Steve3007 wrote: ↑October 1st, 2018, 2:43 amWhen I've said "Earth" please take this as shorthand for that starting line.
That's fine - I'm happy with shorthand of this kind where the transformation rules have been explained.
All three experiments are identical from the point of view of different inertial reference frames. The Principle of Relativity observes the fact that the laws of physics are the same in any inertial reference frame. Therefore all 3 experiments are identical.
That is where you're making your fundamental mistake. All three experiments appear identical, but they aren't. If you're using a set zero model, time doesn't run (or indeed exist at all), so there's no direct problem there, but when we're exploring the contradictions we're concerned with specific models which have running time where we allow some clocks to run faster than others rather than having them all run at the same rate as each other at all times (which would take us into the models with event-meshing failures), we are specifically testing set 2 and set 3 models, and what we find here allows us to eliminate the set 2 ones (including Einstein's original SR).
...but if you do that, you're changing the speed of light relative to clocks 3 and 4.
No you're not.
Yes you are. Every time you change frame, you change the speed of light relative to the arena.
The speed of light is observed to be the same when measured against any inertial reference frame. Clocks 3 and 4 are both stationary in inertial reference frames. Observers who are travelling with clocks 3 and 4 will measure the speed of light in a vacuum to be c, regardless of the movements of any other objects that might happen to be around, such as you and me.
This is the big result of the brainwashing - it is very effective in shutting down people's rational thinking, and you're one of an army of such victims. I've set a simple proof in front of you here, but you appear to be unable to process it. In experiment 1:-
If my clock is ticking faster than yours during leg 1 of your trip,
then clock 3 is ticking faster than clock 4. In experiment 3.
If my clock is ticking faster than yours during leg 1 of your trip,
then clock 4 is ticking faster than clock 3.
If both of these experiments are identical,
then clock 3 is ticking faster than clock 4 and clock 4 is ticking faster than clock 3, but that's a mathematical impossibility.
The reality is that
if my clock is ticking faster than yours during leg 1 of your trip in the first experiment,
then your clock is ticking faster than mine during leg 1 of your trip in the third experiment.
When it comes to logical reasoning, you seem to have an entire module missing. You're not alone in that though, because it is very much the norm for people who imagine that SR is valid. Some of them do see the problem though (Minkowski, perhaps) and recognise that set 2 models don't work.
One of the ways in which it can be described (but not the only way) is to point out that when the travelling twin turns around and comes back he switches inertial reference frames.
And that means changing the speed of light relative to the system for each leg, leading to a complete misunderstanding of what's going on.
The speed of light relative to clocks 3 and 4 reveals an asymmetry if clock 3 is ticking faster than clock 4 (or the reverse).
No it doesn't.
Yes it does - you are changing frame and thereby changing the speed of light relative to the system. You're doing bad physics.
The speed of light as measured by observers travelling with clocks 3 and 4 is c.
The apparent speed of light relative to them in each case is c. The actual speed of light relative to them may be different for each.
The rate at which clocks 3 or 4 are observed to be ticking depends on the clock against which they are compared and the relative velocities of the clocks.
We're only interested in how fast they're ticking relative to each other. You've playing a game where clock 3 is ticking more quickly than clock 4, then you change frame and claim that clock 4 is ticking more quickly than clock 3, but you're trying to have your cake and eat it by taking both of these things to be true at the same time.
If we're talking about clocks 3 and 4 measuring their tick rates relative to each other, by sending signals between them, then they will each measure the other to be ticking more slowly than themselves. Those two clocks will never meet again, so that is the only way that they will ever measure their relative tick rates. If you're talking about measuring the tick rate of clock 3 relative to another clock, or clock 4 relative to another clock, then specify which other clock you're referring to.
We only need to compare them against each other, but we can include other clocks in that process. In experiment 3, I start next to clock 3 and move away from it at the same speed as clock 4, so my clock ticks at the same rate as clock 4.
You're playing an irrational game where you change the speed of light relative to the system in order to pretend that experiments 1 and 3 are the same, but they aren't the same. There's an asymmetry there which you're simply ignoring and pretending doesn't exist. This shows that you have bought into the dogma 100%, because it's controlling you - you appear to be incapable of thinking independently of it any more.
Let's lock things down more clearly by doing experiments 1 and 3 at the same time with the help of a couple of friends. We are at rest in a frame in deep space which I call the arena. I'm going to stay in the same place in the arena throughout, so my clock will tick along with clock 3 throughout. Einstein is going to move away from me at v, so he will accompany clock 4 throughout. You are going to stay with me for a while, then you'll race after Einstein to catch up with him, so your clock will tick at the same rate as mine for the first leg of your trip, and then tick at a different rate during the second leg. Lorentz will initially travel with Einstein but then he'll turn round and come back to me. So Lorentz and I are doing experiment 1 while you and Albert are doing experiment 3.
Lorentz's clock runs more slowly than mine over the whole trip, so we can speculate about how that happened. There are five rational possibilities for this when we're testing set 2 and 3 models, as I set out earlier. Those options are:-
(A) My clock ticked more quickly than Lorentz's clock on both legs of his trip.
(B) My clock ticked more quickly than Lorentz's on the first leg and his ticked at the same rate as mine on the second leg.
(C) My clock ticked at the same rate as Lorentz's on the first leg and more quickly than his on the second leg.
(D) My clock ticked more quickly than Lorentz's on the first leg and more slowly than his on the second leg.
(E) My clock ticked more slowly than Lorentz's on the first leg and more quickly than his on the second leg.
Options (B), (C), (D) and (E) recognise the possibility that the frame in which the arena's at rest is not the absolute frame, but if you deny the existence of an absolute frame, then you can assume that (A) must be correct, so you can ignore the other options if you wish. In the same way, there are five possibilities for what happened with your clock and Einstein's, so we can set them out and give them names in the same way:-
(F) Einstein's clock ticked more quickly than yours on both legs of your trip.
(G) Einstein's clock ticked more quickly than yours on the first leg and at the same rate as yours on the second leg.
(H) Einstein's clock ticked at the same rate as yours on the first leg and more quickly than yours on the second leg.
(I) Einstein's clock ticked more quickly than yours on the first leg and more slowly than yours on the second leg.
(J) Einstein's clock ticked more slowly than yours on the first leg and more quickly than yours on the second leg.
There's some symmetry about this, but it isn't complete. Whenever we do this in the same arena, and all the more obviously when we do this at the same time in the same arena, we should be able to see the nonsense that comes out of changing frame in between the experiments to change the speed of light relative to the arena. Einstein's and Lorentz's clocks were ticking at the same rate as each other during the first leg, and my clock and yours were ticking at the same rate as each other during the first leg too. Logic dictates the following asymmetric things:-
If (A) --> not (F), not (G), not (H), not (I).
Therefore if (A) --> (J).
If (B) --> not (F), not (G), not (H), not (I).
Therefore if (B) --> (J).
If (C) --> not (F), not (G), not (I), not (J).
Therefore if (C) --> (H).
if (D) --> not (F), not (G), not (H), not (I).
Therefore if (D) --> (J).
If (E) --> not (H), not (J).
Therefore if (E) --> (F) or (G) or (I).
These rules come from LET, but they have relevance to set 2 models too. Set 2 models simply don't care and ride the contradictions, but no one who pushes a set 2 model should be denying that it generates contradictions. The contradictions are clear. If my clock is ticking more quickly than Lorentz's during the first leg and Einstein's clock is ticking more quickly than yours during the first leg, then my clock is ticking more quickly than yours while they're co-moving (and side by side), and Einstein's is ticking more quickly than Lorentz's while they're co-moving (and side by side). This renders set 2 models magical, ruling them out from real physics.
Those who can't recognise the contradictions here clearly doesn't have an adequate grasp of relativity, so they need to sort themselves out.