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

[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.

 

[Rive]

I'm an engineer and I recognize that nothing I calculate or measure is exact.

With physics it is even worse. It takes a lot of metaphysics (philosophy) to accept that we can't deal with 'reality' (whatever it means). We only have experiments, and theories fitting them. So the whole 'real', and 'right' is a kind of alarm bell, since these are just out of physics.

If you have only experiments, then how can you decide which theory is 'right' if you can't support the distinction (within a range) with experimental data?

Nice - it works. Works - fine. Limited - very good. Useful - even better! Practical - hooray for it!
Right - now, that's very-very suspicious...

 

[sysprog]

<joke>
Just in case you guys were/are still concerned about angel size:
##\ell_{(M,\varphi)}:\Delta^+=\{(x,y)\in \mathbb{R}^n:x<y\}\to \mathbb{A}## where ##\mathbb{A}=\mathrm{[angels]}##
there you go ##\dots##
</joke>

 

[DaveE]

Dunning-Kruger comes to mind here.

I have no idea how this relates to the OP's work since we haven't seen it. Even then I probably wouldn't, but y'all might.

I believe that this effect applies to everyone in each knowledge domain. The question is: do we have the self awareness to know where we are on the graph?

“The first principle is that you must not fool yourself — and you are the easiest person to fool.” - R. Feynman

 

[russ_watters]

And actually quite various as well. I think that was more surprising to me.

With physics it is even worse. It takes a lot of metaphysics (philosophy) to accept that we can't deal with 'reality' (whatever it means). We only have experiments, and theories fitting them. So the whole 'real', and 'right' is a kind of alarm bell, since these are just out of physics.

If you have only experiments, then how can you decide which theory is 'right' if you can't support the distinction (within a range) with experimental data?

Well, where the rubber meets the road, I'm not sure I believe it. There's a 8.5 km supercollider near Geneva, not an 8.5 km Michelson interferometer. There's a reason for that. There's a reason we scoff when someone says they have an idea for a new theory that contradicts Relativity. I don't think it's just that the person isn't qualified to make the claim - I think the reason in both cases is that physicists believe Relativity is Correct. Not "correct within its domain of applicability", but Actually Correct.

 

[f95toli]

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.

I don't think that is true. There are quite a number of scientists who spend their whole career doing more and more accurate measurements to see if they can spot any difference between their measured values and what is predicted by theory. Some of this work is published in high-impact journals (see https://www.nature.com/articles/s41586-020-2964-7 for a recent example.)

We all know that physics isn't "complete"so it is entirely possible that we will one day find a "more complete" theory which also works in situations where existing physics (including SR) isn't applicable or-assuming we one day find an "error"- is able to predict results with higher accuracy.

The key here is realising that these situations would have to be either very exotic OR you are trying to calculate something with a precision which is beyond what we can currently measure. So any new theory would still need to explain existing data.

 

[BWV]

Dunning-Kruger comes to mind here.

I have no idea how this relates to the OP's work since we haven't seen it. Even then I probably wouldn't, but y'all might.

I believe that this effect applies to everyone in each knowledge domain. The question is: do we have the self awareness to know where we are on the graph?

“The first principle is that you must not fool yourself — and you are the easiest person to fool.” - R. Feynman

View attachment 276494

seems like everyone who sees that graph thinks they are an expert on Dunning-Kruger

 

[Vanadium 50]

not an 8.5 km Michelson interferometer

No, that's only 6km, and it's in Tuscany.

However, I think the point you are trying to make is valid. Nobody would say it's worth doing a billion dollar experiment to add one more zero to the null result of Michelson and Morley in lieu of a billion dollars worth of other experiments.

If SR were wrong, would a better Michelson-Morley experiment find it? I think the answer is probably not. You would need some sort of incomplete ether drag, so that the ether wind is a fraction of a meter per second, but then you run into problems with Michelson-Gale-Pearson type measurements.

Trivia question: which Nobel prize winner was a proponent of partial ether drag theories?

 

[Dale]

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."

I certainly could be understanding it wrong, but I have always understood it as a shorthand for the limit as v/c goes to zero.

In this case since there are two velocities it is equivalent but easier to take the limit as c goes to infinity.

 

[Vanadium 50]

The best Michelson-Morley experiment type-experiment appears to be a 2005 Dusseldorf experiment:
https://arxiv.org/abs/gr-qc/0504109 and https://arxiv.org/abs/physics/0602115

Expressed as ether wind, the ether is moving at less than 9 cm/s (0.2 mph). Somewhere between a sloth and the world's fastest snail. I don't see a huge value in measuring this well enough to move the limit to 1 cm/s. Does anyone?

 

[Dale]

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.

That is possible. I tend to use 2., but now that I think of it I am not sure that anyone I have read actually defined it clearly. So 2 is simply what I inferred from context and usage.

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.

You are right. I have an Insights article about Bayesian inference in science. In my opinion that is the best way to evaluate the evidence without resorting to a binary yes no.

But the impression I'm geting is that scientists do not believe there is enough room in those error margins for another theory

I think that there are some beyond the standard model theories that differ from SR but live in those error margins.

 

[gmax137]

My understanding (from reading mostly pop-sci), is that somehow Einstein knew about the anomalous precession of the perihelion of Mercury, and was able to accurately calculate the orbit using his new GR. So there is a place in orbital mechanics where "Newton is wrong" so to speak. Do we now have any examples where SR/GR predictions are known to be incorrect, or better said "not quite in accordance with observations"?

I'm not looking for "well, GR and QM don't get along" as that's too philosophical. A concrete example of observed results that don't match the GR prediction would be nice. Or, do the scientist experts believe SR/GR actually provides perfect predictions?

 

[Dale]

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.

It does mean that they are equivalent when restricted to that special case. An ellipse is not mathematically equivalent to a circle, but an ellipse with both foci at the same point is.

I notice that the people who have been objecting to my language keep on dropping the restriction. The restriction is essential.

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.

Yes, which is why the precision of the experiment needs to be part of the specification of the domain. With new portable optical atomic clocks we should be able to do a similar experiment at walking speed.

 

[Dale]

Einstein knew about the anomalous precession of the perihelion of Mercury, and was able to accurately calculate the orbit using his new GR. So there is a place in orbital mechanics where "Newton is wrong" so to speak. Do we now have any examples where SR/GR predictions are known to be incorrect, or better said "not quite in accordance with observations"?

I think that galactic rotation curves are quite analogous to the Mercury situation. At the time, another planet called Vulcan was proposed as the source of the anomaly. Vulcan was never identified by other means and then GR was developed which explained the anomaly without Vulcan.

 

[russ_watters]

I certainly could be understanding it wrong, but I have always understood it as a shorthand for the limit as v/c goes to zero.

In this case since there are two velocities it is equivalent but easier to take the limit as c goes to infinity.

Ok, that's what I thought -- rather than say v is so small compared to c it may be zero, you're saying limit as c goes to zero, giving basically the same result. But the "<<" operator of "much less than" is qualitative and really means "too small to measure" or "too small to matter", right?

I notice that the people who have been objecting to my language keep on dropping the restriction. The restriction is essential.

Setting aside whether what you said means what I think you said, my objection is that you added the restriction in the first place. It creates a circular argument: they are mathematically identical in special cases we can specify where they are mathematically equivalent. Ok. In other cases they aren't mathematically equivalent, so let's talk about those. Clearly, one can make calculations using either method for cars driving on a highway and get answers that are different from each other. Not a lot different, but different nonetheless. Whether 100 km/hr satisfies "<< c" and we can safely ignore the difference isn't what matters to me. It matters that they are in, in fact, different.

Edit: for two cars passing each other at 30 m/s with respect to the ground, I get answers of 60 m/s and 59.99982 m/s.

 

[russ_watters]

I don't think that is true. There are quite a number of scientists who spend their whole career doing more and more accurate measurements to see if they can spot any difference between their measured values and what is predicted by theory. Some of this work is published in high-impact journals (see https://www.nature.com/articles/s41586-020-2964-7 for a recent example.)

This is great, thanks. The abstract talks big-picture motivation, which is what I'm after here:

The standard model of particle physics is remarkably successful because it is consistent with (almost) all experimental results. However, it fails to explain dark matter, dark energy and the imbalance between matter and antimatter in the Universe. Because discrepancies between standard-model predictions and experimental observations may provide evidence of new physics, an accurate evaluation of these predictions requires highly precise values of the fundamental physical constants. Among them, the fine-structure constant

"...consistent with (almost) all experimental results."
"...fails to explain..."
"...discrepancies..."
"...may provide evidence of new physics..."

Is this wording really much different from the OP?
"... supported by most experiments..." (this is most concerning to me based on how weak it is worded).
"...contradicts..."

Or the post that started this sub-discussion:
"Wanting to disprove Einstein is a noble goal... if you can actually do it."

The only differences I see are differences in the strength of language.

If it seems like I'm flip-flopping positions (SR can be replaced / SR is complete and unworthy of further study) it's because I am, because that's what I'm seeing/reacting to.

We all know that physics isn't "complete" so it is entirely possible that we will one day find a "more complete" theory which also works in situations where existing physics (including SR) isn't applicable or-assuming we one day find an "error"- is able to predict results with higher accuracy.

What about certain pieces of physics? Is the speed of light really invariant or is there room for it to vary? Do scientists think that's realistic? Would they have declared it to be the basis for defining units of length if they believed fluctuation was likely?

The key here is realising that these situations would have to be either very exotic OR you are trying to calculate something with a precision which is beyond what we can currently measure. So any new theory would still need to explain existing data.

Yes, and this is where I perceive the OP goes wrong. It's not the general idea that there could be a new theory that contradicts SR in certain predictions, is better and replaces SR, but rather the likelihood that a person who is almost certainly a layperson could have discovered it.

 

[Dale]

my objection is that you added the restriction in the first place. It creates a circular argument: they are mathematically identical in special cases we can specify where they are mathematically equivalent.

The point is that there does exist such a special case where SR becomes equivalent to Newtonian physics. Not all possible theories have a Newtonian limit at all. Those that do not are invalidated by all of the evidence that validates Newtonian physics. The existence of that limit was critical for establishing relativity as a viable theory.

Whether 100 km/hr satisfies "<< c" and we can safely ignore the difference isn't what matters to me. It matters that they are in, in fact, different.

What matters for the scientific method is whether or not a specific experiment can distinguish between them. That involves not only the predicted difference but also the experimental precision.

 

[HAYAO]

I don't know if I can phrase this right, but no one measures the size of a table with micrometer precision. I hope everyone use a measure for that. Measures are not precise to a micrometer level, but it doesn't mean it's "wrong". It's just a good estimation because that's the realm of what we are concerned about. If a micrometer and a measure are contradictive (i.e. measuring a 1 mm object with micrometer and a measure show completely different measurement), then they are either manufactured poorly or used in a wrong way. In principle, they can't contradict each other.

Similarly, Newton is not "wrong", Einstein's SR or GR is not "wrong", QM is not "wrong", QFT is not "wrong". It is in principle not impossible to come to a similar conclusion of Newton mechanics with QM, but mathematically a very challenging thing to do (and we can't...yet). What we do instead is we incorporate approximation(s) that we perceive to work for a specific case in concern. We continue on and with sufficient approximations, we can reach the same conclusions of Newton mechanics.

Relativity explains the world very well and is very consistent. Let's say whatever you came up with is similarly very consistent with experiments. That means your theory and Relativity are compatible in some way. But it can't fundamentally contradict.

 

[Rive]

Is this wording really much different from the OP?
"... supported by most experiments..." (this is most concerning to me based on how weak it is worded).
"...contradicts..."

Yes, that wording is very different. The quoted text starts with the approval of the domain of validity of the standard model, and expressing their wish to extend it to new areas. They do not want to contradict: they wish to extend.

The concerning part from the OP is, that the root of SR is nothing more than the basic coordinate transformation valid for Maxwell. If you actually contradicts it, that means you are contradicting the existence of your computer, and that's just the very beginning. Not really a promising start.

It is still possible (? maybe just acceptable) to find special circumstances where rules are different and what's not actually part of the valid domain of (classic) electromagnetic. But then you still need to not contradict it in normal circumstances - and this makes that theory not a replacement, but an extension at this point. Just like in that quote.

One other point where the OP goes wrong is, that by now SR is barely considered a 'theory' on its own. It is kind of a transitive tool for education/basic usage between classical and GR physics. Just a slice of the big cake to make digestion smoother. Since it is kind of a 'first shock' for most people it is easy to understand why it is a common target, but that does not makes it a good target. If you shoot for it you shoot for a toy: if you shoot for real, that makes you ... erm... well...

 

[georgechen]

Thank you everyone replied to my post. Appreciate your feedbacks. This post was moved by the admin so I mistaken it from being deleted and only see it today.

For update, I already spent several months checking the math and can't find any error since it is simple math. So I will move forward and send the paper just hope someone may be so open-minded that he will at least take a look and not throwing it away immediately.

 

[PeroK]

Thank you everyone replied to my post. Appreciate your feedbacks. This post was moved by the admin so I mistaken it from being deleted and only see it today.

For update, I already spent several months checking the math and can't find any error since it is simple math. So I will move forward and send the paper just hope someone may be so open-minded that he will at least take a look and not throwing it away immediately.

What experimental tests do you have that your theory is valid?