To say that something is conserved means that it is the same at one time as it is at another time.
If you cannot time travel, and you have a set of objects at 1 PM, then you can compare them to the same set of objects at another time, such as an hour later.
If you can time travel, you can do the same—but terms such as “at another time” and “an hour later” become tricky.
With time travel, the time as measured in the setting is not the same as the time as measured by the objects themselves. If some of those objects time travel from 2:30 back to 1:30, then at 2 PM, 1 hour passed in the setting, you have some objects for which 1 hour has passed, and you have other objects for which 2 hours have passed. If you add those objects up just because 1 hour has passed in the setting you are adding the wrong things. You should be adding the objects for which one hour has passed (ignoring the objects for which two hours have passed) because conservation means that the amount is preserved one hour later—you can’t mix objects from one hour later and from two hours later and expect to get an amount that is conserved. The fact that one hour has passed in the setting is useful in the non time travel case because the time that has passed in the setting is the same as the time that has passed for all of the objects. In the time travel case the fact that one hour has passed in the setting is just a distraction.
Mass is neither created nor destroyed. It is moved.
Assuming you can tell if energy is conserved by checking if it’s still there later, when you have a time machine, is like claiming a bolder has violated mass/energy conservation because somebody broke a piece off.
To say that something is conserved means that it is the same at one time as it is at another time.
If you cannot time travel, and you have a set of objects at 1 PM, then you can compare them to the same set of objects at another time, such as an hour later.
If you can time travel, you can do the same—but terms such as “at another time” and “an hour later” become tricky.
With time travel, the time as measured in the setting is not the same as the time as measured by the objects themselves. If some of those objects time travel from 2:30 back to 1:30, then at 2 PM, 1 hour passed in the setting, you have some objects for which 1 hour has passed, and you have other objects for which 2 hours have passed. If you add those objects up just because 1 hour has passed in the setting you are adding the wrong things. You should be adding the objects for which one hour has passed (ignoring the objects for which two hours have passed) because conservation means that the amount is preserved one hour later—you can’t mix objects from one hour later and from two hours later and expect to get an amount that is conserved. The fact that one hour has passed in the setting is useful in the non time travel case because the time that has passed in the setting is the same as the time that has passed for all of the objects. In the time travel case the fact that one hour has passed in the setting is just a distraction.
None of what you wrote makes any sense to me, sorry.
Here’s how I read it:
Mass is neither created nor destroyed. It is moved.
Assuming you can tell if energy is conserved by checking if it’s still there later, when you have a time machine, is like claiming a bolder has violated mass/energy conservation because somebody broke a piece off.
The whole point is that in GR conservation is local, you should be able to trace the movement of mass through space.
Exactly. You were treating it as general.