David Cooper wrote: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).
I'm not really interested in discussing this in terms of model numbers. For clocks C1 and C2 the experiments are identical because in all experiments they move, relative to each other, in the same way. That's a really simple and obvious fact. There are no contradictions in it. I think the underlying reason why you keep on seeing contradictions where none exist is because you simply refuse to accept that physics is an empirical subject, that statements in physics are only meaningful if they can be related to something that can be measured, that the movements of objects are only meaningful relative to another object and that the tick rate of a clock is only meaningful relative to another clock. Your statements fail to take this into account over and over and over again. The most recent posts of yours, to which I am replying here, will demonstrate this apparent blind spot of yours yet again.
There is no such thing as an event meshing failure in physics. As I said earlier, that stems from your misuse of the concept of a 4D spacetime graph and the concept of a worldline, and your weird notion (on your website) that these 4D spacetime graphs have to be "built" like some kind of Lego model.
Yes you are. Every time you change frame, you change the speed of light relative to the arena.
I don't know for sure what you mean by "the speed of light relative to the arena", but I presume you mean the speed of light from any light source as measured against the starting-line reference frame. That speed is measured to be constant. The speed of light, as measured against any reference frame is constant regardless of the movement of the light source relative to that reference frame.
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.
I disagree that you have provided any kind of proof of anything. I'm not sure you even understand what a proof is.
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.
In all 3 experiments clocks 1 and 2 (yours and mine) are receding from each other at speed v in leg 1. Therefore they each see tick signals from the other as slower than their own tick signals in leg 1.
In all 3 experiments clocks 3 and 4 are receding from each other at speed v. Therefore they each see tick signals from the other as slower than their own tick signals.
Your problem is that you persist in thinking that if clock X measures the tick signals from clock Y as slower than its own, then clock Y must measure the tick signals from clock X as faster
than its own. It doesn't. They each measure the other's as slower. This problem seems to me to stem from your apparent inability to get used to the fact that we have to talk about things in terms of how they can be measured, as stated at the beginning of this post.
For reference, see this post:
for all the details of the relative speeds of clocks 1, 2, 3 and 4. The relative tick rates that each pair of clocks measures depends on those 2 clocks' relative speeds. Nothing else. You can add in as many other clocks as you like, and have them moving around as you like. Adding new clocks doesn't suddenly change the relative tick rates measured between existing clocks. Think about the simple logic of that for a moment.
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.
I think your failure to appreciate that tick rates are things that are actually measured by comparing pairs of clocks stems from your attachment to some form of universal time, and failure to realize that time is what is measured by a clock. That's my theory anyway. It is the only reason I can think of for your statements.
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.
Your assertions do not agree with observed reality.
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 is measured to be the same by all observers. There is no contradiction in that.
Yes it does - you are changing frame and thereby changing the speed of light relative to the system. You're doing bad physics.
I'm not changing the speed of light. See above.
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.
I don't know what you mean by "the actual speed of light". If you're not talking about something that can be measured you're not doing physics
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.
They both measure each other to be slower. This is an empirical fact. See above. I'm not playing any games. I'm sticking to what is measured. i.e. doing physics.
We only need to compare them against each other, but we can include other clocks in that process.
Only if we make measurements against those other clocks.
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.
In experiment 3, the relative speeds of clocks 1 and 3 is v, and the relative speeds of clocks 1 and 4 is zero.
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.
When you refer to "the system" which observer are you referring to? The speed of light is c as measured by all observers. In all 3 experiments clocks 1 and 2 move at the same speed relative to each other in the first leg and then clock 2 changes reference frames. In all 3 experiments clocks 3 and 4 move at the same speed relative to each other throughout. Throughout it all, all clocks measure the speed of light relative to themselves as c. These are simply the facts.
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.
OK. That's what I've called "the starting-line reference frame".
I'm going to stay in the same place in the arena throughout, so my clock will tick along with clock 3 throughout.
OK. You're going to remain stationary relative to the starting-line and clock 3. So let's just call you clock 3.
Einstein is going to move away from me at v, so he will accompany clock 4 throughout.
So let's just call him clock 4. We've added no new observers so far.
You are going to stay with me for a while, then you'll race after Einstein to catch up with him,...
So in leg 1 my speed relative to C4 (Einstein) is -v. In leg 2 my speed relative to C4 is v.
...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.
In leg 1 I am stationary relative to C3 (you). In leg 2 the relative speeds of me and C3, as measured by either of us, are +/-xv (where 1 < x < 2). I was previously referring to this as 2v and you were right to point out that this is incorrect. So in leg 2 me and C3 (you) will each measure the others tick signals as slow compared to our own.
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.
OK. Lorentz is stationary relative to C4 (v relative to C3) in the first leg and -v relative to C3 in the second leg. So C3 (you) and Lorentz are C1 and C2 in experiment 1. I am C2 in experiment 3. Albert is C4 (moving with C1 in experiment 3).
I don't see the point in adding all these extra people. They're covered by various already existing clocks in the existing 3 experiments. So we've added nothing new. Therefore I see no possibility of any new insights from this. But let's go on and see.
Lorentz's clock runs more slowly than mine over the whole trip, so we can speculate about how that happened.
You are C3. Lorentz is C2 in experiment 1. Therefore Lorentz changes reference frames between leg 1 and leg 2 so that he can be re-united with you. You stay in the same reference frame throughout. So we are simply considering the "twin paradox" that has already been discussed by Halc and Tamminen.
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.
None of the above options are valid because none of them refer to what is measured by observers travelling with each clock.
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.
See previous comments about the speed of light as measured by all observers.
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).
All irrelevant because all options are invalid. See above.
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.
As I said earlier, I'm not interested in model numbers.
Those who can't recognise the contradictions here clearly doesn't have an adequate grasp of relativity, so they need to sort themselves out.