Game of Life may be a model for deriving quantum odds from cause-and-effect laws, Nobel laureate ’t Hooft says
Second of two parts (Read part 1)
Quantum physics is like life. Not nasty, brutish and short, but rather unpredictable, occasionally interesting, and often depressing. At least it has been depressing for many scientists, like Einstein, who thought science ought to predict what happens, not just give you the odds for what might happen, like meteorologists forecasting rain.
At least with quantum physics, unlike weather forecasts, the odds are always accurate. But that doesn’t satisfy everybody who wants a truly deep understanding of nature’s laws. So even though quantum theory’s predictions are always remarkably reliable, physicists have for decades been debating what the mathematical apparatus for making those predictions, known as quantum mechanics, really means.
Some interpretations suggest that reality is ill-defined until observations and measurements are made. It’s like turning a spinning coin into either heads or tails by catching and looking at it. Others say there are multiple parallel universes, so all spinning coins turn up as heads in one universe and tails in another. Or maybe — a minority view — quantum coins are just like real coins: whether they turn up heads or tails is completely deterministic, obeying strict laws of cause and effect. If you knew all the forces, the strength of the flip and the gravity and air resistance and everything else, you could predict a coin’s heads-or-tails outcome correctly every time. Some people hope that quantum physics will turn out to be like that, with everything foreordained by tock-after-tick deterministic clockwork, as with classical Newtonian physics.
Sadly for Newton fans, the weird outcomes of many quantum experiments have seemingly ruled out any such return to certainty. Take, for instance, the confusing phenomenon of quantum entanglement. Two particles from a common source can be separated by a vast distance, yet a measurement of one instantly determines what can be measured about the other. No signal can be sent through spacetime for ordinary cause-and-effect to explain that link. It’s quantum magic. Unless some invisible properties, or “hidden variables,” are determining the connection.
Over the years, various experiments have supposedly ruled out such hidden variables. But not necessarily the ones proposed by Nobel laureate Gerard ’t Hooft. If you trace all causes and effects back to the beginning of the universe, then maybe quantum mysteries such as entanglement can be explained in a classical cause-and-effect way, he argues.
“It may well be that, at its most basic level, there is no randomness in nature, no fundamentally statistical aspect to the laws of evolution,” he writes in a new paper. “Everything, up to the most minute detail, is controlled by invariable laws. Every significant event in our universe takes place for a reason, it was caused by the action of physical law, not just by chance.”
’t Hooft calls his view of quantum mechanics the cellular automaton interpretation. In other words, he thinks quantum physics is like Life. A cellular automaton is like a grid on which black and white squares change color on the basis of simple rules. The prototypical example is the game known as Life, invented several decades ago by the mathematician John Conway.
Think of the universe as made up of rows of pixels on a computer screen. The configuration of pixels changes from row to row by applying an algorithm, a set of rules for telling each pixel what color to become based on the current colors of its neighboring pixels. This approach is equivalent, ’t Hooft points out, to saying that the states of nature can be described by a sequence of integers that evolve over time, as determined by an algorithm that tells them how to change.
Such an algorithm, ’t Hooft contends, can reproduce all the mysterious features of quantum physics. All observable phenomena will still obey the probabilities computed using quantum math. In this view, even though the future is determined by the past, humans could never predict the future, because they don’t know the underlying algorithm. And even if they did, they couldn’t calculate it faster than the evolution of the universe itself.
If he is right, the foundations of reality could be described by a deterministic theory. “It will be a theory that describes phenomena at a very tiny distance scale in terms of evolution laws that process bits and bytes of information,” ’t Hooft writes.
Mathematical technicalities abound in his 202-page paper. He shows with elaborate mathematics how his idea can work for “toy” models, such as a world with particles that move in only one dimension and don’t interact with each other. He suggests ways that ideas from superstring theory might help make things work in more complicated systems. He goes on to outline how further work might develop a complete theory capable of explaining the entirety of particle physics, with all its quantum features, from a nonquantum foundation.
Recapitulating ’t Hooft’s 200 pages of arguments into a few paragraphs omits a lot of nuance. But at the core of his approach is the notion that ultimate elements of reality, whatever they are, do not correspond to the templates for reality conceived by the human mind. Concepts such as particles and fields used in today’s standard physics are human inventions. Subatomic particles, atoms, molecules — the things that exhibit quantum weirdness — are templates imposed by human theory on the underlying truly real objects in nature. Quantum mysteries arise because of lack of awareness of the underlying level. An electron can be in two places at once because an electron is not a basic element of reality — it’s a template that subsumes multiple “beables,” the submicroscopic states of true reality.
“It is due to our intuitive thinking that our templates represent reality in some way, that we hit upon the apparently inevitable paradoxes” of quantum physics, ’t Hooft writes. He believes that a cellular automaton can describe the real states underlying the templates deterministically, with math that can be transformed into quantum theory’s seemingly probabilistic descriptions of reality.
“We consider cases where one has a classical, deterministic automaton on the one hand, and an apparently quantum mechanical system on the other,” he writes. “Then, the mathematical mapping is considered that shows these two systems to be equivalent in the sense that the solutions of one can be used to describe the solutions of the other.”
Yet while ’t Hooft makes a lot of progress, he acknowledges that the battle is far from won. There are difficulties to be overcome before he can reproduce all the victories achieved by the standard model of particle physics. Not to mention incorporating solutions to its remaining puzzles, such as how to formulate a quantum theory of gravity.
“It may take years, decades, perhaps centuries to arrive at a comprehensive theory of quantum gravity, combined with a theory of quantum matter that will be an elaborate extension of the standard model,” he writes. Only then will it be possible to identify the beables, the basic ingredients for deterministic theory, and figure out the relationship between the beables and the human templates such as particles and fields. “Only then can we tell whether the cellular automaton interpretation really works.”
’t Hooft has been developing these ideas for many years. So far they have not caught on among other quantum physicists. But his efforts are much more subtle and sophisticated than the many other attempts to restore cause-and-effect determinism to the universe. And even if he hasn’t yet succeeded in establishing that this approach will work, he has offered sufficient evidence that his views should be taken seriously. And that is one of his goals.
“We hope to inspire more physicists to … to consider seriously the possibility that quantum mechanics as we know it is not a fundamental, mysterious, impenetrable feature of our physical world, but rather an instrument to statistically describe a world where the physical laws, at their most basic roots, are not quantum mechanical at all. Sure, we do not know how to formulate the most basic laws at present, but we are collecting indications that a classical world underlying quantum mechanics does exist.”
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