Comment by kcexn | Hacker News Reader

Comment by kcexn | Hacker News Reader

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This is a wild over simplification of what 'chaos' theory is actually studying and the statements it makes.

Chaos theory in general states that for some deterministic systems, small changes in the initial conditions can lead to a wildly different deterministic outcome.

A closer metaphor than the butterfly metaphor is a car on a wet road.

Think of driving your car on a wet road. This is a completely deterministic system, there is nothing we don't know about how cars handle on wet roads. When you take that one corner too fast however, your car loses traction on the road, whether your car spins out or just fish tails for a bit before straightening out depends a great deal on the speed and angle that you entered the corner at. If you don't know the speed or angle that you entered the corner accurately, you don't know if you can bring the car back under control again or not.

I don't think anybody in the field of Quantum Mechanics doubts that it is possible for Quantum effects to be entirely deterministic. But it may be so sensitive to small changes in initial conditions (which may be as far back as the birth of the universe), that even if we knew the exact deterministic equations to solve for Quantum Mechanical systems, they would never make an accurate prediction.

> I don't think anybody in the field of Quantum Mechanics doubts that it is possible for Quantum effects to be entirely deterministic.

That quantum effects cannot be deterministic is not only something people in the field believe, it is the majority position. The alternative goes under the name of "hidden variable" theory, and hidden variable theories aren't doing so well: https://en.wikipedia.org/wiki/Hidden-variable_theory

In gp's particular case, it is the subclass of hidden variable theories known as pilot wave theories.

All the local ones are dead due to Bell. Except super determinism I guess (both "sides" dont agree on whether it is local or non local)

The nonlocal ones live, but have few real supporters

(The article, unlike the grandparent comment, is closer to superdeterminism)

Bernardo Kastrup took Sabine Hossenfelder to task over this and to say that she did not like it would be an understatement.

What are you referring to?

They're a philosopher (Kastrup) and physicist (Hossenfelder) who have been having a long going back and forth internet debate about super determinism and hidden variables. Google it and you will find plenty of YouTube videos from both of them. It's quite interesting if you're into that sort of thing

It's the apparent (as it doesn't really happen) collapse of the wave function that seems to transcend determinism. However that's not intrinsic to the function itself. It's only a supervenience of subjective consciousness as it were. The wave function itself is very much deterministic and nothing can violate that.

The issue isn't that deterministic models are necessarily untrue. But that it's meaningless to investigate the phenomena as a deterministic one.

Even if we knew all of the hidden variables. And had the exact deterministic mathematical formula for the universe. The formula may still be so unstable that it would make exactly 0 predictions.

You'd think something like "the uncertainty principle" by it's name alone would be a pretty good hint.

The name of the "uncertainty" principle is pretty stupid and it has nothing to do with its meaning.

The so-called "uncertainty" is just a trivial property of the Fourier transform. It is the same property which requires a great frequency bandwidth for transmitting a pulse that is short in time.

The fact that certain quantities that appear in quantum mechanics are related by Fourier transforms is something that is completely orthogonal to the interpretation of the wave function amplitudes as probabilities of intrinsically random phenomena or as interaction efficiencies caused by real angles of rotation of the interacting particles/waves, which are unknown due to unknown initial conditions.

Technically you're correct, but you seem to be shortchanging the import of the uncertainty principle being a consequence of the Fourier transform.

That "trivial" property of the Fourier transform fundamentally limits our ability to measure both position and momentum, or time and energy of a particle. Without that aspect of QM we could get effectively unlimited certainty of those various properties. It deeply implies the universe is non-local in nature.

What is the difference between "unknown (and unknowable) initial conditions" and "uncertainty"? You can't go back in time to check the initial conditions.

The uncertainty in the initial conditions has no relationship with the "uncertainty" word used in the phrase "uncertainty principle", which refers to the relationship between the variances of two functions, one of which is the Fourier transform of the other.

I have refrained from using a phrase like "uncertainty in the initial conditions" and I have said "unknown initial conditions", precisely to not imply any connection with "the uncertainty principle", because no such connection exists.

Moreover, "uncertainty" is typically used about the difference between the true value of a physical quantity and its estimated value, but in quantum mechanics problems there are many cases when a value is completely unknown (i.e. all the possible values are equi-probable at the initial time, like the angular coordinate of the position of an electron bound in an atom) and not only uncertain.

Saying "unknown initial conditions" covers such cases.

Max Bohr explained the uncertainty principle in his Nobel laureate speech quite well (and in nontechnical terms) - even though it might be interpreted as some law today, it definitely began as a practical obstacle.

Also, the hidden variable theories seem to be about practicality; for all intents and purposes, because it would be practically impossible to know that such hidden variables exist, they are deemed as non-existent.

> Also, the hidden variable theories seem to be about practicality; for all intents and purposes, because it would be practically impossible to know that such hidden variables exist, they are deemed as non-existent.

Definitely not. Everyone would strongly prefer a model of the universe that was deterministic. Hidden variables don't get ignored just because we don't need them to make predictions. We really really really want them, for their own sake, but we cannot make them work.

> We really really really want them, for their own sake, but we cannot make them work.

Sure we can. Bohmian mechanics showed how back in the 50s.

I think you are folding two things together that are related but not the same. Hidden variables are about the state of an entangled system. The uncertainty principle can be applied to measurements taken of an entangled system but can also just refer to two quantities of a single particle such as it's position and momentum.

> Max Bohr

Max Born

I think the description in the article was actually good. In particular, the part where they say:

> This is the metaphor used to describe the unpredictability of chaotic systems:tiny uncertainties in the initial conditions of a system grow and grow until they completely destroy the accuracy of any forecast

This doesn't seem too far off from you say.

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