Memory theory, fission and faster-than-light influences

Standard memory theories of personal identity says that what is necessary and sufficient for identity is a chain of memories (or, more precisely, quasi-memories) and the absence of fission or fusion of memories. Now suppose:

1. If we keep fixed the laws of nature and miracles don't happen, then what is done five light years from earth at t cannot affect whether I am on earth five minutes after t (keeping a constant reference frame throughout).

Suppose physicalism is true. Then it is in principle possible to perform the following operation: record the state of my memories, freeze me, and send the records to a location five light years from earth. At that location the records can be downloaded into a fresh brain. So, suppose my memories have been recorded, I'm frozen, and the records are five light years from earth, where, at time t, someone is deciding whether or not to download those records into a fresh brain. At the same time (in this frame), I am being thawed. If they download the records into a fresh brain, then at t I will experience fission, and cease to exist according to standard memory theories. But that violates (1): whether they download the records into a fresh brain affects whether I am on earth five minutes after t.

One can get out of this problem, at the cost of other weirdness, by allowing one to survive fission. Another way is to deny physicalism—without physicalism it is not clear that memories can be transfered, as they may not be entirely brain-based.

But one might also try for the following solution. Suppose they do download the memories into a fresh brain. Fission doesn't count as occurring then. After all, reference frames are arbitrary, and so such a "then" would be arbitrary. Fission only counts as occurring when one of my memory-continuants is in the forward light-cone of another of my memory-continuants. And that will happen five years after the operation, and hence will not violate anything like (1). I don't know how attractive this view about fission is. It would be weird to build into a memory view something so tied to the physics of our world. One would need to say something about how the memory view changes in worlds with different physics. I still think a better move is just to deny the memory theory. But this interesting move would be worth thinking about.