@ACB,
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ACB
I assume that the answer has to do with your statement that the distance between the twins is a relevant factor. Any clarification of the specific problem I have raised above would be helpful.
Yes thats right. The thing is that in relativity we cannot seperate time dilation from space and velocity (and acceleration and mass). If we intellectually conceive that space is a kind of inert platform for things to happen, then we are tempted to take an objective perspective such that time dilation and other effects are caused not by space. Its a free floating gods eye view. Rushing intellectually from one observer to another through space would thus be seen as having no effect upon the factors acting within the universe. (Similarly for time, ie rushing backwards and forwards in time would have no effect either on physical measurements.) But that free floating objective classical view ends with relativity. The rushing about in intellectual space and time to have a look at what is 'really' happening has to be accompanied by shifts in frames of reference in relativity and the measurements of reality change with it. (intellectually speaking within the model that is, as well as reality itself).
A scientific model is not reality but a model of reality. If the model means that a change of reference frame changes the appearance of reality in that model then a key aspect of 'objectivity' has been lost. This is why i raise in other threads the concept of 'now'. 'now' according to science is as naive as 'gods make thunder'. We conceive of 'now' (the ever changing present) as simultaneous across the universe. Universal simultaneity is mathematically impossible under relativity. If A is simultaneous with B for observer X, then it can be A before B for observer Y, and B before A for observer Z. This has lead many scientists to actually believe that the 'now' is an illusion in a block spacetime universe. The future and past exist, the naivety of 'now' (that demarcates them) is an illusion.
Quote:ACB
What particularly puzzles me is that the amount by which the earth twin's clock advances (from the traveller's point of view) during the turnaround seems to depend on future events.
Hopefully my previous comments help to at least get the ideas that create your intellectual conflict, which is very understandable. None of us can get our 'naive' heads around it....... it is non classical. And this is special relativity! GR is much more complex.
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ACB
But the traveller could have changed his mind during the return journey, and decided not to go back to earth after all. How could the earlier observed advances of 19.8 or 39.6 years (or whatever the true figures are) be accounted for then?
Because if the traveller
changed his mind and didn't return, then the compared measurements between the twins
remain virtual. As such they can yield contradictory non absolute non classical comparisons. Each can make virtual measurements such that one says M>N and the other N>M. Only when they are in coincident time frames do the
virtual measurements for each
have to sum over the different (and contradictory) histories to reach agreement. Thats why i distinguish between actual and virtual comparisons. Actual measurement comparisons have to be mutually consistent. Virtual ones do not. From one actual comparison to the next actual comparison, the summation of different virtual measurements (history) have to come back to agreement.
This is why the early universe or any other spacetime position in the universe can appear (virtually) to run slower or faster. With special relativity (velocity time dilation) each effect is slower. But when we bring in acceleration and gravity, then one can see slower and the other faster. However, acceleration and gravity are not equivalent. For example sitting in our chairs. According to GR there is no force of gravity. Gravity does not pull us to the ground. It is the ground that pushes us up. Classically if you have an unopposed force on a mass then it will accelerate. That does not
necessarily occur in GR. In GR a net force on a mass will deviate it from its geodesic (which isn't necessarily a classical straight line constant velocity). Our geodesic as we sit on our chairs is to accelerate towards the center of the earth. We don't because a net force (from the springiness of the ground upon us) stops us following that geodesic.
In Newtons theories it necessarily followed that any mass following a path of acceleration (eg an orbit, parabola, etc) had a net force acting upon it, because the geodesic in newton's classical space and time model was motion of constant velocity. (not to be confused with constant speed of course, as with circular orbits). In GR the geodesics can be curved accelerating paths without a net force acting. ie gravity. Gravity is not a force (at least classically speaking) in GR.
I don't think many people realise that GR is also non classical, but in a different way to QM. Einstein accepted GR.
Compared to QM he felt it was classical. But really its a difference in non classicality. The reason is as follows....
If in a region of spacetime there exists two events A and B, such that it is conceivably possible to link them with a light ray, then it follows that one occurs before the other for all virtual observers. If under such conditions A occurs before B for observer X (virtually) then for all other observers travelling less than the speed of light relative to X then A occurs before B. The different observers would generally not agree on the virtual measurement of time between them, but all would agree that A occurred before B (by however short or long a length of time).
This is crucial to retaining a belief in causality. That is why einstein loved GR but hated QM. The non classical probabilistic nature of QM
threatened causality for einstein. He wouldn't let it go.
Spacetime objectivity he could live without, but not the philosophical threat to causality that QM poses.
But GR does undermine our naive intellectual conception of objectivity. The relationship between observer and measurement is non classical in GR. It is also non classical in QM. But they are different. That difference is reflected in the mathematics that tries to encapsulate each different non classical model and is why it makes them very difficult to unite. Not least is the concept of simultaneity. Universal simultaneity is inconceivable in GR.
It is necessary in QM in the understanding of entangled states!
However there is a possible saving grace. The simultaneity in QM
cannot transfer information. That is why information has become central to theoretical physics. It also brings in another
possibly non classical area of physics ...... entropy. Science is wrestling with concepts of classical and non classical forms of information. Classical information
emerges from large scale non classical information.