Apparant 2 directions

Discussion in 'Pseudoscience' started by chinglu, Aug 13, 2013.

  1. chinglu Valued Senior Member

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    1,637
    Let's see, we are trying to understand why SR claims the one and only one SLW moves one direction from (0,yg,0) along the line yg and also moves two directions.

    You never explained this.
     
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  3. chinglu Valued Senior Member

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    Rpenner and AN.

    Although you both have proven you are very good at insulting people, you have both fallen way short on explaining why SR claims one SLW moves one direction from (0,yg,0) and also moves two directions from (0,yg,0).

    I am certainly prepared to handle this debate.

    So, please explain why this contradiction is consistent with nature.
     
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  5. chinglu Valued Senior Member

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    I want to make a proposal to RPenner and AN.

    We open up a thread in RPenner's forum and debate SR where no moderation is allowed.

    I say RPenner's forum AN because I believe as you are losing, you will close the thread if you have moderator status because of fragile ego.

    I'll take both of you on.

    Now, since you both believe you can defend SR against me, I am sure you will take this offer.

    The crowd watching will laugh at me since you both will win and I will be defeated. It will be very funny. AN everyone can see here your disgust of me and you also RPenner, so they know you will take this deal to settle the truth of SR once and for all. See if you are both correct, you will demonstrate your superior intellects.

    I am betting I will tear you both a new one.

    Prove your confidence in yourselves.
     
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  7. rpenner Fully Wired Valued Senior Member

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    I believe I did explain this. In 2011. See [post=2822356]post #11[/post], [post=2822529]post #15[/post], [post=2825893]post #56[/post], and [post=2826531]post #72[/post] of your [thread=110037]"SR is dead" thread[/thread]. See also [post=2791989]post #22[/post] and [post=2794693]post #154[/post] of your [thread=109190]"Special Relativity Is Refuted" thread[/thread]. (I referred to both threads earlier.) Algebraic geometry and multivariable calculus are things I've been able to do for decades. But earlier in this thread I wrote this (which you were unable to understand on your first reading):


    You can't just assert a person's math is wrong, you have to demonstrate it reliably. In 2011, you could not even be relied upon to adequately summarize my post.

    But just answer this one question -- if the wire is not radial with respect to the origin of the Spherical Light Wave (SLW), then how can you assert that the intersection of the light cone and a time-like plane (the worldsheet of the wire) is a SLW when this locus describes a hyperbola in space-time that corresponds to the illusion of a "dot" of light that moves everywhere faster than light? It's not a thing, like a photon or a rubber ball, it's a projection of light against a surface like a spot of illumination from a lighthouse and is not constrained to obey the laws of physical things. The geometric interpretation as a locus of points that form a hyperbola in space-time combines with the hyperbolic rotation of Lorentz transformations in a very natural way. (Even in Euclidean geometry one learns that a plane may intersect a cone to form a hyperbola.)

    You are welcome.
    I try.

    Correcting you and reminding you of history is not necessarily an insult. Do you have a specific complaint? Neither one of us are making (fallacious) ad hominem arguments that because you are stupid your arguments are flawed, we are saying that your assertions and arguments are so flawed that it makes you look stupid. Amicus AlphaNumeric, sed magis amica veritas. And likewise, no one knows why you think Andrew Banks seems persuasive because those that can do calculus, geometry and algebra are not impressed. The truth would make a better friend for you than Andrew Banks.

    And you lack many good qualities in a student. For example if you don't understand something you should ask questions instead of repeating unreliable assertions. We could have settled this in 2011 if you were a better student of physics, math or logic.

    Evidence has shown that you are incapable of following a logical argument in English or a mathematical argument in multivariable calculus. Evidence has shown that you make empty assertions and declare victory. Neither is a good sign when entering a debate.

    Simply put, you have confounded a beautiful and precise model of nature with your own mistaken preconceptions of what nature should say. And when they necessarily conflict, you blame not your own mistake but the model that you have never bothered to understand properly. You even make the basic mistake of assuming a "place" in one coordinate frame is also a "place" in a relatively moving coordinate frame, which wasn't even true in Galilean Relativity.

    A debate is of no value unless both participants value the decision of the judge. You propose no judge, no prize, and no topic of debate.

    Special Relativity is 108 years old and rests on the success of the principle of relativity (circa 1600) and success of Maxwell's theory of electromagnetism (1865). Since then, there has been thousands of new experiments that confirm that the geometry of the universe is very closely approximated by a manifold experimentally indistinguishable from a locally-Lorentz-invariant manifold. You misunderstand the Sagnac effect (which is about a rotating ring inferometer, and since it is rotating it is non-inertial) which is compatible with special relativity.

    http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Sagnac
    http://mathpages.com/rr/s2-07/2-07.htm
    http://mathpages.com/home/kmath169/kmath169.htm

    Because you have raised this issue some 99 years later, I don't trust your ability to read and understand the material. Also, you have the abhorrent habit of quoting an entire post without correcting defects caused by the quoting mechanism or responding to the entire post. Therefore I have no reason to undo your ban from physforums.com from Dec 26 2010.

    An alternate suggestion is that you issue a formal "Proposal" with mutually agreed upon rules and a single limited topic of debate. This is the purpose of the forum "Formal Debates" here on this site. You may even mutually agree on a procedure to elect a judge. One such proposal is that you each volunteer an associate and the two associates decide upon a judge. Most judges of good reputation will not work for free. You might each advance $5000 and the judge will keep 1/2 the money and split the remainder between the participants in proportion to their success. If you have no such funds, you might challenge AlphaNumeric to a 30-day-ban from the site. In such a case Tiassa and James R are the only viable candidates for judges. Details like a posting schedule, who goes first, and other rules would have to be mutually agreed on in the "Proposal" thread before the "Debate" thread in the same forum can begin.

    You have bizarre preconceptions.
     
  8. AlphaNumeric Fully ionized Registered Senior Member

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    6,702
    Why don't you just start a thread in this subforum, where I have no moderator access? Besides, in the past where you and I have 'discussed' things the discussions have often lasted pages and pages. Closures have only occurred in instances where you repeat claims already addressed and/or refuse to answer direct relevant questions, both actions being trolling.

    Firstly I know I can defend SR from you, as I (and Rpenner) have done so in the many many threads like this in the past. Secondly knowing I can best you does not necessarily imply I'll take you up on the offer. Firstly I see nothing new from you, you're just rehashing claims previously shredded by Rpenner and I. Secondly I have seen no indication you're capable of having an informed discussion about relativity since I see no evidence you understand it or can do even the necessary high school level algebra. Thirdly you assume I'm so insecure that I simply most respond to each and every challenge. Fourthly you think that I have nothing else to do with my time.

    I'm happy for Rpenner to paste you, if he so desires. Personally I don't think you're worth the time. In the past I might have had more free time I was willing to waste on you but things are different now, real life responsibilities and circumstances and all that. If I thought you capable of having an informed discussion about SR I'd not have banned you from posting threads in the main forum. I see nothing to alter that decision. If you think you have a true disproof why are you wasting time here? Why aren't you and Mr Banks sending your work to journals? We all know why, they'll laugh the BS out of your ears.

    If you were anything other than an ignorant troll, if there were anything to your claims, you'd have accomplished something by now. How many years you been claiming to have disproven various things? At least the 3 or 4 I've known you.

    I find wilful ignorance and dishonesty disgusting yes. You've been whining about relativity or set theory for years yet you cannot do either one of them. In the years since you and I first crossed paths you could have learnt a lot and put that knowledge to use somehow. Instead you have learnt nothing and continue to learn nothing, despite each and every time getting schooled by someone on the forum.

    Except we've been round this way before. You make a claim, we crush it, you slink off and then return a few months later and we do it all again. Why didn't the last time "settle the truth of SR once and for all"? Or the time before that? Or the time before that? You're a blatant liar, either to yourself if you think you'll really stop after this next time, or to us for saying you will when you won't. That's part of the reason you're not worth the time, you're just pathetic.

    Like we did the last time? And the previous time? And the time before that? Remember, I even typed up a pdf document which went through the explicit example you gave, as well as completely generalising it, to show the depth of your mistake. I'm sure I can go dig it out if you want reminding. Funny how you didn't consider "the truth of SR settled once and for all" back then. If I remember correctly it was about 2 years ago and yet here we are again.

    You've lost that bet every time before.

    We have done. And unlike you I am a professional mathematician so I get paid for being good at it. If you're so confident send your work to a journal. After all if you're right and you're going to beat us why not just save us all some time and go straight to the people who can get your work to the community at large? Because you know you're a hack.

    You know you'll fail peer review and so the best way you can delude yourself into thinking you're competent is to talk smack on a forum, despite each and every time you do it you get your backside handed to you. If anyone wants to see the depths of your delusion and ignorance they need only check your post history. Beyond that a 'debate' with you is not worth my time.
     
  9. Aqueous Id flat Earth skeptic Valued Senior Member

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    I resolved to putting the hardcore cranks on ignore, which still leaves their quoted content visible. Thus I can engage certain questions without being bothered by the useless responses. In this case, the only serious challenge to one's lifelong beliefs is rehabilitating the incorrigible addicts of pseudoscience to the point that they can make sense of a meaningful answer. There never is true dialog in this, but it gives us new ways to says things, and it can be a good workout too. (I would take exception to the use of 'beliefs' as this blurs the distinction between belief and knowledge.)

    Questions of this sort always begin: Assume what is true to be false. Now from this we can prove the following paradoxes (etc.) from which the logical conclusion is that science is broken. Of course the answer from the get-go is the premise was false. Trolls pretending to be mere cranks love to engage thoughtful people this way . . . or should I say bait and switch.

    Questions of this sort are never about the purported topic - such a relativity or aether. Instead they are always about the middle school material in Geometry which covered theorems and proofs. The crank has no idea what a syllogism is, whereas the troll knows but pretends not to. Both prefer to invert this (like on the planet Bizarro where everything is done backwards) giving nothing but invalid logic while claiming that the valid logic of science is false.

    As for protecting life-learned values: I personally think you would not encounter much of that if it were not for the perennial anti-science campaign waged by the churches. There really is no distinction between them and this once you remove the religious content. The only sense of moral indignation that I know of among scientists is due to the fear and loathing of people who have no business meddling in policies that affect scientific progress, education and society. Math and science folks are quick to square off to any problem and recommend a course of corrective action when one is available. Here it's quite simple - just remove the pretense of legitimacy from the crank that claims it. If there is any time-honored value in science, it's honesty. We can't get there by accepting mangled syllogisms, inverted logic and pretense of being scientific.
     
  10. chinglu Valued Senior Member

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    1,637
    I'm sorry, I am not seeing any evidence that you explained how one SLW moves two different directions from unprimed (0,y,0).

    Why not provide a simple coherent answer to that.
     
  11. chinglu Valued Senior Member

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    Well, let's see.

    You have not provided a simple answer as to why one SLW moves two different directions from unprimed (0,y,0).

    Why not start with that.
     
  12. chinglu Valued Senior Member

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    1,637
    Feel free.
    Explain how one SLW moves two different directions from unprimed (0,y,0).

    That way, your opinion has value.
     
  13. Lakon Valued Senior Member

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    Ahh ..

    http://www.etymonline.com/index.php?allowed_in_frame=0&search=science&searchmode=none


    science (n.)

    c.1300, "knowledge (of something) acquired by study," also "a particular branch of knowledge," from Old French science, from Latin scientia "knowledge," from sciens (genitive scientis), present participle of scire "to know," probably originally "to separate one thing from another, to distinguish," related to scindere "to cut, divide," from PIE root *skei- (cf. Greek skhizein "to split, rend, cleave," Gothic skaidan, Old English sceadan "to divide, separate;" see shed (v.)).
    Science, since people must do it, is a socially embedded activity. It progresses by hunch, vision, and intuition. Much of its change through time does not record a closer approach to absolute truth, but the alteration of cultural contexts that influence it so strongly. Facts are not pure and unsullied bits of information; culture also influences what we see and how we see it. Theories, moreover, are not inexorable inductions from facts. The most creative theories are often imaginative visions imposed upon facts; the source of imagination is also strongly cultural. [Stephen Jay Gould, introduction to "The Mismeasure of Man," 1981]
    Modern sense of "non-arts studies" is attested from 1670s. The distinction is commonly understood as between theoretical truth (Greek episteme) and methods for effecting practical results (tekhne), but science sometimes is used for practical applications and art for applications of skill. Main modern (restricted) sense of "body of regular or methodical observations or propositions ... concerning any subject or speculation" is attested from 1725; in 17c.-18c. this concept commonly was called philosophy. To blind (someone) with science "confuse by the use of big words or complex explanations" is attested from 1937, originally noted as a phrase from Australia and New Zealand.
     
  14. Lakon Valued Senior Member

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    I like the way in which you reduce the issue to one succinct point in your last three posts.
     
  15. rpenner Fully Wired Valued Senior Member

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    Then you fail again.
    It's not a coherent request for the two reasons I outlined for you.
    1) Just because you call the intersection of an expanding light cone and a non-radial wire a "Spherical Light Wave" doesn't mean that the spot of light shares any property with a SLW. It's not spherical, it doesn't have fixed speed, it isn't spherical. It's the intersection of a future-facing light cone with a planar worldsheet, and thus is a space-time hyperbola. All its properties including transformation under a Lorentz transform with a velocity parameter parallel to the sheet follow from this correct description.
    2) A "place" in one frame is not a "place" in the other frame because the two frames have relative motion.

    Repetition without the slightest good faith effort to actually read and understand the required material (in this case the conversation) is why chinglu's denialism is trolling. Both the above points I already pointed out in the previous post and chinglu didn't make the slightest acknowledgement that those basic facts rob his repeated point of any meaning.

     
  16. Aqueous Id flat Earth skeptic Valued Senior Member

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    esp. actual knowledge of science

    esp. separation of the wheat from the chaff.

    as opposed to pseudoscience which returns to older cultural contexts long since obsolete.

    While pseudoscience merely turns away from facts and lives in fiction.

    At the time he felt marginalized. But I wonder how he grew to measure his own theories by this standard?

    Both art and science utilize skill. Pseudoscience is the lack of skill parading as talent. I can't think of a parallel in the fine arts, since it invokes unlikely scenarios such as a tone-deaf person with no training in musicology, drama or literature posing as a critic of opera.

    Pseudoscience strays even from this into the boondocks of wild speculation. But it's also fraudulent.

    Pseudoscience is the false pretense of blinding the naive with science, whereas both perpetrator and victim have only been blinded by nonsense.
     
  17. Lakon Valued Senior Member

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    1,117
    esp. separation of the wheat from the chaff.

    Following upon your metaphor, both wheat and chaff have purpose, nor can wheat exist without chaff.

    I won't detract any further from the OP along these lines. Perhaps the issues you raised (which admittedly, you could justifiably say you did raise because of my initial comment) would make interesting material for another thread.

    Please feel free to make a final comment. I'm keen to see chinglu's responses to the recent posts by rpenner, etc.
     
  18. Lakon Valued Senior Member

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    chinglu ?

    Fight or flight ???
     
  19. rpenner Fully Wired Valued Senior Member

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    A space-time hyperbola, hurrah!

    Flat space-time is modeled as vector space with a Lorentzian inner product.

    In flat, space-time with two or more dimensions of space, let us have events O, A, B, C such that A and B are space-like separated, A and C are time-like separated with C in A's future, O is not in the plane given by A, B and C.

    Let us have the space-time metric with (-,+,+,+) conventions. Then it follows that \(\left< (C - A), (C - A ) \right> \lt 0 \lt \left< (B - A), (B - A ) \right>\).

    Then it follows that every event U in the plane ABC is specified by two real numbers r and s, such that \(U - A = r ( B - A ) + s ( C - A )\). Likewise any two real numbers r and s specify a event in the plane ABC.

    The event, O specifies uniquely a light cone which is open in the future direction. All events, V, of the light cone satisfy both \(\left< ( V - O ) , ( V - O ) \right> = 0\) and \(\left< ( V - O ) , ( C - A ) \right> \leq 0\).

    Thus it follows that for every value of r, there is one value of s that such that \(A + r ( B - A ) + s ( C - A )\) is both a U-event in the plane ABC and a V-event in the future-facing light-cone of O. Writing \(s = f(r)\) is justified.

    Same as before, now with four Cartesian coordinates.

    Our conditions are now:

    \( c^2 ( t_B - t_A )^2 < ( x_B - x_A )^2 + ( y_B - y_A )^2 + ( z_B - z_A )^2 t_C > t_A c^2 ( t_C - t_A )^2 > ( x_C - x_A )^2 + ( y_C - y_A )^2 + ( z_C - z_A )^2 \mathcal{U} = \left{ U \quad | \quad \exists r, s \in \mathbb{R} \quad t_U = t_A + r ( t_B - t_A ) + s ( t_C - t_A ) \quad \textrm{and} \quad x_U = x_A + r ( x_B - x_A ) + s ( x_C - z_A ) \quad \textrm{and} \quad y_U = y_A + r ( y_B - y_A ) + s ( y_C - y_A ) \quad \textrm{and} \quad z_U = z_A + r ( z_B - z_A ) + s ( z_C - z_A ) \right} \mathcal{V} = \left{ V \quad | \quad c^2 ( t_V - t_O )^2 = ( x_V - x_O )^2 + ( y_V - y_O )^2 + ( z_V - z_O )^2 \quad \textrm{and} \quad c^2 ( t_V - t_O )(t_C - t_A) >= ( x_V - x_O )( x_C - x_A ) + ( y_V - y_O ) ( y_C - y_A ) + ( z_V - z_O )( z_C - z_A ) \right} O \not \in \mathcal{U}\)

    Thus it follows that \(\mathcal{H} = \mathcal{U} \cap \mathcal{V}\) is a non-empty set and I wish to prove that
    \(\forall r \exists ! s = f(r) \quad H = A + r ( B - A ) + s ( C - A ) \in ( \mathcal{U} \cap \mathcal{V} )\)

    It follows that
    \( s = f(r) t_H - t_O = (t_A - t_O ) + r ( t_B - t_A ) + f(r) ( t_C - t_A ) x_H - x_O = (x_A - x_O ) + r ( x_B - x_A ) + f(r) ( x_C - z_A ) y_H - y_O = (y_A - y_O ) + r ( y_B - y_A ) + f(r) ( y_C - y_A ) z_H - z_O = (z_A - z_O ) + r ( z_B - z_A ) + f(r) ( z_C - z_A ) c^2 ( t_H - t_O )(t_C - t_A) \geq ( x_H - x_O )( x_C - x_A ) + ( y_H - y_O ) ( y_C - y_A ) + ( z_H - z_O )( z_C - z_A ) c^2 ( t_H - t_O )^2 = ( x_H - x_O )^2 + ( y_H - y_O )^2 + ( z_H - z_O )^2 \)

    with solution:

    \( \left< C -A , C -A \right> = -c^2 (t_C-t_A)^2+(x_C-x_A)^2+(y_C-y_A)^2+(z_C-z_A)^2 \left< (1-r)A + rB - O, C -A \right> = -c^2 ((1 - r) t_A + r t_B - t_O)(t_C-t_A) + ((1 - r) x_A + r x_B - x_O)(x_C-x_A) + ((1 - r) y_A + r y_B - y_O)(y_C-y_A) + ((1 - r) z_A + r z_B - z_O)(z_C-z_A) \left< (1-r)A + rB - O, (1-r)A + rB - O \right> = -c^2 ((1 - r) t_A + r t_B - t_O)^2 + ((1 - r) x_A + r x_B - x_O)^2 + ((1 - r) y_A + r y_B - y_O)^2 + ((1 - r) z_A + r z_B - z_O)^2 s = f(r) = \frac{ \left< (1-r)A + rB - O, C -A \right> - \sqrt{ \left( \left< (1-r)A + rB - O, C -A \right> \right)^2 - \left< (1-r)A + rB - O, (1-r)A + rB - O \right> \left< C -A , C -A \right>}}{ \left< C -A , C -A \right> }\)

    With regards to the Lorentz transform

    Since the Lorentz transforms is linear, a given event in \(\mathcal{U}\) has the same linear relation to A, B, C, r and s. Since the Lorentz transform preserves the inner product, it follows that the events in \(\mathcal{V}\) has the same relationship with O and since the relation f(r) is entirely in terms of the inner product, it follows that the same hyperbola of events is described in any Lorentz-boosted frame. Thus what we are doing in algebra is legitimate geometry.

    A numeric example

    In units of seconds and light-seconds (where c=1), let us have the following coordinates in (t,x,y,z) order:
    O: (0,0,0,0)
    A: (0,0,1,0)
    B: (0,1,1,0)
    C: (1,0,1,0)
    \(\mathcal{U} = \left{ (t,x,y,z) \quad | \quad \exists r, s \in \mathbb{R} \quad (t,x,y,z) = (s,r,1,0) \right} \mathcal{V} = \left{ (t,x,y,z) \quad | \quad t = \sqrt{x^2 + y^2 + z^2} \right} \left< C -A , C -A \right> = -1 \left< (1-r)A + rB - O, C -A \right> = 0 \left< (1-r)A + rB - O, (1-r)A + rB - O \right> = 1 + r^2 s = f(r) = \sqrt{1 + r^2} \mathcal{H} = \mathcal{U} \cap \mathcal{V} = \left{ (t,x,y,z) \quad | \quad \exists r \in \mathbb{R} \quad (t,x,y,z) = (\sqrt{1 + r^2},r,1,0) \right} \)
    This is a hyperbola with \(\left( \frac{\partial x}{\partial t} \right)^2 = \left(\frac{t}{x} \right)^2 = \left( \frac{\sqrt{1 + r^2}}{r} \right)^2 = 1 + \frac{1}{r^2} > 1 = c\) thus if interpreted as a world-line this one-dimensional locus of events represents a point of light instantaneously splitting into two points moving away everywhere faster than the speed of light. This is generally true regardless of the numerical values plugged in provided they correspond to the requirements at the top of this post.

    The trick introduced by Andrew Banks is to artificially constrain the "wire" with the worldsheet \(\mathcal{U}\) so that in one particular frame only half of the hyperbola is seen. Since a Lorentz boost is a hyperbolic rotation that "rotates" one description of the hyperbola into another, with the net effect that the "hidden" half becomes visible. This is not mysterious, but is in fact required for relativity to be self-consistent.



    Transforming the Hyperbola

    Let \(\Lambda = \begin{pmatrix} \cosh \rho & \sinh \rho & 0 & 0 \\ \sinh \rho & \cosh \rho & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} \) be our Lorentz transform.

    Then in terms of (t', x', y', z') we have the following:
    \(O: (0,0,0,0) A: (0,0,1,0) B: (\sinh \rho,\cosh \rho,1,0) C: (\cosh \rho, \sinh \rho ,1,0) \mathcal{U} = \left{ (t',x',y',z') \quad | \quad \exists r, s \in \mathbb{R} \quad (t,x,y,z) = (s \cosh \rho + r \sinh \rho ,r \cosh \rho + s \sinh \rho,1,0) \right} \mathcal{V} = \left{ (t',x',y',z') \quad | \quad t' = \sqrt{x'^2 + y'^2 + z'^2} \right} \left< C -A , C -A \right> = \sinh^2 \rho - \cosh^2 \rho = -1 \left< (1-r)A + rB - O, C -A \right> = - r \sinh \rho \cosh \rho + r \cosh \rho \sinh \rho = 0 \left< (1-r)A + rB - O, (1-r)A + rB - O \right> = -r^2 \sinh^2 \rho + r^2 \cosh^2 \rho + 1 = 1 + r^2 s = f(r) = \sqrt{1 + r^2} \mathcal{H} = \mathcal{U} \cap \mathcal{V} = \left{ (t',x',y',z') \quad | \quad \exists r \in \mathbb{R} \quad (t',x',y',z') = (\sqrt{1 + r^2} \cosh \rho + r \sinh \rho,r \cosh \rho + \sqrt{1 + r^2} \sinh \rho,1,0) \right} \)

    All self-consistent.
     
  20. Lakon Valued Senior Member

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    I knew all that .. heh ..
     
  21. AlphaNumeric Fully ionized Registered Senior Member

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    You have yet to do as I asked, namely go through the actual calculations and showing the contradiction you claim exists. No arm waving, no simply repeating assertions, show you can do the relevant Lorentz transformations. If you're unable to do that then you have failed to make your case such a contradiction exists. Furthermore, given your past history, if you cannot demonstrate to a reasonable satisfaction that you're even able to understand the mathematical models involved in any discussion of said scenario then I see no reason to engage in discussion with you. Why should Rpenner or I spent time typing out LaTeX code to go through explicit calculations when all evidence points to you being too ignorant of mathematics and relativity to understand what we type.

    Do the calculations explicitly else I'll assume, based on a mountain of evidence from previous discussions, you are too ignorant to be able to engage in the discussion you ask of us. Go on, step up or shove off.
     
  22. Lakon Valued Senior Member

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    Pot .. kettle ..
     
  23. Lakon Valued Senior Member

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    Withdrawn.
     
    Last edited: Aug 24, 2013

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