On the Definition of an Inertial Frame of Reference

You are correct. Hilbert always gave Einstein the credit but note that Hilbert made it clear that Einstein's contribution wasn't the least bit mathematical.

At a gathering of mathematicians, Hilbert asked:

And also consider this very well-known Hilbert quote:

And even more relevant, please note that Einstein cried like a baby at the thought that Hilbert was going to publish first:

To ‘nostrify’ means to appropriate.

Respected peer reviewed journals do not publish obvious results.

Your lack of appreciation for clear thinking in relativity reminds me of the time I shared my discovery of nonlinear Lorentz-equivalent transformations with Wolfgang Rindler. It was about 15 years ago. The professor's attitude was that my discovery was obvious and uninteresting and therefore not worthy of being published, even though there are many physicists that are totally confused by the subject. My strongest recollection of Rindler's reaction is that all physics journals should only publish on important theories and that all physicists who couldn't figure out the meaning of a nonlinear version of the Lorentz transformation are insufferably stupid and that no time should be devoted to try to educate them.

The paper by V. Berzi and V. Gorini in the Journal of Mathematical Physics, Volume 10, Number 8, August 1969 admits that the question of the linearity of the transformation formulas has long been debated in the literature. That's a published admission of confusion. See footnote 6.

I admit that I was rejected by a physics journal that sometimes publishes incredibly ignorant stuff. That leads me to ask, "Why are referees for the American Journal of Physics so hopelessly confused about special relativity in 1+1 dimensions?"

Why shouldn't terribly confused and ignorant physicists be taught my easy stuff?

 

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Because they aren't as terribly confused and ignorant as you say they are? Relativity is an extremely simple theory. Contrary to what you claim in the abstract in your essay, "Ph.Ds" in physics are not confused about relativity. The fact that you think the twin paradox is still controversial really says more about you than it does about relativity or physicists.

 

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Ask Wolfgang Rindler or any world-famous relativist about my explicit nonlinear Lorentz-equivalent transformation equations. Or ask any mathematician that knows about nonlinear representation theory if my nonlinear transformation equations are correct.

 

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I've already told you: any non-linear transformation is going to rely on a privileged coordinate origin, which is inconsistent with experience. Your non-linear transformation is not a symmetry of the known laws of physics. Quoting all the perceived authority figures in the world won't change that. You're wrong, or at best not correct in any sense that's relevant to physics. Live with that and move on.

 

The Quintessence of Axiomatized Special Relativity Theory resolves the twin paradox thought experiment in the general case of a nonlinear time equation. The reflection on physicists today is that they generally avoid the problem.

The Twin Paradox was one of the longest standing scientific controversies in twentieth century physics. [12].

How all the spacetime clocks of the universe are synchronized has not been revealed to you. Thus, you don't have any experience about the subject to justify your dogmatism.

Sure it is. Time dilation is a known law of physics and the symmetry follows from my nonlinear time equation.

Your quote from Wikipedia on "Argument from authority" states, "Arguments from authority are an important part of informal logic. Since we cannot have expert knowledge of many subjects, we often rely on the judgments of those who do. There is no fallacy involved in simply arguing that the assertion made by an authority is true."

I simply agree with Wolfgang Rinder on this point: Nonlinear Lorentz-equivalent Lorentz transformations are obvious and physicists that can't figure that out aren't very bright.

 

Well then, as someone who holds two degrees in physics and is now starting a Ph.D., please take my word for the following:
1) The twin paradox should be easily resolvable to anyone who understands relativity at undergraduate level and in particular understands the Lorentz transformation and the use of Minkowski diagrams.
2) Your full non-linear transformation is not a symmetry of the most fundamental known laws of physics.
3) Any non-linear transformation is inevitably going to rely on the existence of a privileged point in space-time, which is not observed in nature.

 

A report on the ineffectiveness of standard university instruction in Einstein's theory of relativity clearly proves that tradition in relativity is difficult to distinguish from gibberish and that a new paradigm for the teaching of spacetime physics is needed. [13].

Why is that a problem for mathematicians? I've read that non-relativistic quantum theory works better than the relativistic version. And supposedly there are significant contradictions in other fundamental physical theories, which prevent axiomatization. It's clear that physicists will just have to work harder to get their theories to agree with first principles.

Understand the theory. Both linear and nonlinear spacetime clock synchronizations are unobservable. [14].

 

Your paper hasn't been published because it contributes nothing to the scientific literature. For all the reasons that przyk has pointed out. If it did you wouldn't need to spend 20 years trying to convince folks in science forums. Einstein is the author of GR regardless of your attempts to trivialize his contribution to the scientific literature. You're a buffoon.

 

Like przyk, you have shown absolutely no understanding of The Quintessence of Axiomatized Special Relativity Theory.

 

So what's your point? Yes, introductory texts on relativity aren't very clear. I'm sure most physicists would agree with most of the sentiment described here, and if you can find a copy, I personally agree with J. Bell's "How To Teach Special Relativity". But that's why I said "at university level" - ie. the point where students start to think in terms of Lorentz transformations and Minkowski geometry. As far as I know, discussions of relativity at that level don't bother with the twin paradox simply because it's obvious by that time to students that there's no real paradox. Simply trying to formulate the twin paradox in that language or attempting to illustrate it on a Minkowski diagram will reveal the resolution.

Why do you keep bringing up mathematicians? It's a problem for physics. In physics, unlike in mathematics, we have this black box called "reality" whose behaviour we're trying to imitate in our theories. If you want to try to publish your essay in a mathematical journal, then go ahead and annoy the mathematical community with it. But please quit annoying physicists with it.

It doesn't. It's simpler, but it only works as a low energy approximation to relativistic quantum theories..

So? Yes, you could probably argue that quantum theory isn't convincingly axiomatised. Or that Feynman path integrals still lack a mathematically rigorous definition. Or that the existence of gravitational singularities in general relativity is a problem. Yes, there are cases in theoretical physics where mathematical consistency is an issue, and in general the physicists working in the relevant fields will be well aware of them. They're not ignorant. But special relativity is mathematically trivial and proving its internal consistency amounts to a few exercises in group theory.

I've told you that a non-linear transformation will require a privileged coordinate origin, which contradicts the translational symmetry we observe in nature. What does clock synchronisation have to do with this? We build clocks. We define what it means for two clocks to be synchronised. Einstein himself gave the matter attention as the first section of his 1905 paper. It's not taken for granted.

 

Please, look for the common denominator here.

 

You also told me to not respect self-inflated would-be authority figures and I don't.

That David Hilbert was right? "Physics is much too hard for physicists."?

 

Disingenuous and evasive. I've run out of patience with you.

 

The third option: your theory is absolutely worthless. You did not do your homework to verify that Maxwell's equations are covariant wrt your transforms (like Einstein did with the Lorentz transforms). The trouble is that your transforms do not produce covariant forms for Maxwell's equations. These two defects make your theory worthless.

 

(28) doesn't follow from (18)-(20) as it contradicts the supposition g is odd if \(\epsilon \neq 0\).

You consider solving different sets of expressions independently, they should all be satisfied simultaneously.

 

The solution to the problem requires solving equations (18)-(20) but I confess--I don't know how to do that. So I assumed that \(g\) is odd and found a solution. Then I realized that \(\epsilon + g\) is also a solution.

If you can find a more general solution, then I will rewrite my paper and add a note of acknowledgement that you were the one that solved equations (18)-(20) with great ingenuity and utmost generality. Or if you can prove that my solution is already the most general one, then I will acknowledge that you have devised a mathematical proof of uniqueness.

 

That would be a total waste of time since your transforms fail the covariance condition.

 

I certainly don't believe that all physicists are misinformed, and stupid. Here are two clear-thinking, thoughtful, unbiased physicists that understand nonlinear Lorentz-equivalent transformation equations:

http://lanl.arxiv.org/abs/physics/0510260
http://onlinelibrary.wiley.com/doi/10.1002/pamm.200310502/abstract

 

Yet physically, the Edwards coordinates in physics:0510260 amount to nothing more than a nonlinear realization of the Lorentz group, which is to say that unless the physics of the universe respects the Edwards-preferred-frame, the Edwards coordinates are bad coordinates. Since Nature doesn't care about a relabeling of t (c.f. sundials which define "noon" as something different than an inertial frame would describe as simultaneous) one concludes that in general Edwards coordinate are a bad choice to use to do physics except when the preferred frame is the laboratory frame for in this instance Edwards = Lorentz.

 

Shubee's theory fails one of the basic tests: Maxwell's equations aren't covariant in his formalism.