Does kinetic energy qualify as negative energy in the wormhole of Kip Thorne and Mike Morris?

Question

Referring to Lagrangian methods if potential energy of gravity is considered as positive energy, then kinetic energy should be considered negative.
Recent publications on frame dragging could suggest that kinetic energy resides in a field closely associated with space occupied by a fast moving object.
In other threads I have encouraged a discussion of possible kinetic energy field as recommended by Albert Einstein in 1949 Autobiographical Notes.
Thorne and Morris require negative energy to stabilize a wormhole, which I have proposed as kinetic energy in other threads.
$Rightarrow$ I think that the Universe is made of two major kind of hydrogen, one is sun-hydrogen, and second one is hydrogen that we know on earth or life-hydrogen. the building block of universe is a quantum mechanics phenomenon, and working based on duality. Sun is creating energy, and atom using this energy, if one of them stop what is doing, both will die. Think of oxygen that we use, and tree is produce. If one side stop doing their task, it would kill other side as well.

Andrew · Answer

No.
Here's some more explanation -- I will work in units where $c=1$.
The key ingredient in a wormhole is that the weak energy condition is violated. The weak energy condition states that for any timelike vector $X^mu$, the stress-energy tensor obeys
begin{equation}
T_{munu} X^mu X^nu geq 0
end{equation}
Consider a particle with mass $m$. The stress-energy tensor is
begin{equation}
T^{munu} =  E v^mu(t) v^nu(t) delta(vec{x}-vec{x}_p(t))
end{equation}
where $E=sqrt{p^2 + m^2}>0$ is the energy of the particle, $vec{x}_p$ is the trajectory of the particle and $v^mu$ is the velocity
begin{eqnarray}
v^0 &=& 1 
v^i &=& frac{d x_p^i}{dt}
end{eqnarray}
Evaluating the weak energy condition for an arbitrary timelike vector $X^mu$ we have
begin{equation}
T_{munu} X^mu X^nu = E(X cdot v)^2 delta(vec{x}-vec{x}_p(t)) > 0
end{equation}
This is positive, so an ordinary particle does not violate the weak energy condition, meaning it cannot provide the negative energy needed for a wormhole.

Does kinetic energy qualify as negative energy in the wormhole of Kip Thorne and Mike Morris?

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