Steve3007 wrote: ↑
October 5th, 2018, 6:34 pm
You're just describing two clocks moving apart from each other at speed v. See earlier explanations.
That's all that happens during the first leg, but after a while CS chases after CE and CL returns to CD. We know from the final scores that D>L and E>S overall (and we don't know if D>E or E>D), but what we're interested in is the ticking rates during the first leg. The above shows a naming problem though which is enabling people to sow confusion, so let's rename some of the tick rates. D and E remain fine for both legs individually and combined as clocks CD and CE don't change their motion at any time during the experiment, but we need the names S1 and S2 for CS's tick rates on the 1st & 2nd legs, and SA for the average of both legs, and we need L1 and L2 for CL's tick rates on the 1st & 2nd legs, and LA for the average of both.
I can now clarify the final scores for the stretch of time between clocks separating and being reunited: D>LA and E>SA. These are facts - they do not vary with frame. The other facts we have are that D=S1 and that E=L1 - they do not vary with frame either. Denying these facts would be denying the best measurements that can be made, and that would be a rejection of physics. In addition to the facts, we have measurements made by comparing the apparent ticking rates of clocks while they are separated by distance and not co-moving, but these change depending on which frame is used to make those measurements, so they are not facts - they merely describe how things appear from specific frames.
Because E>SA, we know that either S1 < E or S2 < E (or that both S1 < E and S2 < E) .
Because D>LA, we know that either L1 < D or L2 < D (or that both L1 < D and L2 < D).
Those too are facts. It is mathematically impossible for them not to be correct. Denying them would be a rejection of mathematics. We are getting into conditional facts with "if"s and "else"s, but they are mathematical facts regardless of how unfamiliar you may be with the mathematical rules of logical reasoning. We can continue to derive further facts from the above:-
If D > L1, then S1 > E.
If E > S1, then L1 > D.
From these, we can see that any attempt to have both D > L1 and E > S1 results in contradiction. This is a really simple mathematical proof. Your trick of changing frame to analyse the two parts of the same experiment is not legal mathematically because it generates contradictions, and it isn't legal in physics either for the same reason. No one in physics should be backing it.
Steve3007 wrote: ↑
October 5th, 2018, 8:07 pm
Since, in leg 1, CD = CS (= CA) and CL = CE, the above is really just one inequality concerning 2 clocks separating at speed v. CD to the left. CL to the right. So you're simply claiming that there is some sense in which one of those clocks is ticking faster than the other. You've presumably tossed a coin and decided that it is the one that is moving to the left: CD.
In frame CD, D>L1 and S1>E.
In frame CE, E>S1 and L1>D.
The point is that if frame CD's account is true, then frame CE's account is false, and if frame CE's account is true, then frame CD's account is false. Tossing a coin doesn't determine which account is true, but pretending that there isn't an underlying reality can't make both accounts true. D>L1 and E>S1 are fundamentally incompatible - it's one or other; mathematically impossible for it to be both. You want it to be both, but you can't have that without rejecting mathematics, and if you do that, you've ceased to do real physics.
That was because you changed frame between experiments, and changing frame is an illegal move if you're going to combine measurements from two frames.
Why are you rejecting mathematics? You've been categorically proved wrong - every competent mathematician on and off the planet will back my position on this and tell you that you've got it wrong. The top physicists will also back my position on this if they are forced to choose, because to do otherwise would destroy their reputation. When the maths tells you you're wrong, you need to listen.
The reference frames that matter are those against which measurements are made, not the one against which we decide to describe relative speeds. What I did in the post to which you objected was to show that the relative movements of those reference frames are the same for all 3 experiments.
I am using frame-invariant measurements for my argument. In all frames, D=S1, E=L1, E>SA and D>LA. I don't depend on any other measurements at all for this. The fact that the relative movements of the clocks and frames are the same for the single experiment that we're doing here is no surprise at all - how could they be anything otherwise! Look at the maths and learn from it. The measurements from different frames which disagree with each other (most notably in relative tick rates) demonstrate that most of those measurements are misleading, so we cannot rely on any of them. The measurements that I rely on are the ones that are facts for all frames. I then take you out of your comfort zone into conditional facts, and that moves us into the mathematics of logical reasoning, although it is pretty standard maths when you say things like if a is a whole number less than 10 and greater than 8, it must be 9, so I don't see why you should be so troubled by it.
It's like this: Consider car A moving along road A at 60mph relative to that road. Consider car B moving along road B at 60mph relative to that road. If road A is road B, then the experiments are identical. If road A is moving at constant velocity relative to road B, then the experiments are identical. That is what you appear to be denying.
You're trying to divert things into a place where the contradictions are hidden. That's why I keep pointing you back to the two places where you can't hide from them: the relative ticking rates of clocks and the unhappening/rehappening of events. Both of these things destroy the set 2 models. The reason you lot put up such a determined defence of these invalidated models though is that you depend on model mixing and muddying the waters in order to hide the fact that you don't have any functional SR model. The set 2 ones are gone, and the set zero ones don't contain any time at all - just a pretence of time in the form of a misnamed space dimension in a static block. None of those models are viable. The set 1 models have event-meshing failures, but you can't even bring yourself to look at them, even though the key part of them in which some clocks travel more quickly into the future than others (no clocks run slow in these models) is often attributed to SR, but it can only happen that way in set 1 models, so again you rely on model mixing (mixing incompatible models to pretend that an attribute of set 1 models that's incompatible with all the other sets operates in set zero) to try to maintain the pretence that you have a working SR model. All you're left with is set 3 models with absolute frames, and one of those is LET. The other has a whole stack of superfluous junk in it and every point in Spacetime is zero distance away from every other point in Spacetime for light which never travels any distance at all and which therefore has no speed. Every single one of your models is a mathematical contrivance which adds complexity rather than reducing it.
With experiment 4, it becomes easy to see why changing frame is cheating. Let's change frame and see what it does to experiment 4. The change of frame forces us to use CA2 instead of CA in order to maintain full symmetry (with CA2 being at rest in this new frame):-
// Experiment 4
CD moves at -v relative to CA2 throughout.
CE stands still relative to CA2 throughout.
CL stands still relative to CA2 during leg 1 and moves faster (negatively) than -v relative to CA2 during leg 2.
CS moves at -v relative to CA2 during leg 1 and at v relative to CA2 during leg 2.
The relative velocities of CD, CE, CL and CS are the same in both legs as they were before. Various other clocks, moving relative to these clocks in various ways, may or may not be present. They are irrelevant to our measurements.
Of course they're the same as they were before - that's my point. You seemed to imagine that my argument depended on there being a difference there, but it doesn't. The contradictions don't show up there - they show up when you apply reasoning, investigating the conditional facts, and this is something you have failed to do, because if you had, you'd have found the asymmetries and contradictions for yourself.
The tick rates during the first leg are as follows: D=S, L=E, E>S, L>D.
OK, so as above CD = CS and CL = CE. So you have 2 clocks (CD and CL) separating at speed v, as before. You've tossed your coin again and this time you've decided that it's the one moving to the right that is, in some sense, ticking faster. What is it? Heads = left, tails = right?
Using the new names, that's D=S1, L1=E, E>S1, L1>D. (For the previous frame, we had D=S1, L1=E, D>L1, S1>E.)
You're the one who wants to toss the coin, but you also want it to land both heads and tails at the same time, and that's the place where you make your monumental error. In the underlying reality, only one of the two options can be right. It is mathematically impossible to have both E>S1 and D>L1, but so long as you deny this, you will continue to try to have your cake and eat it. You are tolerating contradictions.
The reason your frame change is an illegal move is that you're taking D>L from the first frame and S<E from the second.
No you are the one asserting relative tick rates here. As I've said, when we gather together all clocks that are co-moving and treat them as single clocks then it's simply 2 clocks separating at speed v in leg 1. You have arbitrarily decided that the left moving clock ticks fastest or the right moving clock ticks fastest with no physical difference between the two, accept for an irrelevant CA or CA2 (or any number of other irrelevant clocks) floating around.
We have frame-independent facts from measurements that show that D>LA and E>SA, so we know for fact that some clocks tick at faster rates than others. Denying that is denying the facts. I have not made any arbitrary decision about which clocks are ticking faster than which at any time - I cover all the possible options (including the possibility not mentioned directly here in which D=L1 and D>L2, and an equivalent case where E=S1 and E>S2). There is a set of possible realities and I have addressed ALL of them. That is what we do when we go through all the "if x then y else z" options. These are standard nuts and bolts of mathematics, and you really ought to be able to apply them.