cos said:
Observers A and B will eventually both agree that A lags behind B and I see no reason why they cannot both agree that A ticked over at a slower rate than B thereby creating this lag.
Only if they both agree to use the frame in which they are currently at rest to make statements about clock rates. There is nothing that prevents them from using some other frame, it's a matter of arbitrary choice. You're talking as though an observer's inertial rest frame can somehow be taken as intrinsically representing that observer's "perspective", but there's no real basis for that; why are you so resistant to actually spelling out what frame you want the observers to use when you make statements like this?
cos said:
I'm not talking about what either of them 'sees' or 'calculates' or 'predicts' or ‘determines’ during that trip but about what they agree to after the trip.
It's misleading to use the word "sees" as if it were synonymous with the other ones which refer to frame-dependent calculations. What you
see visually is determined by when the light from different events strikes you, unlike frame-dependent calculations this is
not a matter of arbitrary choice, all frames will agree in their predictions about what time shows on your clock when you first see the light from a distant event. The rate you see a clock ticking is in general different from the rate you calculate it to be ticking in the frame where you're at rest--for example, as A is approaching B, B will see A's clock ticking faster than his own, even though in B's rest frame A's clock is really ticking slower than his own. In order to determine when things happen in a given frame, you have to take the times you saw events and do some abstract calculations in order to determine when the events "really" happened in that frame, and it's just as easy to do the calculations using a frame where you are
not at rest as it is to do the calculations for the frame where you are at rest.
cos said:
Prior to accelerating A is looking at a pulsar that is 'ticking over' at the same rate as his clock. On the basis that (according to Einstein) having moved - his clock is 'going more slowly' than it was before he started moving he will see that pulsar ticking over at a faster rate than his own clock however for him to be of the opinion that his clock's rate of operation has remained unchanged whilst the far-distant pulsar (some millions of light years away and lateral to his direction of travel) is now (virtually instantaneously) spinning on its axis at a faster rate than it was before he started moving is, in my opinion, (to put it mildly) a 'very silly' attitude.
This is exactly what is true in one particular non-inertial frame where A was at rest throughout this process, there's nothing silly about it, it's just a matter of how you define your coordinate system. Probably this is why physicists typically use words like "real" "physical" to refer only to coordinate-independent facts, because it would
sound kind of silly to say that there was a real, physical change in the pulsar's rate of spinning at the moment A accelerated; but
if you wish to defy convention and use these words to refer to coordinate-dependent facts, then you have to say that there
was a real, physical change in the pulsar's rate of spinning in A's non-inertial rest frame (unless you want to specify that 'real' and 'physical' can refer only to coordinate-dependent statements made in inertial frames, but in that case you won't be able to make any statements about which of two clocks is 'really' ticking faster if the clocks are at different locations in curved spacetime, like clocks at the top and bottom of a mountain, since all coordinate systems in non-infinitesimal regions of curved spacetime are non-inertial).
cos said:
Sections 1 through 3 of STR refer to fully reciprocal phenomena; clock A ‘is’ ticking over at a slower rate than B from B’s inertial frame perspective and clock B ‘is’ ticking over at a slower rate than A from A’s inertial frame perspective however in section 4 he points out that the phenomena is not fully reciprocal; that from A’s non-inertial reference frame B does not tick over at slower rate than his own clock but that his clock exclusively ticks over at the slower rate.
He doesn't say a single thing about non-inertial frames in section 4. If you disagree, please quote some part of section 4 that you think is referring to non-inertial frames.
cos said:
Contributors point out that I should specify to which frame’s point of view I am referring. In your opinion - to which frame was Einstein referring when he effectively, analogously wrote that clock A ‘goes more slowly’ than clock B?
He didn't use the words "goes more slowly" but rather said A "lags behind" B, which might be taken merely to mean that A's reading is less than B's reading when they meet. But even if you interpret "lags behind" to mean "goes more slowly", he did refer to a specific frame in that section, the "stationary" frame K in which the clocks A and B were initially at rest and synchronized:
From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.
Note that in this translation Einstein routinely uses the word "system" to refer to what we have been calling a "frame", and he also made clear that K referred to a coordinate system in section 3.
cos said:
He accelerates to an experimentally maximum attained instantaneous velocity thereby generating a gamma factor of 400 000. At that instant clock B ‘is’, according to his calculations, ticking over at the rate of 400 000 seconds for each of his own seconds.
He flicks a switch extinguishing his rockets and at that very instant clock B reverts from being 400 000 times faster than his own clock and instantaneously[i/] reverts to being 400 000 times slower than his clock!
Is he not likely to be of the opinion that an 800 000 x instantaneous reversal might have some affect on that clock’s mechanism to say nothing of what it might do to an observer accompanying clock B?
You don't appear to appreciate that non-inertial coordinate systems make exactly the same predictions about frame-independent facts as inertial ones in SR, so any purely local predictions you could make about the "clock's mechanism" or an "observer" (like whether any part of the clock breaks, or whether the observer is injured) will be exactly the same in a non-inertial frame as an inertial one. Keep in mind that in a non-inertial coordinate system, coordinate accelerations (even very large ones) need not be accompanied by G-forces as would be true in an inertial frames, because there can be "pseudo-gravitational forces" to cancel them out--again, please read this section of the twin paradox page.
cos said:
On the basis that, whilst still accelerating, A sees clock B (on Earth) ticking over 400 000 times faster than his own clock he must also ‘see’ (i.e. determine) that not only Earth seconds are passing at that enormous rate but also it’s minutes, hours and days. For Earth days to be ticking over at the rate of 400 000 for each of his own days it would have to be spinning on it’s axis at some 640 000 000K-h.
To make matters worse - he stops accelerating whereupon the planet instantaneously stops spinning at 640 million kilometres an hour and virtually stops spinning on it’s axis (it is ‘then’ spinning at some 400 centimeters an hour in lieu of 1 600 kilometers an hour).
People point out that A knows that in B’s reference frame (i.e. the planet’s reference frame) the Earth is not spinning on it’s axis at 640 000 000K-h but at 1 600K-h. If the Earth is not spinning 400 000 times faster than it was then neither is the second hand of clock B yet this is precisely what it is claimed he will ‘see’ (determine, predict).
Yes, these things will be true in one particular non-inertial coordinate system--what's your objection, aside from some sort of aesthetic distaste? As long as one properly applies the laws of physics in this non-inertial coordinate system, all predictions made about coordinate-independent facts (the facts most physicists would refer to as 'physical' ones, even if you don't) will be exactly the same as those made using an inertial coordinate system.
cos said:
If I am located at an axial point (i.e. the North Pole) of a large spinning, massless and transparent sphere in outer space looking at a clock on that sphere’s rim (i.e. it's equator) I will, according to Einstein’s section 4 STR see that clock ‘going more slowly’ (i.e. ticking over at a slower rate) than my clock.
It matters not that a person alongside that clock sees my clock ticking over at a faster rate than his clock. My presentation is from my point of view, not his!
Only if you choose to define "your point of view" as "your inertial rest frame". Again, unlike what an observer sees visually which is intrinsic to his worldline, what happens in an observer's rest frame is a matter of abstract calculations, they could just as easily do the calculations from the perspective of a frame where they are moving at 0.99c and choose to refer to that as adopt the arbitrary convention that this frame shall be referred to as "their point of view".
cos said:
I send another clock along a line of longitude on that sphere toward the sphere’s equator. As I watch it it progressively ticks over at slower and slower rates than my own clock as it’s speed relative to me increases (it is accelerating).
And again, the rate you see it ticking will be different than the rate it's ticking in your inertial rest frame (although they will both be slower than your clock).
cos said:
I have every right to assume that if I were to carry another clock along that same line of longitude that it, too, would progressively be ticking over at a slower and slower rate than a polar clock
You have a "right" to assume that if you want to continue to calculate things from the perspective of the inertial frame where you were at rest at the pole even once you have started moving from the pole. On the other hand, if you want to calculate things from the perspective of a frame moving relative to the pole--perhaps your instantaneous inertial rest frame as you are in motion--then you have an equal "right" to assume your clock is ticking faster than a clock at the pole. Both statements are correct given that you make clear which frame you want to use, but if you don't make it clear, these statements are simply too ill-defined to be right or wrong.
cos said:
I suspect that somebody will respond that from the point of view of observer XYPG on planet Poplex which is in a deadly spiral toward a black hole my clock will not progressively slow down however the views expressed, or opinions held, or determinations made, by that observer have absolutely no affect whatsoever on my observations or determinations and it is MY determinations and predictions to which my postings apply not those of potentially countless hypothetical observers.
No, YOU can make determinations from whatever frame you choose, you don't have to use the inertial frame where you are at rest. And even if you want to (arbitrarily) define "your determinations" as determinations made using inertial frame where you are at rest while at the pole, why don't you then also want to define "your observations" once you have started moving relative to the pole as determinations made in the inertial frame where you are instantaneously at rest at that moment, or even using the non-inertial frame where you have remained at rest throughout the whole journey?
cos said:
People insist that my (actually Einstein’s) comment that clock A will tick over at a slower rate than B is pointless unless I specify to which reference frame I am referring however my comment has always been in reference to ’my’ frame (i.e. observer A’s frame).
That's fine as long as you understand this is an arbitrary matter of choice, there is no intrinsic reason a given observer has to calculate things from the perspective of the inertial frame where they happen to be at rest (and as I said it's puzzling why you continue to refer to the pole's rest frame as 'my' frame even once you have started moving relative to the pole). Aside from this, you have made some statements about non-inertial frames which definitely suggest confusion between coordinate-dependent facts and coordinate-independent ones (like suggesting that a large coordinate acceleration in a non-inertial frame would somehow imply a clock or observer would be damaged).
