Jonathan Barrett - Causal influence in quantum theory

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Jonathan Barrett University of Oxford Any account of causality in the physical world should answer questions such as the following. If A is a cause of B, then what sort of thing are A and B? What does it mean to say that A is a direct cause of B? Do causal concepts involve, in an essential way, interventions by agents? Are causal relations directed in time? What, in the overall picture, is ontic (i.e., factual and independent of the agent), and what is epistemic (i.e., relative to an agent’s knowledge or beliefs)? I will give an account of causality in quantum theory that answers these questions, leading to a formalism for quantum causal modelling. The classical formalism for causal modelling can be recovered from this account, as a special case when quantum channels are all diagonal. Towards the end I will make some more speculative remarks about a possible new direction in the interpretation of quantum theory that is suggested by the work. The talk is based on (bits of): arXiv:1609.09487 arXiv:1906.10726 arXiv:2001.07774 arXiv:2002.12157 arXiv:2011.08120

Keywords: Barrett, Quantum, Casual

Lorraine Ford

The view of physicists and mathematicians seems to be that their equations, including equations with delta symbols, are all that is needed to symbolically represent a viable system, a viable world.

The problem with this view was eloquently expressed by the late physicist John Archibald Wheeler who in 1972 apparently said to his students: “You see, these equations can’t fly. But our universe flies. We’re still missing the single, simple ingredient that makes it all fly.” https://ncatlab.org/nlab/show/John+Wheeler

In 2024, and with computer systems all round them, physicists and mathematicians, e.g. Jonathan Barrett, are still not even vaguely aware that their special symbols, including equations and numbers, don't represent a system that "flies".

What computer systems have shown is that, in order to represent a viable system, that in addition to symbols for equations, categories and numbers, you also need symbols that represent point-of-view on-the-spot logical connectives (e.g. IF, AND, OR, IS TRUE, and THEN).

In other words, in order to have a viable system, there necessarily exists entirely separate point-of-view on-the-spot aspects of the world that can only be represented by statements containing logical connective symbols like IF, AND, OR, IS TRUE, and THEN.

Physicists and mathematicians, e.g. Jonathan Barrett, seem completely unable to take to heart or comprehend what that means about the actual nature of the world.

To put it another way:

Just like symbolic equations are statements that represent relationships that have been experimentally confirmed to actually exist in the world,
Statements containing logical connective symbols (like IF, AND, OR, IS TRUE, and THEN) represent necessary, but not experimentally confirmable, point-of-view on-the-spot aspects of the world.

Lorraine Ford

Lorraine Ford
One of the problems, and it’s a big one, with what Jonathan Barrett is saying, is that he seemingly never thinks to ask why a system moves/ “flies”.

Certainly, the “causal” symbolic equations/ diagrams/ algorithms are moving in the conscious imaginations of mathematicians and physicists, and certainly, the mathematicians and physicists are moving, changing and rearranging the symbols (on paper or screen) using their own hands.

So, we know why the physicist-mathematician-symbol system is moving.

But why is the actual real-world system, that is purportedly being represented, moving/ “flying”?

What is movement?

Well, with physics’ law-of-nature equations, if a couple of the numbers (that apply to categories like the position category) “jump”, then secondarily, other numbers will necessarily change purely because of the mathematical relationship that is represented by the equations.

This secondary number change involves no movement at all, it only involves law-of-nature relationship as a complete explanation. The only genuine movement, the only movement requiring further explanation, was the initial number “jumps”.

Despite the delta symbols, physics’ law-of-nature equations DON’T represent movement in a system, but “number jumps” DO represent movement in a system. And despite the “causal” symbolic equations/ diagrams/ algorithms, only “number jumps” represent movement in a system.

In the physicist-mathematician-symbol system, physicists/ mathematicians can only symbolically represent a number jump as the creation of a new low-level relationship, in which a number is equated/ assigned to a category.

So, in the actual real-world system that is purportedly being represented by the physicist-mathematician-symbol system, a real-life “number jump” is actually the creation of a new low-level relationship.

Try as they may, and with all their “causal” symbolic equations/ diagrams/ algorithms, physicists/ mathematicians can’t ever get over the fact that genuine movement in a genuine real-world system involves the creation of new low-level relationships in which numbers are equated to categories.