Is a length contraction just a visual thing?

Discussion in 'Pseudoscience' started by absolute-space, Feb 22, 2016.

  1. Q-reeus Valued Senior Member

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    2,605
    Having a bad spelling day, just like that poster I was referring to? Notice I ended with to, not too.
    It was actually referring to your buddy, and his false charge of 'never link anything from a text-book, but simply wiki only' as per a post on p16 in:
    http://www.sciforums.com/threads/gravity-waves-detected-for-the-first-time-ever.154848/
    Yet never once complained about your chronic use of and reliance on web references. Nice to have such selective and discrete buddies, huh.
    Decoded: You had not read it through nor grasped it's philosophy before posting. And think that 'validating length contraction' excuses the unnecessary baggage his approach introduces. As usual, ever so kind and gentle and understanding - toward yourself that is. Do carry on.
     
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  3. rpenner Fully Wired Staff Member

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    Definition of inertial frame of reference: All bodies in inertial motion describe linear relations in space-time coordinates.
    Definition of two bodies in same state of inertial motion: Relative to a third body or inertial coordinate system, they have the same velocity as a vector.
    Definition of length of a material body in a uniform state of inertial motion: The difference in position of its two ends as measured simultaneously.

    Thus we have for a body in a state of inertial motion described by velocity \(\vec{u}\) in a certain inertial coordinate system, the following linear relationship for it's endpoints A and B:

    \(\vec{x}_{A,1} - \vec{u} t_{A,1} = \vec{x}_{A,2} - \vec{u} t_{A,2} \\ \vec{x}_{B,3} - \vec{u} t_{B,3} = \vec{x}_{B,4} - \vec{u} t_{B,4} \)

    So for any given time, t, we have
    \(\vec{x}_A(t) = \vec{x}_{A,1} + \vec{u} \left( t - t_{A,1} \right) = \vec{x}_{A,2} + \vec{u} \left( t - t_{A,2} \right) \\ \vec{x}_B(t) = \vec{x}_{B,3} + \vec{u} \left( t - t_{B,3} \right) = \vec{x}_{B,4} + \vec{u} \left( t - t_{B,4} \right)\)

    So the length measured between comoving endpoints A and B at any one time is:
    \( L_{AB} = \left| \vec{x}_B(t) - \vec{x}_A(t) \right| = \left| ( \vec{x}_{B,3} - \vec{x}_{A,1} ) + \vec{u} \left( t_{A,1} - t_{B,3} \right) \right| = \left| ( \vec{x}_{B,3} - \vec{u} t_{B,3} ) - ( \vec{x}_{A,1} - \vec{u} t_{A,1} ) \right| \)

    We can simplify this somewhat if we use the property of real numbers that there is a zero, thus our coordinate system has an origin, even if this origin is purely a fiction of mathematical convenience.

    Then \(\vec{x}_{A,1} - \vec{u} t_{A,1} = \vec{x}_{A,2} - \vec{u} t_{A,2} = \vec{x}_{A,0} \\ \vec{x}_{B,3} - \vec{u} t_{B,3} = \vec{x}_{B,4} - \vec{u} t_{B,4} = \vec{x}_{B,0}\)
    For any given time, t, we have
    \(\vec{x}_A(t) = \vec{x}_{A,0} + \vec{u} t \\ \vec{x}_B(t) = \vec{x}_{B,0} + \vec{u} t\)
    And the length measured between comoving endpoints A and B at any one time is:
    \( L_{AB} = \left| \vec{x}_{B,0} - \vec{x}_{A,0} \right|\)

    So the question of this thread is what is the length of the same material body in a coordinate system where it is not moving.
    Newton and Special Relativity give different answers.

    For special relativity we can transform space-time points \(( \vec{x}_{A,1} , t_{A,1} ) , \; ( \vec{x}_{A,2} , t_{A,2} ) , \; ( \vec{x}_{B,3} , t_{B,3} ) , \; ( \vec{x}_{B,4} , t_{B,4} ) \) and recalculate the length in the new coordinates.

    \(\vec{x}' = \vec{x} + \frac{1 - \sqrt{1 - \frac{u^2}{c^2}}}{\sqrt{1 - \frac{u^2}{c^2}}} \frac{ ( \vec{x} \cdot \vec{u} ) \vec{u} }{ u^2 } - \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} \vec{u} t \\ t' = \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} \left( t - \frac{ \vec{x} \cdot \vec{u}}{c^2} \right) \)

    Using \(\vec{x}_{A,1} = \vec{x}_{A,0} + \vec{u} t_{A,1}\) we get this:
    \(\vec{x}'_{A,1} = \vec{x}_{A,0} + \vec{u} t_{A,1} + \frac{1 - \sqrt{1 - \frac{u^2}{c^2}}}{\sqrt{1 - \frac{u^2}{c^2}}} \frac{ ( \vec{x}_{A,0} \cdot \vec{u} ) \vec{u} }{ u^2 } + \frac{1 - \sqrt{1 - \frac{u^2}{c^2}}}{\sqrt{1 - \frac{u^2}{c^2}}} \frac{ ( \vec{u} t_{A,1} \cdot \vec{u} ) \vec{u} }{ u^2 } - \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} \vec{u} t_{A,1} \\ t'_{A,1} = \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} \left( t_{A,1} - \frac{ \vec{x}_{A,0} \cdot \vec{u}}{c^2} - \frac{ \vec{u} t_{A,1} \cdot \vec{u}}{c^2} \right) \)
    which simplifies to this:
    \(\vec{x}'_{A,1} = \vec{x}_{A,0} + \frac{1 - \sqrt{1 - \frac{u^2}{c^2}}}{\sqrt{1 - \frac{u^2}{c^2}}} \frac{ ( \vec{x}_{A,0} \cdot \vec{u} ) \vec{u} }{ u^2 } \\ t'_{A,1} = \sqrt{1 - \frac{u^2}{c^2}} t_{A,1} - \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} \frac{ \vec{x}_{A,0} \cdot \vec{u}}{c^2} \)
    Similarly, we have:
    \( \vec{x}'_{A,2} = \vec{x}_{A,0} + \frac{1 - \sqrt{1 - \frac{u^2}{c^2}}}{\sqrt{1 - \frac{u^2}{c^2}}} \frac{ ( \vec{x}_{A,0} \cdot \vec{u} ) \vec{u} }{ u^2 } \\ t'_{A,2} = \sqrt{1 - \frac{u^2}{c^2}} t_{A,2} - \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} \frac{ \vec{x}_{A,0} \cdot \vec{u}}{c^2} \\ \vec{x}'_{B,3} = \vec{x}_{B,0} + \frac{1 - \sqrt{1 - \frac{u^2}{c^2}}}{\sqrt{1 - \frac{u^2}{c^2}}} \frac{ ( \vec{x}_{B,0} \cdot \vec{u} ) \vec{u} }{ u^2 } \\ t'_{B,3} = \sqrt{1 - \frac{u^2}{c^2}} t_{B,3} - \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} \frac{ \vec{x}_{B,0} \cdot \vec{u}}{c^2} \\ \vec{x}'_{B,4} = \vec{x}_{B,0} + \frac{1 - \sqrt{1 - \frac{u^2}{c^2}}}{\sqrt{1 - \frac{u^2}{c^2}}} \frac{ ( \vec{x}_{B,0} \cdot \vec{u} ) \vec{u} }{ u^2 } \\ t'_{B,4} = \sqrt{1 - \frac{u^2}{c^2}} t_{B,4} - \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} \frac{ \vec{x}_{B,0} \cdot \vec{u}}{c^2} \)

    So \(\vec{x}'_{A,1} = \vec{x}'_{A,2} = \vec{x}'_{A,0}\) and \(\vec{x}'_{B,3} = \vec{x}'_{B,4} = \vec{x}'_{B,0}\)
    So \( L'_{AB} = \left| \vec{x}_{B,0} - \vec{x}_{A,0} + \frac{1 - \sqrt{1 - \frac{u^2}{c^2}}}{\sqrt{1 - \frac{u^2}{c^2}}} \frac{ \left( \left( \vec{x}_{B,0} - \vec{x}_{A,0} \right) \cdot \vec{u} \right) \vec{u} }{ u^2 } \right|\)

    So if \(\left( \vec{x}_{B,0} - \vec{x}_{A,0} \right) \cdot \vec{u} = 0\) then the motion was perpendicular to the length and there is no change in the length measured.
    But if the directions are parallel, the length measure in the coordinate system where the object is not moving is greater than in the coordinate system where the length was moving with velocity u.
    \( L'_{AB} = \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}} L_{AB} > L_{AB}\).

    So if you accept that the length of a moving object is a thing, then length contraction is real, not illusory, in special relativity.
     
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  5. exchemist Valued Senior Member

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    The first is a very ingenious scenario but I think the problem is that you cannot answer it using special relativity, because the train is accelerating (motion in a circle). My understanding is that Special Relativity only works in situations in which there is no acceleration. I think you need General Relativity to deal with your scenario (and please do not ask me how that works - as a chemist I can get my head round Special Relativity but tensor maths is not something I've ever learned.)

    The second, involving only linear motion, is easier. As I understand it, an observer on the "stationary" train will see the "speeding" one foreshortened, so that the when the fronts are aligned the rear of the "speeding" one is in front of the rear of the "stationary" one. An observer on the "speeding" one will the same thing applying to the "stationary" train, i.e. when the fronts are aligned the rear of the "stationary one is in front of that of the "speeding" one. Each sees the other foreshortened.

    In fact, the interesting thing about this is that the instant at which the ends are aligned appears to occur earlier than the instant when the fronts are aligned but each observer will see the end of the other train aligning earlier. I rather think this is an example of the "relativity of simultaneity", which no doubt you have encountered in your reading.

    But I'd be happy to have a real physicist take over the explanation as I'm far from expert on this subject.

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  7. paddoboy Valued Senior Member

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    Please Register or Log in to view the hidden image!

    Whatever.
    https://www.researchgate.net/profile/Dragan_Redzic
    Dragan Redzic
    University of Belgrade, Belgrade

    Electromagnetism, Theoretical Physics
     
    Last edited: Feb 23, 2016
  8. Q-reeus Valued Senior Member

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    Yes, basically declaring that you judged the article's worth based solely on it's author's formal credentials. Thing is there are lot's of fringe or at least less than ideal articles out there by 'mavericks' who are university affiliated with the same or similar credentials. So my point is - if you are capable of doing so, always judge by actual content not who wrote it.
     
    Last edited: Feb 23, 2016
  9. paddoboy Valued Senior Member

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    No basically declaring that I judged the paper as a arXiv scientific paper that has been reviewed along with the professionalism and author's formal credentials.
    Far better then some of the anti cosmology, SR/GR claims from various mavericks/turkey's that inhabit this site, I'm sure you'll agree..
     
  10. Q-reeus Valued Senior Member

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    2,605
    Ah yes, accepted by the Serbian Astronomical Journal. Which guarantees it's fitness as 'new understanding of longstanding SR puzzle'? So thinks the author of course.
    Oh hell yes. Very very yes!! We have in-principle common ground, but - no names!
     
  11. absolute-space Registered Member

    Messages:
    280
    The train in my example doe's start off stationary and is touching, front bumper to rear bumper, the full length of the circumference, the train is not really travelling a circle, the train wants travel a straight line, the rack redirects the train to travel a circle.


    The second example is much better and an easy experiment to perform.

    Align two lengths, on the front and rear of the trains align two sensors, when the front and the rear of the train align , the sensors detect each other and an alarm sounds. Move one of the trains up the track, then by the stationary train stands the observer, the moved train then returns to pass the stationary train and the observer who see's the moving train contract and observes the stationary train to remain its rest length, should hear the alarm sound if the length has not physically contracted.
     
    Last edited: Feb 23, 2016
  12. The God Valued Senior Member

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    3,546
    Measurement comes from observation and that is frame dependent. But what you are asking is whether a stick of length L really reduces physically ? But for that you have to answer with respect to what ? And you also have to understand that this L in which frame ? So that would involve your SR and almost all the posters are responding from this perspective. But the saner question which you should understand first is the distance between hydrogen atom electron and proton, would this contract ? Assuming that we don't get away with muddled up answer talking about uncertainty principle and electron cloud. In my opinion it will not, because this would involve work/energy which calculations do not consider. Length contraction and time dilation is necessary to keep SR postulate of constancy of light speef, but I don't think it is intuitively easier to appreciate...

    You may like that different frame with different relative speeds will give different values of contraction, so whom to believe ? but then that's relativity killing absoluteness......you are constantly monitoring a stick of length x in your house, it does not change but this x can be any value for a frame/person on aircraft / spacecrafts...So can you conclude anything from this ?
     
    Last edited: Feb 23, 2016
  13. absolute-space Registered Member

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    280
    You seem to have grasped what we are discussing, yes the question is does the ''rod'' physically contract relative to the observer who is experiencing the visual length contraction. I agree the question is unrelated to special relativity in the principle that we have to go deeper and look at the atomic bonds , whether or not the molecules can contract due to relative motion. Personally with kE gain from the moving ''rod'' and gravity ''drag'' , I would of thought the ''rod'' expanded by the work of the kE gain?
     
  14. Q-reeus Valued Senior Member

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    2,605
    Still have the totally wrong conceptual outlook. Some folks decry use of Wiki and Youtube but correctly used they can both be great resources. I suggest you run through the entries here:
    https://www.youtube.com/results?search_query=relativity of length contraction&spfreload=10
    And find the one that finally makes good intuitive sense. Everything exists within spacetime and is subject to it's transformation rules. No exceptions possible (leaving aside controversial issues like 'entanglement' that one or two here build so much into).
     
  15. absolute-space Registered Member

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    280
    My conceptual outlook is that length contraction is just a visual thing, related to the short length and stretched length of light from point A and point B of a ''rod'' in motion relative to to the observer. I have read several things and viewed several videos, people seem to be confused and mention the length of the actual ''rod'' contracts without any evidential merit. Some people say it does contract and some people say it does not contract, so please forgive the confusion, it is not I don't understand the concept, it is I don't understand who's answer is correct.
    You mention space-time, please describe in your own words.
     
  16. Q-reeus Valued Senior Member

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    2,605
    It's certainly not an optical illusion - though optical distortion is an added consideration when taking an actual 'snapshot' of a moving object.
    It's been explained to you that 'actually contracts' is in general a frame-dependent consideration. Rotating disk - Ehrenfest paradox - 'solidifies' that in the sense that effects of contraction (moving rim) are manifested in the non-rotating rest frame. Similarly with clocks - rotation destroys the symmetry applying to relative linear motion situations. Bottom line - relativistic length contraction is real but manifests somewhat differently depending on th specifics of a given scenario.
    Fundamental to any relativistic analysis is the concept of the invariant spacetime interval (you can search for that term). From that the special relativistic transformation laws follow. All experiments confirm that's how the world works.
    Look - these things ARE covered in various of those YT vids, with the added benefit of animated graphics to aid visualization. Go make a start there. A textbook would doubtless be too dry and formal. I will not be held responsible for any loony stuff present in that list - if an author claims SR is wrong, just avoid and choose another.
     
  17. absolute-space Registered Member

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    If it is not an optical illusion then please provide the experimental evidence that differs from the train sensor example?
     
  18. Q-reeus Valued Senior Member

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    2,605
    Please learn and apply something here in regards to decorum. If you wish to refer to something in a past post or thread - provide either the page & post # if in the current thread, or the entire link if in another. Otherwise you place an unreasonable burden on others to have to guess and go hunt for some vaguely described this or that.

    So anyway I wasted some time and it seems post #68 is what you meant, and in particular the latter example there of relative linear motion. Well the moving train certainly will appear contracted from the pov of stationary observer and train. Hence assuming sensors require simultaneous triggering for alarm to sound, it won't.

    Getting back to your circular track example, what happens is that at speed nose and tail of train no longer touch, the moving train having length contracted by the SR factor of sqrt(1-(v/c)^2) relative to the same train when at rest. In the real world centripetal forces and resulting strains vastly exceed such SR effects, but they are still there.
    Dealing peace-meal with such scenarios won't help overall if you continue to just raise one new specific example after another, hoping to 'trick' us into conceding. Go learn from those YT vids!
     
  19. absolute-space Registered Member

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    280
    I have read every single post from every poster in this thread, it is you that needs to learn some decorum, you obviously have not read the thread, the train sensor example was only a page or so back. It is not on me to keep repeating myself sir, it is on you to read the entire thread if you have interest in the discussion.
     
  20. Q-reeus Valued Senior Member

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    2,605
    Is that actually so? Well good luck on what will likely be a very long and painfully frustrating quest.
     
  21. Russ_Watters Not a Trump supporter... Valued Senior Member

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    Ding, ding.
     
  22. origin Trump is the best argument against a democracy. Valued Senior Member

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    You have been given ample evidence that you are incorrect. Apparently you do not like that concept of length contraction (and probably time dilation, no absolute motion, gravity waves, etc.). That is too bad, but the universe is really not concerned with what you want to be true. Your refusal to accept the evidence simply means that you are choosing to remain uneducated so you can hold on to your preconcieved notions of what you think should be. That seems so odd to me, but we have others here that are in your same boat, so at least you have company. [shrug]
     
  23. Russ_Watters Not a Trump supporter... Valued Senior Member

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    Given that you have been holding back here, why don't you tell us what you already know, to save us all some time. For example, do you know about muon decay observations? If not, Google it, read up on it and let us know how it works out for you.
     
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