Let’s say there was some way to change a single moment of time.
We would then need some kind of meta-time over which time could “change”.
The lamp’s state would need to change from “OFF at 7:02am at 3:00meta-am” to “ON at 7:02am at 3:01meta-am”.
But wait! Have you ever seen a lamp change from OFF at 7:02am at 3:00meta-am, to ON at 7:02am at 3:00meta-am? No! A single instant of meta-time never changes, so you cannot change it, and you have no control.
“Have you ever seen?” refers to a state of a (mere) time computer. Your memory is time-caused so it is not reliable evidence about meta-time mechanics. It is an important obliviousness result for chronal beings. It might not be holeless. I don’t know about more general settings but with “propagation” (meta-time change being local in (normal) time), even a chronal mind in the proximity of CTL could occasionally (with some appriciable fraction of meta-time) notice things that are not compatible with a totally frozen timeline (this does need recurring meta-time switching back and forth to not be infinidesimal (in the setting that I know CTL can also provide such a meta-time switching source)).
So with two lamps with different meta-time wire lengths (essentially different proper times) you could have all four states of “A on, B on”, “A on, B off”, “A off, B off” and “A off, B on” cycle and have corresponding chronal observer experience each. None of them see the lamps change in (normal) time, but it still takes place.
“Have you ever seen?” refers to a state of a (mere) time computer. Your memory is time-caused so it is not reliable evidence about meta-time mechanics. It is an important obliviousness result for chronal beings. It might not be holeless. I don’t know about more general settings but with “propagation” (meta-time change being local in (normal) time), even a chronal mind in the proximity of CTL could occasionally (with some appriciable fraction of meta-time) notice things that are not compatible with a totally frozen timeline (this does need recurring meta-time switching back and forth to not be infinidesimal (in the setting that I know CTL can also provide such a meta-time switching source)).
So with two lamps with different meta-time wire lengths (essentially different proper times) you could have all four states of “A on, B on”, “A on, B off”, “A off, B off” and “A off, B on” cycle and have corresponding chronal observer experience each. None of them see the lamps change in (normal) time, but it still takes place.