# Acceleration doesn't cause the Twin Paradox?

JDoolin
Gold Member

Can you draw the spacetime diagrams that will help it make sense? I don't see how it can help because as I pointed out significant events in one frame may not be significant in another frame.

I will do that.

This event at (x=0, t=5) in the original reference frame seems significant to the nonmoving twin, why? Because that is the time he will (later) figure out that the traveling twin turned around. He doesn't see the inbound twin turn around at that time. He won't see the inbound twin turn around until much later, because of the speed of light delay.

Now, I have this temptation to say we should only worry only about "significant" events, events that the traveling twin actually observes. That temptation is probably pretty valid.

But what are those events that the traveling twin is going to observe? Well, if he's interested at all in figuring out Special Relativity, he's going to aim a telescope at Earth and observe EVERY event. He's going to be watching where he came from the whole time. So he WILL eventually see that event at (x=0,t=5), but when and where?

So he's not going to be just asking what his own watch says. He's going too be asking "What news from Earth? How far away am I from Earth?" And this question has a very INTERESTING answer (to me anyway). But you wouldn't know it by reading any of the texts on special and general relativity.

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jambaugh
Gold Member

Pardon my late entry into the discussion. The paradoxical part of the "Twin paradox" stems from the implicit use of absolute time in a theory in which time is relative.

To be correct you must qualify the question "which twin is older/younger/are they the same age?" with some specification of the frame of reference. Each observer moving at a distinct velocity (vector velocity!) has a distinct definition of time and thus also a distinct definition of "at a given time" i.e. simultaneity of events.

The best way to express the paradox in my opinion is to have the triplets, two of whom leave home simultaneously (on their 20th Birthday) in craft traveling in opposite directions at relativistic speeds, say 80%c=4/5 c and the third staying home. Call them Adam, Bob, and Carl (Bob stays home).

You can then analyze the three questions:
When 20 years have passed for Bob how old are his brothers from his perspective?
When Adam is 20 years older how old does Bob and Carl appear to him (also how fast is Carl moving relative to him)?
When Carl is 20 years older how old do Adam and Bob appear to him?

From Bob's perspective the event where Adam and Carl are simultaneous to Bob's 40th Birthday occurs 20 years and 16 light-years from the common launch event so Adam and Carl will each have experienced $\tau = \sqrt{ 20^2-16^2}=12$ years. They will be as Bob sees it, 32 years old.

From Adam's perspective Bob is moving away at 80%c so on Adam's 40th birthday the simultaneous event in Bob's life is 20 years and 16 light-years away from the launch event and that's 12years along Bob's lifeline so on Bob's 32nd birthday.

To see how Adam perceives Carl's events we need the relative velocities. Note that 80% (of c in c=1 units) is approximately $c\tanh(1.0986123)$, doubling the pseudo angle yields: $c\tanh(2\times 1.0986123) \approx 0.97561c$.

To add relativistic velocities ( as a percent of c) express them as hyperbolic tangents of a boost parameter and add the parameters. Thus Adam see's Bob moving at 80% c and sees Carl moving at about 97.561% c (boosted twice as much via the parameter.)

From Adam's perspective Carl has a simultaneous event 20 years and about 19.5122 light-years away (97.561% of 20y) from the launch event and that occurs when Carl has experienced $\sqrt{20^2 - 19.5122^2} \simeq 4.39$ years. Adam see's Carl as only 24.39 years old on Adam's 40th birthday.

Carl see's Bob and Adam in the symmetric way as Adam sees Bob and Carl.

This is the correct relativistic analysis and by making it symmetric we've removed issues of who has or hasn't accelerated. Specifically Adam and Carl each has experienced symmetric opposite accelerations.

JDoolin
Gold Member

The best way to express the paradox in my opinion is to have the triplets, two of whom leave home simultaneously (on their 20th Birthday) in craft traveling in opposite directions at relativistic speeds, say 80%c=4/5 c and the third staying home. Call them Adam, Bob, and Carl (Bob stays home).

You can then analyze the three questions:
When 20 years have passed for Bob how old are his brothers from his perspective?
When Adam is 20 years older how old does Bob and Carl appear to him (also how fast is Carl moving relative to him)?
When Carl is 20 years older how old do Adam and Bob appear to him?

In short, when each triplet reaches 40 years old,
As Bob calculates it, Adam and Carl are 32 years old.
As Adam calculates it, Bob turns 32, and Carl turns only 24.39
As Carl calculates it, Bob turns 32, and Adam turns 24.39

What you are calculating is the "current age of distant objects." What you probably don't know is that there is a raging controversy on this topic; (well maybe just a one-man-raging-controversy.) Namely Mike Fontenot is arguing that this is an important concept. I agree that it is an important concept. You, apparently agree that it is an important concept.

But General Relativity Experts are claiming that it is NOT an important concept. They apparently think that the "current age of distant objects" is a fabrication.

This, along with the other blatant fabrications introduced by Michael Fontenot, should be removed, and no mention should be made here or anywhere else in the encyclopedia of his uncited paper from the unreliable source Physics Essays, which has failed for over 10 years to generate the slightest interest from professionals in the field.

Why do professionals in the field not have an interest in figuring out such a simple question?

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The paradoxical part of the "Twin paradox" stems from the implicit use of absolute time in a theory in which time is relative.

To be correct you must qualify the question "which twin is older/younger/are they the same age?" with some specification of the frame of reference. Each observer moving at a distinct velocity (vector velocity!) has a distinct definition of time and thus also a distinct definition of "at a given time" i.e. simultaneity of events.

Wow that's well said. I think that's the clearest & most accurate comment in this thread regarding the twin paradox.

JDoolin
Gold Member

Can you draw the spacetime diagrams that will help it make sense? I don't see how it can help because as I pointed out significant events in one frame may not be significant in another frame.

Here is a space-time diagram created by WWoods for Wikipedia's Twin Paradox Article.

You can see discussion of that here:
here, here, and here

WWoods did a good job at picking out the events A, B, and C. B is simultaneous with the turn-around event in the home-frame. A is simultaneous with the turn-around-event in the outbound frame, and C is simultaneous with the turn-around event in the return-bound frame.

jambaugh
Gold Member

What you are calculating is the "current age of distant objects." What you probably don't know is that there is a raging controversy on this topic; (well maybe just a one-man-raging-controversy.) Namely Mike Fontenot is arguing that this is an important concept. I agree that it is an important concept. You, apparently agree that it is an important concept.

But General Relativity Experts are claiming that it is NOT an important concept. They apparently think that the "current age of distant objects" is a fabrication.

It is an important concept in SR but ill defined in GR. A distant event is separated in space and in time. The concept of "current age" is an attempt to ignore the spatial distance which is problematic in SR (hence confusion over the twins) and down-right impossible to do in GR.

In GR we cannot extend the t=constant point on the observer's world line as a plane due to curvature of space-time. One can at best define a geodesic "now" hyper-surface tangent to local linear space but that can be topologically peculiar and altered dramatically by intervening masses, not to mention changing over time. Its not the kind of thing one can project out in the absence of distant observations. For example geodesically extending the "right now" space into a black hole will manifest as a time-like surface (with a space-like normal). Also in a deSitter space-time topology you'll have coordinate singularities (all of my past and future "right now" hyperplanes meet at a certain distance.

I see no problem simply rejecting any concept of "current time at distant objects" in GR scale physics. It is very theory dependent and far from operationally meaningful.

JDoolin
Gold Member

It is an important concept in SR but ill defined in GR. A distant event is separated in space and in time. The concept of "current age" is an attempt to ignore the spatial distance which is problematic in SR (hence confusion over the twins) and down-right impossible to do in GR.

The only problematic thing about "spatial distance" in SR is that there are multiple meanings for it.

"Simultaneous Distance"
"Image Distance"

The confusion mostly lies in not distinguishing between the meanings.

Dolby Gull are calculating Radar Distance.
WWoods, and Mike Fontenot are figuring out Simultaneous Distance.
For stellar aberration, and superluminal jets, you work with image distance.

The point is, they are all compatible if you say what you mean, but there is a lot of argument because people all think their meaning is "the best" meaning, or "the only" meaning.

I see no problem simply rejecting any concept of "current time at distant objects" in GR scale physics. It is very theory dependent and far from operationally meaningful.

How big is GR scale physics? Is that on a larger scale than stellar aberration, or Ole Romer's calculations? Or are stellar aberration and Ole Romer's calculations operationally meaningless?

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JDoolin
Gold Member

Re: Current age of distant objects...

It is an important concept in SR but ill defined in GR. A distant event is separated in space and in time. The concept of "current age" is an attempt to ignore the spatial distance which is problematic in SR (hence confusion over the twins) and down-right impossible to do in GR.

What exactly do you mean by "ill defined" and what exactly do you mean by "impossible to do in GR"

In GR we cannot extend the t=constant point on the observer's world line as a plane due to curvature of space-time. One can at best define a geodesic "now" hyper-surface tangent to local linear space but that can be topologically peculiar and altered dramatically by intervening masses, not to mention changing over time. Its not the kind of thing one can project out in the absence of distant observations. For example geodesically extending the "right now" space into a black hole will manifest as a time-like surface (with a space-like normal). Also in a deSitter space-time topology you'll have coordinate singularities (all of my past and future "right now" hyperplanes meet at a certain distance.

You probably didn't mean for me to address this point-by-point, but I can say for sure that we have distant observations, some of them up to forty-six billion light-years away, I believe.

Also, to the best of my knowledge, we actually have located some black holes in the universe. Maybe we don't know exactly how far away they are, but we can estimate. I don't want to extend "right now" INTO the black hole, but I would certainly like to get a good approximation of where the black hole IS.

When you talk about extending "right now" into a black hole are you talking about the Painleve coordinates? There are some strange coordinate systems that define objects falling into a black hole as co-moving. So yes, that is what I would call ill-defined, and in that situation, yes, doing such a thing makes using the Lorentz Transformations invalid.

I see no problem simply rejecting any concept of "current time at distant objects" in GR scale physics. It is very theory dependent and far from operationally meaningful.

It is theory dependent, in the sense that if you define a coordinate system based on objects which are accelerating relative to one another (Painleve coordinates) or moving away from each other (FLRW metric) then you cannot use Special Relativity in that coordinate system. But if you have a coordinate system where the coordinate system is NOT shrinking or expanding or accelerating, etc, (for instance the Schwarzschild metric.) then the coordinates are defined in the same way as Special Relativity, and subject to the same operations; i.e. rotation, translation, Lorentz Transformation.

jambaugh
Gold Member

The only problematic thing about "spatial distance" in SR is that there are multiple meanings for it.
exactly.
How big is GR scale physics?
that depends on the precision at which you're distinguishing events, the distance/durations over which you are comparing them, and the degree to which the intervening space is curved. When GR corrections become significant at your level of precision... there you go.
What exactly do you mean by "ill defined" and what exactly do you mean by "impossible to do in GR"
In SR an (inertial) observer frame is defined by a set of rectilinear coordinates, typically ortho-nomal ones are chosen, as we see in the TP the spatial separation as well as time separation of two events in one frame is needed to establish the same in another frame and hence compare simultaneity of events. In GR there are no global inertial frames and by "frame" we mean a set of curvilinear coordinates with the operational meaning noted by Einstein as a network of clocks and measuring rods. It is not sufficient to compare observer frames to just know where each observer's position and velocities in the other's frames. The "observer" is no longer locally defined as in SR. Indeed comparing velocities of two objects becomes problematic as one must ask "over what path?" and carry out parallel transport.

Listen, I don't want to hijack the thread on this. If you want to discuss it further start a new thread and pm me a link or post it here.

Nice formulas and diagrams... [stares confused, he only knows how to code]

On the related note, I thought that logic tells me that traveling at high speed causes slowing of the clocks... Why would "acceleration" cause the time difference when we consider this example:

Consider the case when twins traveled in parallel near the speed of light in 2 separate space ships and being close to Earth, the first one decided to land on earth and the second one on a planet 30 LY away a few seconds later... They both send their pictures as they land.

For the second twin, the picture arrives a few moments later. The first one receives it after 30 years when she is 30 years older. It's obvious that they concluded that not acceleration but travel at near the speed of light caused the "differences in age".

Unless I am wrong, I didn't violate any GR/SR principles in this thought experiment, but I don't see the problem with this "perception" of clocks.

JDoolin
Gold Member

Nice formulas and diagrams... [stares confused, he only knows how to code]

On the related note, I thought that logic tells me that traveling at high speed causes slowing of the clocks... Why would "acceleration" cause the time difference when we consider this example:

Consider the case when twins traveled in parallel near the speed of light in 2 separate space ships and being close to Earth, the first one decided to land on earth and the second one on a planet 30 LY away a few seconds later... They both send their pictures as they land.

For the second twin, the picture arrives a few moments later. The first one receives it after 30 years when she is 30 years older. It's obvious that they concluded that not acceleration but travel at near the speed of light caused the "differences in age".

Unless I am wrong, I didn't violate any GR/SR principles in this thought experiment, but I don't see the problem with this "perception" of clocks.

The twin paradox really doesn't happen in your example. For the paradox to occur, you have to have one of the twins go away and come back. You have to have them meet up in the same place they started.

The twin-paradox has a particular problem set-up:
One twin stays home while the other one goes on a journey and comes back. (That being said, I leave it to any General Relativity Experts to explain how this can be accomplished without any acceleration, as per their frequent claim.)​

I've added one detail. Instead of having the twin just go out to an arbitrary point in space, this twin actually has a destination, Planet X. I have a couple of "quizzes" based on the paradox with 99% of the speed of light right here:

The key to understanding the problem is the asymmetry involved. Whereas the stay-at-home twin merely sees the traveling-twin turn around and come back, the traveling-twin, during acceleration, sees the image of the stay-at-home twin suddenly jumps back! Whereas the stay-at-home twin sees the image of the traveling-twin departing for a large amount of time, and approaching for a small amount of time, the traveling-twin sees both parts of the journey take an equal amount of time.

Why is it controversial?

General Relativity Experts will always claim that this (the sudden lurching away of the image) is nonsense. • They will say the Lorentz Transformation is local and has no effect on faraway events. • They will claim that straight lines do not exist. • They will claim that coordinate systems are a religion. • They will say there is no clear meaning for distant "location" or "velocity" or "now," or that these notions are ill-defined. • I've even seen them argue that "reality" is an ambiguous concept.​

And I certainly agree that these concepts are ill-defined, but that is not a problem with the concepts. That is a problem of the text-book writers whose responsibility should include giving clear definitions.

The point is, though, that I do not understand the General Relativity Expert's arguments. Because I don't understand their arguments, the assumption is that I lack the education to understand their arguments, which I can acknowledge. Those arguments I listed don't make sense to me. But when we say "it doesn't make sense" we need to figure out what that means.

We can classify the various arguments of the General Relativity experts, and in exactly what way they don't make sense:

• the Lorentz Transformation is local and has no effect on faraway events (Wrong. The Lorentz Transformation affects every event in spacetime.)
• straight lines do not exist. (Not even wrong. How would you know that no objects move in straight lines if the concept of straight lines doesn't exist?)
• coordinate systems are a religion (total non sequitur)
no clear meaning for distant "location" or "velocity" or "now," (wrong, certainly wrong in the context of Special Relativity)
• these notions are ill-defined. (Right. But that fault lies with the definers.)
• Reality is an ambiguous concept. (total non sequitur. Doesn't that sound more like a religion than coordinate systems?)

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Janus
Staff Emeritus
Gold Member

The key to understanding the problem is the asymmetry involved. Whereas the stay-at-home twin merely sees the traveling-twin turn around and come back, the traveling-twin, during acceleration, sees the image of the stay-at-home twin suddenly jumps back!

Whereas the stay-at-home twin sees the image of the traveling-twin departing for a large amount of time, and approaching for a small amount of time, the traveling-twin sees both parts of the journey take an equal amount of time.

I'm not not quite sure what you mean by "the image of the stay-at-home twin suddenly jumps back". Nothing special happens to the image other than the traveling twin seeing it go from receding to approaching. In other words, the traveling twin also just sees the stay -at-home twin turn around and come back. The difference is that the traveling twin sees this happen immediately upon turn around, while the stay at home twin must wait for the light carrying the information about the turn around to travel the distance between them. This is what leads to the unequal times each sees in the halves of the journey.

JDoolin
Gold Member

Nothing special happens to the image other than the traveling twin seeing it go from receding to approaching.

Can you verify that with some math, perhaps? You're wrong, but unless you actually perform the Lorentz Transformation on the relevant events, you won't see why. But even without doing the math, you should be familiar with the idea of "stellar aberration." It's the same phenomenon, but to the side, instead of directly in front of you.

(Of course, after a Lorentz Transformation is done, common consensus of General Relativity Experts is that you should disregard the distance coordinates of events after Lorentz Transformation as meaningless, or nonsensical, as described in my previous posts.)

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JDoolin
Gold Member

Nothing special happens to the image other than the traveling twin seeing it go from receding to approaching.

Take care, also, to distinguish, also between image distance and simultaneous distance. If you change this sentence to "The simultaneous distance to earth is the same before and after the transformation" then it would be true.

But the image distance changes.

Attached is a space-time diagram distinguishing between radar-distance, image distance, and simultaneous distance.

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PAllen

Can you verify that with some math, perhaps? You're wrong, but unless you actually perform the Lorentz Transformation on the relevant events, you won't see why. But even without doing the math, you should be familiar with the idea of "stellar aberration." It's the same phenomenon, but to the side, instead of directly in front of you.

(Of course, after a Lorentz Transformation is done, common consensus of General Relativity Experts is that you should disregard the distance coordinates of events after Lorentz Transformation as meaningless, or nonsensical, as described in my previous posts.)

When I did this a long time ago, I concluded that if each twin were holding a clock that could be seen at great distance, the turnaround twin, at moment of turnaround would see the distant clock:

1) Change color from redshift to blueshift
2) Shrink in size, and become brighter
3) change rate

However, there would be no jump in the hands on the clock - just rate change.

I gather, by 'image distance' you are referring to interpreting the image size (a direct observable) as a distance based on knowledge of rest frame size and some model. However, you have a choice of models, including which optical effects you compensate for or not. The image size is an observable. Any particular image distance is a model dependent interpretation.

[Edit: And I think parallax distance would be the same as naively interpreted image size distance]

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JDoolin
Gold Member

When I did this a long time ago, I concluded that if each twin were holding a clock that could be seen at great distance, the turnaround twin, at moment of turnaround would see the distant clock:

1) Change color from redshift to blueshift
2) Shrink in size, and become brighter
3) change rate

However, there would be no jump in the hands on the clock - just rate change.

Yes, yes, yes, and yes. All correct.

I gather, by 'image distance' you are referring to interpreting the image size (a direct observable) as a distance based on knowledge of rest frame size and some model. However, you have a choice of models, including which optical effects you compensate for or not. The image size is an observable. Any particular image distance is a model dependent interpretation.

[Edit: And I think parallax distance would be the same as naively interpreted image size distance]

That's not exactly what I'm referring to. I'm referring to the intersecton of the observer's past light-cone with the world-line(s) of the object. The distance to the image is mathematically identical to the distance to the event that produced the image. If you're doing everything right, (i.e. if you choose the right model) it should work out the same.

Here is a conceptual animation of what I would do to find the image distance to an object:

with some discussion of it here:

http://www.spoonfedrelativity.com/pages/Is-Lorentz-Contraction-Invisible.php

PAllen

It seems like this equivalent to the following wording:

I pretend I was always moving the way I am now, then I figure out what distance I would have been from the object at the time its image was emitted. Distance here may be taken to be Lorentz 'ruler distance' based on my current simultaneity extended back in time.

Assuming you are now moving inertially, I believe this distance will be the same as image size distance (naively interpreted) and also the same as parallax distance. It will also be the same as radar distance to the emitting event determined by someone who really was always moving the way I am now.

So then we get into philosophy. Is it reasonable to interpret observations according to a counterfactual model (I wasn't always moving the way I am now)? I've expressed the view that it is perfectly feasible to do this, but not required or preferred.

JDoolin
Gold Member

It seems like this equivalent to the following wording:

I pretend I was always moving the way I am now, then I figure out what distance I would have been from the object at the time its image was emitted. Distance here may be taken to be Lorentz 'ruler distance' based on my current simultaneity extended back in time.

Assuming you are now moving inertially, I believe this distance will be the same as image size distance (naively interpreted) and also the same as parallax distance. It will also be the same as radar distance to the emitting event determined by someone who really was always moving the way I am now.

So then we get into philosophy. Is it reasonable to interpret observations according to a counterfactual model (I wasn't always moving the way I am now)? I've expressed the view that it is perfectly feasible to do this, but not required or preferred.

Yes, well said.

The same thing is done with a rotation transformation. You start with the mapping of events in space, then you ask the question, what would things look like if I had ALWAYS been facing to my left? And boom, there you are, facing left. And the light is reaching you as though you had always been facing left.

Similarly, The Lorentz Transformation Equation is mapping that counterfactual into the factual.

When you jump on a passing trolley, you are now in the reference frame of that trolley; your experience of events will be exactly the same as the other people on board that trolley. There is nothing about your history that can affect your current experience.

So the question to ask then is whether it is "just feasible" to do this, or is it "required?"

I think it is required.

Is there some kind of loophole where your immediate experience after jumping on a trolley, or turning your head left is affected by your experience before jumping on a trolley, or turning your head left?

PAllen

Well, if you change direction quickly enough, you will see extremely superluminal changes in image distance. You might argue that turning your head can create a superluminal illusion, but that's just it - everyone takes it to be illusion because you can feel rotation.

Similarly the always (or long time) inertial observer has every reason to treat the straightforward interpretation of measurements as being 'as real as anything gets' in physics. In contrast, someone going through extreme G-force to reverse direction has no rational reason to believe their direction change caused distant objects to move superluminally. They might prefer to equate their situation to the the head turner, and treat the visual changes as optical rather than physical phenomena. The very simplest way to do this is to pick any inertial frame for the analysis of the whole trip, translating measurements to it. Then, you have no surprising interpretations. Alternatively, you can choose any number of global coordinate schemes that mesh changing local frames together in such a way as to avoid particular undesirable interpretations (e.g. superluminal motion).

We've been down this road before. Many here grant that your preferred approach is a feasible way analyze any SR situation. We differ only when you want to insist it is the only or strongly preferred approach.

JDoolin
Gold Member

We've been down this road before. Many here grant that your preferred approach is a feasible way analyze any SR situation. We differ only when you want to insist it is the only or strongly preferred approach.

The alternatives I can think of are:

(1) Coordinates of distant events are observer dependent.
(2) Coordinates of distant events are theory dependent.
(3) Coordinates of distant events are ambiguous and undefinable.

I'm trying to make point #1 here, and I think you are either trying to make point #2 or point #3.

As for point #3, I don't know how to respond to that, but...

As for point #2, If you use spherical coordinates, Rindler Coordinates, Painleve Coordinates, FLRW coordinates, Schwarzschild Coordinates, Cartesian Coordinates, Minkowski Coordinates, then YES the coordinates are theory dependent. Coordinates are arbitrary in this sense. Description based coordinates can be defined whimsically. Once defined whimsically, description based coordinate systems can become difficult or even impossible to Lorentz Transform.

But Lorentz Transformation and Rotation are transformations of a completely different character. They don't change the description of the coordinates; they change the observer.

And in a transformation that changes the observer, you can't just shrug off changes in the positions of events as illusionary. They are real changes in the observer's perspective.

If you want more information on what I mean by "description dependent" vs "observer dependent" transformations, see http://www.spoonfedrelativity.com/pages/Types-of-Transformations.php.

JDoolin
Gold Member

The very simplest way to do this is to pick any inertial frame for the analysis of the whole trip, translating measurements to it. Then, you have no surprising interpretations.

When surprising ideas are defined with clarity, they may appear to be ridiculous. However, if an idea is true, it should be possible to defend the idea, even if, at first, it appears ridiculous.

Alternatively, you can choose any number of global coordinate schemes that mesh changing local frames together in such a way as to avoid particular undesirable interpretations (e.g. superluminal motion).

When we have an a priori idea of what represents an "undesirable interpretation" do you think it is appropriate to take extra steps to hide the facts so that this interpretation is hidden, or wouldn't it be more appropriate to acknowledge the facts, and expand our vocabulary of ideas until we can explain WHY this doesn't break the laws of Special Relativity?

The correct answer is going to "sound" ridiculous. But if it is expressed with clarity, it can be defended.

The fact is when I am on a merry-go-round, distant objects DO move faster than the speed of light RELATIVE TO ME. But in no way does that mean that the distant objects have traveled faster than the speed of light in any static reference frame. When I am on a merry-go-round, my reference frame is continuously changing.

(1) We can continue to make the claim that the experience of the person on the merry-go-round represents a single local reference frame, and just ignore the non-local objects which are (mathematically, but not really) moving faster than the speed of light.
(2) Or we could be bold, (stand up to ridicule,) and make the claim that the person on the merry-go-round is continuously changing their reference frame, and acknowledge the objects which are moving faster than the speed of light relative to the observer, but NOT relative to any static reference frame.