=Al68;2794254]I've mentioned before that Einstein's 1918 resolution addresses it from the non-inertial frame of the ship. I know most consider the standard resolutions adequate because they provide the correct answer, but Einstein realized full well that a 100% correct resolution isn't necessarily a satisfactory one.
Hi Al68
I don't even remember if I ever read that paper let alone the contents but I have some questions on principle:
1) As I understand it G time dilation in an accelerating frame only has an effect within
the frame itself . A relative dilation between differnt locations in the frame.
It does not have any effect relative to inertial frames {clock hypothesis]
The relationship with other frames is simply derived from the instantaneous relative velocity. As per your statement below ((2))
2) Even in a round trip with only a relatively short acceleration phase compared to total trip length;- m the overall trip time the cumulative diilation is based on both accel. ICMF velocity and inertial velocity
but the inertial phase dilation (from velocity), which would normally be reciprocal [relative] has now become real , actual.
{Catalytic effect}
3) There is no corralation between the relative percentage of the trip that is accelerated and the end result . Quite unusual for a physical phenomenon wouldn't you say?
For a relevant parameter to vary with no consequence to the end result??
IMO The reason many people are unsatisfied with the resolution is:
It seems like you should be able to analyse the picture from either frame in an identical manner. Assume the accelerating frame as at rest and the Earth is accelerating etc.
Draw an Earth worldline that is curved in areas and straight while inertial and apply all the relevant math on that basis. This of course can be easily calculated and in actuality wouldn't the calculations also be identical,?
Then there would be symmetrical Minkowski diagrams [reciprocal mirrow images] and all the analysis that is commonly used in resolutions would be identical.
But this is not allowed. It is denied on the basis of somewhat ad hoc pricipals
a) Acceleration is real as opposed to inertial motion which is purely relative [unreal]
b) Because of a) only inertial frames are considered valid.
c) Because a world line which changes direction makes it longer and accelerated . ANother version of
a) and b)
Regarding :
a) It is true that there are measurable differences between accelerated and inertial motion.
Unquestionable.
But does there simply being a difference mean there must be a specific effect attributable to that difference?
There is no physics principle or concept suggesting that acceleration would result in real dilation or how it might catalytically turn relative dilation into real or explaining how it possibly could effectuate this result.
So it is not because there aren't valid resoluions to the "paradox" that there remains the dissatisfaction [if anything there are too many]
it is because some seemingly valid ways of looking at it are negated on grounds that are themselves not completely satisfactory or consistent.
Basically, ((2)) you can break the period of acceleration into as many segments as you want, and calculate Earth time for each one in the ship's (co-moving inertial) frame. Or just use the equivalent of an infinite series of co-moving inertial frames: gravitational time dilation.
((1))
Einstein's resolution just uses the simple gravitational time dilation equation for linear acceleration to calculate elapsed time on Earth's clock in the ship's frame during acceleration. And, unsurprisingly, gets the same answer as the standard resolutions
I am going to have to read the 1918 paper (again?)
Judging by this it seems to indicate that G-dilation is exactly equivalent to velocity dilation [ICMF's etc.]
COnsistent with clock hypothesis
But this seems strange if G-dilation is constant but instantaneous velocities are varied.
ANy ideas ?
Thanks
