Timeline for How does the clock postulate apply in non-inertial frames?
Current License: CC BY-SA 4.0
13 events
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| Apr 23, 2022 at 23:54 | comment | added | Dale | @GumbyTheGreen you cannot have time dilation without a coordinate system. Time dilation is the rate of change of proper time with respect to coordinate time: $1/\gamma=d\tau/dt$. You cannot avoid introducing a coordinate system, that is where the $dt$ comes from. Because of the freedom of choosing your coordinates there is no 1-to-1 correspondence. You might benefit more from a discussion format than a Q&A format. I am active at physicsforums.com if you want | |
| Apr 23, 2022 at 22:33 | comment | added | Gumby The Green | I only brought the coordinate system into the mix because you said that $g$ "is a property of the particular coordinates chosen". My argument is primarily physical - the fact that there's a 1-to-1 correspondence between acceleration and "gravitational" time dilation in the accelerating frame. I suspect that a philosophical difference regarding the nature of causality is at play here that would be tough to resolve. | |
| Apr 22, 2022 at 2:31 | comment | added | Dale | @GumbyTheGreen no specific coordinate system is ever needed. You can do a twin’s analysis in inertial coordinates or in Rindler coordinates, or in any other coordinates you choose. It is not a matter of cause and effect, but simply a matter of convenience or inconvenience. Some coordinates will be easier than others, but none are caused by the physics, they are chosen. Pick any problem you like and I can work it in different coordinates, thus showing that there is no cause and effect relationship, no chain of causality | |
| Apr 22, 2022 at 2:05 | comment | added | Gumby The Green | Sure thing! Hmmm, I'll need to stew on all that. Since acceleration is what causes such a coordinate system to be needed, it seems clear to me that there's a chain of causality between it and time dilation. And this "gravitational" time dilation happens in flat spacetime if and only if there's acceleration. So saying that there's no causal link between them seems like a nonphysical math/accounting/semantic trick to me. But I think you've probably made the case as well as it can be made. | |
| Apr 22, 2022 at 2:05 | vote | accept | Gumby The Green | ||
| Apr 21, 2022 at 22:45 | comment | added | Dale | @GumbyTheGreen thanks for the edit, good catch! | |
| S Apr 21, 2022 at 20:09 | history | suggested | Gumby The Green | CC BY-SA 4.0 |
Fixed a math blunder
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| Apr 21, 2022 at 19:40 | review | Suggested edits | |||
| S Apr 21, 2022 at 20:09 | |||||
| Apr 21, 2022 at 11:22 | comment | added | Dale | @GumbyTheGreen yes, you are right on that last point, I will update the wording. On the rest, no, for the reasons already given. First, it is the “gravitational” potential not the acceleration, second it is a function of position, and third the g is a property of the coordinates not the objects in the coordinate system regardless of an object’s proper or coordinate acceleration they have a time dilation that depends only on the object’s position and velocity in the coordinates. There is no causal link as you say. We choose the coordinates for convenience, and could make a different choice | |
| Apr 21, 2022 at 11:07 | history | edited | Dale | CC BY-SA 4.0 |
added 177 characters in body
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| Apr 21, 2022 at 10:00 | comment | added | Gumby The Green | When the traveling twin is a given distance from Earth, there's a direct causal link between his thrust and his accounting of the speed of Earth's time. Isn't that enough to say that from a physical standpoint, acceleration causes time dilation, at least in part? Finally, you said that "although $g$ has units of acceleration, it is a property of the spacetime", but would it be more correct to say that it's a property of the coordinate system since everything is technically still in flat Minkowski spacetime? If so, does that change anything? | |
| Apr 21, 2022 at 10:00 | comment | added | Gumby The Green | Thanks for the detailed, direct replies to my questions and points. I'm following but I can't shake the feeling that it's a matter of interpretation, wording, and the way that the math of relativity has been framed by us humans. If acceleration determines the metric, and the metric—along with position—determines time dilation, can't we say that acceleration determines time dilation as much as position does? | |
| Apr 21, 2022 at 3:53 | history | answered | Dale | CC BY-SA 4.0 |