"For a Galton board with any given number of rows, the number of different paths a marble can take to reach a bin placed at a given row is exactly equal to the corresponding number in Pascal’s triangle"
Because there's no such thing as random or chaos; Everything follows a pattern, a protocol, a law; We may perceive it as random or chaos but it is not; Everything we call random, is in fact pseudo-random; If there's a Law, an algorithm behind everything, then who or what coded it ? That's the rabbit hole;
This article seems to be starting from a conclusion and then working its way up to an explanation. That's not how science works. There is lots of experimental evidence that on a quantum scale there is inherent randomness.
Anyone can claim that there are deterministic causal factors leading to what appears to be randomness. What are those factors? I could claim that invisible unicorns are the underlying factor for deciding which slit the photon goes through and this explanation wouldn't be any less supported than the reasoning presented in this article.
> it might come from subtle factors, including, perhaps, the exact initial location of the marble, its angle of motion, or the manner in which the marble bounces off the subtle imperfections of the peg’s surface. These are all deterministic factors with a clear causal chain that decides which way the marble goes. The path selected seems random to us only because of our ignorance of these details.
One thought experiment that comes to mind is, imagine a perfect Galton board where all the pegs are perfectly identical in a closed perfectly isometric system. Without subtle factors like air currents or imperfections in the pegs or the marbles, where does the marble land? I think personally if all other factors are ruled out the thought experiment reduces to the double slit experiment.
All experiments involving quantum theory affirm the mathematics, but are interpreted differently based on how one translates the mathematics into physical reality.
For example, in Everettian interpretations there is no fundamental randomness. There is a universal wave function evolving continuously and deterministically, but decoherence processes lead to the appearance of randomness.
In some Copenhagen type interpretations it only makes sense to talk about a wavefunction in the context of the system it describes, and there is a real physical collapse of the system's wavefunction which results in genuine fundamental randomness.
Still other interpretations are agnostic about whether randomness is fundamental or merely apparent.
No experiment to date has proved the supremacy of one class of these interpretations over the others.
> This article seems to be starting from a conclusion and then working its way up to an explanation. That's not how science works.
No, it's starting from a phenomena and providing a possible hypothesis for why that phenomena is occurring. This is explaining an existing, untested hypothesis.
> There is lots of experimental evidence that on a quantum scale there is inherent randomness.
No, there isn't, at least not as far as I know. The experimental evidence I'm aware of shows that we cannot, with current measurements, model the phenomena on a quantum scale, except probablistically. It does not show that there isn't any determinism, it only shows that, with current techniques, we don't have access to the determinism (if it exists).
In short, this is explaining the "Team E" position:
> [W]e debated whether randomness or determinism lies at the heart of quantum mechanics, which I characterized as team B (Niels Bohr) versus team E (Albert Einstein). Team B sees the unpredictability of particle behavior as evidence that at the fundamental level of the universe, determinism is replaced by intrinsic, objective randomness. Team E contends that this randomness is merely a sign of our ignorance of a deeper level of deterministic causation.
To be clear, I'm not saying that quanta are deterministic. I don't know.
> One thought experiment that comes to mind is, imagine a perfect Galton board where all the pegs are perfectly identical in a closed perfectly isometric system. Without subtle factors like air currents or imperfections in the pegs or the marbles, where does the marble land? I think personally if all other factors are ruled out the thought experiment reduces to the double slit experiment.
Assuming a perfectly drop as well, my hypothesis is that the ball would land on the top peg and balance there, perhaps after bouncing if we're assuming some elasticity in the components of the system. A "perfect drop" being in this case, one where the ball is perfectly centered, with no spin or side-to-side motion.
But I think this is getting into why analogies aren't a very good way to talk about science--analogies don't prove anything, and always fall apart on some details.
Bell's Theorem is really about locality rather than randomness. It's possible to define quantum theory in terms of deterministic but non-local random variables. In fact, this is a pretty apt description of the de Broglie-Bohm interpretation.
I don't think it's that simple. A fair amount of work has been done on relativistic extensions of de Broglie-Bohm type theories, e.g. https://arxiv.org/pdf/quant-ph/0406173.pdf
> No, it's starting from a phenomena and providing a possible hypothesis for why that phenomena is occurring. This is explaining an existing, untested hypothesis.
There is no hypothesis presented, merely that there are deterministic factors that we don't know of. That's not a hypothesis.
> No, there isn't, at least not as far as I know. The experimental evidence I'm aware of shows that we cannot, with current measurements, model the phenomena on a quantum scale, except probablistically. It does not show that there isn't any determinism, it only shows that, with current techniques, we don't have access to the determinism (if it exists).
I think you are presenting a semantics argument that has little value.
> the uncertainty principle actually states a fundamental property of quantum systems and is not a statement about the observational success of current technology
Science doesn't work backwards from conclusions. If you think that there is determinism, there needs to be a testable theory that explains what these deterministic factors are. Like I said, we can simply attribute this supposed determinism to invisible unicorns and it'd be an equally valid explanation.
> There is no hypothesis presented, merely that there are deterministic factors that we don't know of. That's not a hypothesis.
How is that not a hypothesis?
How is it any less valid a hypothesis than "it occurs randomly"?
> Science doesn't work backwards from conclusions.
And neither does the article.
> If you think that there is determinism, there needs to be a testable theory that explains what these deterministic factors are.
If you think that there is randomness, that is inherently not a testable hypothesis (nor is it a theory: please do not use "hypothesis" and "theory" as if they are interchangeable--in scientific discussion they are not interchangeable terms).
I don't think that there is determinism: that would be a conclusion.
I think it's possible that there is determinism. That's a hypothesis.
I also think it's possible that there is not determinism. That's also a hypothesis.
Given current technology, I don't think we have the means to test either hypothesis. I'll also point out that randomness is inherently untestable.
> Like I said, we can simply attribute this supposed determinism to invisible unicorns and it'd be an equally valid explanation.
This is also a valid argument against inherent randomness.
As an atheist with a good amount of atheist reading under my belt, I am quite familiar with this argument, and in general agree with it when applied to i.e. God. The problem in this case is that BOTH hypotheses are untestable: you cannot test whether the underlying mechanism is random OR deterministic.
Here's a thought experiment for you: I've generated the following sequence of numbers:
I generated this sequence of numbers via a widely-used secure pseudorandom generator, so they are not random. But if I didn't tell you that, you'd have no idea, and these pseudorandom generators are time-tested to be very hard to distinguish from random numbers if you don't know the seed (otherwise you'd be able to break a lot of modern encryption). So by your logic, since you can't tell me what the deterministic factors are, you can only conclude that the numbers are truly random. But that's wrong, the numbers aren't random.
EDIT: This was downvoted faster than anyone can read, I'd wager.
> Attributing quantum phenomena to randomness also makes no falsifiable predictions.
“Any research effort will find no deterministic explanation” is, I suppose, falsifiable, but mostly I agree; randomness as explanation is the absence of an explanatory hypothesis, not a substantial hypothesis.
My thinking on this is basically, hypotheses don't have to be falsifiable, but they aren't very useful if they aren't, because you can't design an experiment to test them.
Neither the determinism nor nondeterminism hypotheses are falsifiable, so there's no reason to prefer one over the other right now.
However, non-determinism will never be falsifiable, whereas determinism is only currently non-falsifiable because a plausible, testable mechanism has not yet been hypothesized. So while there's no reason to favor determinism as something we believe, there's reason to favor it in research, because research has the potential to yield further information.
I mean, things could be that way. It's not so hard to imagine a universe where some events just happen without any causation or correlation with past events. The astonishing thing is that there is any causation at all! That events at different times are related to each other.
You think a billiard ball that just starts moving for reasons of randomness is less astonishing than a billiard ball that moves because it was struck by another ball?
Of course we are already used to things being that way.
But a priori, order is what needs explanation, not orderlessness.
The interesting thing is that there is movement. That there is temporal structure. It's not like one instant is totally different from the previous. And that there are simple laws governing how the previous snapshot relates to the next snapshot.
Why isn't the universe simply white noise, like when you tune on a non-existent channel on old TV's and you get totally independent, random images at each instant.
But that is clearly the wrong reduction. Start position will determine the final position every time if we assume a perfect board. Marbles are not wave particles. You get a distribution based on the input distribution.
It's a thought experiment. If we assume a perfect board with perfect marble with all other factors like imperfections/air currents removed and with the same initial position, and let's say the perfectly spherical marble hits the peg dead center every single time, does the marble fall to the left side of the peg or right or does it not fall to the either side?
I can assure you I don't know. That moves the problem from platonic shapes to real interactions of quantum particles. Atoms are not equivalent to perfect spheres.
"For a Galton board with any given number of rows, the number of different paths a marble can take to reach a bin placed at a given row is exactly equal to the corresponding number in Pascal’s triangle"