Abstract
It is well known that the local kinetic energy density can be negative in quantum field theory. This is a “quantum effect” that is in contrast to classical physics where the kinetic energy density is always non-negative. It has been proposed in the literature that there exist “quantum inequalities” which place limits on this negative energy density. In this paper we will examine a type of quantum inequality call the spatial quantum inequality. The spatial quantum inequality is a lower bound on the weighted average of the kinetic energy density. It will be shown that for a massless scalar field in 1-1 dimensional space-time we can formulate a quantum state which violates the quantum inequality. In addition, we will look into the quantum interest conjecture. The quantum interest conjecture states that a negative energy pulse must always be closely associated with a positive energy pulse of greater magnitude. It will be shown that the quantum interest conjecture is violated.
Highlights
In quantum field theory the kinetic energy density can be negative over some region of space (Epstein et al, 1965)
This is a “quantum effect” that is in contrast to classical physics where the kinetic energy density is always non-negative
This is a “quantum effect” that is in contrast to classical physics where the kinetic energy density is always positive
Summary
In quantum field theory the kinetic energy density can be negative over some region of space (Epstein et al, 1965). The quantum inequalities provide a lower bound on the weighted average of the kinetic energy density integrated over some region of space and time. They apply to “free field” systems, that is, systems where all external potentials are zero. I have proposed in a number of papers that one can formulate counterexamples to the quantum inequalities (Solomon, 2010; 2011A; 2011B; 2011C) The basis of these counterexamples will be described as follows: Consider a massless scalar field in 1-1 dimensional space-time and assume that all external potentials are zero. This paper we will demonstrate the existence of a “free field” quantum system for which a region of negative kinetic energy density is “isolated” and violates the spatial quantum inequality
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