How Deterministic Is Determinism?

[psionl0]

In theory, due to quantum effects, we could not make up that final 10^-1000th of a percent to make the result of a coin toss a certainty.

In practice, quantum effects are nothing compared to the other factors you would have to control to guarantee the result of a coin toss. We may be able to control enough factors to guarantee the result of a coin toss to a high probability but I seriously doubt that we would get to the point where only quantum effects were left to worry about.

 

[JoeMorgue]

You seem to be suggesting that a coin toss is a classical and not a quantum mechanical system.

I'm saying it's an irrelevant distinction in the context being used. "Random" is a concept we apply to the areas of our knowledge in which we don't have all the information because it only works in that context.

As already noted determinism is just a matter of having all the information. Yes when we get down to the quantum level the idea of what data is can get... weird to say the least but it's still information. That concept exists on the quantum and classical levels.

At the end of the day if a coin lands a certain way something cause it to do so and if we had the information beforehand we could predict it.

A coin toss is deterministic because everything is deterministic because effects need causes.

I've long been annoyed by the fact that the very concept of "materialism" exists because it just seems like a way to make "reality exists" into some subjective opinion there are other valid opinions on and I'm sorta getting that way with "determinism" because it seems to be doing the same thing with "cause and effect."

 

[jimbob]

We have created electrical systems to deliberately generate specific types of random macroscopic effects from quantum randomness. There will be natural systems where this happens as well.

JoeBentley, I am not sure that I agree with you about simply needing all the information. Excluding magic, I would argue that you can't have the information to predict with certainty whether a particular radioactive atom will decay in any particular half-life period.


I know that there is discussion about hidden variables, but I feel that the most parsimonious explanation for the various quantum double slit experiments is that the universe doesn't "know" what will happen until the experiment is performed and the measurements taken.

It also provides an explanation for how structure could arise given the complete uniformity of the big bang.

 

[Roboramma]

I think jimbob said what I would have said and probably better than I would have said it, so I'll just add: +1.

With a small addendum that we can get a sort of determinism back with the Many Worlds Interpretation.

The physicist Sean Carroll has a pretty interesting blog post on this subject: http://www.preposterousuniverse.com/blog/2011/12/05/on-determinism/

I wasn't really sure what the best quote to take from the post is, and it's probably best to read the whole thing, but here's a short sample:

Quantum mechanics is where things get interesting. When a quantum state is happily evolving along according to the Schrödinger equation, everything is perfectly deterministic; indeed, more so than classical mechanics, because the space of states (Hilbert space) doesn’t allow for the kind of non-generic funny business that let non-deterministic classical solutions sneak in. But when we make an observation, we are unable to deterministically predict what its outcome will be. (And Bell’s theorem at least suggests that this inability is not just because we’re not smart enough; we never will be able to make such predictions.) At this point, opinions become split about whether the loss of determinism is real, or merely apparent.

 

[caveman1917]

(from the original thread)

http://www.perlikowski.kdm.p.lodz.pl/papers/PR2008.pdf

does that work for you?

Neat. Admittedly I've mostly just skimmed it, but it appears to me they're only modelling a coin which is initially non-rotating except along the symmetry axis (bottom of page 81: ωη = 0, ωζ = 0). The coin then acquires a rotation along the other axes as it falls down, but it starts out with zero rotation. Normally though when we toss a coin we give it a fast initial rotation.

The reason this is relevant is because such fast rotation can create local turbulence in the air surrounding the coin, making the Navier-Stokes equations describing it go chaotic and negating a couple of simplifying assumptions made about the coin-air interaction in that paper. So it's a neat paper, but it seems to exclude a priori the conditions that would make the coin toss chaotic.

ETA: Nevermind, they do account for initial rotation, I should've determined the coordinate system from the equations rather than from the picture. It's still just a model though, approximating air resistance coefficients from the non-rotating case and applying them to the rotating case.

ETA2: Of course this point of whether a coin toss is chaotic or not is still entirely separate from whether it is deterministic or not. All systems are quantum systems, Newton's laws are approximations.

 

[Hercules Rockefeller]

I'm saying it's an irrelevant distinction in the context being used. "Random" is a concept we apply to the areas of our knowledge in which we don't have all the information because it only works in that context.

As already noted determinism is just a matter of having all the information. Yes when we get down to the quantum level the idea of what data is can get... weird to say the least but it's still information. That concept exists on the quantum and classical levels.

At the end of the day if a coin lands a certain way something cause it to do so and if we had the information beforehand we could predict it. A coin toss is deterministic because everything is deterministic because effects need causes.
I've long been annoyed by the fact that the very concept of "materialism" exists because it just seems like a way to make "reality exists" into some subjective opinion there are other valid opinions on and I'm sorta getting that way with "determinism" because it seems to be doing the same thing with "cause and effect."

No. There is no way, neither in practice nor theory where it is possible to have that information. What you are talking about is causality.

 

[William Parcher]

(I have a feeling though that the heads side is probably heavier. And if the flip involves landing on a floor and not a catch, that would cause it to land face down more, so if it is 50.0000001 % anything it would be tails.)

Coins often bounce when hitting the floor or grassy ground and sometimes they roll before falling on a side.

 

[jt512]

No. There is no way, neither in practice nor theory where it is possible to have that information. What you are talking about is causality.

Are you saying it's impossible to predict a coin flip? There are machines that can flip a coin to land on a predetermined side with 100% accuracy.

 

[Hercules Rockefeller]

Are you saying it's impossible to predict a coin flip? There are machines that can flip a coin to land on a predetermined side with 100% accuracy.

Yes. I would take a ridiculously amount time; much much longer than the current age of the universe, but a some point a random fluctuation will cause the experiment to fail.

https://en.wikipedia.org/wiki/Quantum_tunnelling

 

[Planigale]

The split between classical physics and modern physics is determinism. In classical mechanics in theory if you know the starting state then you can predict the outcome. In quantum mechanics prediction becomes probabilistic not deterministic. (On this basis relativity is classical physics).

On the other hand even ignoring quantum effects, there is not a solution for all starting states within classical mechanics. The classic example is the three body problem.

In terms of physics assuming a perfect disc excluding external forces and tossing in a perfect vacuum with a constant force then coin flips should be entirely predicable.

 

[TubbaBlubba]

Are you saying it's impossible to predict a coin flip? There are machines that can flip a coin to land on a predetermined side with 100% accuracy.

Assuming a perfect flip (coin has only vertical linear momentum and horizontal angular momentum) it is a fairly simple matter, and corrections can be made for non-ideal conditions.

However, as the coin spins through the air, it interacts with the air molecules, performing work on them, and losing some linear and angular momentum.

Consider a coin with a diameter of an inch; it displaces air in a volume that is about 65 ccm. Let's use a simplified model where it experiences drag as if it moved face-forward at the instantaneous velocity of its spinning at the edge. What's the instantaneous velocity? Let's say it spins 100 times in a coin flip lasting 1 second, that's 0.01 seconds to move a distance of 5*pi which gives 500*pi cm/s, bringing in the other parameters we get a drag force of about 0.015 dynes, and a total work of about 25 ergs, or 2.5*10^-6 J. For comparison, the rotational energy of the coin is around 0.5 J. You can't be off by more than about 0.25% if you want to predict the side it lands on (with a bunch of quasistatic assumptions made).

However according to this very simplified calculation the air resistance saps only like 1 part in 10^-5 of the rotational energy of the coin. Of course you're going to have secondary effects as well (e.g. the coin wobbling), but it's very hard to see how the air, energetically, could do all that much. Provided you can get close enough to ideal conditions, it seems like it would take some pretty ridiculous parameters for turbulence to affect the coin enough to interfere with the prediction.

 

[TubbaBlubba]

On the other hand even ignoring quantum effects, there is not a solution for all starting states within classical mechanics. The classic example is the three body problem.

There's no analytic solution. Numerically it can be solved to abritrary precision.

 

[caveman1917]

Consider a coin with a diameter of an inch; it displaces air in a volume that is about 65 ccm. Let's use a simplified model where it experiences drag as if it moved face-forward at the instantaneous velocity of its spinning at the edge. What's the instantaneous velocity? Let's say it spins 100 times in a coin flip lasting 1 second, that's 0.01 seconds to move a distance of 5*pi which gives 500*pi cm/s, bringing in the other parameters we get a drag force of about 0.015 dynes, and a total work of about 25 ergs, or 2.5*10^-6 J. For comparison, the rotational energy of the coin is around 0.5 J. You can't be off by more than about 0.25% if you want to predict the side it lands on (with a bunch of quasistatic assumptions made).

See the link in the quote in post 25, it fully develops the model in the same way you seem to be doing it.

However according to this very simplified calculation the air resistance saps only like 1 part in 10^-5 of the rotational energy of the coin. Of course you're going to have secondary effects as well (e.g. the coin wobbling), but it's very hard to see how the air, energetically, could do all that much. Provided you can get close enough to ideal conditions, it seems like it would take some pretty ridiculous parameters for turbulence to affect the coin enough to interfere with the prediction.

It's not so much about how much (in absolute terms) the air affects the coin, but whether there are chaotic regions in the state space such that even a tiny error in the air-coin interaction gets magnified to the point where it affects the result of the coin eventually landing heads or tails. It seems obvious that in the limit of large angular and linear momentum the system will become chaotic, the question really is how large an angular and linear momentum that has to be, and whether actual coin tosses can get to that point.

 

[caveman1917]

There's no analytic solution. Numerically it can be solved to abritrary precision.

Not exactly. Well, technically you can solve the equations to arbitrary precision, but the three-body problem has chaotic regions in its state space where any non-zero error will lead to wildly different outcomes.

 

[TubbaBlubba]

It's not so much about how much (in absolute terms) the air affects the coin, but whether there are chaotic regions in the state space such that even a tiny error in the air-coin interaction gets magnified to the point where it affects the result of the coin eventually landing heads or tails. It seems obvious that in the limit of large angular and linear momentum the system will become chaotic, the question really is how large an angular and linear momentum that has to be, and whether actual coin tosses can get to that point.

Yeah. I think the translational energy will be smaller, around 10^-3 J. So that makes the drag closer to the right order to interfere, depending on how the turbulence works out.

 

[jt512]

Yes. I would take a ridiculously amount time; much much longer than the current age of the universe...

That sounds like a pretty good definition of deterministic.

 

[Hercules Rockefeller]

That sounds like a pretty good definition of deterministic.

No.

 

[jt512]

No.

Just because something has a non-zero probability doesn't mean that it can happen in the real world. There is a positive probability that you can scramble and egg, drop it to the floor, and it form a whole egg, but it will never happen.

 

[davefoc]

It certainly seems likely that it is impossible to completely remove randomness from a system due to quantum mechanical issues at least.

But that doesn't rule out the possibility that things are completely deterministic, we just don't know how to figure out the result before hand because it is impossible to get that information.

Suppose nothing is random. The entire universe is set on a deterministic path and there is nothing that can be done to change it in the least. We think we are in charge. We work to optimize results for ourselves by figuring out which is the most likely path to provide the best results for ourselves, but it doesn't matter. The universe is set up in a particular way and what will happen, will happen including the thoughts we might have about the decision facing us.

I think the theorizing above is worthless because the theory postulated seems to preclude ever being able to test it. But maybe somebody has some thoughts about it?

 

[lomiller]

Now since a sadly percentage of the population understand "Quantum Mechanics" only enough to think it means "Weird stuff happens so science doesn't understand everything therefore my Woo is true neiner neiner neiner" quantum mechanics operates even to the degree it does only on quantum level, meaning it's not a factor in what we're discussing to degree we need to be discussing it. Yes at some point in the future we might (hell probably) use quantum mechanics intentionally to produce true randomness, but it's not something we have to factor in (or acknowledge to appease the pedants) on any day to day level.

Yeah sure it's technically theoretically possible that a quantum event could "cause" a coin to land a certain way beyond normal physical deterministic factors. It could also quantum tunnel through the planet and wind up in China. It's just not going to. A coin landing on its side is a near infinitely more likely outcome (a US nickel is wide enough to land on its side on average every 1 in 6000 fair flips) and we don't worry about that.

Chaotic systems amplify small changes in initial conditions, and this amplification can increase progressively over time. The exactly a sufficiently chaotic system over sufficient time could indeed be truly random and impossible to predict. While chaotic a coin toss can be more or less reset to similar conditions every time, so it would not be an example of a system where quantum effects come into play. Some chaotic systems feed back into themselves essentially indignantly with no “resets” like you would see in a coin toss.

Keep in mind, however that in many, possibly most, chaotic systems even if the exact behavior is impossible to predict it’s expected behavior can be fully described using statistics. Eg Weather models can’t predict the exact weather more than a few days in advance but climate models can predict the average weather decades, and perhaps centuries in advance. IOW you would not expect to see a radically results just different ones that are all within the normal range.