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Events in the world can be described on the macro scale or the micro scale. For events that occur in the macro scale, such as the shape of a particular rock that forms, would the rock have formed in the same way at the same time if we replayed the entire universe?

In other words, what would the probability of a particular event such as a person being assassinated today be if we knew everything there is to know about the universe initially? Would it be 0 or 1, or atleast close to 0 or 1?

Put another way, if we rewinded the universe, would world war 2 for example have started on the same day? I don’t see why it’s not possible for the probability of world war 2 happening on the day that it did be close to 1 despite the indeterminism in quantum mechanics, since you can still have multiple branches of reality resulting in the same macro scale event. With that being said, I’m not sure, and it’s hard to conceptualize these probabilities.

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    Many aspects of the world are unstable to perturbations, so even small deviations along the way will snowball, they call it butterfly effect. A simple example is hyperbolic divergence in weather dynamics which makes long-term forecasts impossible (conjectured by Kolmogorov and proved by Arnold). Macrodynamics of deterministic "chaotic" systems does almost all the work, even infinitesimal QM perturbations are enough.
    – Conifold
    Nov 30, 2023 at 8:52
  • @Conifold I thought the butterfly effect in quantum mechanics doesn’t exist. Or are you saying that because small changes in initial conditions affect the end result in chaotic systems, those changes can be caused by QM perturbations, and thus cause a change in the end result? If so, what is the end result, and within what margin of error would the probability change? In a deterministic chaotic system, the probability of rain a year from now today is still 0 or 1. Now, given quantum mechanics, what percentage of the branches of reality from today would result in rain a year from now?
    – user62907
    Nov 30, 2023 at 9:08
  • You are essentially asking if determinism is a fact; determinism is just a speculative theory, it is not proven, it can't be proven. Unless someone is able to experience multiple universes or pasts to verify it.
    – RodolfoAP
    Nov 30, 2023 at 9:20
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    Most random quantum events have no discernible effects at a macro scale. No doubt there are all kinds of probabilistic quantum interactions in my laptop, but pressing the Z key always seems to produce a Z. I always laugh (rolling on floor uncontrollably and clutching sides) when I read people talk about Shrodinger's poor cat as if 'dead' was a single quantum state. Nov 30, 2023 at 9:26
  • Some sequences of events are more susceptible to small changes in conditions than others. A butterfly that was in my study last year beat its delightful little wings repeatedly with no discernible effect on the time evolution of my slate floor, for example, but for all I know might have triggered nine typhoons over the Pacific. Nov 30, 2023 at 9:30

7 Answers 7

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To my eye, it looks like multiple questions are being asked at once, so I'm going to try to pick them out and answer them:

  1. Is quantum mechanics deterministic, or probabilistically random? You'll read a lot of opinions online, but the reality is, this is still UP FOR DEBATE among experts. There are many different interpretations of quantum mechanics, and they all pretty much make the same predictions, but they have different ideas of what's going on "under the hood" so to speak. I would say the three big schools of thought are probably Copenhagen, within which randomness is probably real, Many Worlds, which is deterministic but which appears effectively random to a person within the system - at the level of human experience, it's random, but it has a sort of 'meta-determinism' - and the third is Bohmian Mechanics, which is just straight-forwardly deterministic (or at least most people consider it deterministic, some argue it's not). Copenhagen is probably the most popular, but that's arguably because it's taught by default since it was kinda the first intepretation. There are more interpretations than these 3, but these are the most popular it seems among experts.

  2. Can quantum randomness "average out" to macroscopic events being effectively determined? YES, certainly over small timescales, but not over large timescales. You asked if WWII would start at the same time if we restarted the universe - if quantum randomness is real, then the answer is "if we restarted the universe, WWII probably wouldn't even happen, human beings would likely not exist at all". But if instead of rewinding to the beginning of the universe, we instead rewound to the beginning of 1939 (that's when it started, right?) then I think there's an argument to be made that the probablity is pretty high things would play out pretty close to the same way at the macro level, so that it does start on the same day.

We know quantum randomness can average out to macroscopic "determinism"-like situations, because that's why our macroscopic experience is so consistent to begin with. It's why as you're looking at this screen, you can reliably see the words I've typed instead of seeing random noise - because the quantum randomness that's present in every single photon arriving at your eyes averages out to a consistent image. If your eyes relied in any individual photon arriving in the correct way from the correct place, vision wouldn't work, but vision is a bit more robust than that - because it instead relies on millions and millions of photons accumulating - that's how they have the opportunity to "average out" across all their randomness.

Here's a little write-up on the topic: https://www.askamathematician.com/2012/05/q-is-quantum-randomness-ever-large-enough-to-be-noticed/

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  • “if we restarted the universe, WWII probably wouldn't even happen, human beings would likely not exist at all“ I guess my question is then how does one know this? If they likely wouldn’t exist, that would mean that if one were to enumerate all possible branches from the beginning of the universe on the quantum scale, less than 50% of them would contain the existence of humans. Why?
    – user62907
    Nov 30, 2023 at 9:43
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    @tkol that's my kind of no-nonsense answer. A well deserved +1 Nov 30, 2023 at 9:49
  • @thinkingman first let me clarify that it's my opinion. I think it's a thought-out and informed opinion, but an opinion nonetheless, and if I found that the majority of relevant scientists disagree with me, I'd immediately change my mind.
    – TKoL
    Nov 30, 2023 at 10:31
  • @thinkingman that being said, I think Humans (and any other specific species) are, in fact, incredibly specific. Evolution is full of accidents that stuck, and human beings are full of such accidents. The conditions that created us specifically aren't guaranteed to exist again - I think it's likely that some intelligent species would exist, but that it would be specifically human? I think that claim - that specifically Humans are for some reason inevitable, or highly likely - would need some very special support.
    – TKoL
    Nov 30, 2023 at 10:33
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It depends on the nature of the events. Some physical systems are very susceptible to microscopic changes and others are not. Take a Geiger counter connected to the launch console of the US nuclear missile fleet in such a way that a click of the counter would wipe out civilisation. There you have an instance (an imaginary one, thankfully) of a single quantum event, happening at random, bringing about large scale change at a macroscopic level. At the other extreme, consider the orbit and rotation of the Earth; I suspect they can be accurately predicted millions of years in advance, notwithstanding the countless splurtillions of random quantum interactions that take place in the meantime.

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  • Good answer. Are there examples like the imaginary scenario that you pointed out that exist in nature already? Single photons or single quantum effects controlling some phenomenon at a larger scale? When I say nature, I mean things not controlled by humans, since of course, one can attach a Geiger counter to conceivably any phenomenon by design
    – user62907
    Nov 30, 2023 at 10:01
  • @thinkingman "Single photons or single quantum effects controlling some phenomenon at a larger scale?" Our sense of vision. If you can see, you can detect photons.
    – Olivier5
    Dec 2, 2023 at 15:12
  • @Olivier5 good point. Wish I had thought of it! Dec 2, 2023 at 15:14
  • @MarcoOcram First I thought of proposing the luminescence of fireflies, the fluorescence of gellyfish... then it downed on me that, leaving aside light emission, simple light detection fits the bill.
    – Olivier5
    Dec 2, 2023 at 16:17
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An attempt to answer your title question “How does quantum mechanics affect the probability of macro events?“ is the mechanism of decoherence.

  1. On the level of microphysics quantum mechanics rests on the principle of superposition: Superposing different quantum states with different normalized weights provides again a possible state. The Schroedinger equation is a linear differential equation. Hence the dynamics of the resulting state is the superposition of the dynamics of the different component states, which now interfere.

    On the way from the micro-level to the meso-level the coherence weakens due to the many interactions with the environment. As a result there is no longer any interference on the meso-level.

    At about 1995 the state of the art was presented in Guilini et al. Decoherence and the Appearance of a Classical World in Quantum Theory. Possibly an update is the book from 2010 by Schlosshauer Decoherence and the Quantum-To-Classical Transition.

  2. Concerning your thought experiment to rewind the universe and asking for the possibility that a particular event happens again: Taking into the quantum fluctuations in the first fractions of a second the probability of the same result after 13.6 billion years seems quite small.
    Even that a restart of the biological evolution on earth produces the same species has only a marginal probability.

Added: The paper by Schlosshauer The quantum-to-classical transition and decoherence, last revision 2019, is "a pedagogical overview of decoherence". From its introduction:

Formally, decoherence can be viewed as a dynamical filter on the space of quantum states, singling out those states that, for a given system, can be stably prepared and maintained, while effectively excluding most other states, in particular, nonclassical superposition states of the kind popularized by Schroedinger’s cat. In this way, decoherence lies at the heart of the quantum-to-classical transition.

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As currently written, the OP is not conceptually consistent. It starts well, with "Events in the world can be described on the macro scale or the micro scale." Evidently true.

Almost immediately though, you throw away this perfect framing: "For events that occur in the macro scale, such as the shape of a particular rock..."

No event occurs on a macro scale, or on a micro scale. They happen at all scales at once in a way, but we chose to describe them using a specific scale. Scale is in the eye of the observer; it belongs to the domain of symbolic description.

The reason scales exists (for observers, as an description tool) is to be found in the relationships -- the dialectic if you wish -- between a map and the territory it describes. A map of a territory in real size would be quite useless, as it would physically extend over the whole territory it describes. Similarly, a map of a molecule in real size (at scale 1/1) would be quite useless because nobody could read it. So we need scales, but the universe doesn't. They are not ontic.

Take the example of the sun. To my knowledge, our only theoretical tools to understand what happens in the sun, all these nuclear reactions between hydrogen producing helium, etc. is QM. The sun is a gigantic quantic ball of atoms in fusion, as currently described by science. And without it, none of us would be alive since life on this planet depends on it.

The very carbon life is made of, originates from other stars, where it was forged with (almost) all the other elements, and then ultimately expulsed into space when those stars died supernova style. The very matter composing the cells of your body today originates from quantic events at the heart of long-dead stars.

The light emitted by the sun come from quantic events. Note that these fusion events do not cancel each other out in any way. Rather, they add up, they link up in chain reactions. And each fusion event is microscopic but the light emitted by them travels far and wide.

So what is the real, ontic scale of such a fusion reaction in the sun, if some of its effects could reach the vicinity of Sirius one day?

There is a logical contradiction between a reductionist outlook, saying that causality comes from below, and a view of the world in which big stuff would be causally autonomous from small stuff, by some fuzzy statistical magic.

Aren't big stuff made of small stuff, after all?

What is the real scale of the shape of your stone? Cannot it be represented at a very fine level of detail, microscopic scale, and shown to have at that scale too all sorts of asperities, holes, crevices, and other shapes?

The shape of the stone exists at all scales. Only you observe it at one scale.

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  • Seem like a quibble. The description 'rock' is a macroscale description. Vs a phenomena characterising a microscale description, like atoms & molecules in it.
    – CriglCragl
    Dec 2, 2023 at 1:11
  • @CriglCragl Conceptual clarity is useful if you want to understand what you are yourself saying. A description is not the same thing as a phenomenon or an event, like the map is different from the territory. A map has a scale; a territory doesn't. You can map it at any scale you want.
    – Olivier5
    Dec 2, 2023 at 8:58
  • @CriglCragl There is therefore no reason to assume that quantic mechanics are confined to "the micro level", a level which exists only as a human representation. My example of the sun -- a gigantic quantic event -- intends to illustrate that point.
    – Olivier5
    Dec 2, 2023 at 9:48
  • What about quantum decoherence & the classical limit? Quantum behaviour is about systems small enough to have at least temporary information-isolation, which when a measurement happens propagates consequences of one of the superposed states out of that system, 'collapsing' the wavefunction.
    – CriglCragl
    Dec 2, 2023 at 15:37
  • @CriglCragl What "classical limit"? Classical physics is long dead. It could not explain how the sun produces energy, for instance.
    – Olivier5
    Dec 2, 2023 at 16:20
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I wait for a Geiger counter to count 100 events, then I go for breakfast. Now I have moved a quantum event into a macroscopic scale. Because I went for breakfast 10 seconds later, I bumped into a person and knocked them over. They broke an arm and went to hospital. Unknown to me the person was a terrorist who had prepared to kill the president, which would have had massive effect on world events leading to a nuclear war. So this quantum event saved the world from destruction.

This is of course highly unlikely and most events have no measurable effect.

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Quantum mechanics is a theory that describes the behavior of nature at the scale of atoms and particles. You describe "macro events" as socio-political manifestations. Interractions between people are not determined or described by physics. The mind with its imagination takes the leading role here. Ideas, and even illusions play a major part in these events. When I design or plan something, that has nothing to do with quantum mechanics, perhaps particles are interracting while I do so, but the output of my intellect is not defined by some "law" or operation in the physical layer, I just visualize something and I make it real. A theory related to matter could perhaps "explain" HOW my visualization became a reality (ex. a sculpture) but cannot "explain" WHY I made this thing. History is the product of the why's, not of the how's. The unfoldment of history cannot be determined or explained by a physical theory.

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This topic is a lot less debatable than some people here are saying. Two main interpretations of quantum theory preserve determinism, Many Worlds, and Superdeterminism - and they are only able to do this with 'extra steps' from our universe, that is other worldliness which we cannot access even in principle, or an 'outside the universe' perspective, respectively. That is to say, within our universe and in terms of experiments we know how to conduct, quantum theory does not preserve determinism.

The 'Butterfly Effect' or non-linear sensitivity to initial conditions, is found in classical physics, where in principle it doesn't prevent exact predictions of systems, but in practice it limits predictions in relation to accuracy of measurement of initial conditions, and the complexity of the system. That generally means there is a cut-off point beyond which predictions become useless, like the proverbial hurricane that could be triggered by the difference made by the flap of a butterfly's wings

(for an intuitive example, consider nucleation sites in a supercritical system, like how droplets form from vapour on dust grains, but in very clean air this doesn't happen - a principle used in cloud-chamber particle detectors to allow even the tiny disturbance of a subatomic particle to leave a visible wake)

There's an interesting example of some cosmological significant impacts, of differences in initial conditions that are below the level of what physicists think is the smallest meaningful length: Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length (paper, link to Arxiv free access version). There is a tension here, in that physicists generally hold to the No-hiding Theorem, which says that information about the past is preserved somewhere, even if it becomes difficult to access. Tensions like this often lead to new discoveries or insights when a reconciliation is found, as per the Blackhole Information Paradox.

There are systems where this cut-off for further predictions doesn't hold. In non-linear dynamics (of which chaos theory is just a part), they talk about attractors, which act against the ordinary dissipative nature of most systems as they move towards equilibrium. And the homeostasis of living systems which 'extract' the Gibbs free energy outside themselves to preserve their order at the cost of accelerating net disorder increase. Knowing the character of person, can allow accurate guesses about their far-future behaviour in a way that we cannot make predictions about weather.

We can't know about a specific rock, but we might expect a whole patch to be very similar. Three-body & other non-linear dynamics mean even the tiny fluctuations of subatomic particles can have macroscopic, and cumulative, effects.

But, there can also be hidden sources of recurrent and persistent patterns or order, and we relate insight into these to true knowledge - gaining heuristics, like understanding the 'character' of the system. So for instance, the available gases minerals and possible biological chemistry, could have allowed pretty accurate guesses about what rocks would be common, and indeed what temperature and acidity the ocean would fluctuate around - but not exactly when a deviation from the average would start or how far it would go. And not neccessary truths, but useful insights.

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