False. I have never made that statement. What I said was SR can handle acceleration but that acceleration is normally a GR function (non-inertial frame) and that Einstein referred to Frame Switching, which is as the result of acceleration or a GR function, when he spoke of the resolution to the Twin Paradox post 1911.
Actually, Einstein referred to handling accelerations through frame switching in his original 1905 paper. I was just reading it last night.
Actually "NO" you haven't quoted the arelevant text. What you have quoted is what he said in 1905 and it was based on relative velocity. That is what led to the issue others dubbed "Twin Paradox". It was post 1911 that Einstien claimed that "Frame Switching" broke that symmetry and is why the traveling twin actually physically stayed younger.
No, the symmetry is broken from the very start. From the astronaut's point of view, the journey to the beacon is a shorter distance than what his Earthbound twin measures. Same for the journey home. For the return trip, from Earth's POV it seems their clock is synchronized with the beacon and they started timing the return trip as soon as the twin started heading home. From the twin's POV, Earth's clock is ticking slow, but Earth also started timing the return trip before the astronaut reached the beacon, i.e. they "cheated" and will ultimately measure more time as having elapsed. Einstein knew this all in 1905, to him it was so obvious he didn't even need to consider accelerations, the coordinate change itself contains all the necessary information.
I posted the relevant text which showed that Einstein relied on a non-inertial frame (GR) to resolve the paradox.
And like I say, there's nothing wrong with the SR solution he gave in 1905. There's no ambiguity to the problem whatsoever, no matter what coordinate frame you choose to be stationary. From this point on, if you want to demonstrate that an ambiguity exists without GR, you'll have to set up some coordinate systems and show me how applying the Lorentz transformations leads to two contradictory results without further assumptions. Otherwise I'm not going to argue about the results of a calculation neither of us has done (here), I've already shown plenty of calculations and examples.
Smart to a degree but certainly not invincible. You do recall he fudged his formula to force the universe to be static until he was proven wrong.
His attempt to stabilize the universe didn't work anyhow. A little nudge either way sends it rapidly inflating or else catastrophically collapsing according to his own calculations.
Just as I claim he is forcing v = c to be a velocity limit to fit his theory by introducing the velocity addition formula. It may be true but I really have my doubts and certainly believe it has been advanced merely as a mathematical construct to appease his preconvieved ideas.
Like I say,
Fizeau. Michelson and Morley also duplicated the experiment with an improved apparatus. From what I've read, Einstein didn't even know about this experiment until after it was published, so if that's actually true it would be even more impressive.
You have missed the point. The differential "v" wasn't in vectors of the traveling twin but the differential between the actual velocity of the traveling twin vs the inertial rest v = 0 of the stay at home twin.
And if it turned out the Earth had actually been moving with velocity "w" the whole time as seen by observer "C", C's measurements (and later direct verification) would all show that the astronaut who left Earth returned substantially younger than his twin.
I have no problem with that. As long as you don't claim that the traveling twin's view of his stay at home brother being younger is physical reality.
Oh, but I do claim it's physical reality, insofar as physical reality is based on what you can sense, perceive, interact with and measure. I even gave a scheme by which each astronaut could, in principle, prove that the other one has a slower ticking clock. The question of whose clock was started first or whose clock ticks faster depends entirely on the reference frame from which you choose to answer these questions.
Not a clear statement. Are both astronauts moving apart from each other? Or did one accelerate away and leave the other behind?
The two astronauts were parked next to each other, then one of them turned on his rocket engines for a while. But the results would actually be the same even if the other one turned on his engines, or both of them turned on their engines and cranked it to different thrust levels. They don't even have to fire their rockets in the same direction, their accelerations could be perpendicular. All that matters is that they have a stable relative speed at some point in the distant future when both of them have run out of fuel or otherwise turned their engines off.
You fall into the same trap others have. Because accelerators propell particles using EM waves; which propagate at v = c, it is inherent that nothing can be pushed past v = c. However in those cases you have v = c as a differential between the particles and the propelling source. If an object is propelled by a source traveling with it there is no relavistic affect between thrust, fuel and load..
That doesn't explain anything at all. I already said it doesn't matter how the particles got up to speed in the first place. You produce them, you get them up to a certain speed by one means or another, you wait for them to cross a certain starting line, then you measure how many of them make it past a series of checkpoints, in order to measure their average rate of decay. It doesn't matter where you put the starting line, pick any point you want in the accelerator, and any particles passing that line will have statistical lifetimes from that point on which depend only on what their velocity is after they cross the starting line (there are no accelerations performed on the particles after they cross this line, and even somewhat beforehand).