10-29-10, 07:23 PM #221
In the Lorentz covariant formulation we accept that the electric and magnetic fields are frame-dependent.
Last edited by Tach; 10-29-10 at 09:28 PM.
10-29-10, 07:27 PM #222
10-29-10, 08:56 PM #223
I never said, hinted or implied that Guest ever made a mathematical mistake in his entire life.
Is there no end to your misrepresentations?
That's false. I equate obvious righteous indignation that is clearly rooted in proven ignorance as the very definition of bigotry.
Shameless slurs confirm words. You have condemned yourself.
I'm not soliciting comments from superficial readers and non-thinkers.
The Black Knight understood what you did not. And his mathematical abilities are at the average high school level. I know. I've seen one of his self-published papers. He goes by the name Dono at google groups.
Journals don't publish obvious results that high school students can understand even though professional physicists cannot.
I tire of programmed responses without discernment like your cut-and-paste stuff out of the same material I learned in graduate school. You obviously failed to understand my questions and comments.
I'm certain that I have said that I only trust mathematicians. That's not an invitation for physicists to intrude where they're not welcome and to find entertainment value in behaving like judgmental trolls.
I don't know of any physics journal that caters to bright high school students.
Been there, done that. Personal conversations with Professors Frankel (UCSD), Rindler (UTD) and others confirm my position.
Yes. I can see how much you must enjoy pontificating and acting like a willfully close-minded troll.
I am certain about high school level algebra. My paper was obviously too difficult for you.
It's funny that you condemn me for what you are guilty of.
10-30-10, 03:58 AM #224
10-30-10, 06:34 AM #225
10-30-10, 06:54 AM #226
As I have already pointed out, it is very easy to prove that a nonlinear model of the Lorentz transformations is an extraordinarily simple idea that physicists are confused about and it is precisely this determined confusion and ignorance that justifies Sir Knight in his holy crusade against me. He has been hounding me for years.
10-30-10, 07:13 AM #227
However, if you write the wave equation in the form
with , then this is obviously the same equation, but the form it is written in is preserved under general coordinate transformations. So we have expressed the equation in a generally covariant form - i.e. a form that is preserved under arbitrary coordinate changes.
The fact you're finding it so difficult to understand is ridiculous. You continue to beat your chest and insist everyone else is wrong! Let's look at some of the clangers you've dropped whilst insisting you know what you're on about:
- Complete ignorance of transformation laws for tensors under coordinate changes.
- Utterly confused, even after having the concept explained to you, of coordinate transformations and the corresponding laws for tensor transformations.
- Complete confusion over the difference between Lorentz covariance and the notion of General covariance.
- Become bewildered by a simple definition of a function of 4 variables.
- An embarrassing lack of understanding of the chain rule, claiming the need to "differentiate with respect to f".
- Confused by the notion of the definition of a coordinate via some implicit definition.
- Strangely worried because something is defined using the composition of other functions.
- Once again indicate you're unable to use the chain rule, now claiming to need to "differentiate S with respect to itself". (for reference: the chain rule is taught in high school)
- Indicate complete unfamiliarity with basic calculus of curvilinear coordinates, and in particular, covariant derivatives.
- Complete lack of understanding of differential geometry.
- Completely unfamiliar with doing coordinate changes in flat space time, and worrying confusion over the notion of polar coordinates in this setting.
- Indicate, once again, a complete non-understanding of the concept of general covariance,
- Complete ignorance of the use of g_ij and related Christoffel symbols in the subject of curvilinear coordinates.
- Again [i]again, demonstrate a complete non-understanding of the concept of general covariance.
- Demonstrate, once again, total confusion regarding the difference between Lorentz covariance and the principle of general covariance.
- Then the same again, to really cement home the fact you don't understand what you're on about.
10-30-10, 08:43 AM #228
Tach, you appear to have either completely ignored almost all of my post or you simply didn't understand it. I'm leaning towards the former because even you should have managed to understand it when I repeatedly said I wasn't defending Eugene's work but making a broader point, yet you continue in your reply to say "Show me how Eugene's equations are right!!!", both failing to grasp the points I'm making about covariance and the very clear statement I made about how Eugene's work is irrelevant to the point I'm making.
I'm well aware of how Maxwell's equations are Lorentz invariant. This is not the same as saying "The only coordinate transformations valid are Lorentz ones". You can write Maxwell's equations in polar coordinates (and many physicists do for things like magnetohydrodynamics), which aren't a Lorentz transformation away from Cartesians, and still have valid expressions.
Maxwell's equations are Lorentz invariant in the sense of the inner product invariance. It's a little over the top but the most general way of writing down a Yang Mills gauge theory Lagrangian is along the lines of where 'a' is the Lie algebra generator index. The Lie algebra structure has a particular kind of symmetry, to do with the Killing form, and the space-time indices have a different kind. I am willing to go into the Killing form kind if you wish but lets stick to the space-time indices for the time being. The Lagrangian density can be rewritten as . Suppose now we act on the space-time indices with a linear operator in the manner of and . Doing this for the F indices and factorising in a particular way it follows (the algebra is too lengthy to type here, I dislike typing excessive LaTeX on forums) that the Lagrangian density is invariant if (if you don't see why, ask).
Thus the form of Maxwell's equations picks out a set of linear operators as 'special', which due to the form of the equations can be reexpressed as those linear operators which leave the metric (ie the associated inner product) invariant. Galilean transforms, in general (though the rotational subgroup does), don't do this specific thing.
However, if you wish to do a coordinate transformation via a Galilean transform, you're welcome to do so on Maxwell's equations. The specific form of the individual equations will change, this is not a surprise. For instance, the form of the Laplacian changes completely when you go into polars (too long to type out, see here). The fact the form has changed isn't a problem, it doesn't mean writing the parameters of space in terms of spherical polars is wrong, just as using a Galilean transform to construct new space parameters will lead to a new expression which isn't 'wrong' either.
In the case of the inner product preserving Lorentz transformation if you have a set of equations involving say the electric and magnetic fields E and B in terms of parameters t,x,y,z then afterwards you'll have a set of equations which are exactly the same but with E changed to E', B to B' and (t,x,y,z) to (t',x',y',z'). That's 'special' because if you changed to polar coordinates you obviously don't just change x to r, y to etc but never the less the coordinate transformation is a valid one and one which doesn't change the tensor structure of Maxwell's equations.
Despite repeated explanation from myself, Guest and przyk you haven't demonstrated you even see the distinction, never mind understand it.
Seriously, how many times do I have to say something as simple as "Eugene's work is irrelevant to the point I'm making" before you get that its irrelevant to the point I'm making?
When you come back from your ban please don't come out with this "Show that Eugene's equations work!!" strawman again. Repeatedly I've said your mistake is nothing to do with Eugene's equations and I've explained it in the much wider context of tensor calculus and inner product spaces. This isn't a matter of "Opps, I forget to carry the two, turns out that transformation doesn't leave the metric invariant", its a matter of "The validity of a coordinate transformation is independent of the metric".
Originally Posted by Eugene
10-30-10, 08:55 AM #229
Shubert's transformation, assuming it's well defined (I don't care enough to check) leave the components of this metric invariant. In terms of the decomposition of his transformation, brings you back to the Minkowski metric, the Lorentz transformation leaves the Minkowski metric invariant, and takes you back to the metric above. That's the least trivial interpretation of Shubert's transformation that could be considered in any way "correct".
Now that you've got the metric, working out the Christoffel symbols is tedious but straightforward. If you really need them (as opposed to demanding people do calculations for you in the hope of stalling the thread while you try to get your act together), they're given in terms of the metric components by
Last edited by przyk; 10-30-10 at 09:19 AM.
10-30-10, 09:27 AM #230
Go to your resting place ghost. It is obvious to anyone that has read my paper, your responses, post #189 or has seen the gruesome video reenactment, that Sir Knight put his sword through your head and that you have already died in shame and defeat and that you will only be remembered, if at all, as a bumbling jouster that received his just reward.
Last edited by Eugene Shubert; 10-30-10 at 09:54 AM.
10-30-10, 09:54 AM #231
10-30-10, 10:05 AM #232
I thought it would be fun to explain this thread to a general audience that might not grasp the intricacies of high school algebra and general covariance.
10-30-10, 02:45 PM #233
Tach's claims about covariance have been completely refuted and explained again and again by myself and others. Your claims have not gained any hold, you've convinced no one. Where's the defeat? So my comment about that specific part of your work wasn't correct, does that mean I was wrong about covariance and coordinate transforms? No. Does it mean your work is 'flawless'? No. Does it mean you're taken any more seriously? No.
When I've tried to engage you in conversation, giving detailed replies to your questions, you ignore me or reply with some cryptic response which suggests you didn't understand what I'd just explained to you.
My mistake was not giving you enough attention, it was not because I got something fundamentally wrong. In regards to getting something fundamentally wrong Tach has had his mistakes explained again and again. I have nothing to be 'shamed' about in that regard.
Tach doesn't think your work is valid either, so you're hardly putting yourself in a better position siding with him against me. No one here thinks your claims of 'flawless' work have merit. You couldn't get published in a reputable journal, you can't even convince people on the internet. If you want to talk about shaming I'd say that's pretty shameful. How many years have you been pushing your work now? I asked before but you didn't answer. I guess you're ashamed of the answer so you don't want to say.
I have no reason to hide or slink away. I stand by everything I've said to Tach about covariance and transformations and the moderators seem to have a similar view, along with Guest and przyk. As for wading through your work, like przyk says, I have no real wish to waste my time. The sorts of questions you ask, the responses you give and your clearly bitter and twisted view of how mainstream physics is done and the people who do it tells me enough to know that your work is very unlikely to be worth the time and effort of going through with a fine tooth-comb.
If you're so confident in your work and you think I'm in such a shameful position why aren't you responding to direct questions? Whenever I try to raise the level of discussion by asking direct questions of a technical nature both you and Tach ignore them and reply with something either irrelevant or which demonstrates you haven't actually understood (or perhaps even read) what I have said. It would seem the ones who are ashamed of the questions they are asked are you two.
So are you willing to answer direct questions or are you going to forever just make references to Monty Python? Its no skin off my nose either way at the end of the day, unlike yourself the contributions I've made to science amount to more than pushing pdfs I've written on forums, so it doesn't bother me if I didn't read your pdf with enough attention, I can at least say I've contributed to science.
10-30-10, 04:19 PM #234
10-31-10, 07:52 AM #235
I'd like to hear your opinion. In the mathematical model called Lorentzian spacetime, is it possible to define inertial frames of reference in a coordinate-free way? Is the existence of inertial frames of reference in that mathematical model a law of physics? If so, is that law of physics generally covariant?
Last edited by Eugene Shubert; 10-31-10 at 08:00 AM.
10-31-10, 09:24 AM #236
My own answers, based on my understanding of relativity:
In the mathematical model called Lorentzian spacetime, is it possible to define inertial frames of reference in a coordinate-free way?
If you mean "inertial frame" in some weaker sense than "inertial coordinate system" then it may be possible to define an "inertial frame" in a partially coordinate free way. I gave an example of how you might do this in an early post in this thread (not that I consider the result terribly useful). You only need a time-like geodesic parameterised by its proper time, which is a weaker requirement than a complete coordinate system.
Is the existence of inertial frames of reference in that mathematical model a law of physics?
If so, is that law of physics generally covariant?
Why do you need Guest's approval for all of this? If you don't feel competent enough to evaluate the answers I'm giving you and you'd rather hear them from a mathematician, then fine, and a good mathematician may well give you more elegant responses than I could. But then why are you filling this thread with inflammatory remarks like "physics is too hard for physicists" when you're obviously unable to evaluate what physicists are capable of?
11-02-10, 10:08 AM #237
First off, thank you for taking the time and attempting to do the calculations. As you will see, my request had a purpose.
1. I suspect that you started from the Minkowski metric and you passed it through the Shubert transforms, right?
If this is the case then the calculations are incorrect. A quick examination shows that you missed the fact that . But this is the least of the problems.
Shubert's transformation, assuming it's well defined (I don't care enough to check)
leave the components of this metric invariant.
In terms of the decomposition of his transformation, brings you back to the Minkowski metric,
the Lorentz transformation leaves the Minkowski metric invariant, and takes you back to the metric above. That's the least trivial interpretation of Shubert's transformation that could be considered in any way "correct".
Now that you've got the metric, working out the Christoffel symbols is tedious but straightforward.
If you really need them (as opposed to demanding people do calculations for you in the hope of stalling the thread while you try to get your act together),
 C. Moller, Theory of relativity (pp.94-96)
 C. Moller, Theory of relativity (pp.377)
Last edited by Tach; 11-02-10 at 12:32 PM.
11-02-10, 11:44 AM #238
It is clearly obvious Sir Knight that you are asking for something that is impossible. The persons seemingly most capable of judging my paper are actually most incapable of doing so fairly. They don't want to be ostracized by the community that greatly reveres Albert Einstein.
11-02-10, 11:57 AM #239
11-02-10, 12:04 PM #240
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