Excellent. I'm ready to follow whichever representation system provided it is internally consistent. According to your suggestion, clocks will be said measuring “time” intervals and thus the twins will effectively "age" differently. Clocks will follow geodesic lines in a 4-dimensions manifold...
I think the last post by stevendaryl was very helpful insofar it becomes clear that a clock delivers an invariant measure of a space-time interval along a one-dimensional curve. Since this curve does not, in general, coincide with the time coordinate axis, I think it is misleading to claim that...
No, I mean that I've never seen a statement whereby the measure S of a space-time interval varies depending on the path followed end-to-end, I've never seen a statement whereby what a clock measures is nothing else than S along a definite path. These are things you don't find in presentations of...
I thank you and stevendaryl for your inputs. Your confirmation that my proposal is fully backed-up by the most generic mathematical formalism of the SR and GR theories is a major step.
Due to the logical precedence of the “space-time” concept over its time and space coordinate components, I felt...
Hmmm... Let me express some doubts. Considering the responses proposed in #71, 72, 73 and 74, it appears there is no consensus about the actual meaning of the wording “proper time”. Does it refer ...
1- to an amount of “space-time” (here I mean the compound quantity S which is mathematically...
It took me some time until I could formulate an answer to this. Indeed I have a strong “aversion” to wordings such as “proper time, proper length, clock slowing down” or “running slow”, being “late”... and several more. On second thoughts, I think these wordings are remnants of an ontology - the...
I'm afraid the “cause and effect” relationship is not properly spelled out: there are two facets of the same relationship. On the ontological side, the difference between the values displayed by both clocks is due to the constraint which imposes different paths through space-time. On the...
Thanks for your input. I see a lot of interesting comments there. I noted in particular your definition of the “elapsed time”, according to which a clock measures a (composite) space-time quantity. As a minimum, its naming convention is misleading and hides a lot of non-intuitive consequences. I...
Let's come back to facts:
all things equal, the numerical value displayed by the accelerated clock is lower than the numerical value displayed by the inertial clock.
This is experimentally true. How should we understand this?
Often physicists state that “the elapsed time is what gets measured...
Wowww! It's clear I'll have difficulties in answering so many strong criticisms at a time. Thanks to all for your inputs anyway. I'll do my best to address the most pressing ones.
Let's consider first the “inertial” clock. It travels from location A to location B at constant speed. The rest...
Thanks for this clarification of your position. On the one hand you concur that time dilation cannot be a physical effect, but on the other hand most presentations of the twins experiment tend to show that this genuine physical effect is a consequence of time dilation. Hence your perplexity. …...
To be honest I'm not sure we disagree . We are debating on the meaning of “time dilation”. My claim is that “time dilation” relates to a change of the inertial frame of reference, and that an IRF sets a space-and-time framework into which the relative motion between physical objects gets...
I did not state, as you seem to believe, that a change of coordinate dependent quantities is relevant to metaphysics. It seems that some misunderstanding is developing here. I qualified as “metaphysical” such statements like “we have jumped into the future or in the past”, “the time flows...
It's a matter of consistency with other coordinate quantities. If the theoretician decides to move the origin on the time axis, all dates change value but we don't conclude that we have jumped into the future or in the past. Only the formal representation of history has changed.
In the same...