# [ExI] QET

scerir scerir at libero.it
Wed Feb 17 21:55:03 UTC 2010

```Henrique:
> By non-local gravitational fields you mean putting gravity on a spaceship
for instance? Now that would be interesting.

Paul Simon sings: < "The problem is all inside your head", she said to me /
The answer is easy if you take it logically [...] > (from '50 Ways To Leave

So, let us start from the beginning.

In "Relativity and the Problem of Space" (1952), Albert Einstein wrote:
"When a smaller box s is situated, relatively at rest, inside the hollow space
of a larger box S, then the hollow space of s is a part of the hollow space of
S, and the same "space", which contains both of them, belongs to each of the
boxes. When s is in motion with respect to S, however, the concept is less
simple. One is then inclined to think that s encloses always the same space,
but a variable part of the space S. It then becomes necessary to apportion to
each box its particular space, not thought of as bounded, and to assume that
these two spaces are in motion with respect to each other. Before one has
become aware of this complication, space appears as an unbounded medium or
container in which material objects swim around. But it must now be remembered
that there is an infinite number of spaces, which are in motion with respect to
each other. The concept of space as something existing objectively and
independent of things belongs to pre-scientific thought, but not so the idea of
the existence of an infinite number of spaces in motion relatively to each
other."

If we follow Einstein, and encode gravity in the geometry of space-time,
matter curves space-time, and its metric is no longer fixed. However, space-
time is still somehow represented by a *smooth continuum*. To restore coherence
of physics or - to say it better - to get a perfect coherence between GR and QT
(not just the present  "peaceful coexistence") one has to abandon the idea that
space-time is fixed, immune to change. One has to encode gravity into the very
geometry of space-time, thereby making this geometry *dynamical*.

Thus, while spacetime can be defined by the objects themselves, and their
dynamics, it is well known the nonlocal (rectius: nonseparable) behaviour of
entangled particles, and these entangled particles should live in the Hilbert
spaces but also in a well-designed space-time. Now, a simple question would be:
if spacetime is defined by objects, and if the nature of these objects may be
quantal, can we say that spacetime may be 'nonlocal' (or 'nonlocally causal')?
Does it make any sense?

For, general relativity completely ignores quantum effects and we have learned
that these effects become important both in the physics of the *small* and in
the physics of long
distance *correlations* (even between *spacelike separated* regions of the
universe, at least in principle).

It has been said that primary goal of *quantum gravity* is to uncover the
quantal structure of spacetime, and coarse-graining, backreaction, fluctuations
and correlations may play an essential role in such a quest. Quantum gravity is
not equivalent to a local field theory in the (bulk) spacetime and there's a
lot of powerful evidence that quantum gravity is not strictly local or causal
(holography; getting the information out of the black hole; there is no
connection operator in LQG and as a result the curvature operator has to be
expressed in terms of holonomies and becomes non-local, etc.).

Summing up. It is not about 'putting gravity on a space-ship'. It is more
about thinking the space-time as something strictly dependent of the dynamics
of massive objects and of quantal objects, it is more about the possibility of
changing the gravitational field at-a-distance, via quantum entanglement
correlations coupled to massive objects, or via more efficient quantum gravity
mechanisms. (Quantal randomness and related a-causality might still preserve
the no-signaling postulate.)

```