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Suppose you have a dice. The “probability” of a dice landing on 1 is defined to be 1/6. However, many say that this is a function of ignorance. If we knew everything about the initial conditions, we could predict with certainty whether or not it will land on 1. Given this knowledge, the “probability” now changes to 0 or 1. Probability disappears as a concept completely.

However, on a quantum scale, atleast according to some standard theories, quantum events happen probabilistically. It is claimed that even if one were to know everything about certain conditions, you could not predict quantum events with certainty.

But quantum events add up to macro events, no? How then can we determine with certainty where a dice will roll but not quantum events?

Is the probability that a dice will roll on 1, given knowledge of all initial conditions, 0/1 or merely close to it given the unpredictability of quantum events? And does this change depending on when you have this knowledge? For example, is the probability of the dice landing on 1 given all knowledge of conditions of the world 3 seconds before the dice roll the same as having all knowledge 10 seconds before?

This is what I’m having trouble wrapping my head around.

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  • Physical determinism is not the same as philosophical determinism. Experience might prove that we can't predict a QM wavefunction collapse, but perhaps it, as everything else, is already determined, so finally we don't have free will. We can only speculate.
    – RodolfoAP
    Jul 7, 2023 at 3:43
  • @RodolfoAP What do you mean by "everything is already determined"? Determined randomly, when? Determined deliberately, by whom? And what is this off-topic nonsense about free will? This question has nothing to do with free will. Jul 7, 2023 at 5:39
  • To "know everything about the initial conditions" you would need something as complex as what you were simulating / predicting. A universe is the best simulator of a universe. In other words, there is no free lunch.
    – Scott Rowe
    Jul 7, 2023 at 10:29
  • @PerttiRuismäki I understand you don't believe in determinism, that's ok, I'm not defending it, just presenting the philosophical approach. Historically, the problem of free will has been contested with determinism. If the world is determinist, my sins are not the result of my decisions, my behavior would be just the result of a causal chain of events (even quantic, because we can't prove otherwise). See Laplace's Demon.
    – RodolfoAP
    Jul 7, 2023 at 12:21
  • @RodolfoAP Determinism is not a matter of belief. It is just a theoretical idea. This question is not about free will. In a hypothetical deterministic world there would be no life and the laws of physics would be different. Jul 7, 2023 at 12:47

3 Answers 3

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There is a strong "wish it were so" inclination in us humans for the universe to be simple and understandable. This is the motivation for wanting the universe to be predictable and deterministic. It is always a good idea to fight a fallacy that one knows one is tempted by, and be VERY suspicious of views that satisfy one's "wish it were so"s.

Physics at its basic level is indeterministic. QM is probabilistic, and events are random within probability envelopes.

when one builds up to macro scales, then the properties of the structure one is building up, matters.

For most structures, there is a "law of large numbers" that begins to superimpose on the QM indeterminacy. A large number of random events, can be treated as a probabilistic distribution, and when the individual events have a trivial magnitude at the macro scale, they can be approximated as a force rather than events. Pressure for gases, and gravity, are the best known of these "force" approximations to multitudes of quantum events. These force approximations can usually be treated as deterministic at the macro scale.

However, some macro scale structures don't interact as simply as pressure or gravity seem to, and some of those structures have the property of being chaotic. what part of the rim of a faucet a drop falls from, or where and how big a new tropical storm will be -- are classical examples of chaos phenomena. Chaos events are highly sensitive to tiny changes in initial condition, so it is reasonable to expect quantum events to leverage up to macro scales when a system demonstrates chaos behavior.

LIFE has this characteristic of chaos sensitivity. Tiny input changes at the quantum level, have macro scale consequences. Such as -- a cosmic ray produced by QM processes 3 billion years ago in another galaxy, could strike one of my chromosomes, inducing a cancerous change, with drastic consequences for my life.

Our lives are therefore not predictable. But the future of our universe, MAY be predictable, but we think it probably isn't. IF the values of the Standard Model of QM are stable, and never change, then gravity will dominate over the future of the universe, and that is simple enough to be deterministically predictable. However, if the Standard Model changes values over time, and we have reason to suspect it does, because the Cosmological Constant is changing value, THEN it is reasonable to suspect that probabilistic quantum phenomena are driving the changes in our physical "laws", and we would therefore not be able to predict the future of our universe.

So to summarize:

  • Our universe is probabilistic at small scales.
  • for much of our macro scale phenomenon, the law of large numbers allows us to approximate this probabilistic physics with deterministic laws.
  • But for complex structures like life, chaos leverages up the quantum unpredictability
  • And while gravity currently dominates our universe, and gravity is deterministic, our best guesses of the underlying physics principles are that our physics will change, so our future is -- unpredictable.
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    It's always funny/sad when the people who believe the much more emotionally appealing option accuse others of believing something because they "wish it were so". In what world is "our actions are nothing but a product of our environment and biology" more appealing than "we're free to do as we wish within physical limits, regardless of environment or biology"? You're saying it's more appealing based on one factor (predictability) while ignoring another (agency). I'm always "VERY suspicious" of people who rely on incoherent definitions (free will) and who deny evidence (neuroscience+psychology).
    – NotThatGuy
    Jul 7, 2023 at 8:37
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    You've argued elsewhere that accepting determinism would literally be too hard for people, and we should lie to them even if it's true (even if that's a dubious and arguable claim and questionable reasoning). ... and part of that discussion happened literally yesterday. That directly contradicts your claim that determinism is actually the preferable option.
    – NotThatGuy
    Jul 7, 2023 at 9:23
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    +1 for "there is a strong inclination in us humans for the universe to be simple and understandable. " And also for the "reasonable" approach to human knowledge: we know something, and we do not know other thing. That's life. Jul 7, 2023 at 9:45
  • Is gravity deterministic though? Three-body dynamics of interacting blackholes create uncertainties below the Planck length. Paper: arxiv.org/abs/2002.04029 Discussion article: universetoday.com/145463/…
    – CriglCragl
    Jul 7, 2023 at 18:52
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    @CriglCragl -- yes, there are a few examples of gravity sustaining complex enough structures to support cases of indeterminism. But gravity in almost all cases is deterministic, and this includes the case of the ultimate fate of the universe (either disperse to zero net density, or collapse to a black hole). For a more complete answer on the indeterminacy of our universe, see: philosophy.stackexchange.com/questions/68224/…
    – Dcleve
    Jul 7, 2023 at 18:58
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One can make (or find in nature) a detector for a quantum event. A detector is a machine that converts a signal that is hard to detect (including a specific part of another signal) into a state that is easy to detect.

A quantum event produces a tiny change. To make a tiny change detector, balance a system on a local equilibrium that takes very little energy to perturb away from the domain in which the system returns to the local equilibrium state. When energy is transferred to the system by the tiny change, it pushes the system into a domain in which the system moves farther away from the local equilibrium, releasing more energy (which was stored earlier, not provided by the detected event). Such a detector "amplifies" the quantum event to macroscopic significance.

For a purely macroscopic example, a mouse trap has an equilibrium state (spring locked back and secured with the trigger pin) that takes only a small amount of energy to perturb away from the equilibrium (trigger pin bumped out of position by an unfortunate mouse) in such a way that it moves rapidly farther away from the equilibrium, releasing a large amount of energy (as the kinetic energy of the accelerated metal bar that kills the mouse).

For a real example, a Geiger counter detects quantum events - the spontaneous decay of radioactive elements, using a circuit for its "mouse trap". Potential difference takes the role of the spring, the signal from the circuit takes the role of the metal bar, and an ionization chamber takes the role of the trigger pin. This amplifies stochastic quantum decay probability to the stochastic macroscopic "Geiger counter click" probability (with some measurement error).

Natural detectors are messier and less easy to trace the precise correlation. A human being appears to be a decent single-photon detector (as long as the photon actually makes it to a light-detecting cell in the retina, just like a mouse trap doesn't 'detect' any mice that don't make it to the bait). A photon interaction is stochastic quantum event; a human who has been instructed to push a button upon seeing a weak flash of light amplifies the interaction probability to a stochastic macroscopic probability (with some measurement error).

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The Universe is not deterministic at any level. The probabilistic behaviour of micro scale particles are seen as inaccuracy in the behaviour of macro scale objects.

Absolutely accurate measurements are not possible, therefore it is impossible to know everything about the initial conditions.

But the key element in the randomness of die-rolling is the manual throwing action. The human neuromuscular system is so inaccurate that even if the thrower knew exactly (which he doesn't) how to throw a six, he could never perform the throw with sufficient precision.

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    +1 for Absolutely accurate measurements are not possible. This can be asserted without going to quantum scale: We cannot predict weather, market, asteroid-strike. And as you correctly say every physics measurement is correct to (at most) least count of measuring meter. It's surprising how few people really grok that numbers in physics and math have utterly different ontologies — whatever could the billionth digit of π mean to a physicist?
    – Rushi
    Jul 7, 2023 at 8:28
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    @Rusi We can predict weather to a reasonable degree (especially if we're talking about movements of hurricanes and climate changes over time), but we can't predict it precisely because we can't even begin to get close to modelling a fraction of the particles on Earth that affects the weather. This has pretty much nothing to do with determinism and everything to do with the limited knowledge of humans. Similar for financial markets. As for asteroid strikes, we predict a good amount there (but, again, we're limited by knowledge).
    – NotThatGuy
    Jul 7, 2023 at 8:48
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    Aren’t you confusing practicality with hypotheticals? The question of whether or not we can physically find out all initial conditions before a dice throw is different from whether or not we can predict a dice throw IF we did have this knowledge. In the QM case, isn’t it the case that even if we did hypothetically DID have all knowledge of initial conditions, the result would still be probabilistic? Whereas in the case of the dice throw, it would be deterministic? Or am I missing something?
    – user62907
    Jul 7, 2023 at 9:11
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    @NotThatGuy Your conflation of (my) predict with (your) reasonably predict is amusing in a question on determinism! I respect your direction to decouple (human) prediction from (ontic) determinism. With the caveat that such decoupling only works within fairly strong Platonic commitments. Myself, I consider a modest,reasonable(😉) platonist. Ie I'm fine with a mathematical realm that's outside of spacetime. But when it goes toward ontic existence of entities that are fundamentally outside human intuition, I fear we've reached angels-on-a-pin arguments
    – Rushi
    Jul 7, 2023 at 10:26
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    Again, your responses are highlighting our physical inability to find out initial conditions, not whether or not we would predict things given full knowledge hypothetically. The first does NOT rule out determinism. The second one may. @PerttiRuismäki
    – user62907
    Jul 7, 2023 at 12:27

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