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Thread: Length Contraction of Space Between Objects

  1. #1 Length Contraction of Space Between Objects 
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    When people explain length contraction they usually explain how a rocket ship or a car appears to be shorter in the direction it's moving in as it approaches the speed of light, and that this is true of all objects. If a rocket ship is moving near the speed of light relative to an observer, and the rocket ship appears to be contracted, the space between the atoms of the rocket ship must also be contracted because if they weren't, only the atoms would contract and the length of the rocket ship would remain the same? How does this work? Also, as the rocket ship moves away from the observer is the space between the rocket ship and the observer also contracted?
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    Quote Originally Posted by Scheuerf
    When people explain length contraction they usually explain how a rocket ship or a car appears to be shorter in the direction it's moving in as it approaches the speed of light, and that this is true of all objects. If a rocket ship is moving near the speed of light relative to an observer, and the rocket ship appears to be contracted, ..
    It's much more than merely appearing to be contracted. It is contracted, physically. And for any speed, not just as it approaches the speed of light of for large speeds. In electrodynamics the Lorentz contraction relevant to charge density plays a large role in the fact that there's zero charge density in the rest frame of a current carrying wire and a normal sized charge density in a frame moving parallel to the wire at normal speeds. That's due to the huge amount of electrons in the wires.

    Quote Originally Posted by Scheuerf
    ..the space between the atoms of the rocket ship must also be contracted because if they weren't, only the atoms would contract and the length of the rocket ship would remain the same? How does this work?
    You're right. The atoms and the electron orbitals also contract. A paper was done in the 1950's on this and it was shown to be the case. I'm trying to find that paper now but am not having an easy time finding it.

    Quote Originally Posted by Scheuerf
    Also, as the rocket ship moves away from the observer is the space between the rocket ship and the observer also contracted?
    It's hard to say what that means since one end is moving and the other end isn't. However I can tell you that the total distance to be traveled is shorter due to contraction.
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    Quote Originally Posted by Scheuerf View Post
    Also, as the rocket ship moves away from the observer is the space between the rocket ship and the observer also contracted?
    Good question. The distance between two static points in the observers frame will be length contracted in the rocket frame, but as Physicist says here one point is static in each frame. I would expect that the situation would be symmetric from both frames. I've not found an answer to this question yet that makes any sense.
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  4. #4  
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    Also, as the rocket ship moves away from the observer is the space between the rocket ship and the observer also contracted?

    Physicist: It's hard to say what that means since one end is moving and the other end isn't. However I can tell you that the total distance to be traveled is shorter due to contraction.

    cinci: Maybe I'm missing something, but the distance between the an observer and a ship moving away is not contracted for that observer, is it? An observer on the rocket ship would measure the distance to be contracted.
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    Quote Originally Posted by cincirob View Post
    Also, as the rocket ship moves away from the observer is the space between the rocket ship and the observer also contracted?

    Physicist: It's hard to say what that means since one end is moving and the other end isn't. However I can tell you that the total distance to be traveled is shorter due to contraction.

    cinci: Maybe I'm missing something, but the distance between the an observer and a ship moving away is not contracted for that observer, is it? An observer on the rocket ship would measure the distance to be contracted.
    Here above, cinci, you are NOT applying reciprocity. If the spaceship moving away is not seen to have the distance between it and the external observer contract, then an observer in the ship would NOT notice length contraction between the external observer and himself - though he would presumably find length contraction of the earth or whatever object the external observer was standing on.

    The contraction of distances between objects (including mutually stationary objects moving relative to another observer and seen by him) is one fraught with paradox & confusion - a mental minefield!

    TFOLZO
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    Quote Originally Posted by Jilan View Post
    Good question. The distance between two static points in the observers frame will be length contracted in the rocket frame, but as Physicist says here one point is static in each frame. I would expect that the situation would be symmetric from both frames. I've not found an answer to this question yet that makes any sense.
    It is not complicated at all:

    If observer O measures distance L in his frame, then observer O' moving at speed v wrt O measures the same distance to being .

    Conversely, if observer O' measures distance D' in his frame, then observer O moving at speed v wrt O' measures the same distance to being .
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    LOL, then the distances then get smaller and smaller with each iteration. Don't you see a problem with this?
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  8. #8  
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    Quote Originally Posted by Jilan View Post
    LOL, then the distances then get smaller and smaller with each iteration.
    No, they don't. The only thing that my post illustrates is the fact that length contraction is symmetric, just like time dilation.


    Don't you see a problem with this?
    The only problem I see is your inability to understand a simple explanation.
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    X0x, with respect that is what your formulae are saying. L' is smaller than L which is smaller than L' which is smaller than L etc etc.
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    Pick a frame and apply the formula to get the correct result.

    Pick the other frame and apply the formula to get the correct result.

    You can't be in both frames at once. There is no frame of reference which covers both frames unless both frames are at rest in relation to each other, in which case they share the same frame.
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    Quote Originally Posted by Jilan View Post
    X0x, with respect that is what your formulae are saying. L' is smaller than L which is smaller than L' which is smaller than L etc etc.
    ...and you are STILL incapable of understanding.

    O has a ruler measuring length L in HIS frame.
    O' has his OWN ruler measuring length D in HIS frame.
    Do you get it now?
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    Not really, the moving observer sees the length contracted by a factor gamma. The stationary observer sees that distance contracted by another factor gamma because he is moving wrt to the other one. Etc. etc. this just cannot work sorry. There must be a better answer.
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    TFOLZO: Here above, cinci, you are NOT applying reciprocity.

    cinci: maybe it doesn't apply.

    TFOLZO: If the spaceship moving away is not seen to have the distance between it and the external observer contract, then an observer in the ship would NOT notice length contraction between the external observer and himself

    cinci: Unless I mis-spoke, I said the observer in the ship sees the distance contract.

    Think about it this way. If his speed is constant both observers can measure the time in transit and calculate his distance. Spaceship clock runs slower by the factor(1 - (v/c)^2)^.5. The observer back on earth calculates his distance as

    d = vt.

    Spaceship guy measures

    d' = vt(1 - (v/c)^2)^.5.


    - though he would presumably find length contraction of the earth or whatever object the external observer was standing on.

    The contraction of distances between objects (including mutually stationary objects moving relative to another observer and seen by him) is one fraught with paradox & confusion - a mental minefield!
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    Quote Originally Posted by Jilan View Post
    Not really, the moving observer sees the length contracted by a factor gamma. The stationary observer sees that distance contracted by another factor gamma because he is moving wrt to the other one. Etc. etc. this just cannot work sorry. There must be a better answer.
    Not only is there no better answer, there is no other answer, given the 2 postulates of special relativity true. If one takes the time to learn Minkowski spacetime diagrams, these 2 spacetime figures below present WHY both observers hold each other's moving clock to run slower, while yet BOTH agree that the clock that's located >>> at <<< BOTH events (B in this case) always records the least duration for the defined interval. Also, why both record moving lengths as contracted, while the proper length between any 2 simultaneous events (including a body length) is always the largest recordable length, and all agree.

    We have inertial observers A & B, a planet X at rest in the A frame, and a string of 5 equally separated clocks between the 2 events at rest in the A/X frame. All clocks of each frame synchronized with each other per the Einstein/Poincare clock sync method. The defined interval is between event A/B flyby and event A/X flyby (B flies inertially from A to X). Here's the spacetime figures ...



    Note ... the B observer holds that interval to take 2 hr, the A/X frame clocks always running half as fast.
    Note ... frame A/X observers hold that interval to take 4 hr, even though the B clock always runs half as fast.

    wrt time dilation ... Notice that B holds any individual A/X frame clock to tick slower than his own, by 50%. That's true no matter if the clock is at flyby with B, or remotely located, as the figure shows. Yet, each passing A/X frame clock (on flyby) is advanced wrt his own clock, by double, upon its flyby event with B. >>> That's <<< why it all works. Note that the 5 clocks (at tB = 12am) are desynchronised per B. They are desynchronized "to just the required tune" that the clocks are "advanced by double per B on flyby", even though "they tick half as fast as B's own clock" per B.

    wrt length contraction ... Note on the A/X POV figure, the A/X separation is 3.464 at any time. On the B POV figure, the A/X separation "marked between the 2 events" when both the A & X clocks read tA/X = 12am is a dilated 6.982 range per B (due to the time dilation). However at tB = 12am, B holds the current A/X separation as contracted to 1.732, the A & X clocks being desynchronized since they are viewed in motion per B (the X clock reading 3am-X, the A clock reads 12am). Looking back at the A/X POV figure, where the X clock reads 3am, B is then (3.464-2.598) = 0.866 away per any A/X frame observer, which is 50% contracted wrt the 1.732 noted by B at tB = 12am per himself.

    It all works.

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    I'm the one who misspoke cinci...
    Quote Originally Posted by cincirob View Post
    TFOLZO: Here above, cinci, you are NOT applying reciprocity.

    cinci: maybe it doesn't apply.

    TFOLZO: If the spaceship moving away is not seen to have the distance between it and the external observer contract, then an observer in the ship would NOT notice length contraction between the external observer and himself

    cinci: Unless I mis-spoke, I said the observer in the ship sees the distance contract.

    Think about it this way. If his speed is constant both observers can measure the time in transit and calculate his distance. Spaceship clock runs slower by the factor(1 - (v/c)^2)^.5. The observer back on earth calculates his distance as

    d = vt.

    Spaceship guy measures

    d' = vt(1 - (v/c)^2)^.5.
    ...in that we have two observers, one on the spaceship, the other being the 'external observer' imagined as being on a planet (e.g. earth) or some sort of 'pseudo-stationary' object.

    Hence due to reciprocity we would have to conjecture that both mutually moving observers would observe the distance between them to contract - or neither would. If you state that the distance contracts (& time dilates!) for only ONE of the observers then you are invoking an preferred reference frame (Lorentzian ARF etc) relative to which a moving object (& observer) length contract & time dilate.

    Would you agree with this reciprocity situation or alternatively would you care to elaborate on what sort of 'preferred reference frame' you might have in mind?

    (Please ignore SYA's 'Roadkill-style comments' as none of us want to go back to that thread do we?)

    TFOLZO
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    Dear Jilan...
    Quote Originally Posted by Jilan View Post
    Not really, the moving observer sees the length contracted by a factor gamma. The stationary observer sees that distance contracted by another factor gamma because he is moving wrt to the other one. Etc. etc. this just cannot work sorry. There must be a better answer.
    ...if you want me to discuss SYA's Minkowskiesque reply with you, please open another thread on the Personal & Alternatives Section as I am not permitted to discuss Einstein's relativity critically in detail on this part of the forum - or I'll be banned!

    However it sounds like you might have quite a few questions to ask here first!

    TFOLZO
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    Quote Originally Posted by TFOLZO View Post
    Dear Jilan...
    ...if you want me to discuss SYA's Minkowskiesque reply with you, please open another thread on the Personal & Alternatives Section as I am not permitted to discuss Einstein's relativity critically in detail on this part of the forum - or I'll be banned!
    Lol. That's like the fellow with 3 DUIs complaining he cannot drive without a license

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    SYA, thanks for the diagrams. So if both observers see their relative distance contracted will they agree on their mutual separation?
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    I don't want to jump the gun too much on this Jilan...
    Quote Originally Posted by Jilan View Post
    SYA, thanks for the diagrams. So if both observers see their relative distance contracted will they agree on their mutual separation?
    ...but I think SYA & perhaps even cinci will probably agree that both observers see (or find) that the intervening distance is shortened.

    However, despite SYA complaints - in defence of which he will no doubt use a Minkowski Muddlegram - the two observers will NOT agree as to whose spacecraft or planet is relatively length contracted since each one sees the other's spaceship/planet length contracted relative to one's own!

    TFOLZO
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    TFOLZO: ...in that we have two observers, one on the spaceship, the other being the 'external observer' imagined as being on a planet (e.g. earth) or some sort of 'pseudo-stationary' object.

    cinci: I think the space thing screws you up here. Let's say you're standing on a road. A care leaves your position at high speed and he arrives 1 mile down the road. The car doesn't change where you the 1 mile marker or the distance from you to the one mile marker; you are not moving relative to the road so it always looks and measures the same. For the observer in the car, the 1 mile piece of road has relative motion and so he would see it contracted.

    Hence due to reciprocity we would have to conjecture that both mutually moving observers would observe the distance between them to contract - or neither would. If you state that the distance contracts (& time dilates!) for only ONE of the observers then you are invoking an preferred reference frame (Lorentzian ARF etc) relative to which a moving object (& observer) length contract & time dilate.

    Would you agree with this reciprocity situation or alternatively would you care to elaborate on what sort of 'preferred reference frame' you might have in mind?

    (Please ignore SYA's 'Roadkill-style comments' as none of us want to go back to that thread do we?)

    TFOLZO
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    I had asked: Would you agree with this reciprocity situation or alternatively would you care to elaborate on what sort of 'preferred reference frame' you might have in mind?

    Hooray cinci, I think we're getting somewhere!
    Quote Originally Posted by cincirob View Post
    TFOLZO: ...in that we have two observers, one on the spaceship, the other being the 'external observer' imagined as being on a planet (e.g. earth) or some sort of 'pseudo-stationary' object.

    cinci: I think the space thing screws you up here. Let's say you're standing on a road. A car leaves your position at high speed and he arrives 1 mile down the road. The car doesn't change where you the 1 mile marker or the distance from you to the one mile marker; you are not moving relative to the road so it always looks and measures the same. For the observer in the car, the 1 mile piece of road has relative motion and so he would see it contracted.
    The answer you give, whether you realize it yet or not, is that of a preferred reference frame - an explicitly Lorentzian answer - one considered 'stationary' since it is treated as a 'road'. (E.g. the observer in the car would only see the distance of 1 mile contracted if the car was still moving. Once the car stopped the distance would 'sproing' back to its normal length.)

    So I might be "screwed up" about space - but considering observers moving mutually in space without earth & road is perfectly legitimate, as no doubt others will agree!

    When considering two mutually moving observers (and removing questions of inertia/acceleration etc.) we have to consider them without invoking one system as preferred or stationary - two observers moving about in outer space for example. When one thinks of 'earthly' type situations such as road & road-runner or wheel one unconsciously inserts a bias whereby the 'earth' is considered stationary and objects on it considered to move. This notion covertly suggests Newton's absolute space (earth being naively treated as being at rest) and of course the stagnant ether.

    So if I now ask you the question again - considering two observers moving past each other in space, will there be mutual length contraction observed (& thus mutual time dilation) or will you assert that this somehow cannot be so because there is some sort of preferred frame (of yet-undetermined type) operative in the situation?

    The point of course is that by referring it again to a 'road surface' & car you would be invoking a preferred reference frame. So what do you do when your observers are drifting past each other (e.g. a long line of clocks with observers for each reference frame)? How will you resolve that situation?

    A bit different to arguing about a rolling wheel on a road surface isn't it!!!!

    TFOLZO
    Last edited by TFOLZO; 09-02-2014 at 02:56 AM. Reason: Emphasized red comment added
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    Quote Originally Posted by Jilan View Post
    SYA, thanks for the diagrams. So if both observers see their relative distance contracted will they agree on their mutual separation?
    Here's the problem with this question, it tacitly assumes that there is some moment that both observers agree on is the "Now" when they make the measurement.

    To illustrate further:

    Give both observers a clock. each clock reads zero at the moment the two observers are next to each other.

    You want to determine the distance each observer measures their separation to be at some later point. Now here is the rub, what do you use to determine that moment in time?

    Let's say you decide on the moment that the non-ship observer's clock reads 1 sec. If the relative velocity between the two is .8c, then he will measure the distance as 0.8 light sec at that moment.

    So what does the ship observer measure measure at that moment? Well it depends on which "moment" you are talking about. According to the non-ship observer, the ship clock runs at a rate 60% that of his own, so when his clock reads 1 sec, the ship clock reads 0.6 sec. According to the ship, when its clock reads 0.6sec it is 0.48 light sec away from the other observer, so he sees the distance as being shorter.

    On the other hand, we can just use the "moment" when the non-ship clock reads 1. In this case, according to the ship, the non-ship clock is the one running slow, so when it reads 1 sec his own clock reads 1 2/3 sec and he is 1 1/3 light sec away from the other observer and is sees the distance shorter.

    In other words, while for the non-ship observer, his clock reading 1 sec and the ship clock reading 0.6 sec is a single moment, they are two separate moments according to the ship observer.

    Another way to to consider this is by using clocks instead of just 2. the clocks are paired with each pair synchronized and separated by 0.8 light sec according to their own frames.

    We start with the two observers next to each other. And the two other clocks their furthest apart.

    So at the start, each observer sees his own clock reading 0, paired with another clock reading 0 and 0.8 light sec away. He also sees the other observer's clock reading zero. However the other observer's paired clock will be only 0.48 light sec away (length contraction) and reads 0.64 sec (relativity of simultaneity).

    Let's call one observer Red and the other Green.

    So this is what happens according to Red:

    Both his and Green's clock read 0 as they pass, Green is heading towards Red's paired clock and Green's paired clock is heading towards Red both at 0.8c. Green's paired clock starts out reading 0.64 sec and takes .6 sec to reach Red, during which, due to time dilation, it accumulates 0.36 sec. Thus when Red and Green's paired clock meet, Red's clock reads 0.6 sec and Green's paired clock reads 1 sec.

    Green hasn't reached Red's paired clock yet, and doesn't do so until Red's clock and his paired clock reads 1 sec (0.8 light sec/0.8c). Green's clock will have run slow due to time dilation, and will have accumulated 0.6 sec. Thus when Green and Red's paired clocks meet they read 0.6 and 1 sec respectively.

    Note that if we switch to Green's frame, we get the exact same end results, the only difference is the Green will say that he met up with Red's paired clock before Red met up with Green's paired clock. But this has no effect of the final outcome. In fact, if both Red and Green had an infinite number of clocks strung out along the line joining them with their pair, and you compared each of Red's clock to Green's clocks as they passed each other, Both Red and Green ( and anyone else for the that matter) would agree as to what any two clocks read at the instant they passed each other. Different frame will disagree on the respective readings of clocks that are separated from each other, but always agree on their respective readings if they meet up.
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    Janus, that's smashing! I had wondered if the lack of simultaneity would resolve the situation. So what happens when the moving observer decelerates to a stop? Does the distance travelled appear to expand quickly so that both observers then agree on their mutual separation?
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    Quote Originally Posted by Jilan View Post
    Janus, that's smashing! I had wondered if the lack of simultaneity would resolve the situation. So what happens when the moving observer decelerates to a stop?
    "To a stop" with respect to what?


    Does the distance travelled appear to expand quickly so that both observers then agree on their mutual separation?
    "Mutual separation" with respect to what? You see, you simply fail to understand that distances, time, simultaneity, are all measured wrt. to specific frames of reference, as I tried to explain to you in two earlier posts (#6 and #11), in this thread. Sorry, I failed.
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    Quote Originally Posted by x0x View Post
    "To a stop" with respect to what .
    With respect to the stationary observer
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    Quote Originally Posted by Jilan View Post
    SYA, thanks for the diagrams. So if both observers see their relative distance contracted will they agree on their mutual separation?
    Well, no, it's not that simple actually. While the relativistic effects are reciprocal, the LT solns are not. That's the nature of Lorentz symmetry. The physical equations are invariant under a rotation from one inertial frame to the other differing frame, but the LT solns (input versus output) differ for those 2 differing POVs, when considering each other. This is only to say that they disagree on "the measure of" space and time. So while the LT solns differ the eqns do not, which means the principle of relativity is upheld. While the solns differ with a relative v, they differ in such a way that ...

    (1) they can agree on their disagreements, using the LTs.
    (2) all observers agree on the time-readout of a clock momentarily co-located at an event, no matter how the inertial observers or clock move.

    In relativity theory, observers are allowed to disagree, because they must disagree as to what are simultaneous events when in relative motion at relativistic rates. Yet, the 2 statements above always hold true per SR.

    Thank You,
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    EDIT: The underlined verbiage was added for clarity
    Last edited by SinceYouAsked; 09-01-2014 at 08:39 PM.
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    Good, I am trying to understand why a traveller at 0.86c going to A Centuri will only measure his maximum distance to be half of the real distance. I am struggling with why the stationary observer will also not see that maximum distance to be less also.
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    Quote Originally Posted by Jilan View Post
    Good, I am trying to understand why a traveller at 0.86c going to A Centuri will only measure his maximum distance to be half of the real distance. I am struggling with why the stationary observer will also not see that maximum distance to be less also.
    I don't understand why you're having a problem with this Jilan. It's just that the distance between A Centuri and Earth is Lorentz contracted to 1 half its rest value. Think of lying a rod down in space with one end on earth and the other end on A Centuri. Then to the traveling observer this rod is moving and the length of this rod is 1 half its rest value.

    See what I mean?
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    Quote Originally Posted by Jilan View Post
    With respect to the stationary observer

    Good, you are starting to learn. How about the answer to my second question?
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    Quote Originally Posted by Jilian
    Good, I am trying to understand why a traveller at 0.86c going to A Centuri will only measure his maximum distance to be half of the real distance. I am struggling with why the stationary observer will also not see that maximum distance to be less also.
    Good question.

    Let's say that observer A sits on earth with his clock and ruler, while another inertial observer B travels colinearly between earth and Centauri A at v = √(3/4) = 0.866c carrying an identical clock and ruler. Per earth, the earth-centauri separation is 4.37 ly. We ask ...

    (1) how does observer A record the earth-centauri separations?

    First, the contraction factor is the reciprocal of the dilation factor. The dilation factor is the gamma factor ...

    γ = 1/√(1-v/c)

    So the contraction is defined by its reciprocal ...

    1/γ = √(1-v/c)

    Since earth and Centauri move at v=0 wrt the earthbound measurer's (A's) ruler, the earth-centauri separation is a stationary length, and the contraction of the separation is then ...

    1/γ = √(1-v/c) ... and since v = 0 and c = unity, then
    1/γ = √(1-0/1)
    1/γ = √(1-0)
    1/γ = 1

    This is just to say that there are no relativistic effects (including contraction) if there is no relative velocity between the measurer and what's measured.

    And so the stationary length is 100%, a totally uncontracted length. So per the observer A, the earth-centauri stationary separation = 4.37 ly x 100% = 4.37 ly. That's called the "proper length", which is the longest recordable length given simultaneous measurements to take the measurement.


    Now, consider observer B flies past earth colinearly toward Centauri A at v=0.866c inertial. At any time, he can then take his measurement. Observer B holds himself as stationary, and both the earth and Centauri A traveling colinearly at v = -0.866c. As such, that's a moving length, and not a stationary length as before, and moving lengths are contracted per SR ...

    (2) how does observer B record the earth-centauri separation?

    1/γ = √(1-v/c) ... and since v = -0.866c and c = unity, then
    1/γ = √(1-(-0.866c)/1)
    1/γ = √(1-0.75)
    1/γ = 0.5

    EDIT 1: And so the moving length is 50%, a contracted length. That's a contracted length wrt its proper length. So per the observer B, the earth-centauri moving separation is = 4.37 ly x 50% = 2.185 ly.

    Bottom line, stationary lengths are uncontracted (proper) while moving lengths are contracted wrt their proper length. The proper length of a body never changes, even as it accelerates. For example, the A & B rulers are identical at the start, sitting in a coffee shop in Bern. B departs and returns for later flyby of A to travel to Centauri A inertially at 0.866c. B will declare his ruler has never changed in size wrt his departure event from A on earth. A will disagree, recording it at 50% its length before departure. On flyby, B will also hold that A's ruler contracted by 50% wrt departure. All are correct. Bottom line, no ruler (or clock) ever changes in and of itself due to a change in it's own state of motion ... the proper length is an invariant in relativity theory.

    EDIT 1: The term COORDINATE LENGTH was removed from the paragraph even though it is often enough used, as it's not defined as a relativity term and is redundant to the existing term "contracted length".

    Thank You,
    SinceYouAsked

    PS: To understand why relativistic effects come to be, the easiest way is to learn the geometry of spacetime as presented in spacetime figures. It's all on that page I posted for you, and one need only study it until they see it. There is no better way to fully grasp the nature of relativistic effects than to study them geometrically by spacetime diagrams. Generally, everything gets quicker, easier, and simpler using them.
    Last edited by SinceYouAsked; 09-02-2014 at 06:06 AM.
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    Quote Originally Posted by SinceYouAsked
    That's called the "coordinate length", ...
    called by whom? I've never seen anybody use that term and an internet search didn't pull one up. Please show me a source which uses the term as you just did. Thanks.
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    The important issue here Jilan is that the Earth and A-Centauri are roughly at rest wrt each other.
    Quote Originally Posted by Jilan View Post
    Good, I am trying to understand why a traveller at 0.86c going to A Centuri will only measure his maximum distance to be half of the real distance. I am struggling with why the stationary observer will also not see that maximum distance to be less also.
    In contrast, the spaceship is moving very fast (0.86c) relative to Earth & A-Centauri, spaceship observers finding that the distance to A-Centauri contracts (according to Lorentzian & Einsteinian relativity)!!!!!

    One would therefore think that the spaceship observers should reach A-Centauri (4.3 ly away) in LESS than the 5 years that one would expect from the 4.3 ly distance at 0.86c, the round trip thus being 10 years for earthbound observers.

    Hence we have the separated twins paradox again. One twin travels to A-Centauri, the other stays on Earth. What will be the ages of the twins when they meet up again on Earth? Will it be young stay-at-home twin with old travelled twin or vice versa? If one takes the Sun & A Centauri as a preferred frame then the travelled twin should be younger on return! Strict reciprocity instead implies that the universe has divided into two daughter universes - one with old stay-at-home & young travelled twin (seen by Earth observer), the other with old travelled twin & young stay-at-home (seen by Spaceship observer).

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    Quote Originally Posted by SinceYouAsked View Post
    That's called the "coordinate length", ...

    Quote Originally Posted by Physicist View Post
    called by whom? I've never seen anybody use that term and an internet search didn't pull one up. Please show me a source which uses the term as you just did. Thanks.
    Very good Physicist. Indeed, the term (while used) is not an official relativistic term.

    I had actually gone through this online with Burt Jordaan of ScienceChatForum back in November, and had already forgotten We were discussing whether new terms commonly used (and/or in the literature) should be requested for addition to the related Wiki page. We, and others, had long (and often enough) used the term "coordinate length", meaning the measure of a moving length (to distinguish it from proper length). Also, I had figured that if the term COORDINATE TIME was defined, then I saw no good reason not to have a COORDINATE LENGTH term.

    Burt was himself interested in adding a PROPER FRAME term as in relation to EVENTs, however a PROPER FRAME definition already exists that's defined a little differently. He desired something like PROPER FRAME-EVENT. I was interested in adding COORDINATE LENGTH and COORDINATE DISTANCE, however since the terms CONTRACTED LENGTH and CONTRACTED DISTANCE already exist, that makes them redundant and so we decided it best to leave things as they were. Ultimately, it's better to have a minimally required number of defined terms, so long as they get the job done. As such, that was the end of that.

    So where I said COORDINATE LENGTH, that should be taken to mean MOVING CONTRACTED LENGTH, if preferred. Thanx.

    Thank You,
    SinceYouAsed
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    So I guess you see what I mean now, cinci!
    Quote Originally Posted by SinceYouAsked View Post
    Very good Physicist. Indeed, the term (while used) is not an official relativistic term.

    I had actually gone through this online with Burt Jordaan of ScienceChatForum back in November, and had already forgotten We were discussing whether new terms commonly used (and/or in the literature) should be requested for addition to the related Wiki page. We, and others, had long (and often enough) used the term "coordinate length", meaning the measure of a moving length (to distinguish it from proper length). Also, I had figured that if the term COORDINATE TIME was defined, then I saw no good reason not to have a COORDINATE LENGTH term.

    Burt was himself interested in adding a PROPER FRAME term as in relation to EVENTs, however a PROPER FRAME definition already exists that's defined a little differently. He desired something like PROPER FRAME-EVENT. I was interested in adding COORDINATE LENGTH and COORDINATE DISTANCE, however since the terms CONTRACTED LENGTH and CONTRACTED DISTANCE already exist, that makes them redundant and so we decided it best to leave things as they were. Ultimately, it's better to have a minimally required number of defined terms, so long as they get the job done. As such, that was the end of that.

    So where I said COORDINATE LENGTH, that should be taken to mean MOVING CONTRACTED LENGTH, if preferred. Thanx.

    Thank You,
    SinceYouAssed
    It is indeed jargon - necessary jargon as SYA rightly says - but terms such as 'COORDINATE' & 'PROPER' have had to be introduced to cover up the fact that the situations being described are objectively unresolvable.

    With these words SYA is actually helping you thru the jungle - but his machete & his goal are not the same as yours, as you have rightly at last begun to suspect.

    TFOLZO
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    Quote Originally Posted by x0x View Post
    Good, you are starting to learn. How about the answer to my second question?
    By separation I mean the distance B records A being at relative to B in the B frame and vice versa.
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    Quote Originally Posted by TFOLZO View Post
    Strict reciprocity instead implies that the universe has divided into two daughter universes - one with old stay-at-home & young travelled twin (seen by Earth observer), the other with old travelled twin & young stay-at-home (seen by Spaceship observer).
    Nonsense. The two twins are not equivalent and the travelled twin is unequivocally younger than the stay-at-home twin. The non-equivalence is because the travelled twin changed inertial frames of reference (accelerated) while the stay-at-home twin did not.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by Jilan View Post
    By separation I mean the distance B records A being at relative to B in the B frame and vice versa.
    This is not how "separation" is understood. This is why you are so confused.
    A and B are initially at rest in some frame, "separated" by a distance D. It is in THAT frame that the notion of separation is considered.
    A and B "close" the distance D between them, if they move in opposing directions.
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    Quote Originally Posted by x0x View Post
    This is not how "separation" is understood. This is why you are so confused.
    A and B are initially at rest in some frame, "separated" by a distance D. It is in THAT frame that the notion of separation is considered.
    A and B "close" the distance D between them, if they move in opposing directions.
    So there is no notion of separation in other frames between two objects if they are moving relative to each other? That's a novel way out of conundrum, I'll give you that!
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    Quote Originally Posted by Jilan View Post
    So there is no notion of separation in other frames between two objects if they are moving relative to each other? That's a novel way out of conundrum, I'll give you that!
    There is. I gave you the meaning of proper separation distance. In all other frames, the separation distance is contracted by the appropriate factor. If you don't understand things just ask, don't get fresh.
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    Quote Originally Posted by TFOLZO View Post
    Strict reciprocity instead implies that the universe has divided into two daughter universes - one with old stay-at-home & young travelled twin (seen by Earth observer), the other with old traveled twin & young stay-at-home (seen by Spaceship observer).
    Well, that was a good episode

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    Quote Originally Posted by SinceYouAsked View Post
    Very good Physicist. Indeed, the term (while used) is not an official relativistic term.

    I had actually gone through this online with Burt Jordaan of ScienceChatForum back in November, and had already forgotten We were discussing whether new terms commonly used (and/or in the literature) should be requested for addition to the related Wiki page. We, and others, had long (and often enough) used the term "coordinate length", meaning the measure of a moving length (to distinguish it from proper length). Also, I had figured that if the term COORDINATE TIME was defined, then I saw no good reason not to have a COORDINATE LENGTH term.

    Burt was himself interested in adding a PROPER FRAME term as in relation to EVENTs, however a PROPER FRAME definition already exists that's defined a little differently. He desired something like PROPER FRAME-EVENT. I was interested in adding COORDINATE LENGTH and COORDINATE DISTANCE, however since the terms CONTRACTED LENGTH and CONTRACTED DISTANCE already exist, that makes them redundant and so we decided it best to leave things as they were. Ultimately, it's better to have a minimally required number of defined terms, so long as they get the job done. As such, that was the end of that.

    So where I said COORDINATE LENGTH, that should be taken to mean MOVING CONTRACTED LENGTH, if preferred. Thanx.

    Thank You,
    SinceYouAsed
    The term "coordinate time" is best referred to as time. When you see someone say "The amount of time it took was.." just know that it means the same thing as "The amount of coordinate time it took was..". The "coordinate" should always be left out and assumed to be there when it's not a proper time. Otherwise it gets messy rather than being elegant.

    Here's how things should work in a perfect world

    frame dependent ------ invariant
    ______________________________
    mass ------------------- proper mass
    lifetime ---------------- proper lifetime
    length ------------------ proper length

    Of course it should be noted that things such as the distance between two events doesn't always have a proper length to it nor is there always a proper time corresponding to two events.

    The frame dependent quantities use Latin symbols while the proper quantities use Greek symbols
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    You are arguing two different things, KLW.

    I had written:Strict reciprocity instead implies that the universe has divided into two daughter universes - one with old stay-at-home & young travelled twin (seen by Earth observer), the other with old travelled twin & young stay-at-home (seen by Spaceship observer).

    Quote Originally Posted by KJW View Post
    Nonsense. The two twins are not equivalent and the travelled twin is unequivocally younger than the stay-at-home twin. The non-equivalence is because the travelled twin changed inertial frames of reference (accelerated) while the stay-at-home twin did not.
    So there is supposed to be time dilation due to mere motion ONLY for the travelled twin - which situation would then imply a preferred (Lorentzian or absolute) reference fame for the Earth & A-Centauri. The question of a superadded time dilation due to the inertial forces (centrifugal, accelerational) involved in turning the spaceship around does NOT resolve the issue. This is because the distance covered from Earth to A-Centauri is an INDEPENDENT variable from the time dilation produced by the inertial forces of turning the spaceship around. I.e. the mere fact that ONLY the travelled twin experiences these inertial forces does NOT explain the time dilation observed by the earth observer when the travelled twin returns relative to stay-at-home twin.

    Now I know that Einstein used the Naturwissenschaft article to insert GR into explaining away SR paradoxes but the situation there is contrived due to his discounting of the independence of the distance variable effect on time dilation and that of the inertial (or GR-induced) effect on time dilation; it becomes merely an evasive way of claiming that Earth & A-Centauri comprise a preferred reference frame (e.g. an ARF) & hence Lorentzian relativity. The issue of reciprocal time dilation - necessarily implied by Einstein's application of the LTs - is simply sidestepped & ignored rather than the question being addressed frankly.

    As it is, your claim that the inertial forces explain the time dilation for the travelled twin is merely a cover for the hidden implication that there is a preferred system relative to which the Earth & A-Centauri are more or less at rest meaning that objects that travel fast relative to it (e.g. the spaceship with the travelled twin) are more time-dilated. The application of SR alone indicates that there has to be reciprocal time dilation with only some modification due to only one twin enduring the inertial forces from turning the spaceship around for the return journey.

    TFOLZO
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    TFOLZO: The answer you give, whether you realize it yet or not, is that of a preferred reference frame - an explicitly Lorentzian answer - one considered 'stationary' since it is treated as a 'road'.

    cinci: The only preference to the road frame is that the observer chose to stand on it.

    TFOLZO: (E.g. the observer in the car would only see the distance of 1 mile contracted if the car was still moving.

    cinci: I didn't indicate that the car stopped so all my comments refer to the situation where the car is moving.

    TFOLZO: Once the car stopped the distance would 'sproing' back to its normal length.

    cinci: Yes. When both observers are at rest with the road both will measure distances the same.

    TFOLZO: When considering two mutually moving observers (and removing questions of inertia/acceleration etc.)

    cinci: An inertial observer cannot determine that he is moving. So for two inertial observers there is no such thing as mutually moving for either observer. If you introduce a third observer, he can measure mutual motion but you will find that all motions will produce the correct observations for each observer according to relativity.

    TFOLZO: So if I now ask you the question again - considering two observers moving past each other in space, will there be mutual length contraction observed (& thus mutual time dilation) or will you assert that this somehow cannot be so because there is some sort of preferred frame (of yet-undetermined type) operative in the situation?

    cinci: Well now you've changed the question. The answer to this question is yes, each will see the other time dilated and contracted. In terms of my road example, the car will be contracted relative to the observer standing on the road; the observer on the road will be thinner as observed the observer in the car. Reciprocal time dilation will be observed also. But the distance between them is not involved in either of these phenomena; that distance was the subject of your first question. The reciprocal phenomena will be observed if the two observers are at the same point in space or if they are a billion miles apart. Different questions, different answers.

    TFOLZO: A bit different to arguing about a rolling wheel on a road surface isn't it!!!!

    cinci: I don't know because I haven't asked you a question. If I did and you answered it, that would be different.

    By the way, if you don't understand my explanation, then try SYA's: Well, no, it's not that simple actually. While the relativistic effects are reciprocal, the LT solns are not. That's the nature of Lorentz symmetry. The physical equations are invariant under a rotation from one inertial frame to the other differing frame, but the LT solns (input versus output) differ for those 2 differing POVs, when considering each other. This is only to say that they disagree on "the measure of" space and time. So while the LT solns differ the eqns do not, which means the principle of relativity is upheld. While the solns differ with a relative v, they differ in such a way that ...

    See?
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    TFOLZO: The answer you give, whether you realize it yet or not, is that of a preferred reference frame - an explicitly Lorentzian answer - one considered 'stationary' since it is treated as a 'road'.

    cinci: The only preference to the road frame is that the observer chose to stand on it.

    That 'preference' is trivial since the mere presence of the road creates a bias of 'something stationary' = the road, and something moving e.g. a spaceship or wheeled vehicle. You have instead to consider mutual motion between observers in space. You can give them straight lines in space armed with equally spaced clocks for example - and have the line of clocks pass each other to compare the times.

    TFOLZO: (E.g. the observer in the car would only see the distance of 1 mile contracted if the car was still moving.

    cinci: I didn't indicate that the car stopped so all my comments refer to the situation where the car is moving.

    TFOLZO: Once the car stopped the distance would 'sproing' back to its normal length.

    cinci: Yes. When both observers are at rest with the road both will measure distances the same.

    But if you think of observers mutually separating in outer space you are going to have to consider their mutual velocity and mutual length contraction - not merely the contraction of an 'absolutely moving' observer compared to an 'absolutely stationary' one.

    TFOLZO: When considering two mutually moving observers (and removing questions of inertia/acceleration etc.)

    cinci: An inertial observer cannot determine that he is moving. So for two inertial observers there is no such thing as mutually moving for either observer. If you introduce a third observer, he can measure mutual motion but you will find that all motions will produce the correct observations for each observer according to relativity.

    For Galileo that was only true if the inertial observer CANNOT observe the outside world i.e. all motion is relative, hence linear motion without inertial forces can only be detected by examining the outside world, unlike the person in Galileo's ship with the window closed. We however have the windows open in space so our inertial observers CAN determine their relative motion!

    Hence two inertial observers can observe their mutual motion without the need for a third observer. So I see that we've already run into trouble EVEN BEFORE starting on applying SR. This question is necessary however - since it seems to me that you are denying mere relative motion, such that when you think of motion you keep putting in a 'road' or some large stationary system relative to which another moves. Treating the different mutually moving observers as merely undergoing mutual motion is going to reveal to you something very different.

    TFOLZO
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    TFOLZO: The answer you give, whether you realize it yet or not, is that of a preferred reference frame - an explicitly Lorentzian answer - one considered 'stationary' since it is treated as a 'road'.

    cinci: The only preference to the road frame is that the observer chose to stand on it.

    TFOLZO: That 'preference' is trivial since the mere presence of the road creates a bias of 'something stationary' = the road, and something moving e.g. a spaceship or wheeled vehicle. You have instead to consider mutual motion between observers in space. You can give them straight lines in space armed with equally spaced clocks for example - and have the line of clocks pass each other to compare the times.

    cinci: Exactly. Since it's trivial it doesn't violate relativity's stricture against preferred frames.

    TFOLZO: (E.g. the observer in the car would only see the distance of 1 mile contracted if the car was still moving.

    cinci: I didn't indicate that the car stopped so all my comments refer to the situation where the car is moving.

    TFOLZO: Once the car stopped the distance would 'sproing' back to its normal length.

    cinci: Yes. When both observers are at rest with the road both will measure distances the same.

    TFOLZO: But if you think of observers mutually separating in outer space you are going to have to consider their mutual velocity and mutual length contraction - not merely the contraction of an 'absolutely moving' observer compared to an 'absolutely stationary' one.

    TFOLZO: When considering two mutually moving observers (and removing questions of inertia/acceleration etc.)

    cinci: An inertial observer cannot determine that he is moving. So for two inertial observers there is no such thing as mutually moving for either observer. If you introduce a third observer, he can measure mutual motion but you will find that all motions will produce the correct observations for each observer according to relativity.

    TFOLZO: For Galileo that was only true if the inertial observer CANNOT observe the outside world i.e. all motion is relative, hence linear motion without inertial forces can only be detected by examining the outside world, unlike the person in Galileo's ship with the window closed. We however have the windows open in space so our inertial observers CAN determine their relative motion!

    cinci: I didn't say he couldn't observe relative motion; I said he can't observe his own motion. Therefore any motion he does observe IS relative.

    TFOLZO: Hence two inertial observers can observe their mutual motion without the need for a third observer. So I see that we've already run into trouble EVEN BEFORE starting on applying SR. This question is necessary however - since it seems to me that you are denying mere relative motion, such that when you think of motion you keep putting in a 'road' or some large stationary system relative to which another moves. Treating the different mutually moving observers as merely undergoing mutual motion is going to reveal to you something very different.

    cinci: Your hence is wrong. Each can observe only the relative motion of the other. And that is no problem for SR since that is one of the assumptions upon which it is based.
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    Quote Originally Posted by Physicist View Post
    The term "coordinate time" is best referred to as time. When you see someone say "The amount of time it took was.." just know that it means the same thing as "The amount of coordinate time it took was..". The "coordinate" should always be left out and assumed to be there when it's not a proper time. Otherwise it gets messy rather than being elegant.

    Here's how things should work in a perfect world

    frame dependent ------ invariant
    ______________________________
    mass ------------------- proper mass
    lifetime ---------------- proper lifetime
    length ------------------ proper length

    Of course it should be noted that things such as the distance between two events doesn't always have a proper length to it nor is there always a proper time corresponding to two events.

    The frame dependent quantities use Latin symbols while the proper quantities use Greek symbols
    Well, it's not that I disagree with you there. For those who understand the theory well, there is no need to refer to anything other than these ...

    time,
    length,
    distance,
    frame,

    proper time,
    proper length,
    proper distance
    proper frame,

    However, COORDINATE TIME is a long lasting defined relativistic term in the literature, and it'd more confusing to try and remove it now than to continue using it.

    Those trying to learn the theory, who have difficulty in understanding what PROPER TIME is, will use TIME for the clocks of both frames since all clocks record time. It exists to help distinguish the frames when students always have so much difficulty keeping track of the frames while learning. COORDINATE TIME being a tool to help students remain on track, and speed up the education process.

    I was wondering, did Minkowski define the term COORDINATE TIME when he defined the PROPER terms? Or, was it introduced later by educators?

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    Quote Originally Posted by Physicist View Post
    Of course it should be noted that things such as the distance between two events doesn't always have a proper length to it nor is there always a proper time corresponding to two events.
    Indeed. It all depends upon how the events and POVs are defined, or occur/exist.

    Quote Originally Posted by Physicist View Post
    The frame dependent quantities use Latin symbols while the proper quantities use Greek symbols
    I was not aware of that. Is this a GR convention? OEMB used only Greek symbols. Are you saying that Minkowski used Latin symbols, or is this a convention that was introduced later over the years? Do you have an example?

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    Quote Originally Posted by SinceYouAsked
    However, COORDINATE TIME is a long lasting defined relativistic term in the literature, and it'd more confusing to try and remove it now than to continue using it.
    While it's true that its used in the literature it wouldn't be missed if it was gone because most people simply refer to it simply as "time."
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    Quote Originally Posted by Physicist View Post
    While it's true that its used in the literature it wouldn't be missed if it was gone because most people simply refer to it simply as "time."
    I'd just as well use the term TIME alone too Physicist, vs COORDINATE TIME. However, universities seem to like to use it, because it helps bring the students up to speed quicker. I've had gazillions of discussions with folks learning relativity, and I've found the term "coordinate time" very useful ...

    For example, if one wants to talk about "the recorded time by a clock that was not located at both events", they simply talk "coordinate time". They do not have to say each time ... "the recorded time by a clock that was not at both events". When these things are restated repeatedly in discussion, it's quick and convenient to have short buzz phrases ... like "proper time" for example, versus saying each time ... "the recorded time by a clock that was located at both events".

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    I see I have misled you again cinci!

    TFOLZO: The answer you give, whether you realize it yet or not, is that of a preferred reference frame - an explicitly Lorentzian answer - one considered 'stationary' since it is treated as a 'road'.

    cinci: The only preference to the road frame is that the observer chose to stand on it.

    TFOLZO: That 'preference' is trivial because the observer's choice of merely standing on the road is NOT the fundamental issue. The fundamental issue is the insertion of the road itself!

    That is, the mere presence of the road creates a bias of 'something stationary' = the road, and something moving e.g. a spaceship or wheeled vehicle. You have instead to consider mutual motion between observers in space. You can give them straight lines in space armed with equally spaced clocks for example - and have the line of clocks pass each other to compare the times.

    Hence your subsequent claim does NOT follow from it.


    cinci: Exactly. Since it's trivial it doesn't violate relativity's stricture against preferred frames.

    Rather, the exact opposite is true. Since as you say SR claims there is no preferred frame you have no right to insert one by turning the issue into a 'road race', the road & the 'earth' beneath it becoming the preferred frame. Capiche? A fair comparison means considering space ships passing in space.

    Hence two inertial observers can observe their mutual motion without the need for a third observer - as I think you will now agree - since each observer can label himself as being at relative rest & see the motion of the other.

    So I now ask you the question again without inserting a road: - considering two observers moving past each other in space, will there be mutual length contraction observed (& thus mutual time dilation) or will you assert that this somehow cannot be so because there is some sort of preferred frame (of yet-undetermined type) operative in the situation?

    Certainly a jet engineer would know what I mean - though evidently not the commandant of Stalag Thir...

    TFOLZO
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    In reply to TFOLZO, re: your posts.

    Glad you are back!!! (now be good...leave off w/ "the side references" of politics/religious stuff! You are better than that! Please!?!? I'm bored when you're not here! There's no one sympatico

    enough to argue with!!!)

    Cheerio! (I gotta' go shopping now)
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    cinci: Exactly. Since it's trivial it doesn't violate relativity's stricture against preferred frames.

    TFOLZO: Rather, the exact opposite is true. Since as you say SR claims there is no preferred frame you have no right to insert one by turning the issue into a 'road race', the road & the 'earth' beneath it becoming the preferred frame. Capiche?

    cinci: I understand what you're unwilling to understand. Distance along a road, distance in space. No difference.

    TFOLZO: A fair comparison means considering space ships passing in space.

    Hence two inertial observers can observe their mutual motion without the need for a third observer - as I think you will now agree - since each observer can label himself as being at relative rest & see the motion of the other.

    So I now ask you the question again without inserting a road: - considering two observers moving past each other in space, will there be mutual length contraction observed (& thus mutual time dilation)

    cinci: Yes. Happy now? But it doesn't mean that both will see the distance between them contracted which was the first assertion in this discussion.

    or will you assert that this somehow cannot be so because there is some sort of preferred frame (of yet-undetermined type) operative in the situation?

    Certainly a jet engineer would know what I mean - though evidently not the commandant of Stalag Thir...
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    In reply to TFOLZO, re: your #50 post.

    Is there any real possibility (other than a numerical posit) that would prove "time dilation" as a true event? I simply don't see this as an actual event.

    (Thanks for reading!)
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    Your suspicions are correct GerryN...
    Quote Originally Posted by Gerry Nightingale View Post
    In reply to TFOLZO, re: your #50 post.

    Is there any real possibility (other than a numerical posit) that would prove "time dilation" as a true event? I simply don't see this as an actual event.

    (Thanks for reading!)
    ...but we'll have to discuss this question on the Personal & Alternatives Section since the attempt to discuss it here 'in a samizdat way' would render the discussion incomprehensible.

    Thanks for writing!

    TFOLZO
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    TFOLZO: Since as you say SR claims there is no preferred frame you have no right to insert one by turning the issue into a 'road race', the road & the 'earth' beneath it becoming the preferred frame. Capiche?

    cinci: I understand what you're unwilling to understand. Distance along a road, distance in space. No difference.

    TFOLZO: A fair comparison means considering space ships passing in space.

    Hence two inertial observers can observe their mutual motion without the need for a third observer - as I think you will now agree - since each observer can label himself as being at relative rest & see the motion of the other.

    So I now ask you the question again without inserting a road: - considering two observers moving past each other in space, will there be mutual length contraction observed (& thus mutual time dilation)

    cinci: Yes. Happy now? But it doesn't mean that both will see the distance between them contracted which was the first assertion in this discussion.

    Aha! Very interesting cinci! Now we are getting somewhere. You admit mutual length contraction of objects but you demur on claiming contracted distances between objects. Some people might decide to jump down your neck at that - especially as this situation is dualistic since if we now consider an object in motion relative to another, we need to consider the first object's atomic constitution i.e. the distances between the atoms of the object will contract as the object length contracts. Very obvious - very logical. But...

    If we now have two objects e.g. spaceships, at distance x from one another and traveling at the same speed relative to a third observer (say on earth), would the earth observer also consider the distance between the two spaceships to be x (as implied by your above discussion) or less than x (according to applying the LTs)?

    More fun & more logical than a rolling wheel with shortened circumference but full-sized spokes eh cinci ! I hope you'll be wearing your engineer's hat for the answer too - not the Luftwaffe one...

    TFOLZO
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    I never read the OP, so here's may response ...

    Quote Originally Posted by Scheuerf View Post
    If a rocket ship is moving near the speed of light relative to an observer, and the rocket ship appears to be contracted, the space between the atoms of the rocket ship must also be contracted because if they weren't, only the atoms would contract and the length of the rocket ship would remain the same? How does this work? Also, as the rocket ship moves away from the observer is the space between the rocket ship and the observer also contracted?
    Part of the problem here, is in the scenario described. While it's a fine scenario, it is somewhat insufficient to readily make clear what's going on in collective. Let's add a 2nd identical rocket out in front of the 1st rocket, both 100m long per themselves (proper length), traveling colinearly and at the same velocity per the observer. The rockets separated by 2 light-seconds (2 ls) per themselves, traveling at v = 0.866c wrt the observer, and so the gamma factor = 2.

    Per the observer, he records both rockets moving, and length contracted by 1/gamma = 1/2, so by 50%. So, both moving rockets are 100m x 50% = 50m per the stationary observer. The rockets (of course) hold themselves stationary, and the observer moving at v = -0.866c, and so the observer appears 50% length contracted per they.

    Now, let's talk "separation". The rockets are defined as separated by 2 ls per themselves. What must their separation be per the observer? The observer must record them separated at 2 ls x 1/gamma = 2 ls x 1/2 = 1 ls. Why? Because the entire x'-axis of the rocket frame is length contracted by 1/gamma relative to the observer's own frame. This means that stationary space as defined by the rockets (x'), is contracted relative to the spacetime system of the observer, and as such, the atoms of the rocket length-contract right along with the space that they declare themselves to be at rest in. Said another way, it's "the measure of space and time" that differs with relative motion. The atoms of the rocket length-contract, because the space they are at rest in length-contracts, per the observer. Now space is transparent, however the measure of space is empirical. The LTs will allow the observer to determine that the ships hold themselves stationary and at 2 ls separation, even though the observer holds them moving at 1 ls sep. If one assumes all atoms were round, and their spherical boundaries touching when Born rigid, then the observer sees the atomic spheres (instead) as 50% contracted ellipsoids, still touching.

    Thank You,
    SinceYouAsked
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    Well, SYA, your punches might nominally be aimed at poor nave honest Scheuerf...
    Quote Originally Posted by SinceYouAsked View Post
    Now space is transparent, however the measure of space is empirical. The LTs will allow the observer to determine that the ships hold themselves stationary and at 2 ls separation, even though the observer holds them moving at 1 ls sep. If one assumes all atoms were round, and their spherical boundaries touching when Born rigid, then the observer sees the atomic spheres (instead) as 50% contracted ellipsoids, still touching.

    Thank You,
    SinceYouAsked
    ...but it sounds like cinci is meant to be on the receiving end.

    But that doesn't matter, so long as cinci keeps his engineer's hat on - and doesn't trade it for the Colonel's... again!

    So here's a little bit o' physics cinci, in order to keep your engineer's hat on! Philipp Lenard discovered that atoms are mostly empty space - by passing cathode rays thru lead. Were atoms spherical and touching - like they do in the SYA substance of the quote above (whether face-centered cubic or body-centered cubic) - the volume of the atoms would exceed the volume of the intervening space, against the experimental evidence.

    TFOLZO
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    TFOLZO: Aha! Very interesting cinci! Now we are getting somewhere. You admit mutual length contraction of objects but you demur on claiming contracted distances between objects. Some people might decide to jump down your neck at that -

    cinci: Yes, but some people's only purpose in life is to jump down someone's neck. Some of them keep jumping even when there's no neck.

    TFOLZO: ....especially as this situation is dualistic since if we now consider an object in motion relative to another, we need to consider the first object's atomic constitution i.e. the distances between the atoms of the object will contract as the object length contracts. Very obvious - very logical. But...

    If we now have two objects e.g. spaceships, at distance x from one another and traveling at the same speed relative to a third observer (say on earth), would the earth observer also consider the distance between the two spaceships to be x (as implied by your above discussion) or less than x (according to applying the LTs)?

    cinci: Your statement implies that the third observer measured the distance between them as x. Relativity says you have to believe what you measure. The LTs don't enter into making a measurement.

    TFOLZO: More fun & more logical than a rolling wheel with shortened circumference but full-sized spokes eh cinci ! I hope you'll be wearing your engineer's hat for the answer too - not the Luftwaffe one...

    cinci: Nah, the rolling wheel is the gift that keeps on giving. I get a new laugh every day.
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    Now we are getting somewhere. You admit mutual length contraction of objects but you demur on claiming contracted distances between objects. Some people might decide to jump down your neck at that -

    cinci: Yes, but some people's only purpose in life is to jump down someone's neck. Some of them keep jumping even when there's no neck.

    TFOLZO: ....especially as this situation is dualistic since if we now consider an object in motion relative to another, we need to consider the first object's atomic constitution i.e. the distances between the atoms of the object will contract as the object length contracts. Very obvious - very logical. But...

    If we now have two objects e.g. spaceships, at distance x from one another and traveling at the same speed relative to a third observer (say on earth), would the earth observer also consider the distance between the two spaceships to be x (as implied by your above discussion) or less than x (according to applying the LTs)?

    cinci: Your statement implies that the third observer measured the distance between them as x. Relativity says you have to believe what you measure. The LTs don't enter into making a measurement.

    But that's my point cinci, I don't know what result I am meant to find if the third (earth) observer measures the distance between the two (length contracted) spaceships. I suppose the distance could be a little greater - due to length contraction of the spaceships themselves, but my question to you is whether the space between the spaceships is length contracted - since the space within the spaceships certainly is, as you, I and even SYA agree (the space within the spaceships contracting according to SR via the LTs).

    So tell me cinci what will the third (earth) observer find of the space between the two mutually moving spaceships. Will he find the space contracted (I mean by that what he actually measures - I don't mean multiplying it by √[1-v^2/c^2] or some similar equation) or will he not? If your answer is "I don't know" then please say so!

    TFOLZO


    PS: Why did the chicken get run over?
    cinci: ... the rolling wheel is the gift that keeps on giving. I get a new laugh every day.
    Answer: So cinci could claim that what I meant by "colonel's hat" referred to Colonel Sanders!
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    TFOLZO: If we now have two objects e.g. spaceships, at distance x from one another and traveling at the same speed relative to a third observer (say on earth), would the earth observer also consider the distance between the two spaceships to be x (as implied by your above discussion) or less than x (according to applying the LTs)?

    cinci: Your statement implies that the third observer measured the distance between them as x. Relativity says you have to believe what you measure. The LTs don't enter into making a measurement.

    TFOLZO: But that's my point cinci, I don't know what result I am meant to find if the third (earth) observer measures the distance between the two (length contracted) spaceships.

    [B]cinci: Yes you do. If the third observer measures the distance between them, whatever he gets is the distance between them. Again, the basic philosophical change that relativity gives us is that all observers do not have to agree and that each observer must believe his own measurements. [B]

    TFOLZO: I suppose the distance could be a little greater - due to length contraction of the spaceships themselves, but my question to you is whether the space between the spaceships is length contracted - since the space within the spaceships certainly is, as you, I and even SYA agree (the space within the spaceships contracting according to SR via the LTs).

    cinci: Yes the spaceships contract for the third observer but the distance between them does not.

    TFOLO: So tell me cinci what will the third (earth) observer find of the space between the two mutually moving spaceships. Will he find the space contracted (I mean by that what he actually measures - I don't mean multiplying it by √[1-v^2/c^2] or some similar equation) or will he not? If your answer is "I don't know" then please say so!

    cinci: He will find the distance to be whatever he measures it to be. Look at it this way. The ships are at two points in the sky; the distance between these two points doesn't change because the spaceships are there.
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    TFOLZO: If we now have two objects e.g. spaceships, at distance x from one another and traveling at the same speed relative to a third observer (say on earth), would the earth observer also consider the distance between the two spaceships to be x (as implied by your above discussion) or less than x (according to applying the LTs)?

    cinci: Your statement implies that the third observer measured the distance between them as x. Relativity says you have to believe what you measure. The LTs don't enter into making a measurement.

    TFOLZO: But that's my point cinci, I don't know what result I am meant to find if the third (earth) observer measures the distance between the two (length contracted) spaceships.

    cinci: Yes you do. If the third observer measures the distance between them, whatever he gets is the distance between them. Again, the basic philosophical change that relativity gives us is that all observers do not have to agree and that each observer must believe his own measurements.

    TFOLZO: I suppose the distance could be a little greater - due to length contraction of the spaceships themselves, but my question to you is whether the space between the spaceships is length contracted - since the space within the spaceships certainly is, as you, I and even SYA agree (the space within the spaceships contracting according to SR via the LTs).

    cinci: Yes the spaceships contract for the third observer but the distance between them does not.

    Aha! Thank you cinci - the answer I was looking for!

    cinci: He will find the distance to be whatever he measures it to be. Look at it this way. The ships are at two points in the sky; the distance between these two points doesn't change because the spaceships are there.

    Well I certainly agree 100% with you on that cinci - but this means that the distance between the two spaceships is objective i.e. independent of observer motion. Thus if I measure this distance from earth (as the 3rd observer did) then the distance remains the same. If I measure this distance from another spaceship moving relative to earth & the two commoving spaceships this distance will remain the same - i.e. it exists objectively, independently of observer motion

    As you can see however, this situation also LIMITS the applicability of SR. SR is now only applicable to physical bodies, NOT to space itself. Would you now agree with my underlined statement or would you qualify it in many ways?*

    TFOLZO

    *Please treat any subsequent SYA-type spam separately from my question as the SYA fraternity will try to prove superior in their well-recognized capacity to distract from the thrust of the argument.
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    cinci: Yes the spaceships contract for the third observer but the distance between them does not.

    TFOLZO: Aha! Thank you cinci - the answer I was looking for!

    cinci: I doubt it.

    cinci: He will find the distance to be whatever he measures it to be. Look at it this way. The ships are at two points in the sky; the distance between these two points doesn't change because the spaceships are there.

    TFOLZO: Well I certainly agree 100% with you on that cinci - but this means that the distance between the two spaceships is objective i.e. independent of observer motion.

    cinci: You didn't specify any motion for the third observer so you cannot logically draw that conclusion.

    TFOLZO: Thus if I measure this distance from earth (as the 3rd observer did) then the distance remains the same.

    cinci: Only if the third observer is at rest relative to the Earth.

    TFOLZO: If I measure this distance from another spaceship moving relative to earth & the two commoving spaceships this distance will remain the same - i.e. it exists objectively, independently of observer motion.

    cinci: No, we already said that the distance between the ships when measured by observers on the ships is contracted. You cannot ascribe measurements made by one observer to a different observer if they have relative motion. Each observer must make his own measurements and he must believe them to be true.

    TFOLZO: As you can see however, this situation also LIMITS the applicability of SR. SR is now only applicable to physical bodies, NOT to space itself. Would you now agree with my underlined statement or would you qualify it in many ways?*

    cinci: Nothing in the discussion allows you to draw this conclusion. As for affecting space, that is not at issue. What is at issue is our ability to measure space with the stricture that light speed is the same for all inertial observers. If you apply mathematical logic to that one requirement, special relativity follows as surely as night follows day.
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    I had written above: As you can see however, this situation also LIMITS the applicability of SR. SR is now only applicable to physical bodies, NOT to space itself. Would you now agree with my underlined statement or would you qualify it in many ways?

    I presume you will agree with my underlined statement above hence...

    So let me put forward an added scenario. You remember we had the two commoving spaceships moving relative to an (earth) observer who finds that though both spaceships are length-contracted, the space between them is not.

    Now adjacent to the two commoving spaceships we have a gigantic spaceship, commoving with the two spaceships. When measured on earth before liftoff, the giant spaceship stretched the whole distance* between the two spaceships such that the back of the giant spaceship was level with the rear small spaceship & the front of the giant spaceship was level with the front small spaceship. Hence the earthly arrangement is:

    III>.............................................. ....................................III> two small spaceships
    IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIII> giant spaceship

    So we now launch the three spaceships so that after acceleration ceases and a steady velocity is maintained relative to earth, we must ask what the earth observer will see. Will the giant spaceship be length contracted relative to the earth observer?

    Over to you, cinci - and I'm looking for a straight answer here, not seven different blurbs & splices!

    TFOLZO

    *This distance being the same as that between the two small spaceships when they are maintaining a steady velocity (relative to the earth) in space.
    Last edited by TFOLZO; 09-05-2014 at 05:18 AM. Reason: Grammar
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    cinci: Yes the spaceships contract for the third observer but the distance between them does not.

    TFOLZO: Aha! Thank you cinci - the answer I was looking for!(The third observer being the earth observer)

    cinci: I doubt it.

    He will find the distance to be whatever he measures it to be. Look at it this way. The ships are at two points in the sky; the distance between these two points doesn't change because the spaceships are there.


    TFOLZO: Well I certainly agree 100% with you on that cinci - but this means that the distance between the two spaceships is objective i.e. independent of observer motion.

    cinci: You didn't specify any motion for the third observer so you cannot logically draw that conclusion.

    That is NOT true cinci, since it was already given that the two spaceships were moving relative to the (earth) observer. That is all that is required of my statement so the conclusion stands.

    TFOLZO: Thus if I measure this distance from earth (as the 3rd observer did) then the distance remains the same.

    cinci: Only if the third observer is at rest relative to the Earth.

    Not so, cinci, since you are privileging the earth observer as someone who sees the space between the spaceships remain the same, despite the fact that he is moving relative to the spaceships. Hence this situation must also apply to other observers, no matter what their motion relative to the spaceships AND relative to the earth observer. Get the message?

    TFOLZO: If I measure this distance from another spaceship moving relative to earth & the two commoving spaceships this distance will remain the same - i.e. it exists objectively, independently of observer motion.

    cinci: No, we already said that the distance between the ships when measured by observers on the ships is contracted. You cannot ascribe measurements made by one observer to a different observer if they have relative motion. Each observer must make his own measurements and he must believe them to be true.

    That highlighted statement is NOT correct cinci, since the two spaceship-observers are not mutually in motion hence they will see the distance between them to be unchanged and thus NOT subjected to length contraction - as we had agreed earlier. You also agreed that the earth-observer found the distance between the ships NOT to be contracted either!


    cinci: What is at issue is our ability to measure space with the stricture that light speed is the same for all inertial observers. If you apply mathematical logic to that one requirement, special relativity follows as surely as night follows day.

    Indeed so cinci, the obverse spirit of the poem ending "...then Newton appeared, and all was light." "Then Einstein appeared and all was, once again, night!" Ha ha!

    But before dealing with this, cinci, you need to correct your 'benighted' errors or alter your claims above! Life does not depend on mathematical logic alone!

    TFOLZO
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    Quote Originally Posted by cincirob View Post
    The LTs don't enter into making a measurement.
    Wow!!! Cinci doesn't know the length contraction formula is derived from the Lorentz Transformations?
    Cinci, what are the LT for if they are not to find out the coordinates (=measurement) in another frame?

    JT, SYA, have you read this cinci quote?
    And this is the guy selling his rolling wheel?
    Cinci, go back play with your airplanes, boy.
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    cinci: The LTs don't enter into making a measurement.


    VeeDee: Wow!!! Cinci doesn't know the length contraction formula is derived from the Lorentz Transformations?
    Cinci, what are the LT for if they are not to find out the coordinates (=measurement) in another frame?

    cinci: Finding the coordinates in another frame does not = "making a measurement".
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    Quote Originally Posted by cincirob View Post
    cinci: Finding the coordinates in another frame does not = "making a measurement".
    Indeed. Using transformations allow one, given locations in a coordinate system, to determine what someone would, in principle, measure in a different system of coordinates, were such a measurement possible. One need not use them in making a measurement, unless making that measurement relies upon knowing the location of events that are given only in different coordinate systems.
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    Quote Originally Posted by cincirob View Post
    cinci: The LTs don't enter into making a measurement.


    VeeDee: Wow!!! Cinci doesn't know the length contraction formula is derived from the Lorentz Transformations?
    Cinci, what are the LT for if they are not to find out the coordinates (=measurement) in another frame?

    cinci: Finding the coordinates in another frame does not = "making a measurement".
    It absolutely does. What gave you the impression otherwise?
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    In reply to AIP's this thread, re: contracture.

    I like this thread! It reminds me of "how many angels can dance on the head of pin?" The answer? ALL of them, if they exist...angels are extra-corporeal beings (no matter) and therefore

    all of them will "fit" in the assigned FoR. But what of the "space" of the pinhead...should it not expand or contract in relation to that which is in it's continuum? No...because the space

    involved, of itself, can easily be given an infinite identity. Remove the angels/rockets/observers from the FoR of space and what remains is space. The idea of contraction/expansion

    aspects to space itself, that it can be influenced by the presence of "something in it moving about" is false (imo)

    ......

    Coordinates only apply to things made of matter...not to space itself. Velocities only apply to matter, not to space itself. Measurements apply only to real matter, not to space.

    (the idea of bending/warping/twisting "space" via the mechanism of velocity of an object is completely w/o merit or substance, IMO.)


    (Thanks for reading!)
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    Quote Originally Posted by TFOLZO View Post

    As you can see however, this situation also LIMITS the applicability of SR. SR is now only applicable to physical bodies, NOT to space itself.
    Explain the results of a muon experiment (such as Rossi-Hall), from the frame of the Muon, without a length contraction of the distance between the emitter and the detector.
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    cinci: The LTs don't enter into making a measurement.

    VeeDee: Wow!!! Cinci doesn't know the length contraction formula is derived from the Lorentz Transformations?

    Cinci, what are the LT for if they are not to find out the coordinates (=measurement) in another frame?

    cinci: Finding the coordinates in another frame does not = "making a measurement".

    Physicist: It absolutely does. What gave you the impression otherwise?

    cinci: Well I took my tape and measured the length and width of a room yesterday in advance of laying tile in it. It didn't involve the LTs or length contraction.

    My comment didn't have anything to do with length contraction in the first place. But since you and VeeDee brought it up, you can only make measurements in the frame in which you are at rest. If you're measuring, say the length of a moving object, you can use relativity to determine the coordinates of the ends of the object in the frame of that object (You will find that it is longer in that frame than you measured it in your own frame). The input to that determination is what you measure in the frame in which you are at rest. So measurements and finding coordinates in another frame can be related, but they are in no sense equal.

    In the particular case that my comment referred to (taken out of context as people on the this forum seem to be addicted to) is the distance one observes between two objects in space. You do not have to apply length contraction or the LTs to that situation. What gave you the impression otherwise? Please do me the favor of an answer (not answering questions is another foible people on this forum seem to be addicted to.)
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    PhysBang: Indeed. Using transformations allow one, given locations in a coordinate system, to determine what someone would, in principle, measure in a different system of coordinates, were such a measurement possible. One need not use them in making a measurement, unless making that measurement relies upon knowing the location of events that are given only in different coordinate systems.

    cinci: Thank you.
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    cinci: Yes the spaceships contract for the third observer but the distance between them does not.

    TFOLZO: Aha! Thank you cinci - the answer I was looking for!(The third observer being the earth observer)

    cinci: I doubt it.

    He will find the distance to be whatever he measures it to be. Look at it this way. The ships are at two points in the sky; the distance between these two points doesn't change because the spaceships are there.

    TFOLZO: Well I certainly agree 100% with you on that cinci - but this means that the distance between the two spaceships is objective i.e. independent of observer motion.

    cinci: You didn't specify any motion for the third observer so you cannot logically draw that conclusion.

    TFOLZO: That is NOT true cinci, since it was already given that the two spaceships were moving relative to the (earth) observer. That is all that is required of my statement so the conclusion stands.

    cinci: Your statement is for two spaceships moving relative to each other being observed by a third observer. You can't apply anything else to it. If I introduce a 4th observer moving relative to the 3rd, he will not agree on the distance between the ships.

    Look, I'm familiar with the FBI and Congressional Committee practice of asking dozens of related questions and drawing improper inferences between them to imply that someone is wrong (or in their case, lying; lying to either body constituting a crime). Don't try to use it here. I will patiently take you back to basics and repeat my answers. Your inferences do not trump the facts. ;-)


    TFOLZO: Thus if I measure this distance from earth (as the 3rd observer did) then the distance remains the same.

    cinci: Only if the third observer is at rest relative to the Earth.

    TFOLZO: Not so, cinci, since you are privileging the earth observer as someone who sees the space between the spaceships remain the same, despite the fact that he is moving relative to the spaceships. Hence this situation must also apply to other observers, no matter what their motion relative to the spaceships AND relative to the earth observer. Get the message?

    cinci: I already have the message. I'm trying to give it to you. You need to start reading my answers as they are and don't bias them according to you own prejudices.

    TFOLZO: If I measure this distance from another spaceship moving relative to earth & the two commoving spaceships this distance will remain the same - i.e. it exists objectively, independently of observer motion.

    cinci: No, we already said that the distance between the ships when measured by observers on the ships is contracted. You cannot ascribe measurements made by one observer to a different observer if they have relative motion. Each observer must make his own measurements and he must believe them to be true.

    TFOLZO: That highlighted statement is NOT correct cinci, since the two spaceship-observers are not mutually in motion hence they will see the distance between them to be unchanged and thus NOT subjected to length contraction - as we had agreed earlier.

    cinci: Cute, but this is not what I agreed to earlier.

    TFOLZO: You also agreed that the earth-observer found the distance between the ships NOT to be contracted either!

    cinci: You are mixing cases. I'm not sure whether you are confused or are trying to confuse the issues. In any case, you are not confusing me. I don't have the time to straighten you out now, but I promise I will try later. (Mama wants me to lay some tile...NOW! :-) )


    cinci: What is at issue is our ability to measure space with the stricture that light speed is the same for all inertial observers. If you apply mathematical logic to that one requirement, special relativity follows as surely as night follows day.

    TFOLZO: Indeed so cinci, the obverse spirit of the poem ending "...then Newton appeared, and all was light." "Then Einstein appeared and all was, once again, night!" Ha ha!

    But before dealing with this, cinci, you need to correct your 'benighted' errors or alter your claims above! Life does not depend on mathematical logic alone!

    cinci: And life does not depend on whether or not somebody thinks I've made 'beknighted' errors. Later!
    Last edited by cincirob; 09-06-2014 at 01:00 PM.
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    Again, with the "SR" being applied to "space/matter/velocity" as being a true condition.

    ......

    As Lennon wrote..."semolina pilchard/climbing up the Eiffel Tower!" It's funny, when I write a rebuttal that deals w/reality "as it is" rather than "flights of fancy supported by elaborate

    equations" I am told "you're dealing w/personal agendas of misconception!" But any thought-concept that is coupled w/ a "Wiki" link and some numbers that say nothing is "true".

    Very good...just as I thought.


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    Gerry, can you please state, clearly and concisely, what you actually mean by "true condition"? Come on, spell it out in rigorous terms that leave nothing to ambiguity!
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    Only Gerry can really say of course, but I have always taken it to be "physical reality".....
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    In reply to posts #75 & #76.

    I am not being all that disingenuous...if you want an example of concisely "what I mean" then I'll state it as plainly as possible. "Time" of itself is an abstract concept...it does not and cannot

    be used to "define the reality of reality". Time is a numerical concept and nothing more than that. I thought A.E. made this completely clear w/"Relativity" in that "all matter and energies

    are relative w/respect to each other" and I cannot see any possibility of a numerical concept such as "time" being used in an "SR" FoR to deny that "GR" is no longer in-place w/regard

    to bodies at relativistic velocities. In essence, "SR" is being used as an excuse to state that "time differences between A,B, and C serve to prove that "time" shifts dramatically in response

    to sub-light velocities". I have never been able to accept this concept at all because it DENIES the reality of the continuum of the Universe!

    Not only does this deny the physical reality of the Universe, it implies that "Time" is a real thing-of-self which can be distorted by the velocity of a given object!

    My mind refuses to accept this as true...that time is real of itself. I have tried for years to find a way to make it possible for me to acknowledge that time can be bent/twisted/distorted and

    so on...but I just can't "see it!"

    This why it means little for me to study...I just cannot reconcile myself to the idea of time as "real", that it exists as real function of the Universe.

    I wish I could just accept things, but I don't know how.


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    Quote Originally Posted by Gerry Nightingale View Post
    In reply to posts #75 & #76.

    I am not being all that disingenuous...if you want an example of concisely "what I mean" then I'll state it as plainly as possible. "Time" of itself is an abstract concept...it does not and cannot be used to "define the reality of reality". Time is a numerical concept and nothing more than that. I thought A.E. made this completely clear w/"Relativity" in that "all matter and energies are relative w/respect to each other" and I cannot see any possibility of a numerical concept such as "time" being used in an "SR" FoR to deny that "GR" is no longer in-place w/regard to bodies at relativistic velocities. In essence, "SR" is being used as an excuse to state that "time differences between A,B, and C serve to prove that "time" shifts dramatically in response to sub-light velocities". I have never been able to accept this concept at all because it DENIES the reality of the continuum of the Universe!
    It is true that no one really knows what time is. Many great physicists today debate whether time is real, and/or what it is. That said, what we do know is that we quantify time very well. Add, without that which we call time, we could calculate nothing. Yet, great physicists continue working on it.

    The relative nature of the measurement of time as a function of relative velocity, is a mathematical requirement given the 2 postulates of relativity true. While the relativistic effects seems bizarre in relation to our everyday experience, tests and analyses for >100 years have confirmed it. Now, if we could travel at relativistic rates everyday in a starship, we would then say ... "sure, how could it be any other way". We'd say that simply because "it would then be everyday experience". It would no longer be bizarre. Reality, is just not what we tend to think it is. It's always been that way, it'll probably always be that way. Our definition of reality will likely change and improve, without end.

    Quote Originally Posted by Gerry Nightingale View Post
    Not only does this deny the physical reality of the Universe, it implies that "Time" is a real thing-of-self which can be distorted by the velocity of a given object! My mind refuses to accept this as true...that time is real of itself. I have tried for years to find a way to make it possible for me to acknowledge that time can be bent/twisted/distorted and so on...but I just can't "see it!"
    What relativity does, is defines a perceptible 4 dimensional continuum in which matter and energy exists. In fact, curved space/time exists only because matter/energy exists, and vice versa. They all arose in unison, as the result of the inherent properties of the very medium. We consider time real, because we experience it and can consistently measure it. However, time is not a separate independent thing of existence. It's a particular aspect of existence, as are space, matter, and energy. Time is interwoven with space, and one has no meaning without the other. To discuss the realness of time, one must talk the realness of space. Then, one must talk about that which produces real curved space-time, and as such the realness of matter/energy. It's all connected, linked at the hip, and it's all measurable.

    Quote Originally Posted by Gerry Nightingale View Post
    This why it means little for me to study ... I just cannot reconcile myself to the idea of time as "real", that it exists as real function of the Universe. I wish I could just accept things, but I don't know how. (Thanks for reading!)
    Well, it's certainly fair to say that we do not understand the nature of time. Many great physicists today are still trying to better define it. They admit that no one really knows what time is. Some argue that time is not even real. Yet, no matter what time is, we quantify it very well. It's modeled very well. If time is not real, then it must be replaced by something else that is real. Not matter what that something else may be, it must do everything that we know time to do, and maybe something a little extra. That's what relativity theory did wrt classical mechanics, it handles relativistic rates, but reduces to classical mechanics for the scope under which Newton developed it (for POVs of everyday rate).

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    In reply to SYA, re: your #78 post.

    I stand with what I wrote, and as per many of my other posts, I do agree that the postulated behaviors of theoretical particles stipulate that "time" is measurable as a "true thing".

    The problem here is that I do not agree w/ the existence of many, many theoretical particles that exist only for excruciatingly small fractions of measure. This also is one of my many

    disenchantments wrt modern theory! "Posit a thing, enumerate a thing, and the thing becomes real" does not "work" for me...no matter how many support the thing.

    I appreciate the effort you put into your reply to me (really, you went to this much effort for someone who is almost "personae non grata" as far as credibility is concerned!) and I am not

    unappreciative of your efforts to explain the "timespace continuum" to me. But I think I could live another thousand years, and still never accept the posits that have come from "SR".

    (I doubt A.E. would accept them either, but he is dead and can longer write "Scoundrels! Who think they know!" )


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    Quote Originally Posted by Gerry Nightingale View Post
    But I think I could live another thousand years, and still never accept the posits that have come from "SR".
    Then there is little point in your being on this forum, is there?
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    Gerry Nightingale: This why it means little for me to study...I just cannot reconcile myself to the idea of time as "real", that it exists as real function of the Universe.

    cinci: Perhaps you would be interested in a book by Lee Smolin, "Time Reborn". He claims physics is stymied at the moment because they physicists have effectively eliminated or limited the role of time from our theories.
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    TFOLZO: You also agreed that the earth-observer found the distance between the ships NOT to be contracted either!

    cinci: You are mixing cases. I'm not sure whether you are confused or are trying to confuse the issues. In any case, you are not confusing me. I don't have the time to straighten you out now, but I promise I will try later.

    cinci: OK, back to basics. First, using the Earth is a poor choice because it isn't really inertial but it can be assumed to be inertial without introducing much error if the problem involves relativistic velocities and long distances. To eliminate confusion, I will discuss the three observer problem (two spaceships and a third observer) as being located in deep space (away from any significant gravitating source).

    All three elements (the two spaceships and the third observer) will be considered to be dimensionless points; this also introduces ignorable errors for large separations of the elements.

    First let's name the spaceships S1 and S2 and the observer is O. S! and S2 are on a straight line collision course; O is somewhere off that line.

    The occupy three points in space at any given instant.

    YOU chose an instant when O knows S1 and S2 are separated by a distance x.

    That statement implies that O has the ability to determine distance x and that he determined it as a distance that is stationary relative to O. This requires some technology: he could have beacons in space that he placed stationary to himself and can observe when the ships pass them by some means. Note, he may not be able to determine this at a given instant and may only know it some time after the ships pass the beacons but he can, with suitable technology determine that at a particular time on his clock, the spaceships were separated by a known distance x.

    Next, YOU chose to acknowledge that O could also determine the velocities of S1 and S2 when they were separated by the distance x. Also technologically possible.

    So now, YOU have specified that O knows a distance x, V1, and V2 and I have shown that he could technologically collect this data.

    Note, that none of this data is subject to relativistic effects as far as O is concerned. The First Postulate confirms this in that it says the laws of physics hold good in a frame where the mechanics hold and they hold in an inertial frame. So no contraction of x.

    S1 is also inertial. He can also make measurements. Since he is inertial, he cannot determine his own motion, but he can measure velocities relative to himself. So here is what he measured.

    He can measure the distance to S2 but he gets a value x1 which is different than x as measured by O.

    S2 gets a value for the distance to S1, let's call it x2.

    TFOLZO, let the question begin.
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    Quote Originally Posted by cincirob View Post
    cinci: OK, back to basics. First, using the Earth is a poor choice because it isn't really inertial but it can be assumed to be inertial without introducing much error if the problem involves relativistic velocities and long distances. To eliminate confusion, I will discuss the three observer problem (two spaceships and a third observer) as being located in deep space (away from any significant gravitating source).

    All three elements (the two spaceships and the third observer) will be considered to be dimensionless points; this also introduces ignorable errors for large separations of the elements.

    First let's name the spaceships S1 and S2 and the observer is O. S! and S2 are on a straight line collision course; O is somewhere off that line.

    The occupy three points in space at any given instant.

    YOU chose an instant when O knows S1 and S2 are separated by a distance x.

    That statement implies that O has the ability to determine distance x and that he determined it as a distance that is stationary relative to O. This requires some technology: he could have beacons in space that he placed stationary to himself and can observe when the ships pass them by some means. Note, he may not be able to determine this at a given instant and may only know it some time after the ships pass the beacons but he can, with suitable technology determine that at a particular time on his clock, the spaceships were separated by a known distance x.

    Next, YOU chose to acknowledge that O could also determine the velocities of S1 and S2 when they were separated by the distance x. Also technologically possible.

    So now, YOU have specified that O knows a distance x, V1, and V2 and I have shown that he could technologically collect this data.

    Note, that none of this data is subject to relativistic effects as far as O is concerned. The First Postulate confirms this in that it says the laws of physics hold good in a frame where the mechanics hold and they hold in an inertial frame. So no contraction of x.

    S1 is also inertial. He can also make measurements. Since he is inertial, he cannot determine his own motion, but he can measure velocities relative to himself. So here is what he measured.

    He can measure the distance to S2 but he gets a value x1 which is different than x as measured by O.

    S2 gets a value for the distance to S1, let's call it x2.

    TFOLZO, let the question begin.
    Okay, so what time is spaceship S1 supposed to measure distance X1 for it to be a meaningful comparison to distance X? Likewise, what time is spaceship S2 supposed to measure distance X2 for it to be a meaningful comparison to distance X?
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    Quote Originally Posted by Gerry Nightingale View Post
    In reply to SYA, re: your #78 post.

    I appreciate the effort you put into your reply to me (really, you went to this much effort for someone who is almost "personae non grata" as far as credibility is concerned!) and I am not unappreciative of your efforts to explain the "timespace continuum" to me. But I think I could live another thousand years, and still never accept the posits that have come from "SR".
    Yup, I can remember long ago when I was thinking it didn't make sense, when I was trying to come to grips with the meaning of relativistic effects and how and why they exist. Man am I glad I got over that hurdle. It's very liberating, I must say. I've seen others spend 10 to 30 years trying to fully understand it, and they never have. You see, I never presumed that all the relativists were wrong, that relativity was wrong, or that the whole world was wrong, and I right. I presumed that I fell short of a complete understanding. I then restudied, and tried harder, again and again. Until one day, Voila. That's the ticket. Everyone comes to that understanding in their own good time. It'll happen much faster if one does not assume the adversarial role, because of pride.

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    JT: Okay, so what time is spaceship S1 supposed to measure distance X1 for it to be a meaningful comparison to distance X? Likewise, what time is spaceship S2 supposed to measure distance X2 for it to be a meaningful comparison to distance X?

    cinci: My post is a continuing conversation with TFOLZO. If you want me to explain things like this to you why don't you start a new thread.
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    Quote Originally Posted by cincirob View Post
    JT: Okay, so what time is spaceship S1 supposed to measure distance X1 for it to be a meaningful comparison to distance X? Likewise, what time is spaceship S2 supposed to measure distance X2 for it to be a meaningful comparison to distance X?

    cinci: My post is a continuing conversation with TFOLZO. If you want me to explain things like this to you why don't you start a new thread.
    As I suspected, you probably have no idea what the correct answer is to my question. Carry on.
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    JT: As I suspected, you probably have no idea what the correct answer is to my question. Carry on.

    cinci: Yes, and as I suspected you here only to try to make claims about me. You are nothing if not predictable.

    JT: JT: Okay, so what time is spaceship S1 supposed to measure distance X1 for it to be a meaningful comparison to distance X? Likewise, what time is spaceship S2 supposed to measure distance X2 for it to be a meaningful comparison to distance X?

    cinci: Since I didn't put numbers on any of this, most people who understand relativity would pick an instant in time, a couple of sets of coordinates whose origins are coincident at
    t = 0 and write the "meaningful" equations. Or simply use length contraction and time dilation equations to do the same.

    Apparently what you would do is ask somebody what time it is.

    My example was designed to answer some questions TFOLZO is asking. If you want a platform to criticize me, then start one yourself instead of interrupting TFOLZO and me.
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    In reply to SpeedFreek, re: your post #80.

    Do you mean the "forum as whole" or just this thread? Or are you saying you just want "book-thumpers" on the entire site, people who never write anything except endless "quotes"

    from "Wiki" (knowing full well there is zero chance of being refuted, and thus not risking their "internet phys. sites" credibility)


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    In reply to SYA, re: your #84 post.

    Are you applauding yourself, or chastising me w/this post? I write "what logic and reason and Einstein" tell me is true...you are insinuating that some factor of "pride" is involved on my part, as

    in "pride cometh before the fall". Wrong for two reasons.

    (1) Such "pride" as I have involves my schoolwork in medical training (4.O avg) and not physics theory.

    (2) I never intended to win "Miss Popularity" here or anywhere else, including "real life". If expressing and writing "what I think" is unpalatable to you or anyone else, they or you can just

    put me on "ignore". I think you should do this, it will make "comprehension, complete w/built-in blinders" much easier. I am as I am, SYA, and there little is I can do to change "who I am"

    this late in life.

    It may interest you to know that I despise and loath being me...hopefully death will cure this at some point. I have many, many excellent reasons for disliking the fact that "I am me".

    I have lived alone virtually my entire life, without friends or family, and this did have one benefit, if you want see it that way...I read many, many books. And I understand far more than

    you give me credit for. I think your judgment of "pride" is rather harsh...try "surety" instead. That would be true.

    Shall I tell you one more thing? Being "really smart" is a CURSE...not a gift! I am certain of this. Being "smart" is okay...but "really smart" is instantly disliked.

    I would trade my intellect and all that it means or does not mean for even ONE DAY of being...happy. (I am insanely envious of people who are content, who like their lives and wake-up

    feeling "good" everyday)


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    Dear cincirob,
    You have given us a specific scenario in which spaceships S1 and S2 are on a collision course, and observer O is located in the middle.


    Of course O can measure the distance between S1 and S2 at any TIME, that is true.

    Of course S1 can measure the distance between S1 and S2 at any TIME, that is true.

    Of course S2 can measure the distance between S1 and S2 at any TIME, that is true.



    So, what are the TIMES that you think they all should make these measurements, so that they might give the same results as the 'LENGTH CONTRACTION' method?
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    JT: You have given us a specific scenario in which spaceships S1 and S2 are on a collision course, and observer O is located in the middle.

    cinci: First, I didn't give "US" anything. I posed a situation for TFOLZO where I think I can unravel some of his misgivings about relativity, things that he seems to believe are contradictory, and I don't think numbers will help.

    Second, O isn't in the middle. If you want to show off your prowess for solving numerical problems like this with the LTs then make one up and "prowess" away. We'll all be thrilled.
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    Quote Originally Posted by cincirob View Post
    JT: You have given us a specific scenario in which spaceships S1 and S2 are on a collision course, and observer O is located in the middle.

    cinci: First, I didn't give "US" anything. I posed a situation for TFOLZO where I think I can unravel some of his misgivings about relativity, things that he seems to believe are contradictory, and I don't think numbers will help.

    Second, O isn't in the middle. If you want to show off your prowess for solving numerical problems like this with the LTs then make one up and "prowess" away. We'll all be thrilled.
    One of TFOLZO's 'misgivings' about relativity is that there is reciprocal length contraction and reciprocal time dilation. Yet all, you've offered him is the simple fact that anyone can measure anything at any time.
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    Quote Originally Posted by Gerry Nightingale View Post
    In reply to SYA, re: your #84 post.

    Are you applauding yourself, or chastising me w/this post? I write "what logic and reason and Einstein" tell me is true...you are insinuating that some factor of "pride" is involved on my part, as in "pride cometh before the fall".
    That was not my intent Gerry. I was just hoping that you did not fall into that category, a category I have seen in others too many times.

    Quote Originally Posted by Gerry Nightingale View Post
    Wrong for two reasons.

    (1) Such "pride" as I have involves my schoolwork in medical training (4.O avg) and not physics theory.
    Excellent, that's most commendable. Very few attain that kind of success in their higher education at university. Very good!

    Quote Originally Posted by Gerry Nightingale View Post
    (2) I never intended to win "Miss Popularity" here or anywhere else, including "real life". If expressing and writing "what I think" is unpalatable to you or anyone else, they or you can just put me on "ignore". I think you should do this, it will make "comprehension, complete w/built-in blinders" much easier. I am as I am, SYA, and there little is I can do to change "who I am" this late in life.
    Fair enough then.

    Quote Originally Posted by Gerry Nightingale View Post
    It may interest you to know that I despise and loath being me...hopefully death will cure this at some point. I have many, many excellent reasons for disliking the fact that "I am me".

    I have lived alone virtually my entire life, without friends or family, and this did have one benefit, if you want see it that way...I read many, many books. And I understand far more than you give me credit for. I think your judgment of "pride" is rather harsh...try "surety" instead. That would be true.
    Well again, the pride factor was a general statement. While you are very smart in medical school, you certainly do not understand relativity theory. If pride is the issue, and in some cases it is, the good thing is that that can be fixed with a choice. Far as being alone, to each their own. However, it would be better and healthier to make friends, and still read many many books. That's just an opinion, mind you.

    Quote Originally Posted by Gerry Nightingale View Post
    Shall I tell you one more thing? Being "really smart" is a CURSE...not a gift! I am certain of this. Being "smart" is okay...but "really smart" is instantly disliked.
    One can be really smart, and keep it a secret.

    Quote Originally Posted by Gerry Nightingale View Post
    I would trade my intellect and all that it means or does not mean for even ONE DAY of being...happy. (I am insanely envious of people who are content, who like their lives and wake-up feeling "good" everyday).
    Believe me when I tell you, I don't have a day worth waking up to. Yet, I realize I must play the cards dealt me, and that life is not always fair. The first thing one must do to be happy, is to eliminate all denial and blame, and then appreciate the fact that life is a gift. There are 2 choices ... continue, or make a serious attempt to improve oneself. The choice is up to the individual, even if not easy ... there is always a way. Far as being content goes, while it may be good in ways, I'm not so sure that's a great thing. To strive, is a better thing.

    You seem to believe you will never accept relativity theory. If you don't mind my asking, how long have you studied the theory? Another thing, there are some great physicists who accept relativity, but deny that time is real, or fundamental. Do you reject relativity on the LT solns, or in regards to your belief that we have the dimension of time ill defined IYO?

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    When one understands the spacetime continuum geometrically, it is very clear why the measure of space (and time) is relative per POV. Geometrically, all relativistic effects (including length contraction) arises from the angular orientation differentials of spacetime systems (ie POVs) within a fused 4 dimensional continuum of 3-space + time. One cannot ignore time dilation when considering length contraction, and vice versa. When considered in unison, and well enough pondered, one realizes that moving contracted bodies are time desynchronized per the stationary observer. Said time desynchronization within a 4d continuum, explains why and how a moving length can be contracted (wrt proper) without altering the fact that the proper length never changes ... both measurable, and thus real, per POV.

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    Quote Originally Posted by SinceYouAsked View Post
    When one understands the spacetime continuum geometrically, it is very clear why the measure of space (and time) is relative per POV. Geometrically, all relativistic effects (including length contraction) arises from the angular orientation differentials of spacetime systems (ie POVs) within a fused 4 dimensional continuum of 3-space + time. One cannot ignore time dilation when considering length contraction, and vice versa. When considered in unison, and well enough pondered, one realizes that moving contracted bodies are time desynchronized per the stationary observer. Said time desynchronization within a 4d continuum, explains why and how a moving length can be contracted (wrt proper) without altering the fact that the proper length never changes ... both measurable, and thus real, per POV.

    Thank You,
    SinceYouAsked
    Correct. Einstein relativity is about 3D cuts through 4D spacetime. The invariant is not 3D space but 4D spacetime. Spacetime diagrams shows you how different 3D cuts automatically give length contraction and time dilation.
    But lots of people never will - or don't want to - understand or accept this.

    Interesting Einstein quotes:

    << From a "happening" in three-dimensional space, physics becomes, as it were, an "existence" in the four-dimensional "world". >> (Albert Einstein. "Relativity: The Special and the General Theory." 1916. Appendix II Minkowski's Four-Dimensional Space ("World") (supplementary to section 17 - last section of part 1 - Minkowski's Four-Dimensional Space).

    << Since there exists in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence. >> (Albert Einstein, "Relativity", 1952).

    Your post #84
    Yup, I can remember long ago when I was thinking it didn't make sense, when I was trying to come to grips with the meaning of relativistic effects and how and why they exist. Man am I glad I got over that hurdle. It's very liberating, I must say. I've seen others spend 10 to 30 years trying to fully understand it, and they never have. You see, I never presumed that all the relativists were wrong, that relativity was wrong, or that the whole world was wrong, and I right. I presumed that I fell short of a complete understanding. I then restudied, and tried harder, again and again. Until one day, Voila. That's the ticket. Everyone comes to that understanding in their own good time. It'll happen much faster if one does not assume the adversarial role, because of pride.
    Glad you experienced that wonderful moment of 4D insight.
    SinceYouAsked likes this.
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    Well, cinci, I did warn you not to fall for the provocations of SYA, this website's Vincent Price...
    Quote Originally Posted by cincirob View Post
    cinci: The LTs don't enter into making a measurement.


    VeeDee: Wow!!! Cinci doesn't know the length contraction formula is derived from the Lorentz Transformations?
    Cinci, what are the LT for if they are not to find out the coordinates (=measurement) in another frame?


    cinci: Finding the coordinates in another frame does not = "making a measurement".
    ...but now you've fallen for the provocations of that sniggering Peter Lorre character, VeeDee. All we need now is Boris Karloff - yes that Boris Karloff!

    TFOLZO
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    Thank you for this opportunity, SpeedFreek...
    Quote Originally Posted by SpeedFreek View Post
    Explain the results of a muon experiment (such as Rossi-Hall), from the frame of the Muon, without a length contraction of the distance between the emitter and the detector.
    ...but I will post it on the Personal & Alternatives Forum lest I make you show not merely your index finger.

    TFOLZO
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  98. #98  
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    Quote Originally Posted by Gerry Nightingale View Post
    In reply to SpeedFreek, re: your post #80.

    Do you mean the "forum as whole" or just this thread? Or are you saying you just want "book-thumpers" on the entire site, people who never write anything except endless "quotes"

    from "Wiki" (knowing full well there is zero chance of being refuted, and thus not risking their "internet phys. sites" credibility)


    (Thanks for reading!)
    The rules for this site are pinned at the top of the "Announcements" forum.

    8. This forum is reserved for the discussion of established science only, and does not permit the posting of "personal theories", or of any material which is obviously in contradiction to current scientific consensus, into the main sections. Such posts will be moved to the "Personal Theories" subforum, or to the trash can. It is the responsibility of the moderator and administrator team to appropriately categorize forum posts.
    Special Relativity is "established science" and whilst it is fine to discuss the various aspects of the theory and to have questions about your understanding of the theory, if you think that you "could live another thousand years, and still never accept the posits that have come from "SR"", then if I were you I would steer clear of posting any of your views regarding this in any discussion that enters the domain of applicability of SR. This would mean discussions in the Special & General Relativity forum, and any other related discussions like those involving Quantum Electrodynamics, for instance.

    No we don't just want "book thumpers" on the site, but "book thumpers" don't just quote "wiki", they quote the standard texts on these subjects. Some members don't "book thump" at all, they work the mathematics up from the basic principles. Some members have never read a science text, but are just here to learn. But what they are here to learn is established science. This forum is not for people who want to argue against established science.
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    I agree Jilan...
    Quote Originally Posted by Jilan View Post
    Only Gerry can really say of course, but I have always taken it to be "physical reality".....
    ...but just this weekend I passed thru a place called Jilakin Rock - but I doubt that you have relatives living there merely because it has that name!

    TFOLZO
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    cinci: OK, back to basics. First, using the Earth is a poor choice because it isn't really inertial but it can be assumed to be inertial without introducing much error if the problem involves relativistic velocities and long distances. To eliminate confusion, I will discuss the three observer problem (two spaceships and a third observer) as being located in deep space (away from any significant gravitating source).

    All three elements (the two spaceships and the third observer) will be considered to be dimensionless points; this also introduces ignorable errors for large separations of the elements.


    Hard to believe a spaceship can be a dimensionless point, but I don't consider that to be a fundamental issue.

    First let's name the spaceships S1 and S2 and the observer is O. S! and S2 are on a straight line collision course; O is somewhere off that line.

    The occupy three points in space at any given instant.

    YOU chose an instant when O knows S1 and S2 are separated by a distance x.


    If S1 & S2 are on a collision course then they are not mutually at rest but approaching one another - but I will presume from what you say below that S1 & S2 are mutually at rest)!

    That statement implies that O has the ability to determine distance x and that he determined it as a distance that is stationary relative to O.

    In that case you have set up an entirely different situation. O is now at rest relative to one (or both) of the spaceships.

    This requires some technology: he could have beacons in space that he placed stationary to himself and can observe when the ships pass them by some means. Note, he may not be able to determine this at a given instant and may only know it some time after the ships pass the beacons but he can, with suitable technology determine that at a particular time on his clock, the spaceships were separated by a known distance x.

    Next, YOU chose to acknowledge that O could also determine the velocities of S1 and S2 when they were separated by the distance x. Also technologically possible.


    At the moment the velocity of one of the ships relative to O is zero!

    So now, YOU have specified that O knows a distance x, V1, and V2 and I have shown that he could technologically collect this data.

    Note, that none of this data is subject to relativistic effects as far as O is concerned. The First Postulate confirms this in that it says the laws of physics hold good in a frame where the mechanics hold and they hold in an inertial frame. So no contraction of x.

    S1 is also inertial. He can also make measurements. Since he is inertial, he cannot determine his own motion, but he can measure velocities relative to himself. So here is what he measured.

    He can measure the distance to S2 but he gets a value x1 which is different than x as measured by O.


    Are S1 & S2 mutually at rest or are they approaching on a collision course? Since if the latter is the case they will have to do their distance measurement simultaneously in order to get comparable answers!

    S2 gets a value for the distance to S1, let's call it x2.

    TFOLZO, let the question begin.


    At the moment I am presuming S1 & S2 are mutually at rest, therefore the distance between them will be uncontracted. This is also true for O since he too is at rest relative to the two spaceships. Therefore x1 & x2 will be of equal length - and since there is no velocity between S1, S2 & O (they are all mutually at rest) then SR does not so far come into the picture.

    But you'll have to forgive my suspicions as to what you're gonna come up with next as you start moving O, S1 & S2 relative to one another!

    TFOLZO
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