echidna

I’m tired & I should log off, but …

Is anyone aware of the mathematics of calculating the accuracy required to make a Deterministic Universe work purely deterministically ?

That is, accounting for chaotic processes, how rapidly do we require Initial Condition data to be more accurate. How quickly does the accuracy required descend below the Planck Scale ?

Planck Length = 1.6 x 10-33 cm
Planck Time = 5.4 x 10-44 s

I realise that it is very system dependent, in that some systems are more stable than others. Weather is the classic unstable system, however the brain might be the other cliche of course. My question is poorly given, but is anyone aware of any work which has been done in this area ?

I am only aware of anecdotal explanations that quantum events can chaotically amplify their effects to result into a macro non-deterministic universe. Is there any mathematics behind this ?

Apologies if my question is incoherent. Maybe I can join the dots on Monday.

echidna

I'm also curious about what other significant macro systems might be subject to quantum influence.

Starboy

One time long ago I used to view things as you do. Over time I came to understand that there is a big difference between a system that is completely random and a system that has a random component. Physical processes at the plank scale are not completely random. There are states that have zero probability. If the process were completely random all available states would have the same probability of occurrence. Your thinking is flawed.

Starboy

[ August 24, 2002: Message edited by: Starboy ]</p>

echidna

Um, my post didn’t even contain the word “random”.

OK, QM is open on whether it is deterministic or not, however its laboratory behaviour to date appears unable to be deterministically predicted.

So where is the flaw :

P1. Quantum events cannot be deterministically predicted to date.
P2. The chaotic “Butterfly effect” can amplify microscopic differences in initial conditions to macroscopic events.
C1. Quantum events can have macroscopic effects.
C2. Macroscopic events can be non-deterministic.

[ August 25, 2002: Message edited by: echidna ]</p>

fando

Uh, like everything? The burning sun in our sky is an emergent phenomenon of nuclear fission, a process which is effectively quantum by virtue of operating at the scale where QM is dominant. If you think about it, every generic process observed in the 'macroscopic' world is an emergent phenomenon of the physics of finer scales. There is no way to say that such and such a macroscopic physical system is completely uninfluenced by QM.

I'm probably missing something. Could you elaborate what you mean by macro systems that are subject to quantum influence?

echidna

Some systems behave very stably, whether or not they are emergent functions of QM processes. I hope my chair I’m sitting on, doesn’t suddenly virtually vanish and reappear across the room for instance.

However other systems are incredibly sensitive to initial conditions. Microscopic differences in initial conditions can with time result in dramatic shifts in behaviour.

Weather is the classic unstable system, making longterm prediction impossible. The butterfly effect cliché is that if a butterfly flaps its wings in Hong Kong, a hurricane happens in Honduras.

I see no reason why such effects should not also be applied down to the quantum / Planck scale.

echidna

How widely accepted are the following statements :

1. Until Quantum Mechanics can be proven deterministic, we live in a non-deterministic universe where macro causality is strictly limited by system sensitivity to chaotic effects.

Or in layman’s terms …

2. Shit happens for no reason.

I was prompted this way by another thread where someone claimed that we lived in a macro-deterministic universe.

Is determinism officially dead and buried and I was just dozing when it was announced ?

fando

Oh ok, that's much clearer. I'm not really sure what the consensus is in the physics community. All I have are quips and one-liners uttered by professors in half-forgotten lectures. If my current feeling about determinism is a reflection of these minute influences, then I believe that there really is no consensus. Determinism is currently a philosophical matter and hasn't been replaced by any solid theory yet.

For instance, there are some that say that the universe is truley deterministic and that things like the uncertainty principle are merely inconveniences of the real world that prevent us from seeing the finer clockwork. But there are others who feel that the uncertainty principle is as deep as it gets, and that the universe is inherently non-deterministic beneath the Heisenbergian veil.

Personally, I don't think the issue is black and white. First, there is no such thing as pure non-determinism. A system that appears purely non-deterministic can always be broken down into components that would allow one to treat the system as deterministic. And those components don't have to be the most fundamental and microscopic laws of nature, they just have to be of sufficient granularity to describe our system for the majority of cases. That's not to say it would be easy, it's actually fairly improbable that such a reduction might be made in the lifetime of the universe for most systems. As the Computer Scientists would say, some of these reduction problems are NP-hard. Obviously the determinism arrived by this process of reduction is incomlete, something which I'll get to next.

Second, if something appears purely deterministic, it will no longer be so upon closer examination. There will always be an exception that breaks the determinism. Physics near the speed of light breaks Newtonian determinism. Black Holes and the very early universe break the clockwork determinism of general relativity. There is no way to say something is purely deterministic when all we have are models of reality that are sure to be incomplete. We need to know first how to tell model from reality before we can claim to be equiped to say something is purely deterministic. Philosophically, I don't think we'll ever get to that point because our conception of reality is what we model from our measurements and nothing more. We are solipsistic slaves forever bound to the only cosmos we know and can know.

I'd like to give one concrete example of what I mean by reduction from non-determinism to determinism and the idea that you can't have 100% of either. Consider the evolution of galactic clusters over time. This is essentially an N-body problem where N can be very large. The evolution would appear to be chaotic, and it would be a futile task to construct a computer that can crunch a solution for us before our species goes kaput. However, let's imagine that we were a super advanced civilization with the ability to simulate arbitrary universes with sophisticated quantum computers. Gedankenexperiment. To compute the evolution, we can formulate a universe consisting of N bodies in a simplified fashion (point masses, closed system) and feed this to the computer and ask it to find the state after time T. It will then happily return the results after a bit of chugging. Ta-da, determinism! However, this is not 100% pure determinism as it is merely an incomplete simulation; There will undoubtedly be inaccuracies at the boundaries and at high resolution because the real thing does not consist of point masses and is not a closed system. In fact, the only way to get pure determinism is to recreate our universe exactly and observing its evolution. Not very practical, and probably not possible. Because we can't model the system exactly and because we can't claim to know the system is purely deterministic, we end up not being able to decide whether galactic superclusters follow a purely deterministic pattern of behavior. Where's the model that says so?

[ August 26, 2002: Message edited by: fando ]</p>

Starboy

echidna, what do you mean by deterministic? Do you mean classical determinism? Even in a classical deterministic universe we cannot compute the future with any certainty. There are two big reasons:

1) It is not possible to measure the entire universe with sufficient accuracy to predict out to any length of time.

2) Even if you did know the exact initial conditions the n-body problem is intractable and can only be solved for the simplest cases or statistically.

The universe was never completely predictable. Quantum mechanics just made it more so.

Starboy

[ August 26, 2002: Message edited by: Starboy ]</p>

ohwilleke

Your analysis is precisely the same as my own. I find no flaw in your logic. Moreover, I think it is fair to say that the most "interesting" systems (i.e. those that involve good and bad things happening to particular people and societies) are precisely the kinds of complex system where chaotic behavoir is present in spades.