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Length contraction of space with multiple reference frames

  1. Mar 7, 2013 #1
    My understanding is that as I move, from my FoR all objects and space itself (according to Einstein) contract along the direction of my movement. This length contraction occurs for all space and objects in front of me for an infinite distance. Furthermore, relative motion is relative, and the severity of a thing's contraction depends on its speed relative to me, or my speed relative to it. Same difference.

    Given all this, imagine that there are three objects in space: Me, Ball A, and Ball B. I am moving at .8c relative to Ball A, and .9c relative to Ball B. I understand that from my FoR, Ball B would be contracted than Ball A. What I'm having trouble understanding is how it would be possible for space to contract to two varying degrees from my FoR. I'm sure there's some error in my thought process here.

    Any help getting this straightened out is appreciated. Thank you!
  2. jcsd
  3. Mar 7, 2013 #2


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    Distance contraction is all about simultaneity. I'll get to that in a moment. From your point of view, there is no distance contraction. Any object is contracted in your rest frame according its motion in your rest frame. Distance contraction, from your rest frame, can be described as follows:

    - It two objects are moving at the same speed towards (or away) from you, but separated, you will measure the separation between them as less than either of them would measure it (and they would each measure it the same, since they are comoving).

    Now you introduce two objects moving at different speeds towards you (for example). Well, you measure some distance between them, at some time (simultaneity!) - their position at some same time per you. Each of them considers that you have compared their positions at different times; however they disagree with each other about how large the difference is. Let's say you make your measurement at the moment one of the passes you. Then you measure e.g. 1 meter between them. If each of them measures the distance between them at the simultaneity they ascribe to the passing event, then B will say it is longer than one meter, and A will say it is even longer. Each sees a different degree of 'error' in the way you have made the measurement.
    Last edited: Mar 7, 2013
  4. Mar 8, 2013 #3
    I see! I think... Here's the point I'm still confused about:

    I thought that distance contracted along with objects from my FoR. I'd love some more clarity on this, if possible.

    As for simultaneity, I think I have a good grasp on how it can lead to different observations from different reference frames without them contradicting each other. I think what I'm confused about here is the apparent contradiction from my own, single frame of reference. Or do I have multiple reference frames depending on what I measure my motion as relative to (e.g. I'm stationary relative to my desk right now, but moving at hundreds of miles per hour relative to a plane flying by)?

    I've attached little diagram that hopefully explains where my thinking is at. What I'm wondering in my picture if if the dotted lines representing the distance from the balls would be the same from my reference frame even though I am moving at different speeds relative to the different balls.

    Thanks for all of your help, PAllen.

    Attached Files:

  5. Mar 8, 2013 #4


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    You need to explain what 'contradiction' is bothering you. I have no idea what it is. FYI, in your diagram:

    - if you imagine that A and B are as pictured, then A, B, and you, all agree on the distance between A and B. (We can fix a common simultaneity for part of the scenario be imagining that A and B pass through a tissue wall at rest with respect to you, orthogonal to A and B motion; then you, A and B are all in agreement that the A crossing tissue is simultaneous with B crossing tissue. This is because this surface orthogonal to all relative motion).

    - As for distance between you and A, and you and B, all three disagree on both distances and simultaneity. The discrepancy in distance measures is coupled to the disagreement on simultaneity. Specifically, the point in your history you consider simultaneous with A/B tissue crossing is a completely different time in your history than what A thinks is simultaneous with tissue crossing; and both are different from the point in your history B thinks is simultaneous. Because of relative motion, this disagreement in which point in your history to measure to/from directly leads to 3 different measures of distance.
  6. Mar 8, 2013 #5
    The "contradiction" that I see is that the space/distance in front of me can be contracted to two different degrees simultaneously from my perspective, even though I only have one reference frame. Or can I have as many reference frames as objects that I am moving relative to, and they can all exist without contradiction because of the relativity of simultaneity? I think that's where I'm stuck.
    Last edited: Mar 8, 2013
  7. Mar 8, 2013 #6


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    Let go of thinking about space being contracted. Instead think about distance between comoving points contracted (an object being a collection of comoving points; a pair of stars also fits). Then, one collection of comoving points is contracted differently that a different collection, comoving differently. Nothing happens to space. And note that the contraction is relative to what the comoving points would measure as their mutual distances.

    You can use the muon example here, but lets make you a neutrino. Earth goes by at (c-ε), and its atmosphere seem 1" thick to you. Then, some other earth clone planet goes by at (c-4ε), and its atmosphere seems 2" thick to you.
  8. Mar 8, 2013 #7
    Is the following correct:

    Object A is at rest relative to me.

    If I accelerate towards A, distance between me and A contracts.

    If A accelerates towards me, distance between me and A does not contract.
  9. Mar 8, 2013 #8
    So the distance between comoving point contracts, which could be a single "object" composed of comoving particles, or an entire galaxy (which is, in a sense, one big object). Correct?

    I'm feeling pretty good about this, but I'm still wondering about whether or not I can have more than one reference frame. For example, in my attached diagram, would I have two reference frames (one for each ball) because I'm referencing two different objects with two different velocities? I hope I'm not getting lost in the weeds here.
  10. Mar 8, 2013 #9
    I'm going to take a shot at this and say "no." Wether you consider A as accelerating towards you vs you as accelerating towards A is an arbitrary distinction since motion is, by its nature, relative. That's why we call it "relative motion."
  11. Mar 8, 2013 #10


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    This is not correct. The error is hidden by saying that "motion" is relative. What is true is that speed is relative. Acceleration is not. The accelerating object will feel a 'force' while the non-accelerating object will not.
  12. Mar 8, 2013 #11
    Thanks for the correction. I'll get it one day :)

    So is jartsa correct?

    I'm also pasting my previous comment here so it doesn't get lost in the shuffle:

    Last edited: Mar 8, 2013
  13. Mar 8, 2013 #12


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    This is basically correct, and (depending on how you define your coordinates) can show up as A approaching you at faster than c in coordinate speed in the case where you accelerate towards A. No such thing would happen if A accelerates towards you. Note, that coordinate speed faster than c does not mean faster than light - in such an accelerated coordinate system light from A would travel towards towards you faster than c by a greater amount than A does.
  14. Mar 8, 2013 #13


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    You have only one rest frame. You 'exist' or are represented in all reference frames. In your diagram, you have one rest frame, A has one rest frame, and B has one rest frame. A and B are also 'in' your rest frame; you and A are also in B's rest frame; etc.
  15. Mar 10, 2013 #14
    The degree of contraction of the world outside your frame (of reference) depends on the effect of your time dilation, which depends on your speed relative to the universal fixed frame.[1] It’s your speed compared to light speed, v/c, that term that appears in the Lorentz factor, aka gamma, that modifies so many equations of physics for relativistic effects.
    Your speed is by choice, so there is no causative effect from the differences in your speed and that for A or B, otherwise you could manipulate the world. Your motion only affects your frame, so any change in the outside world is a change in your perception.
    Imagine the fixed frame has distance markers every light second (ls) and you are moving at .9c. On earth using t=x/v, you calculate a destination of 90 ls should take 100 sec. At arrival your clock reads 44 sec (time dilation). Since you cannot find fault with your clock or any time dependent devices, including your biological sense of time, you solve the issue by assuming your measured speed v is true, leaving distance x in your direction of motion, which must be contracted. The result is not a physical change in the outside world, but a physical change in the mind of the observer altering their perception.

    [1] Lack of detection does not imply non-existence.
    The MM experiment only demonstrated that the ‘ether of 1900” did not affect the results. If the particles of quantum physics had not existed, they could not have been discovered.
    New varieties of sea creatures have been discovered in the ocean depths.
  16. Mar 10, 2013 #15


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    I don't have the time to refute this point by point, but it is nearly all wrong and contrary to SR.

    Relativistic effects are caused by relative velocity between two FoR. It has nothing to do with 'physical changes in the mind of the observer'.

    There is no absolute velocity as you seem to be saying.
  17. Mar 13, 2013 #16
    Relativistic effects are caused by absolute velocities. The speed of light is
    an absolute value, therefore object speed relative to light speed is absolute.
    The problem is, an observer can't measure their speed relative to light,
    because they would have to move faster than light to detect the same
    signal they sent, so they do the next best thing, measure the round trip
    time. This relates to the note, that lack of detection does not imply
    non-existence. What an observer measures for relative motion is the relative
    differences in speed, time, length, etc. All measurements are made against a
    standard, but standards are defined.

    If the mind of the observer is not affected, why isn't he aware of his slow
    clock rate?

    If his perception isn't altered, what physical cause instantly produces a
    contracted world outside his frame?

    If a local experiment accelerated some particles to near light speed, literally
    contracting the universe, how could anyone outside the local frame perform
    an isolated experiment?

    One can always describe the physics for two moving observers A & B
    relative to a fixed frame, then remove the absolute variables, and describe
    the physics of A relative to B.

    SR is a theory of measurement, therefore it doesn't give explanations in
    terms of physical phenomena.
  18. Mar 13, 2013 #17


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    SR does not say that. In fact absolute velocity is a redundant concept. We only need *relative* velocity.

    Because it isn't slow. Relativistic effects happen in *other* frames.

    When measurements are translated between frames, moving rods have shorter lengths measured in stationary coordinates.

    I don't understand this.

    Only measurements show relativistic effects. There are no physical phenomena associated with them.
  19. Mar 13, 2013 #18
    Part of what you're implying is that measurements that involve relativistic effects are not *true* measurements, but that true measurements could be arrived at by subtracting or otherwise removing relativistic effects from the equation, so to speak.

    This is contrary to everything I've learned since joining these forums, and while I don't have the chops to dispute in a more technically, I believe it's erroneous.
  20. Mar 13, 2013 #19


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    This is not what I said. Do you understand 'change of coordinates' ?

    (I'm assuming this post is addressed to me.)
  21. Mar 13, 2013 #20
    Hi Mentz144. My post was addressed to phyti. Sorry for the mixup!
  22. Mar 13, 2013 #21
    If I find the relativistic effect that your clock is moving slower than mine, and you find the relativistic effect that my clock is moving slower than yours, then these are not "true" effects in the sense of being coordinate-independent or frame-independent. They are not like rest-mass is, the same for all observers.
  23. Mar 13, 2013 #22
    Right. I think for once I'm actually clear on all of this. I was just disputing phyti's post and trying to process what he was saying. Thanks for clarifying, though.
  24. Mar 13, 2013 #23


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    No worries.
  25. Mar 14, 2013 #24
    I share your concerns. I think SR presentations are incorrect insofar there is no such thing as physical objects shrinking down just because they are in motion in respect to yourself. The same for space in general: you cannot be in motion in respect to space unless one comes back to the concept of an absolute space.
    All this should be geared back to measurement protocols using a measuring device which propagates through open space at a finite speed in respect to you. Should you wish to measure the distance to a remote object, you won't have any choice but measuring the two-way travel time of – let's say – an electron. All things equal, the outcome of your measurement will vary depending on the relative speed of the object in respect to you, because the measurement protocol will take some time, thus the object will move (away from or toward you) during the process itself, so the distance to be covered by the electron will vary accordingly. However converting the measured duration into a distance to the object is not obvious and will require several hypotheses or postulates. This tricky problem vanishes thanks to the postulate of invariance of the speed of propagation of light: whatever the context, one can always assume this speed is equal to c. Thus, assuming one uses light rays instead of electrons, one can convert the measured duration into a distance.
    If a remote object is at rest in respect to you, you will be able to measure its length by difference of two distance measurements targeting each end of the object, assuming you use two-way light rays as a medium. But if the same object is in motion in respect to you, the same measurement protocol (all things equal) will deliver a different value, because light rays will have to cover a longer or shorter distance as compared to the static case: the outcome of the process in the dynamic case will be different from the length of the object. One may state that the object appears to have a different length, but this is misleading because the key events of both light rays (emission, reflection, reception) cannot be all synchronous: this cannot account for a measurement of the length of the object.
    The only possible rationale view is to admit that the measurement protocol based on two-way light rays will deliver the correct value for the length of the remote object in the static case, whereas it will deliver a biased value in the dynamic case. Nothing is shrinking down, neither physical objects nor space.
  26. Mar 14, 2013 #25


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    Then, imagine traveling along with muon created in the upper atmosphere by a cosmic ray. Its life time is two microseconds. The earth's atmosphere and the earth appear to be going by at near c. Only 600 meters of air can go by before the muon is likely to decay. Yet almost all muons make it to the ground. From a frame comoving with the muon, what explanation is there besides that the atmosphere is extremely compressed (many miles into 600 meters or so)?
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