johanfprins wrote:rcain wrote: 1) '... relative to another' - NEVER - unless it is the same actual clock.
So there is no stationary clocks at all? Galileo stated that all items moving along within a single inertial reference frame are stationary within this reference frame. So you are claiming that Galileo stated BS?
- yes, there are NO stationary clocks at all.
- Galileo - maestro, mephisto and genius that he was, did not yet know about the nature of the velocity of light and thus too had no familiarity with Special Relativity - a priori or a posteriori.
- so NO, i am not proclaiming him a BS'er - he described what he saw and he interpreted it well, but not completely.
johanfprins wrote:
they are all moving and they anything else is an approximation.
An approximation of what?
but we can come pretty close to it.
Close to what?
an 'approximation' to some 'possible future' meeting point - a 'targeted' 4d-volume in space time which lies in the causal future of both frames.
'close to' 'at rest'/'of the same frame' - but they never actually can be whilst they are two separate objects. even a (finite/macro) 'solid material body' is just such an approximation, 'local space-time' an abstraction of that.
johanfprins wrote:
2) BOTH -
So you agree that two clocks within two inertial reference frames which move relative to one another with any speed v, MUST show identical elapsed time intervals equal tol (delta)t. I agree with this.
NO - that is not quite what i said (nor what i meant to imply).
what i meant is: for an observer on either A or B, his local clock appears to go at the same rate, it CANNOT EVER be otherwise (relative to itself).
however, what an observer is looking at here is NOT ACTUALLY 'time'; 'time' in this model is actually the 'relationship' between what his local clock appears to be saying and some other (arbitrary) 'reference' time, (in his past or in his future), and therefore it is NOT a single scalar quantity - by definition, EVER, and in reality.
if the other 'reference time' (clock) is in 'approximately' the same space time (ie. at rest wrt us), and ticks at the same rate on the chart, then we we say, 'nothing is moving' 'nothing is dilating' (much).
if two clocks are moving wrt each other, then all we can say is that 'IF AND WHEN' these objects should meet at rest, in some joint future position, each of the participants A and B, will be taking as their LOCAL origin the LEADING EDGE of their respective time lines (whereas they left any possible previous synchronisation at the TRAILING EDGE of their respective INDIVIDUAL and DIFFERENT trajectories.
johanfprins wrote:
if you wish to plan a future meeting between the two clocks and incorporate an 'arbitrary decision' about which clock (frame) catches up or slows down to meet (at rest with) the other.
One clock does not need to "catch up" with the other clock if they BOTH MUST show the same elapsed time (delta)t all the time.
they CANNOT and DO NOT show the same elapsed time ALL the time - by definition, during acceleration/deceleration/change of FOR there is NO SINGLE SCALAR VALUE defined for the 'actual delta-t', because the 'actual delta-t has not happened yet, in either AND BOTH frames.
i visualise, acceleration/deceleration//change of FOR as convolving a rotation of of both 'relative elapsed time' and 'relative distance' curve around 2pi, where the rotation goes also through 2 discontinuities, at which conjuncture, the 'target' (future) magnitudes (of elapsed time and elapsed distance), are 'SAID' to coincide: but, they do not ever truly coincide, only when at 'at rest' and the 'same place', do assume that approximation.
there is in this model therefore effectively an 'advance wave' - but it is ONLY a device for predictive calculation, since everything 'phenomenological' is ONLY ever history.
johanfprins wrote:
ps. ie. it only becomes 'dilated' (dilation only has meaning) relative to another frame.
Correct! So each clock keeps exactly the same time-rate within the reference frame in which it is according to Galileo stationary, equal to the time rtae on another clock which is also according to Galileo stationary within its own inertial refrence frame. This is exactly what I have been saying all along.
'...according to the reference frame in which it is' - YES, but as i have tried to explain, this is actually a meaningless quantity, since epistemologically, it can NEVER be otherwise. all we ever say about our own time-line is whether or not it exactly matches some other, at all times. SR says that it NEED NOT and indeed MUST NOT, in the case of bodies in motion relative to each other, and most noticable at near the speed of light.
johanfprins wrote:
All clocks are moving relative to one another, but each one of these clocks is stationary within its own inertial refrence frame and therefore there is not a unique stationary clock. Since the physics must be the same within each and every inertial refrence frame, this demands that all clocks must keep the SAME time within their respective inertial reference frames. The clock of one twin can thus not go slower or faster within the respective inertial reference frames of the clocks; withih which the twins are also stationary relative to their respective clocks. So how can one age faster than the other?
there IS a UNIQUE stationary clock, according to my interpretation - in fact there are (at least) 6 to be considered in 4d space-time:
- the stationary clocks of A and B as viewed back along the time-tines of each, backwards towards the clock at the origin of their travels.
- the stationary clocks of A and B as they look BACK along their respective trajectories at the final (2nd) meeting (now a historical fact),
- the 'notional' (variable/delta-t) stationary clocks of any/all possible future targeted meetings of the two objects, whilst they were in motion (including the all important 'conjunction' ('synchronisation' opportunity), when one or the other body effectively turns around - ie. is 'instantaneously stationary' wrt the other).
- the idea extends to equivalence with Einstein's multiple clocks network.
- most importantly however, NONE of these can actually be regarded as truly at rest, only approximately - locally flat/linear.
- and most importantly of all, the value read out on such clocks is of absolutely no value to us, on its own - it is the 'tuple's of BOTH clocks at those places/instances we are comparing and evaluating.
the twins 'actually' end up having aged differently, because, one twin OR the other establishes a trajectory TOWARDS, some ILL-DEFINED point in the the future world line of another, taking as its NEW ORIGIN (frame of reference), its own last instantaneous position - ie. its own (historical) LEADING EDGE towards 'some future' leading edge of the other.
which elapsed time is shorter on arrival, depends on this 're-alignment' of 'forward trajectory. (in fact a 'reflection' of the path taken in 'leaving' the origin, hence the (arbitrary) asymmetry according to who completes which parts of the reunion and how fast.
sorry for any laboring of points - as much for my own benefit as yours.