Original post: here.

Einstein does not consider the concept of ‘determinism’ to be as fundamental as it is frequently held to be (as he told me emphatically many times) . . . In the same way, he disputes that he uses as criterion for the admissibility of a theory the question: ‘Is it rigorously deterministic?

-- Wolfgang Pauli

Determinism is a logical fallacy. Everything in the Universe, from the ground up, is non-deterministic. What we often think of as “deterministic” (as in the expected outcomes of a classical physics thought experiment) is called “likelihood”.

How does this change our view of the Universe? It changes everything rather dramatically.

And we do not have to describe how the Universe is non-deterministic in order to know that it is and be able to accept and utilize that fact. For example, we do not have to make a differentiation between “quantum randomness” and “pseudo-randomness” or attempt to accept a myriad of various philosophies around the phenomena like “many-worlds”, etc.

The key to understanding a purely non-deterministic Universe is in differentiating between the restriction to functional relations (i,.e. “functions” and their compositions) and arbitrary finitary relations in our modeling of time. In other words, instead of assuming that causality = given an input there is one and only one possible output, we need to instead assume that there are always many possible outputs for any given input (e.g., a multivalued function), and that it can require many possible and specific inputs to get a possible output or to get some possible set of outputs. Always.

In fact, so much so is this true that saying that the Universe is deterministic at all and in any way is an outright falsehood. The Universe is fundamentally equivalent to a sea of many non-deterministic algorithms interacting non-deterministically. The Universe is not deterministic, it is probable. Across all of time and in all ways. Full stop.

This also makes everything in the Universe fundamentally irreversible. So, there is no "back to the future". There is no "time travel". As any concept of time travel assumes some (often a complete) degree of determinism.

Except, the nice thing about using the concept of finitary relations is that it models the concept of probabilistic sampling from some distribution. Where that distribution could be seen as the weighted set of possible outputs given some set of inputs.

Therefore, our underlying fundamental mental construct of the Universe is a falsehood. It’s not a classic billiard ball table analogy, at all. This false preconception of the Universe, reinforced by Physics 101 classes, is exactly why we assume that Quantum mechanics is “weird”. It’s not weird. Our assumptions that things are rigid bodies purely and deterministically bouncing off of each other exchanging simple momenta values is weird.

Our perception of billiard balls should be “that the classical phenomena observed was the observation - or outcome - that was most likely to occur”. Yet, even that is technically incorrect! Because, it may not necessarily be the most likely.

For example, let’s take the assumption that two billiard balls colliding can have one of three possibilities: 1. they bounce off of each other exchanging momenta 2. One completely absorbs the momenta of the other and spontaneously combusts into a mesmerizing explosion 3. they pass right through each other.

We know that option 1 happens basically “all the time”. But the other two are not actually impossible. They are improbable — highly. And the difference between the concepts is critically important to make. In classical physics, we discuss things using the binary language of possibility and impossibility. But, quantum mechanics tells us this framework is incomplete. For all things that are possible we must provide a spectrum of probability.

Causality is Emergent

A purely non-deterministic Universe working strictly on likelihoods can create a supposedly "reversible" series of events that is merely emergent from an observers' point-of-view and is not actually built into the fabric of reality.

Therefore we like to say that once something has happened that something else prior to it caused that thing. But in a purely non-deterministic Universe, such as the one we live in, this is not actually provable. We can merely interpret the particular outcome given a set of likelihoods as having causal factors.

But a few people might protest that causality is more reminiscent of precedence. Thus, they argue that whatever happened before was the cause of whatever came after. But, this reductionism is exactly why the composionalists (e.g., as found in Category Theory) are obsessed with composition because it reflects a restriction to this world of purely-deterministic causality. Cause and effect. But, we already know that not all things compose. Not all things simply "follow from" the prior.

But, causality is an argument of continuity and if it cannot be proven then that means it also cannot be questioned. So, because no definition of causality exists that can avoid this necessity of provability then it is obvious that either the notion of causality is vague and ill-defined and/or it is not fundamental and simply perceived.

The idea of the existence of a provable notion of causality is exactly why an agreed upon interpretation of quantum mechanics does not exist. It's why we have everything from the Copenhagen interpretation to string theory. They are all avoiding a much more fundamental point: causality can never be proven in a purely non-deterministic Universe. It's impossible to prove that one particle's behavior was the cause for another's ... ever. Thus, causality can only be emergent. Causality can only be perceived or interpreted. It is generated via observation and is not fundamental in the fabric of our Universe. If the Universe were purely deterministic then causality would always be provable, clear, concise, and easily controlled. However, the world works like this in almost no way. Ask any quantum computing company, weather forecasting service, etc.

time and probability befall us all

-- Solomon

Remember, that being right and making good predictions is actually more about getting lucky and/or playing the odds. And now is a good time to study up on how innate Bayesian biases can sometimes be our enemy. Oh, and of course, always remember that causality is caused by (get it?) observation.

The mathematical truth, coming from non-integrable systems, is that everything is the cause of everything else: to predict what will happen tomorrow, we must take into account everything that is happening today.

Except in very special cases, there is no clear-cut "causality chain," relating successive events, where each one is the (only) cause of the next in line. Integrable systems are such special cases, and they have led to a view of the world as a juxtaposition of causal chains, running parallel to each other with little or no interference.

-- Ivar Ekeland

Determinism Does Not Exist

Causality is Emergent

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Genevis

Genevis