# How much energy can we borrow from a vacuum?

Negative energy doesn’t exist; that’s what we learned in school. If it did, then there’d also have to be negative mass – and thus a repulsive gravitational force, because energy and mass are directly linked with each other, as Einstein showed in his theory of relativity. At the micro-level, however, that’s not true (and that’s one of the reasons why physicists are still having a lot of fun trying to unite relativity and quantum theory). In extremely small areas, it is possible for energy to fall below zero for a short time, so that we are essentially borrowing energy from a vacuum. Science fiction authors like to use this idea to fabricate all sorts of cheap energy sources.

But a vacuum is rather stingy. It gives energy credits only up to a certain limit, and even demands a so-called “quantum interest.” The exact value of this amount is currently unknown. In any case, like in traditional banking, the “quantum interest” owed depends on the amount and term of the credit. However, the relationship is not linear, not at all. By all accounts, the universe is an extortioner and the interest amounts quickly balloon even when the term or credit amount increases only slightly. This ensures that going into debt doesn’t become commonplace in a vacuum and existing credits are paid back quickly, so everything remains in balance statistically.

In 2017, physicists proved the “Quantum Null Energy Condition” (QNEC), which specifies certain limits for energy credits. According to this condition, energy can indeed fall below zero, but only in a certain area, only for a certain amount of time, and only within a line of credit that is related to a quantum-physics parameter, the so-called entanglement entropy.

“In a certain sense, this entanglement entropy is a measure of how strongly the behavior of a system is governed by quantum physics,” says Daniel Grumiller of the Institute for Theoretical Physics at the Technical University of Vienna. “If quantum-physics entanglement plays a very large role where an object is located somewhere in the universe, for example, the edge of a black hole, then a negative flow of energy can be produced there for a certain time, so that negative energies become possible.”

Together with Max Riegler and Pulastya Parekh, Grumiller was able to generalize these special calculations. “All previous considerations have been based on quantum theories that follow the symmetries of the special theory of relativity. But now we have been able to show that this connection between negative permitted energy and quantum entanglement is a much more general phenomenon,” explains the researcher. This means that the line of credit provided by the universe for withdrawing energy from a vacuum is not dependent on special properties of quantum theory used to describe the universe, but instead represents a universal property.