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Re: Does Special Relativity contain contradictions?

Posted: September 26th, 2018, 11:21 am
by Steve3007
Yes, if I'm wandering through Spain and I remark that in a New Zealand reference frame I'm upside-down, presumably David would accuse me of implicitly claiming to be upside-down in an absolute sense, and that, since I'm not currently standing on my head, I am contradicting myself.

Re: Does Special Relativity contain contradictions?

Posted: September 26th, 2018, 6:59 pm
by David Cooper
Halc wrote: September 25th, 2018, 8:54 pmThat's fine. Einstein's relativity doesn't assert that the universe needs to 'be generated', so it isn't inconsistent on that front.
Indeed it doesn't assert that. The problem is though that a massive hole is left in the set zero 4D model which leaves it dependent on magical creation. The set 3 4D model doesn't depend on magic, so it should automatically be recognised as a superior model.
This (my bold) is the first I've heard you describe 'Einstein's Minkowski model' as consistent, except for this generation point, which is a philosophical topic on its own that you'll also have to take up with Lorentz who proposed it, even if he didn't complete the work.
I've said before that it's Lorentz Invariant, so I assumed you'd realise from that that the contradictions that are a problem for some models don't directly apply to it. The trouble is that when you try to make the causality real, you have to generate it in order of causation, and that forces you to abandon it in favour of an equivalent model from a different set. Set 3's 4D model is also Lorentz Invariant because it accepts a preferred frame, but it also neatly eliminates the entire need for a block, so it's a much more realistic model than the set zero one, even when you take into account the complication of it having two kinds of time in it, the "time" dimension being distinct from the time of the absolute frame which governs how quickly things can move through the "time" dimension on different paths.
Halc wrote: September 25th, 2018, 9:14 pm David asserts one atypical interpretation and finds any other interpretation contradictory because it is not the one asserted.
The atypical interpretation in question is the model that appears to be Einstein's original SR (before Minkowski pushed it into an extreme place to get rid of the contradictions).
Halc wrote: September 25th, 2018, 10:41 pm
David Cooper wrote: September 25th, 2018, 6:25 pmIndeed - it is only proposing itself to be frame E (the absolute frame) in addition to itself.
Aww... The glimmer went out.
I see no hope of a common language.
Where's the difficulty? If frame E is the absolute frame and all frames are producing measurements that would be absolute truths if that frame happened to be the absolute frame, then all frames automatically serve as proposed absolute frames (whether the person using them intends them to or not).

Re: Does Special Relativity contain contradictions?

Posted: September 26th, 2018, 7:44 pm
by David Cooper
Tamminen wrote: September 26th, 2018, 4:53 amIf a clock in frame A ticks for 4 seconds and simultaneously, measured in A, a clock in frame B ticks for 2 seconds, the clock in frame B ticks slower than the clock in frame A, as measured in A. But measured in frame B the same 2 seconds are simultaneous with only 1 second in frame A, and this means that the clock in frame A ticks slower as measured in B. But it must be noted that the 4 seconds of the clock in A as measured in A are not simultaneous with the 1 second of the clock in A as measured in B, either from the point of view of A or the point of view of B. So simultaneity is frame-dependent. If x in frame A and y in frame B are simultaneous in frame A, they need not be simultaneous in frame B. So two clocks can both never tick slower than the other at the same time, meaning simultaneously. The relation of simultaneity is not symmetric between events in two frames. Counterintuitive perhaps, but not self-contradictory. And all this because the speed of light is the same in all frames.
If I'm standing here with a clock and you move past me with a clock, then you turn and come back to me with your clock, your clock has been ticking while my clock is ticking. There clearly is such a thing as "while" at a distance - it doesn't break because of the two things not sharing the same location. I could have a friend who's standing some distance away from me, again with a clock. You can walk from me to my friend and back with your clock, and your clock has been ticking while mine is ticking. For at least part of that time, your clock has been ticking while my friend's clock was ticking. My friend's clock is ticking while mine is ticking (though it's not known which ticks might be simultaneous, but if we're not standing terribly far apart and we're there for a long time, perhaps holding a conversation by phone throughout, we know that there's a substantial overlap). "While" is a real phenomenon, and it automatically contains the phenomenon of two clocks simultaneously functioning. Those clocks are necessarily ticking at some rate relative to each other.

When you walk away from me and back again, your clock has ticked at a lower rate than mine (on average). When you walk from me to my friend, your clock may be ticking at a lower, higher or the same rate than/as mine. When you walk back towards me, your clock then has to tick at a rate that will lead to the average rate for your clock being lower than mine. Some kind of mechanism governs this in the underlying reality. In the set zero proposed underlying reality, none of the clocks are ticking at all, so there's no direct problem there for set zero models. In the set one proposed underlying realities, your clock has ticked at the same rate as mine at all times, but it's taken a shorter path into the future which makes it look as if it's ticked less, however that's only the average. On the first part of your walk, my clock might have been taking a shorter path into the future than yours, but if so, then on the second part of your walk, yours would have had to take a much shorter path through the time dimension into the future than mine. (Incidentally, this reveals that set 1 models do have an absolute frame hidden in them.) With the set 3 models, the underlying reality has one clock run slower than the other or both run at the same rate, so there are no contradictions. With the set 2 models though (and these are the ones we're interested in when looking at this issue of contradictions), we have a clear contradiction - while you're walking away from me and back, your clock ticks more slowly than mine. We see that in the measurements. What happened to your clock while you were making your trip? If it ticked more slowly than mine throughout your trip, then it ticked more slowly than mine while you were walking away from you, and it ticked more slowly than mine while you were walking back towards me. However, if your clock was ticking more quickly than mine while you walked away from me, it must have been ticking more slowly while you were walking towards me. And if your clock was ticking more quickly than mine while you walked towards me, then your clock must have been ticking more slowly than mine while you were walking away from me. Those are mathematical certainties. If all of those are true accounts of events, then your clock was ticking faster than mine while it was ticking slower than mine. Worse, it would also have had to be ticking more quickly than itself. These contradictions destroy the set 2 models.

Re: Does Special Relativity contain contradictions?

Posted: September 26th, 2018, 7:50 pm
by David Cooper
("while you were walking away from you" should obviously have ended with "from me" rather than "from you".)

Re: Does Special Relativity contain contradictions?

Posted: September 26th, 2018, 8:18 pm
by David Cooper
Steve3007 wrote: September 26th, 2018, 5:10 am One problem, in my opinion, is that David falls into the trap that lots of people fall into when talking about time. It's the trap of misusing temporal language...
Nope - see my reply to Tamminen just above here. I'm using the word "while" correctly.
So now, keeping all of this in mind we can try to make sense of the options David claims to have given us above. It seems reasonably clear now that those two options contain implicit premises. One implicit premise is that there is a third clock (which I'll call clock E) implied by his two uses of the word "while". Another is that there is a third observer (whom I'll call observer E) who is holding that clock and receiving signals from clocks A and B so he can give us his judgement as to which is measured to be ticking faster.
You don't need clock E to explore the while issue between two clocks. We only need to consider how fast they're ticking relative to each other, and we can demarcate the "while" with precision between two points in time where the two clocks are at the same location.
If I say "I am stationary in the reference frame represented by the marks on the inside of the chassis of my car" I am not, either explicitly or implicitly saying "...and I am also stationary WRT another reference frame in which the ether is stationary." Of course I'm not.
Of course you're not also asserting that you are stationary in frame E. The frame is, however, automatically making a proposal that it might be the absolute frame. (Note, I mean that in the same way that I do when I talk about frames making assertions. It's again shorthand for a much lengthier wording in which would avoid treating the frame as an active participant with a mind of its own. The easiest way to get to what I mean would be to imagine an observer as being allocated to the frame, and he is the one who considers the possibility that this frame might be the absolute frame, realising that if it is, then the measurements he's making would be an accurate representation of the underlying reality rather than a misrepresentation of it. So, he can produce correct statements like, "if this is the absolute frame, then that object is stationary in the underlying reality").
Of course, if I'm wrong to think that those premises are implied, then the true premises need to be made explicit in order to render the propositions meaningful enough to be susceptible to analysis. The precise sense in which the word "while" is being used needs to be explained.
It means "while" in the sense that any normal person understands it before they have their head messed with by bad philosophy masquerading as physics.

Re: Does Special Relativity contain contradictions?

Posted: September 26th, 2018, 8:49 pm
by David Cooper
Steve3007 wrote: September 26th, 2018, 8:00 am The Japan/Peru analogy would be a more accurate analogy of lying observers who make false reports as to what they are measuring, which are also self-contradictory.
Very true, but I wasn't trying to create a perfect analogy - I simply wanted you to see clearly that a sentence can contain a contradiction without making one directly itself.
A better analogy would be a person who claims to have spent their whole life upside down with respect to a reference frame that is right-way-up in New Zealand but right-way-up WRT an England-orientated frame. If they are an unadventurous Englishman then their statement is true and not self-contradictory. If they are more adventurous then it's probably a lie, but it's still not self-contradictory.

David, your position would presumably be: No! There is a hidden claim in their words. They're also claiming to have spent their whole life the right-way-up relative to the ether - the absolute frame. I demand that you accept this as true. If you don't, then you lack reasoning power.

Yes?
You haven't managed to create a perfect analogy either. The claim of that individual is either competent or incompetent, depending on whether he can know it to be true. If he's watched years of video evidence of his childhood plus an internal video of himself in the womb, then he might know whether his claim is true or false, in which claim his claim will the a truth or a lie accordingly. A lie is in contradiction to the truth, but producing a lie is not a contradiction in itself. Your frames are weird things that revolve, and the aether has no up or down.

I remind you again that this path that you keep trying to drag things down is a diversion - the business of things moving or not moving is not part of my argument. I do not depend on it at all, but it is resolved by what is found once the argument has been followed to the end. At the moment though, you're still struggling to digest the meaning of "while", so that's something you need to work on.

Re: Does Special Relativity contain contradictions?

Posted: September 26th, 2018, 10:17 pm
by Burning ghost
David -

The whole Japan and Peru business can also be interpreted as non-contradictory. This is an issue of semantics. One could say that someone has to have lived in Peru to have left Peru, so to say “I’ve never been outside Peru” can easily enough be taken in such a way - note: none of that has anything to do with physics.

What puzzles me is the seeming belief that the universe plays out in a rational way (by human standads.) We don’t understand much at all. It is a wonder we understand anything at all. I find it deeply presumptious to assume the universe plays out logically and meaningfully in our small little spark within the inferno we call “life”.

When it comes to abstraction humans are not very good at dealing with things logically.

Analogies in physics are not particularly useful other than for giving a very rough gist to someone who has no idea how mathematics works - and most people have no idea how mathematics works.

You’ve failed to follow through as far as I can see. Make up your mind what you’re task is. Is it epistemic? Semantic? Or physical? The later is not fit for this forum unless you’re talking about “science” from a philosophical perspective.

Re: Does Special Relativity contain contradictions?

Posted: September 27th, 2018, 12:33 am
by Steve3007
David Cooper wrote:At the moment though, you're still struggling to digest the meaning of "while", so that's something you need to work on.
OK, I'll work on it.
Steve3007 wrote:"while" = at the same time.
Time is the thing that is measured by clocks.
viewtopic.php?p=320312#p320312

Finished.

Re: Does Special Relativity contain contradictions?

Posted: September 27th, 2018, 12:54 am
by Steve3007
David Cooper wrote:It means "while" in the sense that any normal person understands it before they have their head messed with by bad philosophy masquerading as physics.
I realize that I've probably had my head messed with by bad philosophy masquerading as physics, and as a result of that my definition of the word "while" is rambling and confused. To set me straight, as a clearer thinker than me, please could you give me your definition of the word "while" in the form of a single short sentence of the form "while means...".

Re: Does Special Relativity contain contradictions?

Posted: September 27th, 2018, 1:19 am
by Steve3007
To Tamminen :
David Cooper wrote:If I'm standing here with a clock and you move past me with a clock, then you turn and come back to me with your clock, your clock has been ticking while my clock is ticking. There clearly is such a thing as "while" at a distance - it doesn't break because of the two things not sharing the same location. I could have a friend who's standing some distance away from me, again with a clock. You can walk from me to my friend and back with your clock, and your clock has been ticking while mine is ticking.
As I've said, I was under the impression that "while" means "at the same time as" but I may be mistaken, so I'm waiting to be corrected about that.

If I turn out to be right, and it does mean that, look at the above and replace all instances of "while" with "at the same time as". Then consider that in order to be meaningful within the subject of physics (and science generally), propositions must (either directly or indirectly) relate to something that can be measured. i.e. they must be falsifiable. That includes propositions about time. So if I make a proposition about time, you are quite justified in asking me: "time as measured by what clock?".

Bearing that in mind, think about what clock David must be implicitly referring to, in the above passage, when he makes such propositions as: "your clock has been ticking at the same time that my clock is ticking." i.e what clock is making that measurement of simultaneity in that sentence? Is it either of the two clocks that are referred to explicitly? Or is it an unmentioned third clock?

Re: Does Special Relativity contain contradictions?

Posted: September 27th, 2018, 4:29 am
by Steve3007
Steve3007 wrote:Please may I refer to "the absolute frame" as frame E.
viewtopic.php?p=320305#p320305
David Cooper wrote:You can if you like, but when frame A is automatically serving as a proposed absolute frame, it means that it's proposing itself to be frame E, so a single measurement is a measurement for both frames at the same time (frame A and the frame that it proposes to be the absolute frame).
viewtopic.php?p=320314#p320314
Steve3007 wrote:If I say "I am stationary in the reference frame represented by the marks on the inside of the chassis of my car" I am not, either explicitly or implicitly saying "...and I am also stationary WRT another reference frame in which the ether is stationary." Of course I'm not.
David Cooper wrote:Of course you're not also asserting that you are stationary in frame E. The frame is, however, automatically making a proposal that it might be the absolute frame.
viewtopic.php?p=320451#p320451

Go figure.

Re: Does Special Relativity contain contradictions?

Posted: September 27th, 2018, 3:29 pm
by LuckyR
Steve3007 wrote: September 27th, 2018, 1:19 am To Tamminen :
David Cooper wrote:If I'm standing here with a clock and you move past me with a clock, then you turn and come back to me with your clock, your clock has been ticking while my clock is ticking. There clearly is such a thing as "while" at a distance - it doesn't break because of the two things not sharing the same location. I could have a friend who's standing some distance away from me, again with a clock. You can walk from me to my friend and back with your clock, and your clock has been ticking while mine is ticking.
As I've said, I was under the impression that "while" means "at the same time as" but I may be mistaken, so I'm waiting to be corrected about that.

If I turn out to be right, and it does mean that, look at the above and replace all instances of "while" with "at the same time as". Then consider that in order to be meaningful within the subject of physics (and science generally), propositions must (either directly or indirectly) relate to something that can be measured. i.e. they must be falsifiable. That includes propositions about time. So if I make a proposition about time, you are quite justified in asking me: "time as measured by what clock?".

Bearing that in mind, think about what clock David must be implicitly referring to, in the above passage, when he makes such propositions as: "your clock has been ticking at the same time that my clock is ticking." i.e what clock is making that measurement of simultaneity in that sentence? Is it either of the two clocks that are referred to explicitly? Or is it an unmentioned third clock?
I totally get what you you are trying to say, but luckily, either wording is fine. The error implied in the post you quoted is in the (unspoken) assumption that by the two clocks being separated (or not separated for that matter) somehow either implies synchronization or a lack of synchronization. Of course the clocks don't care, they will keep time just fine. The reason that folks get confused is with the idea that two clocks which work perfectly well ie they keep time identically, can read two different times depending on the velocity of the individual clock.

Re: Does Special Relativity contain contradictions?

Posted: September 27th, 2018, 4:32 pm
by David Cooper
Burning ghost wrote: September 26th, 2018, 10:17 pm The whole Japan and Peru business can also be interpreted as non-contradictory. This is an issue of semantics. One could say that someone has to have lived in Peru to have left Peru, so to say “I’ve never been outside Peru” can easily enough be taken in such a way - note: none of that has anything to do with physics.
"I've never been outside of Peru" means exactly what it says. If someone has never been in Peru (and has therefore never left Peru, that would mean that they have always been outside of Peru, in which case for them to claim they've never been outside of Peru would not be correct.
What puzzles me is the seeming belief that the universe plays out in a rational way (by human standads.) We don’t understand much at all. It is a wonder we understand anything at all. I find it deeply presumptious to assume the universe plays out logically and meaningfully in our small little spark within the inferno we call “life”.
Our aim in science and philosophy is to understand as much as possible. We have rules of reasoning which are part of mathematics, and we apply those to the world. When we find a rational explanation for something, we prefer that to a less rational explanation of the same thing. For example, when you shout into a cave and hear a voice come back out of it, you can either propose that there's a spirit in the cave or you can do experiments that support the idea that your own voice is bouncing back out at you. We generally consider the latter explanation to be better as the mechanism for it is simpler, while it accounts for the same facts. In the case of relativity, we have a fully rational theory (LET) which doesn't depend on anything weird. Physicists though have gone instead for an irrational theory which has lots of defects which should have ruled it out.
When it comes to abstraction humans are not very good at dealing with things logically.
Then they need to work on improving their skills at applying logic.
Analogies in physics are not particularly useful other than for giving a very rough gist to someone who has no idea how mathematics works - and most people have no idea how mathematics works.
Analogies rarely fit precisely - you are only meant to take from them the part that fits. In the case of the one I used, the only part that was relevant was the existence of a clear contradiction, and I then used that to show how that contradiction can appear at different levels in sentences, allowing one sentence containing it to be true while another sentence containing the same contradiction is false. This part of the discussion is also a diversion away from the issue that's supposed to be being looked at, and you're now allowing yourself to be dragged down that diversion, which shows that it's been an effective tactic. As I've said many times, my argument doesn't depend on the moving vs. not moving issue. If people want to attack my argument, they need to focus on my argument instead of obsessing over a throw-away line in an introduction to a page about relativity (which happens to be correct, but which is only shown to be correct once you've reached the end of the argument - it is not a starting point and should not be treated as one).
You’ve failed to follow through as far as I can see. Make up your mind what you’re task is. Is it epistemic? Semantic? Or physical? The later is not fit for this forum unless you’re talking about “science” from a philosophical perspective.
How have I failed? This is a subject that clearly lies across an intersection between physics and philosophy. Physicists like to claim that it's beyond the reach of physics, but at the same time they arrogantly make all manner of claims which should by the same token be outside their remit. If there is a line to be drawn between the two things, they are crossing it on a selective basis, applying a bias in when they decide to cross it and when they deny others the same right to do so. They won't allow this to be discussed on physics forums, and yet they push their own pet metaphysics relentlessly.

My argument is simply applied reasoning. It is arguably philosophy, it is arguably physics, and it is arguably mathematics: the three things overlap. It's really simple: there are several models that are used for SR, some of them mixtures of different incompatible models. I've shown the divides between different models and pointed out where most of them break or where they have complications which make them less likely to be correct. The set zero models are static eternal block universes which cannot have real causality in them. They are broken. The set 2 models generate contradictions, so they are broken. The set 1 models have event-meshing failures, and the most viable of them contains two kinds of time, making it contrived. The set 1 non-block models are streets ahead of the rest, and the 3D model (LET) is considerably simpler than the 4D one (which contains two kinds of time and is therefore contrived). Anyone rational is forced to recognise that LET should be seen as the main contender and that SR and GR are inferior to it - they are the ones that should be sidelined by Occam's razor, and some of their models should be rejected completely. Anyone who plumps for a 4D model is buying into a mathematical abstraction in which there is no speed of light and where some paths between all Spacetime locations exist that are of zero length. Why would anyone rational favour that over a simpler theory in which things are much closer to what we actually see and where all the right measurements are predicted by that theory?

I've set out my case, and if anyone thinks they can shoot it down it should be easy for them, but what do we get? Diversion tactics and word games. If you want to break a stick in half, you want to pin the ends in place and apply a force to the middle. You can't break it in half by spending weeks arguing about the colour of its bark. However, if you know that you can't break it, you might spend weeks arguing about the colour of its bark as a way of diverting attention from the fact that you can't break it.

Where are the best places to try to break it? One way would be to show that causation can be real in a set zero static eternal block model. That's not going to happen though - time does not run in that kind of model, and process cannot run either - no effect can be caused by its apparent cause because the "cause" did not precede the effect. There is no fix for that other than to accept that such a block needs to be generated in order of causation, and then you have issues with relative rates of causation on different paths, dragging a running time into things. You can achieve that by applying magic or by switching to one of the other sets of models.

Another way to attack my argument would be to show that set 2 models aren't destroyed by contradictions, but they absolutely are - there's no way to save them. This is where the happened vs. not happened issue needs to be looked at, and where the issue of two clocks both running faster than each other comes in. Those aren't going to break.

Another point to attack is my claim that light reduces all paths to zero length and zero time in 4D models, but that claim isn't going to break either. I pinned down a mod at the TNS forum on this point and proved that he was wrong. He was never seen there again, because leaving was the only way to avoid admitting he was wrong, but he's still very much alive, posting on a mathematics forum. Halc claimed I was wrong about that too, so I set out a proof that what I said is correct, and he's said nothing more about it.

Once a model's been shown to fail to function, it's gone. The set zero and set 2 models are out of the running. No one wants the only viable set 1 model because it's too far-fetched. There are only 2 models left on the table, and they're the 3D and 4D non-block ones in set 3. The 4D one contains two kinds of time and has no speed of light. We're only left with LET as a realistic option, and it's faultless: speed of light = c; no contradictions generated; no block needed; a simple aether rather than a denied complex one; absolute truths; accounts for all the relevant experiments. One of the things that supposedly makes GR superior to LET is that it removes the need for gravity to be a force, but LET does the same: the speed of light is lower in the vicinity of mass/energy and this automatically produces the orbits that we see. It even accounts for the appearance of kinetic energy as two objects accelerate towards each other gravitationally, because all of that kinetic energy comes from the slowed functionality of the material involved as it gets deeper in the gravity well - when it's further out of the gravity well, that kinetic energy manifests itself as faster movement within the matter as it functions more quickly (internally).

The big question then is why people insist on asserting the superiority of SR and GR when they should be ruled to be inferior theories using much greater complexity to account for the same facts. What's happening here is that I'm setting out the reality of what these theories are, and other people are defending/denying irrational things in order to try to maintain the inflated status of the inferior theories.

Re: Does Special Relativity contain contradictions?

Posted: September 27th, 2018, 4:39 pm
by Tamminen
David Cooper wrote: September 26th, 2018, 7:44 pm ...while you're walking away from me and back, your clock ticks more slowly than mine. We see that in the measurements. What happened to your clock while you were making your trip? If it ticked more slowly than mine throughout your trip, then it ticked more slowly than mine while you were walking away from you, and it ticked more slowly than mine while you were walking back towards me. However, if your clock was ticking more quickly than mine while you walked away from me, it must have been ticking more slowly while you were walking towards me. And if your clock was ticking more quickly than mine while you walked towards me, then your clock must have been ticking more slowly than mine while you were walking away from me.
I think it is simpler than that. We have 3 frames:

Frame D: you standing with your clock.
Frame T1: I walking away from you with my clock.
Frame T2: I walking towards you with my clock.

You observe with your clock in frame D that my clock in frame T1 ticks slower than your clock.
You observe with your clock in frame D that my clock in frame T2 ticks slower than your clock.

I observe with my clock in frame T1 that your clock in frame D ticks slower than my clock.
I observe with my clock in frame T2 that your clock in frame D ticks slower than my clock.

Re: Does Special Relativity contain contradictions?

Posted: September 27th, 2018, 5:06 pm
by David Cooper
Steve3007 wrote: September 27th, 2018, 1:19 amAs I've said, I was under the impression that "while" means "at the same time as" but I may be mistaken, so I'm waiting to be corrected about that.
"At the same time" can refer to a single instant in time. "While" (and "during") refer to a stretch of time. If you walk away from me with your clock and then bring it back, the ticking that your clock did while you were away occurred while my clock was ticking between the time of your departure and your return. In the same way, your clock was ticking between your departure and return, and while your clock was ticking, so was mine. They've recorded different amounts of (apparent) time passing during that time. Both ends of this time are perfectly synchronised for us as the two clocks were at the same location just before you set out and were at the same location as each other again as soon as you returned.
Then consider that in order to be meaningful within the subject of physics (and science generally), propositions must (either directly or indirectly) relate to something that can be measured. i.e. they must be falsifiable. That includes propositions about time. So if I make a proposition about time, you are quite justified in asking me: "time as measured by what clock?".
There are two clocks involved, and each has measured itself against the other. One has ticked less than the other, and both agree on which one that is.
Bearing that in mind, think about what clock David must be implicitly referring to, in the above passage, when he makes such propositions as: "your clock has been ticking at the same time that my clock is ticking." i.e what clock is making that measurement of simultaneity in that sentence? Is it either of the two clocks that are referred to explicitly? Or is it an unmentioned third clock?
It's both of the clocks that were referred to. Other clocks exist (including your third clock), but we can restrict ourselves to the two that we already know.

What do experiments tell us? You walk away from me and come back while I stay still, and your clock runs slower than mine. If you walk away at a constant speed and I wait for a bit before running after you, when the clocks are reunited, mine's run slow. When we walk along at a constant speed and I then run on ahead, then wait for you, again my clock has run slower than yours while they were apart. When we walk along at a constant speed and I stop, then run after you to catch up, again my clock has run slow while they were apart. In each case, the clock that didn't change speed ticked at a constant rate while the other clock ran slow on average. If the clock that changed speed ran fast on one leg of its trip, it must have run slow on the other leg. If it ran fast on leg one of one trip, it must have run slow on leg one of one of the other trips. There are simple rules about how logic applies to these cases, and what comes out of this are conditions about what must have happened in one case if a clock ran fast in another case. The analysis using different frames provides accounts proposing whether a clock ran fast or slow on different legs of the trip, and different frames produce contradictory accounts. They are simply not compatible. These contradictions drove Minkowski to produce his extreme 4D abstraction in order to escape from them - he recognised a contradiction when it presented itself before him. His solution was that neither clock was running at all. Set 1 models try to solve the problem by having both clocks run at the same speed as each other at all times, but the result is event-meshing failure. Set 2 models fail to solve the problem altogether and are invalidated. Set 3 models solve the problem by having an absolute frame.