Is It Determinism if We Can Calculate Probabilities Exactly?

I set a stretch goal for myself: I want to force myself to keep some posts of mine short.

As a fan of MinutePhysics I am launching a new category: Physics in a Nutshell. I am going to try to tackle a question that has bothered me for a while – hopefully briefly and concisely.


The question of today is:

Butterfly Effect

The Infamous Butterfly. Part of Pop Culture, at least since we had all watched Jurassic Park (Wikimedia)

What is determinism (in physics)?

The extremely short answer is: I don’t know. Or rather: I don’t know if the question makes so much sense as first of all we need to get terminology right and work out a 1 on 1 map between mathematical and philosophical terms. This is an issue I have with those philosophical questions in physics – I am rather a fan of Shut up and Calculate and of Richard Feynman’s pragmatic attitude in general (whether or not the quote can be attributed to him).

Usually we say a system is deterministic if we can predict its future (calculate any property we are interested in) based on its current properties and some fundamental laws.

Classical mechanical systems are deterministic on the fundamental level in the sense that we could predict their behaviors on principle. On principle only, because prediction means calculations, and calculations might be subject to tiny errors adding up when systems turn chaotic. Think turbulence, weather and the infamous butterfly.

Quantum systems are non-deterministic in the sense that the fundamental laws in quantum theory do not give us what we (classically minded) consider the ‘full information’. Think momentum or position versus both, or think entangled particles – we only know both would show the same quantum number when measured, but we do not know which number.

But depending on the system you consider (forces, number of ‘particles’) the quantum mechanical equations may not exhibit chaotic behaviour. So in this case you calculate probabilities, but these probabilities you will know for sure.

We do not even need to allude to spooky quantum stuff – just consider a classical system comprising tons of particles, such as a the air in a room. In this case of a messy classical system we can only forecast probabilities for practical reasons, but statistically defined properties are all that matters anyway. Think temperature.

In real, interesting systems involving lots of forces, matter and stuff, you will encounter both aspects of non-determinism. If you want to tag it that way. I would rather stick with equations, boundary conditions, stability of numerical calculations and other technical terms.


Recommended reading

Richard Feynman, Vol. I of his Physics Lectures. Though sub-titled Mainly Mechanics, Radiation, and Heat it is really about all of physics, including quantum mechanics.

Loosely connected remarks

Ironically, despite Feynman’s explicit depreciation of useless armchair philosophy and reluctance of well-rounded education in liberal arts, many of his statements comprise profound philosophical truths. Sometimes tucked away in a footnote:

Poets say science takes away from the beauty of the stars – mere globs of gas atoms.  Nothing is “mere.”  I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination – stuck on this carousel my little eye can catch one million year old light… What is the pattern, or the meaning, or the why?  It does not do harm to the mystery to know a little about it.  For far more marvelous is the truth than any artists of the past imagined!  Why do the poets of the present not speak of it?  What men are poets who can speak of Jupiter as if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?”

(R. Feynman, physics Lectures, Vol.I, Footnote in section 3-4)


This post was inspired by many current discussions, finally triggered most likely by this discussion on LinkedIn


4 thoughts on “Is It Determinism if We Can Calculate Probabilities Exactly?

  1. The problem between probabilism and determinism/indeterminism is that probabalism is epistemological (addresses what we can or cannot “know”) while determinism/indeterminism are ontological (addresses what exists). Also, predictability or even measurability does not equal indeterminism. Some interpretations of Quantum Mechanics, though entirely unpredictable, are deterministic. For example, Bohmian Mechanics is a non-local hidden variable theory. In physics, if everything is causal (regardless if predictable or measurable) – its considered deterministic. If some acausal events (events that come about which do not have a cause for them) happen, it’s indeterministic.

    For probability, we simply cannot assess a probability for an acausal event except for it happening at some time or never (e.g. we cannot conclude a 30% probability for an acausal event). Therefore, probability really assesses what we can “know” about when or where a causal event might happen (e.g. it’s a 30% probability that the particle will end up at that part of the particle target). What’s important here is that the probability isn’t something that “exists” (it isn’t ontological)…it’s only a model of what we can know.

    If there were three rooms, one with a rabid dog in it. If person X know which room the dog was in it would be a 100% probability based on his knowledge. If person Y knew the dog wasn’t in a specific room but wasn’t sure about the other two, it would be a 50% probability based on his knowledge. And if person Z didn’t know what room had or didn’t have the dog, it would be a 33.33% probability based on her knowledge set.

    In reality, it is a 100% ontological fact that the dog will be in room B, regardless if our epistemic probability is 33.33% or 50%. The same holds true for Quantum Mechanics. Probability is based on what we can and cannot know about where a particle will end up. The fact that we can, however, assign a probability…suggests causality rather than acausality. For those we cannot assign a probability to other than “sometime or never” – there is a possibility of an acausal event and hence indeterminism for such (though we can’t really know such an event happened acausally).

    I’m currently writing a book on (the lack of) free will where I detail out both of these possible universes, and also address what probability means within them. It’s called Breaking the Free Will Illusion for the Betterment of Humankind.

    Take care,

    • Thanks Trick – an interesting and deep comment I will not be able to do justice to in my reply. I am interested in philosophy but I don’t really speak its language – I only speak the language of physics and math so to speak.
      I guess what I actually wanted to say in this post was I find the application of terms like determinism or indeterminism to physics simply troubling. The laws of physics are written in math and that’s basically it. It am wary of these “interpretations” of QM or usefulness thereof.
      You could for example – as quantum computing expert Scott Aaronson explained in his latest book – simply boil down all the strangeness of quantum physics to the fact that probabilities in QM 1) are calculated from complex numbers and 2) are negative. Accounts of QM that point out its probilistic nature usually don’t emphasize that (I didn’t either in this post) – as if classical probability and quantum probability were the same. I don’t see how the very core of QM could be conveyed without math.

  2. As a philosopher you know probably more than me about the exact definitions and classifications of different interpretations (seriously). Wikipedia has a concise table of interpretations of QM – impressive:

    Yes, it is true that there are interpretations based on something like a single, giant wave function that describes the whole universe, started at the Big Bang. Measurements – that would make the wavefunction collapse – do not need to be considered separately in this model. That “collapse” would otherwise disturb a Schrödinger wave function evolving in a predictable fashion in time. The wave function is equivalent to probabilities (so these are predictable) and you need to force the system pick a state at random.
    The fully deterministic interpretation introduces the concept of decoherence and related splitting of reality into multiverses. Yet from the perspective of an inhabitant of a single universe it still looks like a collapse. (Geeky Sci-Fi stuff again – I tried hard to avoid that in this post ;-))

    I think my favorite is the instrumentalist Interpretation which is a verbal description of what’s going on mathematically:
    … although or because
    “instrumentalism explicitly avoids any explanatory role; that is, it does not attempt to answer the question why.”

  3. I’m probably betraying my ignorance of physics here, but aren’t there deterministic interpretations of quantum mechanics? I seem to recall reading that somewhere. We can’t make predictions (because of the complexity of the phenomena and our position as observers) but the outcome is nonetheless determined (from the big bang). In this case the system would only appear to be chaotic. In other words, is predictability a necessary condition for a deterministic system? Or maybe I’m conflating philosophical and physics definitions!

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