Jun21-06, 05:00 AM
I've been thinking about a cool model concerning quantum
gravity, by assuming two elementary particles can get
quantum gravitational entangled, after they have exchanged
two gravitons. A graviton would be a virtual particle which
propagates at speed of light in the vacuum, like any photon
does, although it, instead of carrying classical information,
would carry quantum information.
Suppose two elementary particles with mass, say two electrons,
interact by exchanging gravitons. We want to know how they
gravitationally behave, considering only their masses,
regardless their electric charges. We must claim they only
undergo gravitational interaction after they have exchanged
two gravitons, such that a quantum entanglement has been previously
produced at a distance r, and it eventually collapses. The first
issue would be, that entanglement, produced at a distance r, will
may influence on how the correlated gravitational forces will be
oriented, and this would mean both two elementary masses can,
at random, exhibit attraction or repulsion forces!. Let us set
the convention, state 1 means a force, applied in one of those
two particles, oriented towards the other, and state 0 means it
is oriented in the opposite direction. The collapse of the
entangled state would yield only one of following two possible
The system collapses to
|0>|0>, or it does to
We can adddress this gravitational interaction with only
a unique qubit.
The collaped state |0>|0> means repulsion, and |1>|1>
means attraction. Any of them would occur at random,
depending only on the probability defined by the distance r,
at which the entanglement has been coupled. As a result,
we couldn't take advantage of this phenomemon for
implementing faster than light communication devices,
because we would be unable to predict which outcome
will be produced in a given interaction. Even if we were
able to predict the probability of an outcome for a given
distance entanglement, the inverse will not hold, we will
never know for sure what distance had yielded a certain outcome.
This would be one reason why gravitational waves are so
difficult to be observed, along with the fact that gravitons
would only exchange quantum information.
Observation means classical information, but as a gravitational
interaction would be a product of a quantum entanglement collapse,
there would be no classical information available to be observed,
in the way between both particles. Correlated gravitational forces
would be then simultaneous events, they would occur instantaneously,
but nothing would be communicated at infinite speed.
Call beta the probability for a particle to exhibit a
gravitational force towards the other one, and alpha,
the probability for it resulting on opposite direction,
we can express the collapsed state, |s>, of the entangled
gravitational system as:
|s> = alpha|0> + beta|1>,
such that alpha + beta = 1, must always hold,
and we know |s> may be either
|s> = |0>|0> , or
|s> = |1>|1>
This means that the qubit addresses the signature of the
gravitational interaction. Once we've known whether it is
attractive or repulsive, we can apply the classical
newton's law to address the gravitational force, as the rest
masses are always preserved.
I've claimed above that alpha must be a function of distance r.
Now, I claim that if r = 0, then alpha = 0, and if r = R_h,
where R_h is current Hubble radius, then alpha = 1. This means
those elementary masses, which are coupling quantum gravitational
entanglements at distances close to R_h, should be exhibiting
repulsive gravitational forces, with a higher probability.
Symmetrically, elementary masses, coupling at Planck scales,
would be exhibiting an alpha close to the fine-structure constant!.
This is not too speculative, you can easily deduce it from
quantum mechanics, assuming gravitons are spin-1/2 bosons,
and considering spacetime as the state space of that gravitational
system, formed by two electrons.
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