David, I'm going to deal with this section first because it appears to show that you haven't got your head around the concept of relative motion, and as a result see us as swapping places when we haven't done so. It appears to me to be a good example of your attachment to absolute motion and, possibly, lack of precision about the definition of acceleration getting you in a muddle.
It's from this post:
viewtopic.php?p=320597#p320597
David Cooper wrote:Let's do something else with our clocks.
OK.
We repeat the first experiment and see that your clock ticked more slowly than mine (on average).
OK. To be clear: In this experiment I'm the traveler, in the sense that I'm the one who has to accelerate at some points, while you remain in the same inertial reference frame.
I walk away from you and come back. So I travel at constant speed in one direction and then turn around (i.e. accelerate) and travel at constant speed in the other direction. Let's say the first direction is to the right. Let's call the speed 'v'. So my speed, relative to you and relative to the earth on which we stand is v for half the journey and -v for the other half. Therefore, on turning back, my acceleration causes my speed, relative to an inertial reference frame, to change by 2v to the left. From v to -v. Your speed relative to the earth is zero throughout. You have undergone no acceleration.
Yes?
I then move my clock at the speed you carried your clock at during the first leg of that first trip and you race on ahead of me with yours, then wait for me to catch up.
OK. You move at speed v to the right and I move at speed 2v to the right, both relative to the Earth, on the first leg. So our speed relative to each other is v, as before. I then reduce my speed relative to the earth to zero. I stop. So, as before, I accelerate to the left such that my speed changes by 2v. You do not accelerate. So, in terms of our relative speeds and our accelerations this situation is
exactly the same as the first one.
Yes?
Again my clock has ticked more than yours, so we don't learn much from that.
Not surprising, because the situation is exactly the same and as we know the laws of physics are the same when measured against any inertial reference frame. Measured against an inertial reference frame traveling to the right at speed v, relative to the earth, our movements in this second experiment are
identical to our movements in the first experiment measured against an inertial reference frame that is stationary relative to the Earth.
Do you follow this?
But let's try it again with me walking at the same speed, but this time you stop for a while, then race after me. Again, your clock has run slower than mine.
OK. So, relative to the earth, you're moving at speed v to the right for the whole journey, with no acceleration. Relative to the earth, my speed is zero and then it increases to 2v by my act of acceleration, this time accelerating to the right. In the previous two examples I accelerated to the left. So, in terms our our separation, our relative speeds and our accelerations, again, this situation is
exactly the same as the previous two, except that right and left are swapped. So, again, no surprise that we get the same results.
But look at what's just happened. During this third experiment, my clock was moving through space at the same speed as yours was during the first leg of the first experiment, and your clock was moving through space during the first leg of the third experiment at the same speed as my clock did during the first experiment, so they've swapped places.
No. They haven't swapped places at all. The only things that have physical significance are their spatial separations, their relative velocities and their accelerations. Those have not changed. The second experiment is identical to the first, and the third experiment is the same except that left and right are swapped, which obviously doesn't make any difference. The reason why you think that they've swapped places is because you have this notion that their velocities "through space" are significant when all that is actually significant is their separation, accelerations and
relative velocities.
OK, I'll gradually deal with the other points through this weekend.