# [ExI] FW: Interstellar FedEx

Mon Sep 28 14:55:53 UTC 2009

```Tomaz Kristan wrote:
> It is the same thing. You can pay more, and often you do, but the lower
> limit is 0.

Could you point me to some derivation of this? Because I frankly suspect
it is not true, at least not in empty space.

Consider two stations in space at rest to each other. One has a compressed
spring with a payload in front of it. It releases the spring, and the
payload shoots towards the other station. The first station begins to
drift away in the opposite direction. The payload reaches the other
station, where it meets an identical spring that slows it to rest relative
to the station. Now the other station also is drifting, since it gained
momentum from the payload. The energy that was in the original spring can
be sent back to the first station for example by extending the spring when
connected to a generator, converting the energy into laser light, which is
then received at the first station and used to compress its spring. No
energy has been lost so far. But the stations are now drifting apart at a
certain velocity. To prevent this and retain their relative position both
need to expend momentum just when the payload leaves/arrives. This
momentum seems to be lost forever into a useless form - an entropic cost.

We can certainly imagine that the stationkeeping momentum gets transferred
to other stations that require that same momentum just at that moment. But
this makes it impossible to launch payloads at arbitrary points in time or
with arbitrary velocities. Skipping the stationkeeping makes the system
less useful in the future, since the stations now are drifting apart.
Usually entropy resides in the energy component of a physical model and
sometimes in the positional component, but here it seems that the entropy
ends up in the momentum component of the model.

One can look at it from a reversibility perspective. If something happens
to cause an object to move from A to B where something else happens to
slow it down, then under time reversal the opposite process should be
possible. But the station-keeping under time reversal seems to be one of
those processes where disorganized matter and energy arrive from infinity
to produce a very well-defined outcome.

--
Anders Sandberg,
Future of Humanity Institute
Philosophy Faculty of Oxford University

```