South African cosmologist shows single wave function can't explain observable universe

Can a complex nonlinear world arise from a single universal wave function? This is the question asked by mathematician George F. Ellis, and his answer is "no."

Ellis is emeritus professor of mathematics at the University of Cape Town in South Africa and the author of many books and papers on cosmology and relativity. His article, "Quantum physics and biology: The local wavefunction approach," appears in the online arXiv, Feb. 5. 

In quantum physics a wave function uses mathematics to describe a quantum state and is designated by the Greek letter psi.

Ellis begins by proposing that only local wave functions exist and that  "...there is no single wave function for a living cell or macroscopic objects such as a cat or a brain."

He elaborates on how local wave functions can give rise to complexity. 

"This occurs via adaptive modular hierarchical structures where each emergent level is causally effective because of the meshing of upwards and downwards causation that takes place consistently with the underlying physics via time-dependent constraints," Ellis said.

This process enables "logical branching" to emerge from macromolecular chemistry and the underlying physics. Although quantum effects could occur in a few cases, Ellis writes, "the local wavefunction approach advocated here is applicable in all cases and leads to the highly nonlinear nature of molecular biology that cannot be described by unitary evolution of a single wave function."

Nonlinear dynamics

Ellis explains that nonlinear dynamics results by combining local linear dynamics in nonlinear ways. He uses examples from evolution and development and how they interact, and also the transmission of information in biology, such as in the membrane potassium ion channel.

Instead of reducing something to the properties of its parts, Ellis proposes the concept of emergence. In his view emergence recognizes that the whole has new properties, which are not those of its parts.

As he stresses, the real world isn't linear in its structures or how it functions.

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George F.R. Ellis, "Quantum physics and biology: the local wavefunction approach." arXiv, Feb. 5.

https://arxiv.org/pdf/2301.06516.pdf

Interview with George Ellis

Taking apart the puzzle of quantum linearity

Current Science Daily interviewed Ellis and asked him to elaborate on his ideas of the local wave function approach.

Ellis is a leading world theorist in cosmology. Among his many books, he co-authored "The Large Scale Structure of Space-Time" with University of Cambridge physicist Stephen Hawking, published in 1973. He is a fellow of the British Royal Society. His many honors include being awarded the Order of the Star of South Africa by Nelson Mandela.

What is quantum linearity and why is it a puzzle?

Quantum physics is based in the evolution of the wave function Psi, determined by the Schrödinger equation, which is linear. That means if you add two wave functions, the outcome, the way it evolves with time, is just the sum of the outcomes of each wave function calculated separately, and nothing affects this very simple result. 

But all biology, and computation, is based in conditional branching, depending on context. For example. 

IF {thirsty} (DRINK WATER) IF {satiated} (STOP DRINKING)

IF {credit account over limit $30,000} THEN (Send message: “Over Limit”) AND (Stop further withdrawals) 

Such branching dynamics can’t occur in a linear system. So you can’t have a single wave function with linear dynamics that will give such outcomes, which clearly happen in the real world in biology and in computers. 

The puzzle then is how quantum wave functions obeying the linear Schrödinger equations can lead to such contextually dependent outcomes. 

Can you elaborate on how complexity arises out of local linear dynamics?

You combine the results of separate linear dynamic equations in non-linear ways in an adaptive modular hierarchical structure--such as a digital computer, or a human body.

Thus in a computational example, you split a computation up into simple steps, each such step stated in one line of a computer program. The program consists of many such lines, and contains both branching statements and loops, which make it nonlinear. Then executing the program as a whole enables very complex outcomes, controlled by the conditional branching statements.

Biology works basically in the same way. Gene regulatory networks and metabolic networks combine many simpler steps (“[Turn Gene G1 on] IF [molecular message M1 arrives], ELSE [not]”) and the whole complex interacting set of such steps form a network that can perform amazing things such as turning a single cell into an adult human being.

Emergence takes place, where the various emergent layers and elements that result are nothing like the lower level elements (for example, a heart is unlike a single living cell and is unlike an eye).

Your paper describes the tardigrade experiment. How is it compatible with your paper's thesis?

The tardigrade is a tiny animal that can be put in a state of suspended animation by being cooled to incredibly low temperatures and then resuscitated by bringing the temperature back to normal. A tardigrade was cooled to extremely low temperatures so that it was essentially a rigid solid, and then entangled with superconducting qbits. In that context it was described by a single wave function. It was then brought back to life by returning it to room temperature. Then it could no longer be described by a single wave function.

It was never both entangled and performing the functions of life. 

Please elaborate your view of hierarchy in emergent levels and the importance of an adaptive response to the environment.

We are made of atoms that comprise molecules that comprise cells that comprise tissues that comprise physiological systems that comprise an integral biological entity--a human being as a whole. The numbers are immense, many billions of atoms in each cell, many billions of cells to make a human being, embedded in an unpredictable environment that we must interact with in such a way as to survive.

That is what our physiological systems are for. In particular, homeostatic systems maintain bodily temperature, blood pressure in the face of a changing environment, and sensory systems provide information on what is going on so that the brain can plan a suitable response. 

Every environment is different, and dangers and opportunities are changing all the time. An adaptive response is essential in order to survive and prosper.

Can you summarize your argument that vindicates the local quantum view that you put forward?

It is obviously absurd to propose that all the complexity we see around us, look out your window at plants, trees, people, is based in linear evolution of one single quantum wave function (“the wave function of the universe”), as some physicists claim, as this simply does not allow the kind of conditional branching causation involved, as explained above. Nor is there a single wave function for an entire cat or brain.

Rather, the situation is that local quantum wave functions occur everywhere and determine linear quantum outcomes in a small local context. Putting all these local linear dynamical effects together in highly nonlinear ways generates all the real world complexity we see around us, including cats and brains.

Thus standard quantum physics rules everywhere but only rules locally, in general, in the sense that the relevant wave functions have a limited domain of validity.

Exceptional circumstances allow long-range quantum effects to occur such as were celebrated in last year’s physics Nobel prizes, due to a single wave function existing for the relevant system in its carefully controlled context. But those circumstances cannot occur naturally. They are quite unlike what occurs in biology.

Have you had responses to the article?

One of the top philosophers of science in the United Kingdom, Jeremy Butterfield, has looked at it carefully and is very pleased with it. So has materials scientist Andrew Briggs at Oxford.

Is there anything else you'd like to highlight?

The paper raises major problems for any many-minds multiverse theory, based in the concept of the wave function of the universe.