into the subjective measurements that obtain within the observed body's frame of reference.
     
    Last edited: Mar 3, 2010
  13. Mar 3, 2010 #12
    Hi Grimble,

    I think this link http://en.wikipedia.org/wiki/Andromeda_paradox relates to your thoughts on the difference between subjective and objective measurements.

    In the Andromeda paradox, a slow observer on Earth thinks it is Tuesday on Andromeda and the Aliens have already decided to attack Earth and have launched their fleet. To the fast observer on Earth, it is Monday on Andromeda and the aliens are still deliberating whether to attack Earth or not. To the fast observer there is some uncertainty about the aliens launching an attack while to the slow observer there is 100% certainty that they have launched an attack.

    The paradox is deliberately misleading in a number of ways (but I guess they are supposed to be) but it does help focus on some interesting aspects. Neither of the observers has 100% certainty, because neither has received information that the launch of the attack fleet has actually occurred because of limitations of the finite maximum speed of signal transmission. Now if the slow and fast observers on Earth had corresponding slow and fast observers on Andromeda at rest with their respective partners on Earth, then the secondary observers on Andromeda would agree that the launch of the alien attack fleet took place at the same place in time and space and they only differ in how the launch time differs relative to the observers on Earth. In other words, the slow observer on Andromeda calls the attack launch time "Tuesday" while the fast observer on Andromeda calls the attack launch time "Monday". This difference in what they choose to call the attack time comes about because of the way they have chosen to synchronise their clocks with their respective Earth counterparts (the objective measurement?) while they both agree that they were both there at the same time and place (Attack day on Andromeda) alongside each other when they watched the attack fleet take off (the subjective measurement?).

    Have I interpreted your meaning of subjective and objective measurements correctly?
     
  14. Mar 3, 2010 #13
    Hi Kev, that is an interesting paradox, but as far as I can see, looking at your link, it is related to Relative Simultaneity.

    My subjective and objective measurements arose from consideration of the 'slowing of the moving clock', in that there is just one clock, measuring one time and that clock is measuring the time in its own frame of reference (subjective time); whereas the remote observer has to take that same measurement and 'transform' it (using the Lorentz factor) to arrive at her calculated measurement (objective time).
     
  15. Mar 3, 2010 #14
    Hi again Grimble,

    OK, I might have misunderstood what you were getting at and that is partly because I am guilty of not reading all the preceding posts in detail. I hope you will forgive me, but there is a lot to read there :smile:.

    My gut instinct would be to reverse your use of subjective and objective. Subjective is usually means a measurement that is dependent on the individual making the measurement. For example the question "which is the prettiest girl" would be a subjective descision because it depends on the eye of the beholder. Consider this example in the context of Special Relativity. We have 3 observers. B and C are at rest with respect to each other and moving relative to observer A. Now if C slows down relative to A, observer B will say C's clock is now ticking slower than it was previously and A will say C's clock is now ticking faster than it was previously. Obviously (most people would agree) C's clock can not speed up and slow down at the same time. Therefore the rate that a clock ticks at is dependent on the observer and I would call that a subjective measurement. On the other hand, the rate that C's clock ticks relative to the natural decay of radioactive particles or the characteristic frequency of excited atoms or any other natural process in C's frame is a proper measurement that all observer's agree on and I would call that an objective measurement, but that is just my personal (subjective) interpretation of how those words should be used.
     
  16. Mar 4, 2010 #15
    Kev, I like your honesty, and we all do it, but few admit it! No problem, after all this is all about communication and I do tend to be a bit wordy...

    What you say is so true though I hadn't thought of it that way. I like it!

    I now change my definitions:

    5.By objective measurements I refer to those made directly using rulers and clocks that exist within the observer's IFoR. All observers agree with this measurement.
    6.By subjective measurements I refer to those made using rulers and clocks that exist within the observed IFoR and are a function of their relative velocity.
     
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