[ExI] QET

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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 
Your Lover', 1975)

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.)