Possible to publish a paper that contradicts Einstein's special relativity?

[georgechen]

Summary:: Is it possible to publish a paper contradicting Einstein's special relativity in any high-ranked Journal? Which Journal is the best, i.e. open minded, for such a paper?

I plan to publish a new theory of electromagnetics in a Journal. The findings are purely through strict mathematical derivation without any disputable assumptions and also supported by most experiments. However, the findings clearly contradict special relativity.

The concern is that the editors may simply throw it out due to the deep-rooted belief in Einstein and special relativity. I only hope that the paper can get a chance for a thorough review. I am so sure of the correctness and significance of the results.

Does anyone know any high-ranked journal that may be more open-minded? Any suggestion or comment is really appreciated.

 

[russ_watters]

...also supported by most experiments. However, the findings clearly contradict special relativity.

I am so sure of the correctness and significance of the results.

Does anyone know any high-ranked journal that may be more open-minded? Any suggestion or comment is really appreciated.

It is extremely unlikely to be correct, and extremely unlikely to be published. SR is extraordinarily well tested, so the idea that your idea could contradict SR without also contradicting experiments is slim-to-none, unless your idea actually doesn't differ from SR in its predictions.

We've had a lot of discussions about that issue. The typical cause of this problem is over-confidence in ones' own understanding of the existing theory. The bottom line is that unless you've completed a PhD (at least) or honestly duplicated a PhD learning effort on your own (which never happens), you're very unlikely to understand SR well enough to have a unique and correct idea about it and publish any paper about it.

[edit] Here's a recent thread on the subject:
https://www.physicsforums.com/threads/how-to-get-your-work-published.997913/

 

[berkeman]

Does anyone know any high-ranked journal that may be more open-minded? Any suggestion or comment is really appreciated.

How long is the list of your citations? Your references would surely include articles in the appropriate journals, no?

 

[russ_watters]

Mod note: this thread has been placed in moderation status "Awaiting approval before being displayed publicly." It is likely to generate a lot of harsh criticism. For at least a start, moderators can reply here.

Mod note: I've moved this to career guidance and approved it since we've had similar threads in the past. Let's try not to let this go down a bad road, thanks...

 

[PeroK]

Summary:: Is it possible to publish a paper contradicting Einstein's special relativity in any high-ranked Journal? Which Journal is the best, i.e. open minded, for such a paper?

I plan to publish a new theory of electromagnetics in a Journal. The findings are purely through strict mathematical derivation without any disputable assumptions and also supported by most experiments. However, the findings clearly contradict special relativity.

Any suggestion or comment is really appreciated.

What open question of modern physics does your theory answer?

The concern is that the editors may simply throw it out due to the deep-rooted belief in Einstein and special relativity.

Physicists use SR not because they have a religious devotion to it, but because it produces well-tested results that form the bedrock of modern physics.

 

[Dale]

Is it possible to publish a paper contradicting Einstein's special relativity in any high-ranked Journal?

Yes. The CERN team did so relatively recently. Of course they later found their mistake.

The findings are purely through strict mathematical derivation without any disputable assumptions and also supported by most experiments. However, the findings clearly contradict special relativity.

Then you made a mistake because these are mutually contradictory statements.

 

[Vanadium 50]

Is it possible to publish a paper contradicting Einstein's special relativity in any high-ranked Journal?

Yes.

The findings are purely through strict mathematical derivation without any disputable assumptions and also supported by most experiments. However, the findings clearly contradict special relativity.

Then they're wrong.

Special relativity is mathematically consistent. That doesn't mean it describes the universe we live in, and one could publish the results of an experiment that show that. But the only way you can show SR is wrong mathematically is by making a mistake.

Does anyone know any high-ranked journal that may be more open-minded?

It's not being closed-minded to not want to publish something wrong.

 

[Vanadium 50]

Yes. The CERN team did so relatively recently.

Actually, by the time they published, they found the problem. See https://link.springer.com/article/10.1007/JHEP10(2012)093

 

[Keith_McClary]

supported by most experiments

You have to agree with experiments better than conventional theory.
Have you considered viXra.org ?

 

[Dr. Courtney]

A solid experimental paper would have a much better chance.

A theory paper has the challenge of needing to show significantly better agreement with accepted experimental data. I doubt your paper does that.

 

[PeroK]

A solid experimental paper would have a much better chance.

The problem is that you can't do ground-breaking experiments from the comfort and isolation of your armchair. Whereas, you can revolutionise theoretical physics easily enough.

 

[Vanadium 50]

I'm still not sure why the mods put it here. I guess writing wrong papers has an impact on one's career. (Hasn't seemed to have hurt mine any, though. )

Why is it always relativity (or QM)? Why don't we ever see, I dunno, a new approach to electron pairing in high-temperature superconductors?

 

[Drakkith]

Why is it always relativity (or QM)? Why don't we ever see, I dunno, a new approach to electron pairing in high-temperature superconductors?

It's not as fundamental or 'flashy' as QM or Relativity. I mean, who really cares about electron-pairing (get a room!) when you could talk about spacetime shenanigans or how all of reality is one giant probability wave (well, probably, maybe).

 

[fresh_42]

I'm still not sure why the mods put it here.

Moved.

I guess writing wrong papers has an impact on one's career.

I am less optimistic by what I have seen been published.

Why is it always relativity (or QM)?

Because you need a) a certain level of ignorance and confusion to doubt established results, and b) the illusion that you know what it is about.

Why don't we ever see, I dunno, a new approach to electron pairing in high-temperature superconductors?

It was and is the same in mathematics. Everybody thinks, i.e. condition a) holds trivially, he can approach the 3 classical problems, FLT or RH, since they all fulfill condition b). Even the popular P=NP seems to be already too technical, which by the way makes me wonder why people think RH is not. It is never, "I dunno, a new approach to" nilpotent groups of degree $n$.

 

[Vanadium 50]

Math did have the ABC conjecture and Mochizuki. Not exactly the same thing, since Mochizuki has published extensively, although as far as I know, not his claimed proof of ABC. (The similarity with the OP)

Also, and I am not an expert in the field, my understanding is that the hide-bound defenders of the orthodoxy community's concern is not the proof is wrong but that it is hard to understand, and that Mochizuki is not making it easier.

 

[Dr. Courtney]

Why is it always relativity (or QM)? Why don't we ever see, I dunno, a new approach to electron pairing in high-temperature superconductors?

I've seen a few crank papers on the 2nd law of thermodynamics. There are a few other fields that seem to attract the cranks.

 

[Rive]

The findings are purely through strict mathematical derivation without any disputable assumptions and also supported by most experiments. However, the findings clearly contradict special relativity.

That's a bit of a problem, since the very root of SR (Lorentz transformation) is strict mathematical derivation (based on the Maxwell equations). If you contradict it that means you are bugged against the whole classic electromagnetics (while writing this on a computer and through the internet: both nicely proves that electromagnetics works).

You may want to find something what contains SR and expands its validity to new areas, like GR did: or like the mechanical aspects of SR did with the Newtonian mechanics. That might work.

Also, it is possible to invent alternatives, but the common point with alternatives is, that a 'real' alternative is actually something mathematically equivalent since it still has to comply with Maxwell.

 

[Algr]

The concern is that the editors may simply throw it out due to the deep-rooted belief in Einstein and special relativity.

Even Einstein himself once had a paper rejected. And this was 15 years AFTER he published special relativity and became famous. So don't assume that any rejections you get are about faith. Wanting to disprove Einstein is a noble goal... if you can actually do it.

 

[Rive]

Wanting to disprove Einstein is a noble goal... if you can actually do it.

You can't disprove anything what's working. That's just the complete misunderstanding of how science works.

The best you can do is to extend or redefine it. But then you need to prove that within the (proven) old frames your new approach is mathematically equivalent with the old theory.
To get anything 'revolutionary' approved it's just one of the first steps to prove this kind of equivalence.

Just as like to get the SR based mechanics accepted it was necessary to prove that with low speeds it works exactly like Newtonian mechanics: just as like SR was redefined (accepted) the 'reality' based on the transformation long known before. Just as like as if somebody proposes any 'general theory of everything', he/she needs to prove first that within the validity of the quantum mechanics it works like quantum mechanics: within the validity of GR, it works exactly like (the proven part of) GR.

 

[Algr]

The best you can do is to extend or redefine it. But then you need to prove that within the (proven) old frames your new approach is mathematically equivalent with the old theory.

But Special Relativity is NOT mathematically equivalent to Newtonian mechanics. They just deliver similar results at low speeds. You can't dismiss a new theory simply because it yields a different result then SR - if the results are something that has yet to be tested. To argue if Einstein redefined or disproved Newton is to some extent an issue of semantics. Ask Newton what .8c + .8c is.

 

[PeroK]

Ask Newton what .8c + .8c is.

You can't ask him, but I'll answer. $0.8c + 0.8c = 1.6c$ That's simple algebra.

 

[Algr]

And what would Einstein say about 1.6x the speed of light? Is that extended? Or wrong?

 

[PeroK]

And what would Einstein say about 1.6x the speed of light? Is that extended? Or wrong?

$1.6c$ is a speed. The theory of SR restricts speeds as measured in inertial reference frames to a maximum of $c$ (and $c$ itself only for massless particles or radiation).

 

[Rive]

But Special Relativity is NOT mathematically equivalent to Newtonian mechanics.

Within the area of validity of Newtonian mechanics it is.

 

[Algr]

Ask Newton what .8c + .8c is.

A reasonable person should recognize that as a reference to how speeds are added in SR vrs Newton. If an observer sees two bodies approaching each other at .8c relative to the observer, what will each body observe the other's speed as? In Newtonian mechanics, you simply add the two speeds. Einstein observed that to do so is wrong.

But then you need to prove that within the (proven) old frames your new approach is mathematically equivalent with the old theory.

Which SR isn't.

Within the validity of Newtonian mechanics it is.

Within the validity of twice a day, a broken clock is accurate. ANY theory is right if you exclude the situations where it is wrong.

========================
Edit: It is commonly observed that Newton was "Wrong" in a ridged scientific sense, and yet his contribution to science is widely celebrated and his equations remain highly useful to this day. That is what I was talking about when I said disproving Einstein is a noble goal. It is what Einstein did to Newton. What Rive said above could easily confirm the original poster's worst fears about science.

 

[Rive]

It is commonly observed that Newton was "Wrong" in a ridged scientific sense...

It is wrongly observed, then. Newtonian mechanics is not 'wrong'. It is limited, by its own area of validity, which is now part of the theory itself.

ANY theory is right if you exclude the situations where it is wrong.

Right. That's half of the process of 'proving' something in scientific sense.
Limiting the theory to an area where it's actually right.

Just as GR is limited too: it does not includes quantum mechanics (and a lot more we do not even know about, likely).

But the moment you claim to have a 'general theory of everything', you need to prove that it does have an area of validity, and it is valid both for QM and GR.

 

[Dale]

Which SR isn't.

You should pay attention to what @Rive is saying. He is correct here and above. The very first test that any new theory must pass is equivalence with the old theory within the domain of validity of the old theory.

It is commonly observed that Newton was "Wrong" in a ridged scientific sense,

Actually, it is a rigid philosophical sense, famously described by Popper. Scientifically Newton remains right in the experimentally established domain of validity.

 

[PeroK]

A reasonable person should recognize that as a reference to how speeds are added in SR vrs Newton. If an observer sees two bodies approaching each other at .8c relative to the observer, what will each body observe the other's speed as?

You mean that: $$u' = \frac{0.8c + 0.8c}{1 + (0.8c)(0.8c)/c^2} = \frac{1.6c}{1.64} \approx 0.976c$$
In that calculation, clearly $0.8c + 0.8c = 1.6c$.

If, however, we let $v$ be the separation speed (as measured in the original frame), then: $$v = 0.8c + 0.8c = 1.6c$$

 

[Jarvis323]

Summary:: Is it possible to publish a paper contradicting Einstein's special relativity in any high-ranked Journal? Which Journal is the best, i.e. open minded, for such a paper?

I plan to publish a new theory of electromagnetics in a Journal. The findings are purely through strict mathematical derivation without any disputable assumptions and also supported by most experiments. However, the findings clearly contradict special relativity.

The concern is that the editors may simply throw it out due to the deep-rooted belief in Einstein and special relativity. I only hope that the paper can get a chance for a thorough review. I am so sure of the correctness and significance of the results.

Does anyone know any high-ranked journal that may be more open-minded? Any suggestion or comment is really appreciated.

It appears there is a journal called Physics Essays, which accepts all kinds of papers challenging established physics theories. Some seem to not look at the journal so favorably though. It has been discussed here before.

https://www.physicsforums.com/threads/crackpot-physics-journal.111647/

 

[russ_watters]

I'm still not sure why the mods put it here. I guess writing wrong papers has an impact on one's career. (Hasn't seemed to have hurt mine any, though. )

I moved it to career advice because I wanted to emphasize that in my estimation (as an engineer, not a scientist), publishing a paper is the domain of professional scientists. So not career advice per se, but professional advice. I can see some potential quibbles to that, but the point was to emphasize the seriousness of the endeavor.

Also, I'm the one who originally flagged the post and it sat for a day with nobody else acting on it...

Also noteworthy; the OP hasn't been back since posting this thread.

Why is it always relativity (or QM)? Why don't we ever see, I dunno, a new approach to electron pairing in high-temperature superconductors?

Because most people have heard of them, and they're weird.

 

[Algr]

Right. That's half of the process of 'proving' something in scientific sense.
Limiting the theory to an area where it's actually right.

But in the case of Newton, it was Einstein who did this.

 

[Rive]

But in the case of Newton, it was Einstein who did this.

Yes. It was OK for Newton, though: but in this age we are already a bit more careful with 'all creation included' type of theories, so some initial work from the author is a requirement.
Even if the 'edges' are not visible yet, at least to prove that within the limits of the 'old' theory it works at least just like the old one is the basic courtesy.

 

[russ_watters]

@Algr and @Rive I think there is a fair amount of talking past each other here, but as it reads I agree with the statement that started it, and later logic discussing it via comparison to Newton:

Wanting to disprove Einstein is a noble goal... if you can actually do it.
[separate post]
Ask Newton what .8c + .8c is.

You can't disprove anything what's working. That's just the complete misunderstanding of how science works.

IMO, it's fair to speculate that Newton would answer 1.6C and it is fair to call that "wrong". Broader, it's fair to say that Newton's theory "works" in its domain of applicability and in a handwavey way "works" in the domain in which we use it. But when you do that I think you need to acknowledge that Newton didn't know what that domain of applicability was and almost certainly didn't have a clue as to just how limited/wrong his theory was. Scientists only realized it later when their measurements got more accurate. Newton probably would have said his theory was "working", because as far as he knew, it was -- but he'd have been wrong. And he probably believe his theory was The Correct One.

I do not think it is fair to call Relativity an "extension" or "redefinement" (refinement?) of Newton's laws; it's a replacement (for the purpose of theory; practical use is different). The domain of applicability of Newton's laws is very, very small and we mostly use them today in areas known to be outside their domain of applicability because the math is easier and the error is small enough not to worry about. Their domain are very limited, even single-point special cases at best.

Einstein's theory is much more advanced, with much better experimental data/observation to back it up. But that data isn't infinite in its coverage or precision. There exists the possibility, however remote, that somewhere in those error margins, an experimental result will contradict Relativity. And if that happens, Relativity will be "wrong" and "disproven". Maybe not completely, but within the bounds of the experimental result. In that case, a boundary will need to be drawn or a new theory that matches Relativity's results up to that limit but deviates outside that limit will be needed. Yes, it's extremely unlikely, but if the possibility was absolute zero, then there's be no point in pushing the accuracy of the experimental verification any further. The expectation is that Relativity is 100% accurate in its domain, but it is recognized that it isn't 100% proven, nor can it ever be (though perhaps someday scientists will stop bothering to try to disprove it).

But then you need to prove that within the (proven) old frames your new approach is mathematically equivalent with the old theory.

In my opinion, this is a common statement but an over-statement, and contradicts your previous judgement of the velocity addition example: The velocity addition formulas are not mathematically equivalent. Newton's is wrong, full stop. This is binary. The fact that we use it anyway doesn't mean it isn't wrong.

Extending, the statement then assumes that Relativity is completely accurate instead of acknowledging that by nature experiments can only provide very good approximate verification. I don't think it's hairsplitting because, again, if Relativity were accepted to be 100% accurate, there'd be no need for further testing and the...non-mainstreamers...would be right to point out that we're considering something 100% accurate without 100% accurate experimental verification. A new theory must agree with the existing body of evidence, not the existing theory (except where the two theories and the evidence overlap).

All that said, it's likely the OP doesn't know the overlap and so doesn't know their theory actually does contradict existing experimental evidence.

Note: I define "domain of applicability" as the domain where a theory is believed to be accurate/correct. It does not include the domain where it is known to be wrong but we just don't care because it's close enough. In that sense, as far as I know, Newton's laws of motion have no domain of applicability at all. There is no speed where the Galilean velocity addition formula is believed to be accurate. No speed where it and Einstein's formulas give exactly the same result.

 

[russ_watters]

Since the OP hasn't returned I don't feel bad about hijacking the thread, but if need be we can split part of this off into a new thread discussing "What does 'Domain of Applicability' Mean?" I feel like there are three different definitions people use:

1. The domain in which we use it.
2. The domain in which it is proven accurate.
3. The domain in which it is believe to be accurate.

The definition used will impact how one interprets the statement "correct in its domain of applicability".

 

[Dale]

In my opinion, this is a common statement but an over-statement, and contradicts your previous judgement of the velocity addition example: The velocity addition formulas are not mathematically equivalent. Newton's is wrong, full stop. This is binary.

I disagree with this. Newton's velocity addition formula is mathematically equivalent to the SR velocity addition formula for $v<<c$. In fact, it is critical that the SR velocity addition formula reduce to the Newtonian formula in the limit $v<<c$ precisely because we have a lot of data in that limit that supports the Newtonian formula.

I define "domain of applicability" as the domain where a theory is believed to be accurate/correct. It does not include the domain where it is known to be wrong but we just don't care because it's close enough.

As far as I know, that is not the usual definition. I believe that the usual definition is that the theory's domain of validity is the domain where there is experimental data which validates the theory. There is a lot of experimental data that supports Newtonian physics, including the Newtonian velocity addition. In that domain Newtonian physics is valid (hence domain of validity). SR, to be valid, must also match the established correct predictions of Newtonian physics in that domain.

Note that the precision of an experiment is an important characteristic of the experiment. So the issue is not "we just don't care because it is close enough" but rather than with a certain experimental precision the theories are indistinguishable. They both agree with the data equally. The domain of validity includes not only the experimental velocity but also the experimental precision.

 

[Rive]

No speed where it and Einstein's formulas give exactly the same result.

It is a bit of a problem to support that claim with experimental data.

 

[Jarvis323]

Newton's velocity addition formula is mathematically equivalent to the SR velocity addition formula for $v<<c$.

This might just be a matter of semantics, but I would say, "experimentally equivalent", yes, "approximately equivalent", yes, but "mathematically equivalent", no.

 

[russ_watters]

It is a bit of a problem to support that claim with experimental data.

Huh? The statement is purely mathematical. It has nothing at all to do with experiment. That's one of the key points of the entire post.

 

[russ_watters]

I disagree with this. Newton's velocity addition formula is mathematically equivalent to the SR velocity addition formula for $v<<c$. In fact, it is critical that the SR velocity addition formula reduce to the Newtonian formula in the limit $v<<c$ precisely because we have a lot of data in that limit that supports the Newtonian formula.

@Jarvis323 accurately describes my position.

As far as I know, that is not the usual definition. I believe that the usual definition is that the theory's domain of validity is the domain where there is experimental data which validates the theory.

That's a problem for me, then. Is there another name for what I describe? To me, the distinction matters because in one case we need to keep looking for a better theory and in the other case we don't.

There is a lot of experimental data that supports Newtonian physics, including the Newtonian velocity addition. In that domain Newtonian physics is valid (hence domain of validity). SR, to be valid, must also match the established correct predictions of Newtonian physics in that domain.

Note that the precision of an experiment is an important characteristic of the experiment. So the issue is not "we just don't care because it is close enough" but rather than with a certain experimental precision the theories are indistinguishable. They both agree with the data equally. The domain of validity includes not only the experimental velocity but also the experimental precision.

Since I'm not a scientist, I may not have the theory/process of how errors are dealt with correct, but my understanding was that error bars are not hard limits, so there is no binary yes or no or necessarily an equality of two theories. Isn't there still debate about whether the original Michelson Morley experiment was accurate enough to claim a null result? E.G., it was zero within the error bars, but the error bars were pretty wide?

It also means that for different experiments, Newton's laws have different domains of applicability. That seems very loose/vague to me. I had assumed the domain of applicability was more specific than that, and even independent of the specific experiment. If I'm using my car odometer and you're using a laser interferometer, we can both reasonably claim different domains of applicability of Newton's Laws.

 

[Dale]

This might just be a matter of semantics, but I would say, "experimentally equivalent", yes, "approximately equivalent", yes, but "mathematically equivalent", no.

$$\lim_{c \rightarrow \infty} \frac{u+v}{1+uv/c^2}=u+v$$ So I stand by “mathematically equivalent to the SR velocity addition formula for $v<<c$”

 

[Rive]

the statement is purely mathematical.

That's nice. But somewhere down the line it is exactly the experiments what turns math into physics.

Without experiments supporting the difference in a specific range all what you can say is that keeping the distinction is nice.

Being nice actually still can be a valid point, but being practical can be one too ... And this has nothing to do with 'right'. Limited - yes, that's the one :)

It also means that for different experiments, Newton's laws have different domains of applicability.

For practical reasons, this stands not just for experiments but even for educational levels too.
Indeed, sometimes it is a mess.

 

[russ_watters]

$$\lim_{c \rightarrow \infty} \frac{u+v}{1+uv/c^2}=u+v$$ So I stand by “mathematically equivalent to the SR velocity addition formula for $v<<c$”

Does adding a condition $v<<c$ really provide the same result as $$\lim_{c \rightarrow \infty}$$ ? I thought $v<<c$ meant "so small the deviation becomes immeasurable."

 

[hutchphd]

Of course this is just semantics perhaps, but I would say, "experimentally equivalent", yes, "approximately equivalent", yes, but "mathematically equivalent", no.

I believe the appropriate term here is "asymptotically equivalent" but I don't really care.
I am more concerned with the larger question vis.

Huh? The statement is purely mathematical. It has nothing at all to do with experiment. That's one of the key points of the entire post.

If you really mean this then we can equally debate the number of angels who fit on the head of a pin. I know that you understand this but the statement itself is far too categorical.

 

[russ_watters]

That's nice. But somewhere down the line it is exactly the experiments what turns math into physics.

I'm an engineer and I recognize that nothing I calculate or measure is exact. It was my understanding that mathematicians deal with exact math and that physicists (scientists) sometimes deal with exact math and sometimes deal with inexact experiments and that the difference matters. I'm honestly baffled that it doesn't appear to be the case - that the line appears to be quite blurry.

Again, the main reason why I think this should matter is that it determines whether there is any need/ value in further theoretical development or experimentation or if science could just stop.

 

[russ_watters]

If you really mean this then we can equally debate the number of angels who fit on the head of a pin. I know that you understand this but the statement itself is far too categorical.

I'm really not following you.

 

[hutchphd]

I'm really not following you.

I'm not saying it very well. I really just mean that the behavior of any mathematical theory can be endlessly debated in the realm where the experimental data is not precise enough to differentiate two theories (angels size for instance). It is the hallmark of physics that experimental data always matters and so I disliked the statement categorically.

 

[russ_watters]

I really just mean that the behavior of any mathematical theory can be endlessly debated in the realm where the experimental data is not precise enough to differentiate two theories (angels size for instance).

Agreed. But the impression I'm geting is that scientists do not believe there is enough room in those error margins for another theory, or believe Relativity is exact/correct -- and flip back and forth between the two positions/descriptions. It's a lot more vague than I thought the way scientists think.

 

[hutchphd]

And actually quite various as well. I think that was more surprising to me. It is why we are humans and not machines I guess.

 

[Jarvis323]

I believe the appropriate term here is "asymptotically equivalent" but I don't really care.
I am more concerned with the larger question vis.

If you really mean this then we can equally debate the number of angels who fit on the head of a pin. I know that you understand this but the statement itself is far too categorical.

Well, I don't know because the much less than symbol is not exactly defined as an asymptotic limit. In this case, if you take a limit, then $v = 0$ is probably the appropriate one I guess. Rather than use the concept of a limit, you could just say for $v=0$.

Anyways, if you take it all the way to the limit, as a way to define the domain of applicability, then you have reduced the domain of applicability to infinitesimally small. And you could come up with all kinds of ridiculous equations that are equivalent at $v=0$.

But I get the point.

 

[PeroK]

$$\lim_{c \rightarrow \infty} \frac{u+v}{1+uv/c^2}=u+v$$ So I stand by “mathematically equivalent to the SR velocity addition formula for $v<<c$”

That's more than stretching a point. If "mathematically equivalent" means anything it means they are the same axiomatically (which they are not). Moreover, one system being a special case of the other does not mean they are equivalent. The geometry of circles is not mathematically equivalent to the geometry of ellipses, even though the circle is a special case of the ellipse.

The Hafele-Keating experiment is evidence that Newtonian physics and Relativity are not equivalent, even within what might be expected to be the domain of applicability of Newtonian physics: airline travel.