Causality is one of those difficult scientific topics that can easily migrate into the field of philosophy. Science’s relationship to the concept started out simple enough: one event later causes another event. This was the standard understanding of the scientific community until the introduction of quantum mechanics. With the introduction of the famous “creepy action at a distance,” which is a side effect of the concept of quantum entanglement, scientists began to question this simple interpretation of causality.

Researchers at the Université Libre de Bruxelles (ULB) and the University of Oxford have now developed a theory that further challenges this standard view of causality as a linear progression from cause to effect. In their new theoretical structure, cause and effect can sometimes occur in cycles, with the effect actually causing the cause.

Quantum entanglement. Photo credits: Department of Physics, HKUST

The quantum realm itself, as it is currently understood, is inherently chaotic. There is no real understanding of things on this scale that can be better thought of as a series of mathematical probabilities than actualities. These probabilities also do not exactly lend themselves to the idea of a particular cause-and-effect interaction between events.

The researchers further clouded the water using a tool known as a unitary transformation. Simply put, a unified transformation is a fudge that is used to solve some of the math necessary to understand complex quantum systems. With this function, the famous Schrödinger equation can be solved with real computers.

UT video discussing some of the more interesting implications of quantum theory.

To give a more complete explanation, one needs to study a bit about the “space” in which quantum mechanics works. In quantum mechanics, time is simply another dimension that needs to be considered in a manner similar to how the usual three dimensions of what we consider linear space are considered. Physicists usually use another math tool called Hamilton to solve the Schrödinger equation.

A Hamiltonian, although a mathematical concept, is often time dependent. However, it is also that part of the equation that changes when a unified transformation is introduced. As part of this action, it is possible to remove the time dependency of the Hamilton operator to make it so that the model takes more time instead of going in a particular direction (i.e., making the action and reaction linear) a circle rather than a straight line where action causes reaction and reaction causes action.

Video describing uniform transformations using advanced linear algebra.

Photo credit: Umesh V. Vazirani / Cal Berkeley

If all of this is not confusing enough, there are some extremely elusive implications of this model (and to be clear at the macro level, it’s just a model). An important facet is that this finding has little or no relevance for the daily cause and effect. The causes and effects that would be cyclical in this context are, according to the ULB press release, “not local in space-time”, so they are unlikely to have an impact on daily life.

While it doesn’t have any day-to-day implications right now, this framework could point to a combined theory of quantum mechanics and general relativity that has been the most sought-after prize in physics for decades. If this synthesis is ever fully realized, there will be more implications in everyday life than just the existential questions of whether or not we are actually in control of our own actions.

Learn more:

Eureka Alert: Quantum Causal Loops

Nature communication: cyclical quantum causal models

Florida News Times: Quantum Causal Loop

UT: The three-body problem shows us why we cannot accurately calculate the past

Mission statement:

Artist’s impression of quantum causal loops

Photo credit: ULB

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