On the Definition of an Inertial Frame of Reference

Discussion in 'Pseudoscience Archive' started by Eugene Shubert, Oct 15, 2010.

  1. AlphaNumeric Fully ionized Registered Senior Member

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    Wow, talk about putting your foot in it further!

    \(JJ^T=I\) would imply J is an element of O(N) for the appropriate N, which isn't required. Jacobians don't need to satisfy that, that's just a nice case. The Lorentz transforms don't satisfy that, as they are defined by a metric \(\eta\) invariance. If you were working in complex coordinates than J wouldn't be automatically real but the transformation could still be valid.

    Tach you just keep digging yourself deeper and deeper. Why don't you quit while you're.... well you're not 'ahead' but before you make even more of a fool of yourself, though that'll be hard to manage.

    Who are you trying to convince here? Unlike yourself Guest and przyk clearly paid attention in their courses on vector calculus. You obviously didn't.

    So when you assert something we can see to be utterly false we should let it slide? If you can't accept correction then you move even further into the crank territory Eugene lives in. Guest was right, you're projecting your own faults onto other people. No one here thinks Eugene has a physically viable model but that doesn't mean all your criticisms of him are accurate. We can correct you and still not agree with Eugene, despite you clearly thinking otherwise.
     
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  3. Tach Banned Banned

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    That would have been true if \(S_j=S_j(x,t)\) not for \(S_j=S_j(x-kvt-S_i(x))\).Since this is not the case, you need to pay attention before you start gloating.

    Can you get lamer than that? Sour grapes for being shown wrong?


    I posted a paper for you about inertial frames in flat spacetime. You obviously did not study it. I suggest that you do.
     
    Last edited: Nov 4, 2010
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  5. Tach Banned Banned

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    Yes, they do. I gave you the exact page in the book. The best thing would be for you guys to read the whole chapter 33.

    I don't understand why you insist in claiming something that is so easily proven to be false.You can try the same exercise I gave przyk. He's still sulking about it.
     
    Last edited: Nov 4, 2010
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  7. Tach Banned Banned

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    Let's try something different. Let's see which one of you three (przyk, Guest254, Alphanumeric) manages to be the first one who:

    - derives the speed composition law in Shubert theory

    - proves that it is falsified by experiment (you will have to figure the experiment by yourselves, it is a well-known one, no need to invent anything)

    You can work together on this one if you wish.
     
    Last edited: Nov 4, 2010
  8. AlphaNumeric Fully ionized Registered Senior Member

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    6,702
    I gave you an example, complex coordinate transformations wouldn't always give Jacobians which are elements of the O(N) group.

    But the Lorentz transforms also are a counter example. As I explained to you earlier in the thread they are a special kind of coordinate transformation in that they can be written as a matrix operating on the original coordinates, ie \((x')^{\mu} = \Lambda^{\mu}_{\nu}x^{\nu}\), something which say the transformation from Cartesians to polars can't be expressed as. This means that you get the simple expression for the Jacobian, \(J^{\mu}_{\nu} = \frac{\partial (x')^{\mu}}{\partial x^{\nu}} = \Lambda^{\mu}_{\nu}\). Thus your claim that \(JJ^{\top} = I\) would mean that \(\Lambda \Lambda^{\top} = I\), which isn't the case. The expression \(JJ^{\top} = I\) can be viewed in terms of the Euclidean metric, ie \(J\cdot \delta \cdot J^{\top} = \delta\), ie J preserves the Euclidean metric. Thus your claim implies the Lorentz transforms should preserve the Euclidean metric, they don't.

    If you think this is wrong please explain where I've made a mistake, don't just say "Read that book", because the issue is that you haven't understood the book in question. If I'm wrong you should have no problem explaining where.

    I was just thinking the same thing about you.

    Again, who are you trying to convince here? It seems the only person you're convincing is yourself.

    This is utterly beside the point I'm making. I don't think Eugene is onto anything, no one here is defending him. I'm replying to things you have said which are false. Demonstrably false (as I have just done). Like I said before, should we just ignore it when you say something we know to be false? You clearly have no problem making comments when you think someone has made a mistake, yet you don't want to discuss it when someone notices you have made a mistake.
     
  9. Guest254 Valued Senior Member

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    I simply don't understand how you can't get this. If x' is a function of (x,t) (let's say x'=f(x,t), so it's super clear for you) then how can you not understand that S(x')=S(f(x,t)) is a function of x and t? Seriously - which bit of this is even remotely complicated!?

    You're right - that was a little mean. Friends?

    Is this your way of evading.... again!

    Go on, you know you want to... just compute the Jacobian of the map (x,y)->(Rcos t, Rsin t).
     
  10. dhcracker Registered Senior Member

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    I feel like I just stumbled into a prize fight or something... a debate of real math not just ideas and concepts wow!

    Makes me want to start taking bets.. I give 2 to 1 odds on AN who wants a piece of the action!
     
  11. przyk squishy Valued Senior Member

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    They're not always null. You've had that explained to you multiple times as well.

    Which says absolutely nothing about noninertial coordinate systems in flat spacetime.

    Another hasty retreat?
     
  12. Tach Banned Banned

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    You still refuse to read the paper I linked in. Tough.

    Let's try again: The Shubert formalism is all about inertial frames. You talk about something that you have obviously not read.
     
  13. AlphaNumeric Fully ionized Registered Senior Member

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    That implies Tach is still on his feet. przyk, Guest, Prom and I have already pointed out his mistake about Christofell symbols and no matter how much Tach tries to claim he said something else the posts are there for people to read. Now Guest and I have both given coordinate transformations which have Jacobians which don't satisfy \(JJ^{\top}=1\). If Tach comes back with "Read that book I said" then I would have to question whether he can even do basic calculus as its 5 seconds of work to compute the Jacobians for \((x,y) = (R\cos t,R\sin t)\) and \((x')^{\mu} = \Lambda^{\mu}_{\nu}x^{\nu}\) and both of them contradict his claims. Presently I'm hoping he just didn't read the whole of my post he last replied to, because I did mention Lorentz transforms there. Then he'd just be apathetic rather than unable to work out the Jacobian for a Lorentz transformation, which is mind blowingly easy, as my last post demonstrates.
     
  14. Tach Banned Banned

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    I am getting tired of you guys masturbating the null Christoffel symbols , to the curved spacetime which is really flat in Shubert's formalism and to the non-inertial frames that are really inertial in his formalism so I decided to give you a little practical challenge.

    Good, so you would not have any qualms in solving the little challenge I posted. The computations are really easy, it should take you no more that three lines and 5 minutes. If it takes you more than that, then you are doing something really wrong. Come on, which one of you is going to be the first to solve it?
     
  15. AlphaNumeric Fully ionized Registered Senior Member

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    6,702
    Tach, why did you reply to the second half of my post but not the first half? Why did you skip over the part where I explicitly demonstrated you were incorrect. Do you think no one would notice?
     
  16. Tach Banned Banned

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    I replied, let's try again:

    "I am getting tired of you guys masturbating the null Christoffel symbols , to the curved spacetime which is really flat in Shubert's formalism and to the non-inertial frames that are really inertial in his formalism so I decided to give you a little practical challenge. "

    So, why don't you spend your time working on my challenge? you should have had the answer by now.
     
  17. przyk squishy Valued Senior Member

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    Does it prove that the Christoffel symbols are always null even in noninertial coordinate systems in flat spacetime? Didn't think so.

    I've already told Eugene that his coordinates are, by definition, not inertial.


    Still nothing to say about your problem with variable substitution?
     
  18. Tach Banned Banned

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    Sure, you can come up with a lot of transforms that do not satisfy the conditions metric invariance but these are not the ones that I was referring to. Can you stop writing this type of nonsense and start working on the practical challenge? Just for 5 minutes? You should have had the solution in less than half the time to write the latex for the above.
     
  19. Tach Banned Banned

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    Are you daft? It clearly talks about inertial frames.Meaning that it is perfectly applicable to this thread.

    So, you don't want to read his paper? Go back to post 1 and read it. He clearly constructs inertial frames, just with a weird clock synchronization scheme.

    I have already answered this in my post to Guest254. Now, how about my 5 minutes challenge? You should have had it solved by now. Still struggling? Tsk,tsk.
     
    Last edited: Nov 4, 2010
  20. Tach Banned Banned

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    So, more than one hour has passed and none of the three musketeers has been able to solve a challenge that should take 5 minutes Two of the three musketeers have found time to post elaborate stuff (but not to try solving the challenge). The third one posted the same tripe he always posts (but he hasn't solved it either). Very telling....
     
    Last edited: Nov 4, 2010
  21. przyk squishy Valued Senior Member

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    Why don't you work on your challenge? You want to know what the coordinate velocity transformation associated with Eugene's transformation is, and you are apparently suddenly interested in whether his formalism makes any testable predictions or not, so it's really more appropriate for you to work these things out, or simply ask Eugene. Nobody else actually cares.
     
  22. Tach Banned Banned

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    This was not addressed to you, so why are you responding?

    I have already. It took me less than 5 minutes.

    You mean, you can't. If you could, you would have done it.
     
  23. AlphaNumeric Fully ionized Registered Senior Member

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    Did you even read the post? I wasn't talking about the Christoffel symbols, I was talking about Jacobians, about how they don't have to satisfy \(JJ^{\top}=I\). I gave an explicit counter example, as has Guest.

    At least read my posts rather than simply skipping them and making up what you think they say.

    Rather than trying to change the subject why don't you try actually discussing things? I couldn't care less about Eugene's stuff, the things I'm trying to discuss are things you have said. Every time someone shows you're wrong you try to change the subject.

    So you know that Jacobians don't have to satisfy \(JJ^{\top}=I\)? Then why did you say Eugene's must? Why is that a valid requirement, when its not a requirement in special relativity or anything else?

    It is a pretty transparent attempt to have an excuse for not facing up to the fact you've been corrected again. Like I said, Eugene's claims are irrelevant to the fact I'm replying to things you've claimed.

    Oh please, could you be any more desperate to avoid facing up to your mistakes.

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    Who precisely do you think you're convincing here? przyk, Guest and I have shown we're competent at this sort of calculus and anyone whose been on these forums for a while will have seen enough of our posts to know that. You're trying to make up an excuse to avoid admitting you were wrong again.

    Besides, you're being a bit hypocritical. For instance, Guest asked you to work out the Jacobian for the Cartesian -> Polar transformation to see that your claim \(JJ^{\top}=I\) was false and you didn't.

    Whenever someone demonstrates you're incorrect you make excuses like "Oh you hijacked this thread!", as if no one should correct you because Eugene started the thread. Any competent scientist should welcome constructive criticism, you seem to be utterly unwilling to accept you're mistaken, even when counter examples are put right in front of you. You make broad statements, someone gives a counter example and then you back peddle, trying to claim you meant a particular case, not a general one. You did it with Christoffel symbols and now you're doing it with Jacobians. Clearly you failed to understand the book you keep referencing was talking about particular cases, not general properties.
     

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